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Each student is required to work closely with at least one faculty member to develop and report research with a significant quantitative component, or perform an acceptable application and analysis of quantitative methodologies. MSQA Research Projects are highly variable in nature. You will note that topics of interest include mathematical programming, statistical analysis, simulation, operations management, and many other disparate application and mothodological areas. The underlying commonality of all projects is that they must have a significant component of quantitative analysis, as defined by the candidate's committee. The following list of projects is presented in reverse chronological order. The Committee for each project is listed with the Chair of the Committee first. The date provided for each of the Projects is the date of the Project Presentation; final graduation could have been somewhat later. Where available, abstracts of the projects are provided as well.
Sangeetha Mallya, Applied Bayesian Forecasting of U.S. Medicaid Program Expenditure on Antidepressant, March 4, 2008 (Martin S. Levy, Jeff J. Guo, Christina Kelton)
Mental health drugs expenditure, especially on prescription medicine for depression has been on a steady rise. Depression is among the most prevalent major mental disorders today with about 10% of the US population suffering from Depression. The Social Security Act established Medicaid as a jointly-funded, Federal-State health insurance program. Medicaid plays a fundamental role in the provision of prescription drugs to over 42 million low-income and disabled beneficiaries. The state Medicaid programs spent altogether approximately $2 billion on antidepressant drugs in the US in 2005, across three categories of antidepressants.
To better understand this spending and to safeguard the Medicaid program from excessive expenditure on mental health drugs, state-of-the-art forecasting models can be of great aid. Here, we focus on exploring, building and interpreting forecasting models for Medicaid's expenditure using applied Bayesian modeling methodology. The synthesis of the routine model output with dynamic assimilation of external information is the centerpiece of Bayesian forecasting. Further, a comparative assessment of the forecasts is performed with prior results from classical time-series models. The results from these forecasting processes can be leveraged by Medicaid for research, planning, optimization and inferential purposes.
Rudranil Manna, Development of a Predictive Model for Food Consumption in USA, March 3, 2008 (Norman Bruvold, David Rogers)
The accuracy of the prediction of a household's expenditure in food is a major concern for retailers and manufacturers engaged in food-marketing campaigns. The purpose here is to develop a model to predict the household spending in the major food categories, based on
geographic location and household demographics. The modeling is done with "consumer expenditure diary survey data" obtained from the public domain of the US Department of Labor. A mixed modeling methodology is adopted, which includes a mixture of the fixed effects of the socio-economic characteristics of the household and random effects of each household specific intercepts. This model has taken into account the correlation between the household expenditures for the different food categories. Finally the model predictions are benchmarked against a univariate tobit regression model, widely available in the
literature for similar predictions of household food-consumption.
Qiuhong Zhang, Empirical Verification of Optimal-Portfolio-Based Foreign Exchange Rate Theory, February 29, 2008 (Srdjan Stojanovic, Yan Yu)
The recent optimal-portfolio-based Foreign Exchange Rate theory, introduced by S. Stojanovic in Foreign exchange rates, is implemented and verified using the market data for the economies of: Canada, Japan, UK, and US. The key parameter in the implemented theory is the market (relative) risk aversion parameter ? (or the market sentiment). Therefore, one of the main goals of this empirical study was to estimate the value of the relative risk aversion parameter for the pairs of the considered economies, and to conclude whether it has the same/similar value for all of them. Finally, the statistical hypothesis on whether the Foreign Exchange Rate data conforms to the theoretical model is tested as well.
Feng Yu, A simple discrete-time hazard model for forecasting bankruptcy in construction companies, December 19, 2007 (Martin Levy, Jeffrey Camm, Uday Rao)
The construction industry has played a powerful role in sustaining economic growth and helping the recovery. This industry is inherently very fragile and extremely risky, and the failure of construction firms has had a serious impact on the economy and society. Consequently, the prediction of the failure of construction firms is essential not only for the economy, but also for society. To date, many bankruptcy prediction models have been developed to predict the probability of failure of construction firms based on company financial information and economic information. However, these models have their limitations and disadvantages because of one reason or another, which are reviewed in this study. There is a need to develop prediction models capable of forecasting long-term failure for construction firms of different sizes. In this study, a discrete-time hazard model is proposed to predict the probability of bankruptcy for construction firms in a long time frame. The research is based on a statistical analysis of good and bankrupt construction firms and related financial and economic data in a time frame of about 10 years. A prediction model using survival analysis is developed through this study.
Balkrishna Apte, Worldwide Desktop Computer Supply Chain Complexity and Performance Models for the Hewlett Packard Company, November 30, 2007 (David Rogers, Amitabh Raturi, Michael Stephenson)
In this project is a quantification of supply chain complexity for different business regions across the world for the personal computer desktop business, and its correlation to supply chain performance parameters. Regional supply chain performance is consolidated and quantified with parameters for order cycle time, forecast accuracy, inventory cost, excess, and/or obsolescence. Statistical techniques are utilized to determine if there is a correlation between product line complexity and key supply chain performance measures. Statistical models indicate the impact of change in supply chain complexity for various supply chain performance parameters. Results provide guidelines for management for determining the impact of product line complexity on various supply chain performance measures and ultimately upon profit. Changes for decisions regarding offering additional products by employing the impact of complexity will be posited.
Jeremy Scheidt, Clinical and Surgical Scheduling Across Multiple Facilities Using Integer Linear Programming, November 28, 2007 (Michael Magazine, Craig Froehle, Jeffrey Camm)
Rising health care costs are a complicated issue. Health care organizations have a delicate balancing act of scarce resources with high standards for care and service. Large scale operations can have several advantages for efficiency and service, but the coordination of so many resources using manual methods can be cumbersome, time-consuming, and carries a risk of being less than optimal. Scheduling doctors at several facilities in a metropolitan area is an example of such a problem. Cincinnati Children's Hospital has several locations that share many resources, such as doctors and administrators. The problem considered here is how to efficiently coordinate the scheduling of doctors at various facilities for consistency in quality and service while minimizing the already heavy demands on personnel. The proposed model uses integer programming to choose the schedule that best meets the multiple objectives of a good schedule in this situation. It handles a wide variety of scheduling requests in an automated manner that reduces manual work, minimizes the number of schedule requests that can not be met, minimizes the travel between facilities, minimizes the changes required to accommodate ongoing schedule updates, and provides a consistent space for each doctor to use.
Feng Ji, An Introduction to Credibility Theory With An Actuarial Frequency Case Study, November 21, 2007 (Martin Levy, Jeffrey Camm, Yan Yu)
Credibility theory is a set of quantitative tools which allows an insurer to perform prospective experience rating (adjust future premiums based on past experience) on a risk or group of risks. There is a manual rate which is designed to reflect the expected experience of the entire rating class and implicitly assumes that the risks are homogeneous. However, no rating system is perfect, and there always remains some heterogeneity in the risk levels after all the underwriting criteria are accounted for. Credibility theory provides models which are a compromise between the historical observations and the manual rate, and also a more credible premium. In this paper, three classic credibility approaches, which are Bayesian Methodology, Buhlmann credibility, and Non-parametric Empirical Credibility, are discussed. A case study with a true claim experience from Humana Inc. then shows that credibility premiums outperform either the manual rate or the estimate based on the historical observations.
Yanping Chen, A Case Study on the Linear Modeling Fitting with Outlier , November 14, 2007 (Martin Levy, Norman Bruvold, Jeffrey Camm)
In the application of ANOVA for hypothesis testing, the assumptions such as the homogeneity of errors or normality are often violated because of scale effects, design of the experiments, outliers and the nature of the measurements. This experiment deals with design and statistical analysis on the balance control capability of obese workers. Functional Reach (FR) is a measure of how far a person can reach without losing balance. The hypothesis assumption is that obese workers because of their larger body mass may not be able to reach as far as non-obese people without losing body balance. Except for the obesity_level (obese and non-obese), gender is chosen as another primary factor in the hypothesis testing. However, the plots of the residuals arising from fitting the 2x2 ANOVA show the heteroscedasticity due to the fact that one subject seems to be an outlier. Remedial measures are applied in the project to cure the heteroscedascity, such as the seemingly outlier removal, log, square root, inverse and the Box-Cox algorithm transformations, evaluation on the model adequacy and inadequacy, verification, and the Rank ANOVA. The consequences of these techniques are compared and the ANCOVA model succeeds to reducing the variance and removing the heteroscedasticity for the hypothesis testing.
Yann Ferrand, Forecasting U.S. Medicaid Program Expenditures on Antidepressant Drugs, November 14, 2007 (Christina Kelton, Jeffrey Guo, Martin Levy, Yan Yu)
Healthcare costs and drug prices have been on the rise, and the state Medicaid programs spent altogether approximately $2 billion on antidepressant drugs in 2005. Our goal is to build forecasting models that can be used to predict U.S. Medicaid's future spending on antidepressants. We gather quarterly data (1991-2004, Centers for Medicare & Medicaid Services) on Medicaid national antidepressant expenditure. We use Box-Jenkins forecasting techniques on expenditure time series for specific antidepressants including Prozac®, Zoloft®, Wellbutrin®, Paxil®, Effexor®, and amitriptyline. Intervention analysis is used to determine the effects of patent expiration, new branded-drug entry, and new indication approval. Forecasts are computed and compared to a holdout sample, comprised of the 2005 data, to assess the performance of the models. The Prozac® and Paxil® models incorporate an intervention term corresponding to patent expiration. The model for Wellbutrin® has a pulse with decay intervention term for the increase in Direct-to-Consumer advertising. The model for Zoloft® has an autoregressive factor, and for Effexor® both an autoregressive and a moving average factor. For amitriptyline, the final model is a random walk. Maximum likelihood was used for estimations. Usual checks on the residuals proved to be satisfactory. We find that the drugs studied are affected differently by generic entry. We found no effect of either new branded-drug entry or newly approved indications.
Claudia Rosales, Optimal Inbound Trailer Allocation at a Crossdock - Optimizing Operations and Balancing Workload, August 29, 2007 (Michael Fry, Jeffrey Camm, Rajesh Radhakrishnan)
Transfreight, LLC is a third-party logistics provider that supports Toyota's lean manufacturing operations in North America. Our work provides the optimal allocation of inbound trailers to docks at a crossdocking facility operated by Transfreight. We focus on improving the efficiency of operations as well as balancing workload among crossdock workers. We compare two different implementation tools for our models: a spreadsheet-based solver and CPLEX. Since 2006, Transfreight has successfully used our implementation model for its inbound trailer assignments, leading to considerable cost savings and growth opportunities.
Bhaskar Narayanaswamy , Impact of Interruption and Forgetting in a Knowledge-Intensive Environment on Productivity, August 21, 2007 (Craig Froehle, Jeffrey Camm, Uday Rao)
With the rise of telephone, email, and ubiquitous connectivity, one increasingly common barrier to productivity in professional and knowledge-intensive environments is interruptions. Interruptions cause stoppage of the current task and often induce forgetting on the part of the worker. Beyond the direct delay caused by the interruption, the induced forgetting also causes rework; in order to complete the interrupted task, additional effort and time is required to return to the same level of task-specific knowledge the worker had attained prior to the interruption. Together, these phenomena – interruptions, forgetting, and rework – create significant barriers to productivity in knowledge-intensive work environments. In service environments, interruptions pose an especially significant problem due to the “interruption conundrum” of facing negative consequences from both ignoring and accommodating interruptions. When customer relationships are damaged by both addressing and ignoring a potential interruption, there is no obvious best recourse. This research employs observational and process data gathered from a hospital radiology department as inputs into a simulation model in order to better understand the impact of interruptions, forgetting, and rework. To help mitigate the deleterious effect of interruption-induced rework, we introduce and test the operational policy of sequestering, where one of the service resources is protected from interruptions. Our results suggest two key conclusions. First, sequestering can improve overall productivity and cost performance of the system, but the decision to implement a sequestering policy must consider the costs associated with delaying both interruptions and production work as well as the forgetting rate of the system's human workers. Second, if interruption-induced forgetting is not explicitly considered, the model's results tend to substantially underestimate the benefits of a sequestering policy.
Hsin-Chih Kao , Asymmetric-Response Study among Stock Markets of South Korea, Japan, China, and the US, July 9, 2007 (Martin Levy, Norman Bruvold, David Kelton, Weihong Song)
This project investigates whether asymmetric responses exist among stock-price indices of South Korea, Japan, and China. Magnitude asymmetry and pattern asymmetry are two main foci in the project and are tested by using regression analysis and vector autoregression (VAR) models, respectively. The main findings are as follows: magnitude asymmetry exists as the Japanese index affects the South Korean index. Second, by analyzing impulse response functions derived from VAR models, we find that pattern asymmetry exists among three Asian stock indices. When the possible US effect is accounted for in the analysis, the results show that the movement of index returns of US stocks influence those of South Korea and Japan, but not that of China.
Hua Zou, Developing a Predictive Model for Targeting Potential Donors: Application of Logistic Regression, Classification Trees, and Support Vector Machines in Analysis of Responses to Direct Mailing, May 29, 2007 (Yan Yu, Martin Levy, David Kelton)
Direct-mail campaigns are employed as a core marketing strategy by various organizations, from catalogue-order companies and direct retailers to credit-card and insurance institutions. As the response of a given random selection of prospects is uncertain, many data-mining techniques are used to target good prospects and improve the likelihood of response. In this study, we compare model performance built respectively by binary logistic regression, classification trees and support vector machines (SVMs), and show that lift and gain tables are better than ROC curves, and areas under curves (AUC) to distinguish the optimal model and select the target size because they take profit and gain into account. Finally, support vector machines stand out from other classification algorithms to understand customer behavior and maximize profit in this case.
Raja Nooti, Analyzing Search-Engine Server Patterns, May 25, 2007 (David Kelton, Jeffrey Camm, Uday Rao)
This paper deals with resequencing of server patterns in a search engine with the objective to increase resource utilization and decrease the time taken per query in the search process. A query is a request for information from a database. A server is a computer that holds information and responds to requests for information from it (based on the query). Server patterns refer to the allocation of queries to servers based on query type or frequency. This problem is motivated by the highly competitive search-engine market where each second saved is massive, and there are many potential ways to improve the search process. A base search-engine model is simulated in Arena with a real-world time distribution input to reflect the current search engines' server patterns. Real times are obtained from AOL search logs to develop the model as accurately as possible. Building on this base, an alternate remodeled model is developed incorporating logical constraints on query flow within the model to improve the resource utilization and reduce time taken per search. In addition to proving to be amenable to implementation, this remodeled scenario has several significant advantages over the base scenario, all of which are analyzed. Furthermore, a new model is developed and analyzed that features the enhancements possible and is proved to be more effective than the remodeled scenario.
Guoxiang Xu, What Factors Explain Investor Sentiment?, March 1, 2007 (Brian Hatch, Martin Levy, David Kelton)
The sentiment index recently reported by Baker and Wurgler (2006) reveals dramatic cross-sectional performance patterns in stock returns based on a variety of factors such as Firm Size (ME), Earnings-book Ratio (E/BE), Book-to-Market Ratio (BE/ME), and Sales Growth (GS). When the sentiment index is negative, the subsequent returns are relatively high on small stocks, young stocks, high volatility stocks, unprofitable stocks, non-dividend-paying stocks, extreme-growth stocks, and distressed stocks. Because the sentiment index has some ability to forecast stock returns, it would be valuable to know if there are any factors that explain this sentiment index. Initial efforts reveal that macro-economic factors have little correlation with this sentiment index; however lagged equal-weighted stock index (EW) returns have a strong correlation. Equal-weighted stock index returns annualized from the previous six years (EWP6Y) explain a majority of the variance of the sentiment index. I discuss two possible explanations for this phenomenon, the business cycle and how fund management is evaluated. For further investigation, I used a Hodrick-Prescott Filter to decompose the sentiment index into a general trend and the deviation from the trend. My analyses reveal that the trend and the deviation are composed of different groups of the six variables initially used to synthesize the sentiment index. Logistic regression reveals that EWP6Y has strong predictive power on the sign of the sentiment index.
Prido Lumbantoruan, Univariate and Multivariate Time Series Modeling Application on the Unseasonally Adjusted US Index of Industrial Production, December 8, 2006 (Martin Levy, Norman Bruvold, David Kelton)
The Index of Industrial Production is an important indicator that could be used as a barometer of economic level of a country. In this project we used three monthly economic series, the S&P 500 index (SP), the Unemployment Rate (UR), and the Money Stock Measures (M2) as the input series to model the Index of Industrial Production (IP). Two multivariate frameworks, a dynamic regression with transfer function and a multiequation time-series model, were built to model the Industrial Production Index. Dynamic regression and multiequation time series models are immensely useful in examining the relationship of past values from multiple time series with each other. Additionally, a univariate time-series model was examined and built using the Box-Jenkins method as a baseline model for comparison with the multivariate models results.
Jonathan Healey, A New Model for the Cost- and Priority-Based Carrier-Selection Problem, November 29, 2006 (Jeffrey Camm, Michael Fry, David Rogers)
The three-dimensional bin-packing problem is to pack all or a subset of boxes into one or more bins. In the three-dimensional singular bin-packing problem, the objective is to minimize the wasted bin volume. In the three-dimensional multiple bin-packing problem, the objective is to minimize either some type of bin cost or the number of bins used. Bin-packing problems have many important theoretical and practical implications. On the theoretical side, they have challenged computer scientists and discrete mathematicians for decades because they are NP-hard, and there is no universal algorithm to find the exact solution in a reasonable amount of time. For this reason, heuristics have been developed for attempting to find approximate solutions in a smaller amount of time, some of which I describe. On the practical side, they have many applications in industry, including scheduling and loading cargo into trucks (Sweep 2004). However, many approaches to the three-dimensional bin-packing problem that appear in the operations-research literature are applicable to only a portion of all situations encountered in practice due to their assumptions. The objective of this work is to develop a model for the cost- and priority-based carrier-selection problem and determine the problem sizes that are solvable to optimality in a reasonable amount of time. This model is a more practical approach to the three-dimensional bin-packing problem and builds upon a model by Chen, Lee, and Shen (1995). After showing how the new model works, I present results, observations, and statistical analyses from testing it.
Rossana Bandyopadhyay, A Two-Stage Newsvendor Problem for a Call Center with Downward Substitution, October 12, 2006 (Amitabh Raturi, Uday Rao, Jeffrey Camm)
The call-center industry has a constant demand problem whereby it is difficult to assess the inventory of seats that need to be maintained in order to meet demand and yet not have an overflow of idle seats. Many studies have been done to explore this. Call centers also have different seat types, and customers are specific to certain seat types. So while one seat type experiences idle hours, another may have a demand surge and be unable to fulfill all customer calls. This paper explores how revenue may be affected when we allow substitution of seats between classes. We evaluate the case of a two-stage call center offering high-service-level and low-service-level seats to customers. Upward substitution of seats to callers is generally not a concern. We explore how the effect of downward substitution of seats can affect overall revenue. An integer-programming model is first created to define the process and identify the parameters. Three scenarios are presented for studying the problem. The first determines the effect of variance of demand on the level of substitution. The next experiment evaluates how downward substitution may vary by relative profit rate between the seat classes. Finally, the influence of the differential target service level is evaluated. We use simulation with Crystal Ball to evaluate the process. From the results, we derive the conclusions that downward substitution does contribute to increasing the overall revenue of the firm and so it is a viable option that can be considered. We also find that downward substitution gives marginally decreasing returns and hence we recommend that managers at call centers implement a policy on the extent of downward substitution a priori based on the additional value generated by this flexibility and the marginal cost (such as goodwill losses in either market or the cost of transferring demand).
Andrew W. Lundberg, Modeling a Sports Draft Using Dynamic and Linear Programming, August 25, 2006 (Michael Fry, Jeffrey Ohlmann [University of Iowa], Jeffrey Camm)
We model a professional sports draft using dynamic and linear programming. Our goal is to determine the best drafting strategy for a team competing in a multiple-round sports draft. We formulate the problem first as a stochastic dynamic program using a team's needs at each player position and the current pool of available players to be drafted as the state of the dynamic program. However, this formulation is not generally solvable for reasonably-sized problems. Therefore, we introduce a number of additional assumptions and relaxations that results in a more tractable deterministic dynamic program. To solve our models, we reformulate the problem as a linear program. We develop an easy-to-use application in Microsoft Excel that allows the user to implement our algorithm to determine drafting strategies under a variety of conditions. The application allows the user to change a number of parameters including player rankings and valuations, length of draft, and the team's initial drafting needs. We then compare our algorithm to several competing draft strategies by measuring the performance of each in a fantasy football draft for the 2005 season. Our results indicate that our drafting strategy out-performs these competing strategies in every instance.
Rachel M. LaRosa, Optimal Sequencing in a Multiple Machine Job Shop, August 21, 2006 (Jeffrey Camm, Michael Fry, David Rogers)
In this paper I present an optimization of a specific deterministic Job Shop Scheduling Problem (JSSP). The JSSP studied involves six machines performing a total of eight processes on ten jobs in a real-world company. The schedule was obtained through a model developed with Premium Solver Platform Version 6.5 for Microsoft Excel. Comparison with the current scheduling practices of this job shop revealed many points, including insights into bottlenecking and downtime of machines and operators. As described in the literature, this type of problem is extremely hard and time-consuming to solve. This model may be further developed in the future for implementation in the job shop's schedule planning.
Dongmei Yang, Comparison of Import Vector Machines with Support Vector Machines to Make Predictions in Marketing, July 21, 2006 (David Curry, Martin Levy, Yan Yu)
Many marketing problems require accurately predicting the outcome of a future event. In today's business environment, analysts often face datasets with hundreds of variables related in complex ways so that outcome classes are not linearly separable. In the 1990s, the support vector machine (SVM) was developed for problems of this type by using kernel transformations to transform a highly nonlinear problem (in the original attribute space) into a linear problem in a higher dimensional "feature" space. The SVM performs well (Cui and Curry 2005, 2003) but is limited by the fact what it does not naturally produce probability estimates, it cannot be easily extended to multi-class problems, and it may be computationally "expensive," depending on the kernel selected. In this project, we propose and test a new technique, the import vector machine (IVM) that also employs kernel transformations, but overcomes the shortcomings of the SVM. The IVM provides classification probability estimates, it naturally generalizes to the multi-class case, and it requires less computation than the SVM. We compare the SVM and IVM using data from two sources: (1) a discrete-choice problem based on simulated data, and (2) a large-scale field study involving the prediction of the incidence of client repeat business in the marketing-research industry. Each new technique is also benchmarked against logistic regression. Results indicate that the IVM performs (nearly) as well as the SVM on these problems and that both machine learning techniques significantly outperform logistic regression. Because the IVM provides class-membership probabilities, it leads to deeper understanding than the SVM in both problems.
Kartheek K. Reddy, Regression and Time Series Modeling of the United States Civilian Unemployment Rate, July 6, 2006 (Martin Levy, Norman Bruvold, David Rogers)
The unemployment rate (UER) is an important indicator of the economic performance of a country and there are many ways of forecasting the UER. Economic indicators like the gross domestic product (GDP), the inflation rate (IR), the civilian labor force (LF), and the industrial production index (IPI) may have statistically significant influence upon the UER. The relationship among various economic indicators was examined. Regression and time-series models were developed for the UER. Ordinary least-squares regression methodology was adopted to develop the regression model and univariate autoregression (proc autoreg) and multivariate vector auto regression (VAR) procedures were used to develop the univariate and multivariate time-series models, respectively. The forecasting abilities of regression, univariate, and multivariate time-series models were compared by performing static and dynamic forecasts of the UER.
Elena Bichescu, Bankruptcy Prediction using Logistic Regression and Multiple Imputation, June 29, 2006 (Martin Levy, Jeffrey Camm, Timothy Keyes [General Electric], Yan Yu)
Altman (1968) notes that bankruptcy represents a serious financial distress state that not only affects the bankrupt company, but also has negative social and macroeconomic ramifications. In this context, models that could accurately predict the probability of a company filing for bankruptcy have wide applications, e.g., criteria for bank loans and financial investments, financial turnaround measures, etc. This work proposes the use of logistic regression models and multiple imputation techniques to predict bankruptcy. Our analysis is based on a dataset created by the author and which contains 165 companies, of which 55 have been declared bankrupt. We formulate a logistic regression model where the bankruptcy state is a binary dependent variable and the predictors are continuous financial ratios. Model building is performed on the dataset that results after applying listwise deletion on the initial input data. The models thus obtained are then validated using two approaches: train/test, where the models are validates on separate test sets, and cross-validation. The misclassification rates returned by our logistic regression models average around 10%, a performance similar to models proposed by Altman and Beaver. The proposed logistic models show that among the best predictors of bankruptcy are the financial ratios obtained based on total or current liabilities and on total or current assets. This result verifies both previous work by Altman and Beaver and the intuition that a company's financial health depends crucially on the delicate balance between assets and debt.
Jeremy Jesse, Optimal Warehouse Delay for a Supply Chain Backorders Optimization Model, May 26, 2006 (David Rogers, Amitabh Raturi, Jeffrey Camm)
In this paper a multi-level retailer inventory distribution model with backorders is considered. It is a periodic review system where the optimal base stock levels are determined by minimizing the total penalty cost of backorders subject to delay time constraints. Lead times are deterministic with possible delays, lateral shipments are not allowed, and shipment times are integer constrained to model situations where a fleet of trucks is only able to make one delivery per day. A highly nonlinear mathematical programming model was adapted for this setting. The case of non-identical retailers created a formidable challenge for standard software to yield reliable results. Interval search techniques and optimal selection were utilized within Excel and VBA to provide numerical results for the case of multiple identical retailers.
Yue Wu, An Empirical Study of the Post-Deregulation Electric Utility Wholesale Market, May 23, 2006 (Yan Yu, Martin Levy, Norman Bruvold)
This work explores the volatility structure of daily electricity price returns for 6 markets across the US. Based on daily data from 1998 to 2005, we examine the wholesale electricity prices for Cinergy, Entergy, PJM, Chicago, Michigan, and Ercot with parametric modeling methodology. A family of GARCH type models is implemented to model the return behavior, in which exogenous explanatory variables, seasonality, and asymmetric effects are taken into account. The behavior of electricity prices exhibited a strong tendency to stabilize as a common commodity after deregulation at the end of last century. Several misspecification tests are conducted to evaluate model appropriateness. Different back testing techniques are applied to identify the best model. Finally, a bootstrap simulation methodology is applied to evaluate the model performance of an updated model using data from 2001 to 2005 and an overall model from 1998 to 2005. The updated model turns out to generate a much narrower prediction interval and is more accurate. This supports the conclusion that a structural change happened around 2001.
Robert E. Carter, Estimating Tuition Elasticity Using a Dynamic Discrete Choice Model, May 19, 2006 (David Curry, Jeffrey Camm, Michael Fry)
Prior research on tuition elasticity for institutions of higher learning has consistently found a downward sloping demand curve. That is, as tuition increases, enrollment decreases. However, most published studies relied on aggregate data covering multi-year time frames. Elasticities estimated in prior research reflect the likelihood that a student will attend any college or university. The research does not provide guidance on the choice of college that an individual student may choose to attend. The research presented in this thesis is unique because it employs discrete choice experiments on an individual student basis in order to determine the tuition elasticity for 12 colleges within the University of Cincinnati. Additionally, web-based survey software containing a unique "rules engine" was developed (as none were available commercially) so that the list of competitive schools in the choice set could be dynamic and, hence, reflect the college consideration set for each student. Thus the discrete choice experiment employed here uses a data collection format personalized for each respondent in the study. Results are consistent with prior research in that we identified a downward sloping demand curve. However, our estimated elasticities are considerably greater than those reported in previous research due to the focus on individual student level data as compared with aggregate level analysis. Furthermore, within the University of Cincinnati, we found that students attending the Colleges of Pharmacy, Medicine, and The College Conservatory of Music (CCM) exhibited the lowest tuition elasticity, while students from Business, Engineering, and the College of Education, Criminal Justice, and Human Services (CECH) displayed the highest relative elasticity.
Mayank Seksaria, Portfolio Risk Management Techniques for Electricity Generating Companies, May 19, 2006 (Yan Yu, David Rogers, Martin Levy)
In the past decade electricity markets have been deregulated all around the world. In this new environment energy is traded as any other commodity. Price volatility in deregulated electricity markets is max as compared to any other commodity. Confronted with this extreme price volatility market participants and traders face enormous risks and hence need risk management in electricity markets. With the volatility that fuel prices have encountered in recent past, price risk becomes most paramount for electricity companies risk management. In this thesis we start by calculating the volatility of electricity spot prices using historical simulation methods. Then I used time series models to determine characteristics of spot price returns and also do comparative forecasting of electricity spot prices. Risk cannot be avoided in any market. Modern theory of utility is an approach to decision choice under uncertainty. I developed an optimal portfolio consisting of bilateral contracts and spot pricing. I also used sequential optimization to determine the effect of various factors on the allocation ratio in the portfolio. Besides MPT I also used VaR as a risk control technique and calculate its values. I calculated the VaR for individual asset as well as for the portfolio and compare those values to illustrate the diversification provided by developing an optimal portfolio. I have provided an overall framework of risk management for Generating companies in the competitive electricity market. The proposed energy allocation model provides an analytical and quantitative approach to energy trading.
Zhouzhou Peng, A Dynamic Self-Adaptive Algorithm and Simulation Study for Warehouse Organizing, May 18, 2006 (David Rogers, Amitabh Raturi, Uday Rao)
How well the contents in a warehouse, i.e., the variety of items stored in it, are organized is among the most important factors that determine productivity and efficiency. Current organizing methods are inadequate and cost-prohibitive when facing volatile warehouses where a huge variety of goods are frequently transferred in and out in large and unpredictably fluctuating numbers. The reason for that incapability is twofold: first, current methods tend to focus only on the storing process and ignore the impact of the order-picking function; second, current methods often use a top-down approach and lack the flexibility needed for the ever-changing environment. In this thesis is a new algorithm that integrates both the storing and the order-picking activities and employs a bottom-up perspective to solve the problem, utilizing only basic information readily available within a modern computerized warehouse management system (WMS). A simulation study based upon a real-life case is used to show the algorithm's dynamics and analyze its improved performance over the current method.
Andrew R. Remington, A Study of Unsupervised Learning, April 20, 2006 (Yan Yu, Martin Levy, David Kelton)
Unsupervised learning is a collection of methods that are extremely effective in producing accurate summaries of relationships in a data set. With the recent evolution of computing power and the free implementation of the statistical programming language R, these powerful methods are now readily available to anyone interested in data mining. This project studies association rule analysis, cluster analysis, self organizing maps, principal components, independent component analysis, and multidimensional scaling, offering summaries of each method, descriptions of each method's implementation in R, examples of the application of the method to a real data set, and an assessment of the attributes of each method. Due to the new nature of the field and fragmented documentation of each method, this project crystallizes the process of usage and understanding of each method in a freely available software language to provide novice data miners with a structure of understanding and instructions on the application of each method. This project summarizes journal publications, textbooks, and R code that deal with each method individually. The results of this project show that many unsupervised learning methods are easy to apply, execute quickly, and provide similar results among differing methods. Furthermore, the results demonstrate the redundancy of different methods concerning gene tumor data and the effectiveness of unsupervised learning as exploratory analysis. The significance of the finding is that because the methods are freely available and are easily applicable to a data set, it is prudent that data miners or statisticians apply unsupervised learning methods during their initial exploration of a data set in order to define their starting assumptions more accurately.
Honghua Shang, A Model for Profiling Asian American Association Telecom Services Customers Using Logistic Regression, February 21, 2006 (Martin Levy, Norman Bruvold, James Evans)
Data mining is an information-extraction activity whose goal is to discover hidden facts contained in databases. Using a combination of machine learning, statistical analysis, modeling techniques, and database technology, data mining finds patterns and subtle relationships in data and infers rules that allow the prediction of future results. Typical applications include market segmentation, customer profiling, fraud detection, evaluation of retail promotions, and credit-risk analysis. This project attempts to develop a model for profiling potential customers using statistical methods, such as logistic regression for a given data set. That is, the relationship of some responses and explanatory variables will be explored so that we can determine which variables are the most and least correlated with the response variable. The goal is to segment data provided by the Asian American Association Telecommunication Services into potential customers and non-interested customers. Logistic regression was chosen mainly because of its ability to analyze categorical data. Gender, language, age, dwelling, household income, location, and time zone were variables found to be statistically significant and are therefore important contributors in determining the potential AAATS customers. AAATS will adjust their future marketing campaign based on these findings.
Guohua Wu, A Study of Value-at-Risk Methods, February 7, 2006 (Martin Levy, Jeffrey Camm, Norman Bruvold)
Value at risk (VAR) is a method widely used in financial corporations to measure the risk of holding a portfolio over a period. Three basic methods to get VAR are the delta normal method, the historical method, and Monte Carlo simulation. Among these three methods, Monte Carlo simulation is most powerful while the delta normal method is most popular one since it is economical. However, these methods have a lethal drawback if VAR is forecasted over a volatile period because they assume common variance. Univariate and multivariate ARCH/GARCH models are discussed to deal with heterogonous data. Since the software for the time-varying covariance ARCH/GARCH model is not available currently, the common correlation multivariate GARCH model was used. The vector autocorrelation model is based on the idea that the conditional variances of the portfolio components not only have autocorrelation with themselves but also with other components. Thus, VAR can improve the GARCH model further.
Ying Huang, Development of RFID Technology Measurement Scales, December 2, 2005 (Craig Froehle, Michael Fry, Suzanne Masterson)
Over the past few decades, radio frequency identification (RFID) technology has been used to track and identify goods, assets, and even living things. It is gaining momentum in supply-chain management. Compared with barcodes, it is a more powerful tracking tool in many aspects and can provide more detailed and accurate information in a more timely manner. As the most promising ID technology that might revolutionize the industrial world, it has drawn a lot of interest from supply-chain participants. Millions of dollars have been invested into research to examine its potential and improve its features and benefits. Although a number of surveys have been conducted to explore people's concerns about this hot topic, it is important that RFID technology as a concept be subject to the same serious and careful academic study that has been focused on the technology itself. This could help reveal current and potential RFID users' interests and expectations. Perceptions of RFID are not well understood, likely due in part to a lack of valid measurement instruments. In this paper, we summarize the current state of RFID application. We then propose four important attributes of RFID - reliability, durability, flexibility, and security - and develop multi-item scales to assess the importance of each to managers. Employing a combination of primary field (internet survey) and artificial datasets, we perform reliability and validity analyses using the SAS and AMOS statistical tools. The results of the iterative reliability and confirmatory factor analyses suggest that two of the tested items should not be employed in further applications of the instrument. The results and limitations of the research are then discussed.
Ying Li, Using Bayes Estimation Under BLINEX Loss to determine the Mailing Size for a Direct Mail Marketing Campaign, November 22, 2005 (Martin Levy, Norman Bruvold, David Kelton)
Direct mail marketing is a growing area of marketing practice. Many corporations use a data-mining technique, called scoring model, to estimate the response probability of each household in the mailing list. The selection of targets is based on the assigned probabilities in descending order. The problem that remains unsolved is the size of mailing. In practice, the direct marketers make the decision either based on budget or maximized response rate, which are suboptimal for profit-driven firms. Bayes estimation, which takes cost into consideration, has been applied to find the optimal mailing size. Traditionally, the point estimates are often derived by implicitly assuming a squared error loss (SEL) function, but the SEL may not reflect the actual loss in a direct-marketing problem. This paper use Bayes estimation under bounded linear exponential loss (BLINEX) to find the response rate that corresponds to the optimal mailing size leading to maximized profits. A case study with real data sets from a catalogue company demonstrates the BLINEX loss structure and the financial advantage of BLINEX method over the SEL and the mailing-to-all scenarios.
Pooja Singh, Application of Linear and Non-Linear Modeling with Random effects to Analyze Biomechanical Data, November 21, 2005 (Martin Levy, Jeffrey Camm, Norman Bruvold)
This project deals with design and statistical analysis of biomechanical data. The biomechanical data pertain to a tissue-engineering experiment that aims at accelerating tissue repair. Repair of tendons, ligaments, and capsular structures is common given that these injuries represent almost 45% of the 32 million musculoskeletal cases in the US each year. As a consequence, surgeons and basic scientists have sought to identify new approaches like tissue engineering for tissue repair and returning the patient to pre-injury activities. This experiment sought to understand how the cell-to-collagen ratio affects contraction kinetics of mesenchymal stem cells (MSC) as they mature around posts in a culture. A split-plot design was successfully applied to the experiment and hypotheses were tested using the model. Also, a nonlinear model was fit between the response variable, contraction factor, and time. The model allowed that the random effect in the experiment could enter the model nonlinearly. The analysis was implemented using Proc Mixed and Proc Nlmixed in SAS.
Vinutha Nagesh, Clinical Data Mining: Frozen Shoulder, November 18, 2005 (Martin Levy, Yan Yu, Norman Bruvold)
Data mining, an interdisciplinary research area including artificial intelligence, statistics and databases, is the science of extracting useful information from large databases. In this research project, techniques of data mining were used to analyze the relationships in a clinical condition called frozen shoulder. The data set derived from the clinical database of a shoulder surgeon at Cincinnati Sportsmedicine and Orthopedic Center consists of 65 patients' records. Records include patients' demographics and clinical diagnoses information. The severity of the frozen-shoulder problem is measured in terms of the Simple Shoulder Test score (SST), the range of motion of the aggravated arm in different elevations and the American Shoulder Elbow Score (ASES), which is calculated from the patients' responses regarding the functionality of their shoulder. Treatment included physical therapy or surgery. The data were used to do comparative analyses on pre-treatment and post-treatment measurements using paired and un-paired methodologies. Predictive studies are performed to predict which treatment group a patient is assigned as a function of demographics, pre treatment scores, and clinical diagnoses.
Steven Harrod, Numerical Methods for Realizing Nonstationary Poisson Processes with Piecewise-Constant Instantaneous-Rate Functions, October 24, 2005 (David Kelton, Uday Rao, Martin Levy)
Nonstationary Poisson processes are appropriate in many applications, including disease studies, transportation, finance, and social policy. We review the risks of failing to model nonstationary Poisson processes properly and discuss three algorithms for the generation of Poisson processes with piecewise-constant instantaneous rate functions. We test these algorithms in C programs and make comparisons of accuracy, speed, and stability across disparate rate functions and microprocessor architectures. Choice of optimal algorithm could not be predicted without knowledge of microprocessor architecture.
Vishva Raj Bangad, Bioequivalence and Sample-Size Determination in the Pharmaceutical Industry, October 5, 2005 (Martin Levy, Jeffrey Camm, Uday Rao)
Assessing bioequivalence between the bioavailability of a generic drug product and the innovator drug product has gained a lot of importance in recent years since the generic-drug manufacturer does not need to perform costly clinical trials to demonstrate the safety and efficacy of the generic product if the bioavailabilities of the two drug products are demonstrated to be bioequivalent. However, this bioequivalence must be demonstrated in a statistically sound way to protect the consumer from ineffective and unsafe drugs. Until the 1970s the statistical test of hypothesis of no difference between the bioavailabilities of two drug formulations, usually supplemented by an assessment of what the power of the statistical test would have been if the true averages had been bioequivalent, was used in the statistical analysis of bioequivalence studies. Westlake proposed a new approach based on a confidence interval for the difference between the true means. During the same period, Schuirmann proposed a two-one-sided-test (TOST) method. Anderson and Hauck proposed a new test and claimed that their test was always more powerful than the above two tests. Wilcoxon, Mann, and Whitney proposed a nonparametric version of TOST if the assumption of normality or lognormality is not valid. We will discuss and compare these methods in this paper. We will also determine the power and sample size of Schuirmann's TOST. In the end, we will briefly discuss some of the new approaches that have been proposed in the last decade and define population bioequivalence and individual bioequivalence.
Bogdan Bichescu, Channel Power: Its Implication on Supply-Chain Performance, September 1, 2005 (Michael Fry, Amitabh Raturi, Pradyot Sen, George Polak [Wright State University])
Our work, comprising two essays, examines decentralized supply chains composed of one supplier and one retailer facing stochastic customer demand. We develop models for both periodic (1st Essay) and continuous review (2nd Essay) inventory policies when the decision-making rights are split between supply-chain agents. We seek to answer: 1) when does decentralized decision making result in the greatest loss in supply-chain performance and 2) what effect does the distribution of channel power have on system and individual agent performance. In our first essay, we assume the retailer is responsible for choosing order sizes and the supplier chooses delivery frequency. We find that performance losses from decentralized control are strongly influenced by the relative holding and penalty costs, but somewhat invariant to demand uncertainty due to risk pooling. Furthermore, our numerical results suggest that concentrating channel power with the supplier can lead to supply-chain profits that are very close to a centralized scenario, but also results in lower customer-service levels. Our second essay studies supply-chain performance under a vendor-managed inventory (VMI) agreement where the supplier controls delivery sizes and the retailer sets customer-service levels. Within the VMI setting, we model various power scenarios: equally powerful retailer and supplier, powerful retailer, and powerful supplier. According to our numerical results, the best system performance is achieved when the supplier acts as the Stackelberg leader. Furthermore, somewhat contrary to intuition, we find that individual agent performance is greatest when the agent acts as a follower.
Mohammad Rouholiman, Evaluating Mezzanine Finance in Real Estate: A Monte Carlo Simulation Approach, August 26, 2005 (Jim Clayton, James Evans David Kelton)
Mezzanine finance has emerged as an important source of financing in commercial real estate. It helps to complete the market by bridging the gap between what equity investors are willing to put down and what conventional senior lenders provide. The mezzanine position is structured as a junior debt piece or preferred equity share that takes the first loss after the equity investor, in the event of a default. Due to the riskiness of the position a more rigorous analysis of the property's future cash flows (pro forma) is warranted. Traditional property valuation relies on a static ten-year pro forma. A more risk-adjusted approach is very timely given the aggressive pricing of equity and debt in property markets over the past few years. Real-estate prices have soared and spreads on debt have contracted, leaving investors and bankers with very little room for error. This paper aims to provide a methodology for using Monte Carlo simulation to evaluate the riskiness of a property and aid the mezzanine lender in the decision-making process. The goal is to use Crystal Ball software to provide the mezzanine lender with a better picture of the possible outcomes for the property and see if it meets their initial underwriting criteria. Then OptQuest is used to search for the set of loan attributes that meet the lender's IRR and default risk requirements.
Guoqiang Zhang, Numerical Methods in Valuation of American Options, July 29, 2005 (Michael Ferguson, David Kelton, Martin Levy)
Unlike European options, which can only be exercised at the time of maturity and can be priced with the explicit Black-Scholes formula, American-style options can be exercised at any time before the maturity and there is no closed-form formula to price them. American Asian options, such as arithmetic average American Asian options and geometric average American Asian options, pose more difficulties in valuation since their values depend not only on the underlying assets, but also the arithmetic or geometric averages of the underlying asset over a certain time interval. Numerical methods such as binomial, least-squares Monte Carlo simulation, and finite differences, must be used to valuate American options. The binomial tree method proposed (Cox et al. 1979) provides a simplified numeric approach for valuing options and assumes that the price of the underlying can go up or down by fixed multiples. Each price jump is assigned a probability and a tree of possible underlying prices is built. Working from the tree points or nodes at the option maturity date, the worth of the option can be back calculated until the option can be valued at the desired date. Least-squares Monte Carlo simulation (Longstaff and Schwartz 1997) uses of regression to estimate the conditional expected payoff to the option holder from continuation, and is readily applicable to path-dependent and multifactor financial instruments. Finite differences transform the partial differential equation into a difference equation that can be solved numerically, and is the most commonly used numerical method for solving differential equations. In this project, we discuss the explicit finite, implicit, and Crank-Nicolson methods for the one-factor model and the explicit and ADI methods for the two-factor model such as arithmetic average American Asian options and geometric average American Asian options.
Paul Bessire, Measuring Individual and Team Effectiveness in the NBA Through Multivariate Regression, June 3, 2005 (Michael Fry, Jeffrey Ohlmann [University of Iowa], David Kelton)
At the conclusion of the 2003-04 National Basketball season, the Detroit Pistons, without one player among the NBA's top ten scoring leaders, found themselves atop the NBA with a championship ring. Conversely, Team USA, composed of the most individually talented players in the world, failed to win Gold in the 2004 Olympics. How could this happen? We believe that much of the variation found in a basketball team's success can be explained mathematically through looking at the interactions of the five players on the court and not just individual player abilities. We examine several methods for rating individual NBA players and we utilize multivariate regression analysis to assist in building successful NBA teams. We seek to predict the success of an NBA lineup consisting of the five players on a court at any time. We measure success as the lineup's average scoring margin per minute. In order to predict a lineup's success we consider a set of individual player attributes that serve as our explanatory variables. We use two-way interactions between player abilities to help explain teamwork in the NBA. Applications of the model include examining which players should play at each position, predicting the lineups that should have the greatest team success, and specifying which skill areas the coaching staff should seek to improve through the annual NBA draft, free agency, and trades.
Jason Crabtree, Construction and Tests of an Interactive Genetic Algorithm for New Product Design, June 3, 2005 (David Curry, David Kelton, Yan Yu)
Affinova IDEA(TM) is a commercial software product with marketing applications in the area of new product design. At its core is an interactive genetic algorithm (GA), which provides certain advantages over traditional product design methods, such as conjoint analysis. These advantages include the ability to handle products with many design features and levels to each feature, as well as nonlinear consumer utility functions involving complex effects. The goal of this project is to construct and test an interactive genetic algorithm similar to Affinova. The analysis portion of the project will test the GA over a variety of operating conditions and enlighten the strengths and weaknesses of a genetic-algorithm-based approach to product design.
Neelima M. Reddy, A Route-Sharing Tool for Optimization of Resource Allocation in Logistics Planning, June 3, 2005 (Uday Rao, Michael Fry, David Kelton)
The optimum allocation of resources is one of the biggest challenges faced by a third-party logistics firm during the planning phase of operations. The problem becomes complicated with uncertainty of demand, outsourcing of resources, and dynamic constraints on the availability of resources. The resources in this particular problem are tractors and drivers and they must be allocated to pre-designed routes such that all the routes are run at the design-specified times using a minimum of tractors. Traditionally it has been a slow manual process taking a logistics planner about 2-3 days to come up with a feasible allocation of tractors, let alone an efficient allocation. Also, every time a new route or a set of routes are added or route specifications are changed, the tractors have to be entirely reallocated. The long cumbersome process does not allow comparative studies between scenarios and the possibility of choosing a best cost-effective scenario. In this project, I have developed a software tool called the 'Route-Sharing Tool' for one such Logistics firm (Transfreight) that uses a heuristic approach to the resource-allocation problem and provides a good solution in minutes. It creates a weekly tractor-route flow schedule and is all the more valuable when route specifications change frequently and the resources have to be reallocated. The tool is also useful for comparative studies and can be used during route design to develop an efficient set of routes within the constraints, which reduces the idle time of resources. The tool also gives a visual representation of tractor usage and idle time, which makes it easy to understand and implement the desired changes.
Kanampully Sunny Paul, Analysis of Some Finitized Distributions for Use in Simulation, May 27, 2005 (Martin Levy, David Kelton, Norman Bruvold)
Simulation modeling helps us to replicate real processes using computer programs that are helpful in determining various important parameters of the process. As simulation modeling assumes greater significance today and finds applications in numerous fields, emphasis is being laid on generating accurate, efficient, and faster random-variate-generating algorithms. A new methodology called finitization that converts an infinitely supported discrete power series distribution into another distribution having support of specified finite size has been proposed by Levy and Golnabi. An essential feature of the finitized version is that it preserves the moments of the parent distribution up to the order of finitization. In this paper we seek to explore the possible advantages of using such a finitized distribution in simulating random variates that belong to the family of discrete power series distributions. We also check the accuracy of distributions derived by using the method of finitization compared to the theoretical distribution. We have studied the various methods of simulating random variates and the relative advantages with respect to computational times. We have carried out the simulation in SAS and compared the computational speed with respect to whatever conventional methods SAS uses to generate these distributions. After analyzing the various processing times required for simulation, we could conclude that the method of finitization is advantageous in reducing the processing times by reducing an infinitely supported series into its finitely supported form. We also could conclude that the advantages in processing times may also depend on other factors like the software used, the operating system, and the hardware configuration of the computers used for carrying out simulations.
JianJian Cheng, Projecting the Charge-Off Rate for Consumer Loan Products at HSBC Household, May 23, 2005 (Martin Levy, Norman Bruvold, Yan Yu)
Consumer loan portfolios comprise millions of dollars of receivables at HSBC Household. The ability to understand what the loss, mainly the charge-off, is going to be has become essential. Yet today there are few models available that address this area at HSBC Household. The focus of this paper is primarily on the consumer loan charge-off rate forecasts. The goal is to predict monthly performance from two months ahead to four months ahead. This paper is to answer the question faced by the senior management of HSBC Household 'how can we better project the charge-off for consumer loans?' Given the absence of a formal forecasting model, this paper presents the forecasts of six models including cohort average, Winter's method, linear regression, simple ARIMA time series models, ARIMA intervention models, and ARIMAX models. This case study concludes that, overall, the ARIMA intervention model and Winter's method provide very good forecasting for both two months ahead and four months ahead and they are recommended. ARIMAX model forecasting accuracy is not stable. It produces the best forecasting result for the two-months-ahead window, but is the second worst for the four-months forecasting window. So this model should be used carefully. Linear regression provides good results with stable accuracy. It can be used as a benchmark for other alternative forecasting models, if the delinquency data are accessible.
Peter G. Donley, Intervention Forecasting: How to Forecast Appropriately for Categorical Demand when a New Wal-Mart Superstore Enters a Retail-Dominated Market, May 20, 2005 (Martin Levy, Norman Bruvold, David Rogers)
As Wal-Mart continues to saturate the retail market, other competitive retailers are trying to find ways to adjust for the inevitable changes that they will face in the future. Consumers now have a wider selection of retailers to choose from than the usual local grocery store down the street. As a new Wal-Mart Supercenter enters the market place, there is an obvious change, an intervention, in consumers' shopping patterns. This project is focused on one appropriate method of forecasting consumer demand in a particular category, given that a Wal-Mart Supercenter has entered the marketplace. Using ARIMA intervention modeling, the appropriate steps will be taken in finding an accurate model for forecasting categorical purchases when a Wal-Mart enters and the direct effects of consumer demand are sought.
Nelly Louise Jorgensen Shapero, Human Resources Forecasting Models for Small Companies, March 11, 2005 (David Rogers, Norman Bruvold, James Evans)
Small companies should make data collection for human resource measures a routine task. A trend and regression analysis may work well for short-term forecasts of manpower requirements, even though it may be difficult to get a detailed forecast using these models. A Markov model may be useful for analysis of how many people will be in each position at some future time. The models are fitted to conditions at Transfreight LLC. Two curves are fitted to the trend analysis, an exponential and a linear curve. The trend analysis provided very reliable results for forecast using both of the models. The analysis provided a forecast with an R-square of 0.981 for the linear model and 0.989 for the exponential. A multiple regression analysis may work well for many small companies, but for Transfreight the results were not as good as the trend analysis. Using stepwise regression, the only variable entered was time and an F-test of the single-variable linear model and the multiple-variable regression models does not favor the more complex model. A Markov model was developed and used to describe the system but was not used for forecasting the employee numbers. Many of transition probabilities are very small in this model. The distribution of the standard errors, therefore, becomes very skewed and the normal assumptions necessary for accurate predictions were unreasonable. Predictions made with this model may therefore contain large errors. Several qualitative and quantitative models for human-resource planning are briefly described and evaluated for fit to small companies.
Anand Mathew, Work-In-Process Inventory Entitlement for the Aircraft-Engine Industry, March 11, 2005 (David Rogers, Amtiabh Raturi, Uday Rao)
Understanding, visualizing, and controlling inventory flow is one of the challenges faced by the modern manufacturing industry. Too much or too little of inventory in any form - raw materials, work-in-process (WIP) or finished goods - is undesirable. Of these three types of inventories, work-in-process inventory is an indication of the lack of coordination within the organization. By constantly monitoring and properly managing the work-in-process inventory levels, an organization can substantially reduce its operating costs. Most of the parameters that affect work-in-process inventory are within the organization and hence projects related to work-in-process inventory require a significant amount of impetus and organizational restructuring to succeed. Complexities of modern machineries, unstable and seasonal demand patterns, constant design alterations, and widely dispersed manufacturing locations have made visualization, analysis, and optimization of the work-in-process inventory flow cumbersome and time consuming. This project was undertaken in order to develop a scenario-analysis platform for evaluating the impact of various design parameters upon work-in-process inventory. This new application provides the user the ability to alter the demand schedule, bill of material, product cost, assembly levels, or cycle time of each component in order to analyze its impact on the work-in-process inventory levels. Currently this tool is being used for inventory forecasting and resource allocation at one of the world's largest aircraft-engine manufacturers.
Kelly Herrmann, Optimal Portfolio Allocations for Hedge Funds with Asymmetric Returns, November 24, 2004 (Yan Yu, David Rogers, Norman Bruvold)
'Hedge fund' is a phrase describing a broad range of alternative investment strategies. What they all have in common is a goal to create positive returns in any market environment. They are unregulated and privately organized, allowing for very flexible investment styles (i.e., using leverage). Non-normality and asymmetric returns are usually observed, which make traditional quantitative studies based on Guassian symmetric assumptions difficult to justify. Portfolio allocation, for example, is greatly affected by asymmetric returns. The goal of this project is to determine optimal allocation for a portfolio in hedge funds. The hedge-fund universe is divided into eight strategy categories, and recommendations of the percentage of wealth invested in each strategy are given. Strategies are represented through indices developed by hedge-fund Research. Also, the non-normality of returns will be accounted for using two unique optimization methods, the modified value at risk through the Cornish-Fisher expansion, and Duarte's unifying formulation. These methods will be explained and the portfolios they produce will be compared.
Sujan Balachandran, Bayes Estimation under Bounded Asymmetric BLINEX Loss in a Direct-Mail Decision Problem, November 24, 2004 (Martin Levy, Norman Bruvold, David Rogers)
While unbounded symmetric loss functions, such as squared-error loss, are widely used in Bayesian statistical decision theory because of their mathematical convenience, there are many situations where a bounded and asymmetric loss, such as the BLINEX loss, is more desirable. The aim of a direct-mail marketing problem is to maximize the profitability by increasing the order size and also to increase the market share by familiarizing the potential customers with our products. However, we restrict our problem to the quantitave realm and present an application of Bayes estimation under BLINEX loss to a direct-mail decision problem in which maximum profit is the main decision goal and mailing size is the decision variable. Our aim is to recreate a scenario using a real data set that is very similar to what was previously done using simulation. A scenario to demonstrate and quantify how the profitability of Bayesian estimation can be improved by incorporating the intrinsic boundedness and asymmetry features of the direct-mail loss structure. A algorithm is used to fit BLINEX based upon information elicited from decision makers in general circumstances.
Ning Shao, Semiparametric Estimation for Credit Scoring, November 16, 2004 (Liang Peng, Martin Levy, David Kelton)
Credit scoring is a statistical system used for assessing credit worthiness of potential borrowers and classifying customers into 'good' or 'bad' risk classes. With the explosive growth in the consumer credit market, the credit scoring methods have become increasingly important. They are now standard tools of credit card companies, banks, and mortgage companies, etc. to assess the loan applications, minimizing companies' costs of failure over risk groups. Common classification and regression methods of credit scores are usually linear on explanatory variables. However, in many applications, there is not always evidence of a generalized linear relationship. Data-driven nonparametric/semiparametric modeling techniques such as the generalized additive models, generalized partially linear models, and generalized single-index models, emerge as promising alternatives that offer the flexibility of fitting the curvature and yet retain the ease of interpretability. They are often considered important data-mining techniques in the initial stage of exploratory data analysis. This project investigates various semiparametric modeling techniques on a French bank credit scoring data: generalized linear models (GLM), generalized additive models (GAM), generalized partially linear models (GPLM), generalized partially linear single-index models by P-splines (GPLSIM-P), and generalized partially linear single-index models by kernel smoothing (GPLSIM-K). The response variable of interest is a binary variable indicating default/no default of a loan. The predictors are variables based on the customers' information and credit history etc. The goal of this project is to study different semiparametric models of most recent research using credit-scoring data, to reveal the relationship between variables, and to capture the curvature if any non-linearity exists. Alternatively, methods such as classification and regression trees (CART) and neural network are also discussed.
Keli Feng, Identical Jobs Cyclic Scheduling: Formulation and Solution, October 8, 2004 (Uday Rao, Amtibah Raturi, Norman Bruvold)
We study the computationally-hard, re-entrant flow, cyclic scheduling problem considered by Graves et al. (1983) and Roundy (1992). We present two problem formulations to minimize job flow time (work-in-process), given a target cycle length (throughput). We describe an effcient method to solve the problem to optimality; in computational experiments this method was significantly faster than commercial optimization software (CPLEX 8.0) and solved 40% more of the test instances to optimality within the specified run time and memory limits. We also develop a new ImproveAlignment (IA) heuristic algorithm, which we test against the optimal solution or bounds. Numerical experiments indicate that the proposed IA heuristic quickly produced solutions whose flow times were, on average, (i) 22% better than those from the Graves et al. heuristic and (ii) within 14% of the optimal flow time.
Vladimir V. Pashkevich, The Role of Culture-Level Factors in Shaping Online Purchase Intentions: A Cross-Country Comparison, August 17, 2004 (David Curry, James Evans, Yan Yu)
The primary goal of this research is to enhance our understanding of the moderating role that culture-specific variables - individualism/collectivism and cultural context - play regarding an individual's intentions to use the Internet for obtaining product information and shopping. Specifically, this research (a) operationalizes the concept of cultural context by constructing an index with formative indicators, (b) develops reliable and valid scales for measuring constructs comprising the theory of planned behavior (TPB), and (c) examines the boundary conditions and generalizability of the TPB in Internet-mediated consumption settings. The proposed model is used to examine effects of variables, at the culture level, on the strength of relationships among individual attitudes, experience, subjective norms, and purchase intentions. Predictions under TPB are evaluated across two samples drawn from the United States and Belarus. Findings reveal that subjective norms tend to influence decisions in high context/high collectivist cultures, but not in high individualist/low context cultures. The effects of attitudes and past behaviors on intentions were equal for the American and Belarusian cultures. Results of the proposed study are expected to yield implications for marketing practices across cultures.
Rachna Jaison, Volatility of Demand and its Operational Consequences: A Simulation Study of Systems Dynamics in the Machine-Tool Industry, August 12, 2004 (Amitabh Raturi, David Rogers, Jeffrey D. Camm)
The machine-tool industry, a small but vital sector in U.S manufacturing, suffers high volatility in demand due to a combination of factors. Several trillion dollars worth of inventory lie wasted in the supply-chain pipelines when demand recedes; alternatively, major opportunity losses in business are incurred when firms are unable to deliver during periods of high demand. Machine-tool firms, furthermore, have a severe organizational problem of maintaining a skilled labor force in this highly volatile scenario. Many studies have tried to understand the sources of the volatility and to test alternate policies to reduce volatility, such as reducing order lead-time, information lead time, and capacity planning lead time, altering the work force, and encouraging smoother customer ordering policies. In this study, I use systems dynamics and dynamic simulation to model the non-linear causal, delay, and feedback loops in the machine tool industry. A simple model of a machine-tool maker and a customer is created using Vensim to test various strategies that firms can implement to mitigate the effect of volatility on the industry. From my simulations, I conclude that: (1) the bullwhip effect and the investment-accelerator effect are the two main factors responsible for the extreme amplification of volatility in the machine tool industry, (2) a decrease in the volatility in product orders by the customer increases the average productivity of the machine tool builder significantly, (3) an increase in the customer-order volatility leads to a significant decrease in the average experience level of the machine tool maker's employees, (4) reducing the production lead-time reduces the backlog for the machine tool maker and benefits the entire supply chain. However, the sensitivity tests reveal that reduction in lead time can have unexpected effects on the machine tool maker's production level and capacity, and (5) smoother customer order policies are the most effective vehicle for reducing order volatility significantly compared to other changes in the machine tool operating policies or parameters.
Severine Renault, Forecasting Residual Value Insurance Using Logistic Regression, May 24, 2004 (Martin Levy, Jeffrey Camm, Norman Bruvold)
The purpose of this paper is to develop and assess a logistic regression model to predict the probability of claim for a Residual Value Insurance (RVI) portfolio. This type of insurance is a highly specialized asset-management tool through which an insurance provider assumes the market risk associated with end values of leased assets, automobiles in this case. In the past, the vehicle type, either at the make or model level, has been used to segment data into different groups, for each of which a separate model was built. The focus here is to include a categorical variable representing these groups in the model itself in order to fit a single regression for the entire portfolio. Fitting the model involves looking for confounding and interaction between the categorical variables and other independent variables, testing the significance of each input variable in the model, and finally deciding which one of the vehicle make or model is relevant to represent the vehicle type as a risk factor. The log-likelihood ratio test and the Wald chi-square statistic were used at this stage, the former to compare different regression models and the latter to test individual coefficient estimates. Once a satisfying set of variables has been defined, the next step is to assess the model. We relied for this on commonly used statistics for logistic regression, namely the c statistic for the area under the ROC curve, the Hosmer and Lemeshow ? statistic for goodness-of-fit, and the Osius and Rojek normal approximation to the distribution of the Pearson chi-square statistic. Since this second stage led us to conclude that the model was not a good fit, this paper ends with a brief comparison with results obtained from models where the data were partitioned by vehicle type and the corresponding categorical variable removed.
Karen L. Bickel, Evaluating Intensive Care Unit Mortality: a Comparison of Risk-Adjustment Methods , April 2, 2004 (Norman Bruvold, David Rogers, David Kelton)
Adjusting for differences in patient characteristics present on admission to the intensive care unit (ICU) is essential when comparing ICU outcomes. Mortality risk-prediction models measure variation in patient outcomes for severity of illness and predicted risk of death. Much of the literature refers to the utilization of risk prediction models to evaluate clinical performance and cost-effectiveness of ICUs. Computerization of commonly used laboratory variables in conjunction with the often extraordinary costs associated with manual data entry presents opportunity for the development of an automated, risk-adjusted ICU mortality model. We compare the performance characteristics of two different risk-adjusted ICU mortality models; the National Veteran's Administration (VA) Surgical Quality Improvement Program (NSQIP) surgical risk model, a partially manual data-collection process that identifies pre-surgical risk factors and uses those risk factors in the development of a 30 day mortality model for major surgical procedures, and the Veteran's Administration Intensive Care Unit Risk Adjustment model, (VIR). Assessment of model fit was completed using the Hosmer-Lemeshow goodness of fit statistic, sensitivity and specificity measures, and the c-statistic as performance metrics in evaluating the behavior of each model. Our results indicate that the VIR automated, mortality risk-prediction model produced similar, if not improved, results in model performance vs. a highly used manual data-collection method obtained by the NSQIP model. These results demonstrate that the VIR computerized mortality risk-prediction method yields comparable results to the NSQIP mortality risk prediction model for these data and warrants further study.
Piu Bose, Analysis of Covariance Model to Evaluate the Impact of a $40 Million Ad Campaign in a test Market, Using Retailer-Level Data , March 19, 2004 (Norman Bruvold, Jeffrey Camm, Martin Levy)
Market researchers are concerned with the effects of different interventions or experimental conditions (treatments) on a set of consumers. These experiments are used to reject or affirm a hypothesis, and in case of rejection, provides support for an alternative conclusion. But in the real world, these treatments often get convoluted due to some extraneous factors that constantly play in the market place. As a result, the impact on consumers is a function of both the test treatment as well as the external factors. Therefore it becomes impossible for the researcher to evaluate the true impact of the test treatment and thereby accept or reject the hypothesis. This paper attempts to understand the methodology called ANCOVA or Analysis of Covariance that is used to evaluate a test-treatment while eliminating the influences of extraneous non-test factors. ANCOVA combines two statistical techniques called Regression Analysis and ANOVA. Here the dependent variable scores and treatment conditions constitute the data, but the model includes not only experimental conditions, but also one or more quantitative predictor variables. These quantitative predictors, known as covariates, represent sources of variation that are thought to influence the dependent variable but have not been controlled by the experimental procedures. ANCOVA determines the covariation (correlation) between the covariate(s) and the dependant variable and then removes that variance associated with the covariate(s) from the dependent variable scores, prior to determining whether the differences between the experimental condition (dependent variable score) means are significant.
Yahong Cui, Application of Multivariate Adaptive Regression Splines (MARS) in Direct Marketing, March 15, 2004 (Martin Levy, Jeffrey Camm, Yan Yu)
Increasing costs of direct marketing campaigns coupled with declining response rates have prompted many direct marketers to turn to more sophisticated techniques to model response behavior. The underlying premise is that even a small improvement in prediction accuracy can have significant implications for the bottom line. This study investigates the use of a recently developed technique, Multivariate Adaptive Regression Splines (MARS), together with logistic regression in the context of modeling direct response. In this study, we report a performance analysis among MARS models, logistic regression models, and expectation models, i.e. MARS and logistic regression combined. The MARS procedure builds flexible regression models by fitting separate splines to distinct intervals of the predictor variables. Specifically, our goal is to assess the relative effectiveness of MARS models vis-à-vis logistic regression with original predictor variables in modeling direct response behavior. Our analyses show that the expectation models and the MARS models outperform the logistic model in general, leading us to conclude that MARS offers a number of advantages over a logistic model and MARS can improve the performance of logistic regression models. Direct marketing strategy implications in variable selection, model evaluation, and error variation stabilization are also discussed in this study.
Hui Hui, Comparing Logistic Regression, Classification Trees, and Hybrid Tree-Logit Models on Building Scoring Models for Catalog Mailing Campaign Data, March 10, 2004 (Martin Levy, Norman Bruvold, Jeffrey Camm)
In the last few decades, the direct mailing campaign has become an important field of direct marketing. An effective direct mailing campaign aims at selecting those target groups, offer and communication elements (at the right time) that maximize the profits. Of these four components the list of customers to be selected is considered to be the most important. Therefore, a large amount of direct marketing research focuses on list segmentation or target selection techniques. The scoring model is an effective methodology to realize the purpose of target selection. It assigns every observation in a database a score indicating how likely someone is to respond to a mailing campaign. Thus, according to these scores, the direct marketer can pick a specific number of people to receive a particular offer so that the response to the mailing is maximized. The objective of this project is to compare the performance of three predictive methodologies, Logistic Regression, Classification Tree, and Hybrid Tree-Logit model on building the scoring models to distinguish between the likely responders and nonresponders. By applying these three methodologies to a catalog mailing campaign data set which has 106,284 records and 47 fields, I came to the conclusion that the hybrid model is the best one to create the scoring model in this project, since it can better fit the data, while maintaining similar good performance properties as logistic regression. From the analysis results, I also found that while a classification tree is not as good for building the scoring model, it is the best choice for the classification task here.
Rajesh Radhakrishnan, Interactive Route Builder for Logistics Planning, February 27, 2004 (Jeffrey Camm, Michael Fry, David Curry, Robert Martichenko)
Logistics can be described as the planning, organizing and managing of activities that provide goods or services. Route designing is at the core of the 'planning' phase of operations for a 3PL (Third Party Logistics) company. The first step involves the plotting of all the locations on a map to identify clusters of suppliers (based on their location and freight information). Then routes can be designed that send freight from the suppliers either directly to the plant or to a consolidation center called a 'crossdock.' Route design has traditionally been a slow manual process done on an Excel worksheet with the use of mapping software to print a map of the supplier locations. The designer also has to rely on his or her experience in coming up with a good design on the very first attempt since historically the time taken in the process is usually quite long to allow for multiple designs and comparative studies among them to choose the best one. In this project, I have designed a software tool named the 'Interactive Route Builder' (IRB) to facilitate route-grouping and route design in general. It has made the route design process quicker and more efficient (locations are added to a route by simply clicking on them on an embedded map). The IRB allows the route designer to quickly generate a number of routing scenarios and compare them based on different parameters (such as total cost, cost per cube, etc). This report also includes mathematical and simulation analysis of the parameters to use when geo-locating a crossdock. The solution to the objective function that minimizes the sum of the product of cube and distance of the suppliers from the proposed crossdock is recommended as compared to the cube-center-of-gravity solution.
Samir Kulkarni, An Exploration of the Resource Constrained Scheduling Capabilities of Microsoft Project, February 13, 2004 (Amitabh Raturi, Jeffrey Camm, Michael Fry)
The resource constrained scheduling problem (RCSP) is a significant challenge because of the mathematical complexities that exist within the problem's formulation. Over time, software packages have been developed to aid practitioners with solving the RCSP and programs became increasingly friendly to the user and versatile in how much data the software could incorporate. As the software became more complex, it is claimed that the mechanisms used to determine the best resource constrained schedule began to deviate from what had been proven academically. In this paper, we explore the gap between academic research and the capabilities of scheduling software, specifically in the software's ability to produce a schedule optimal to certain objectives. We study the RCSP literature and analyze the leveling capabilities of Microsoft Project to gain insight to the aforementioned gap. The exact goals of this paper are to: 1) Discuss the major developments in RCSP that have brought the field to where it is today, 2) Discuss the leveling capabilities of Microsoft Project, a leading scheduling software, and the methods that it uses to obtain a feasible resource constrained schedule, 3) Provide insight into the effectiveness of Microsoft Project's leveling algorithm by comparing the results of several problems implemented in both MSP and as mixed integer programs in AMPL/CPLEX.
Huiqing Zhou, Response Models In Direct Marketing, January 21, 2004 (Martin Levy, Jeffery Camm, Norman Bruvold)
Direct marketing (DM) is a key area where scientific methods are often applied to analyze a massive amount of business data. The core of the decision process in DM is a response model which is applied to assess the purchase propensity of each customer in the list prior to the mailing. A variety of approaches have been developed in the direct marketing industry to model response, i.e., RFM (Recency, Frequency, Monetary) variables, tree-structured automatic segmentation methods such as AID (Automatic Interaction Detection), CHAID (Chi-squared Automatic Interaction Detection) and CART (Classification and Regression Tree), and linear statistic models such as logistic regression, etc. In this paper, two popular models (i.e. logistic regression model and RFM model) are introduced, built and evaluated. It is shown that the logistic regression slightly outperforms RFM model, while each model has its own specific advantages.
Hong Gu, Using Data Mining Technology to Build a Predictive Model and to Gain Understanding of Customer Characteristics for a Multi-division Catalog Company, December 1, 2003 (Martin Levy, Jeffrey Camm, Yan Yu)
Data mining techniques enable companies to evaluate historical transaction data from consumer databases and to develop a good consumer model, grouping customers based on visit frequency, profitability, etc. In this project, the data are the catalog purchases from a multi-division company that mails different catalogs to a unified customer base. The dataset contains 96,551 customer records and each record has 163 fields, including life-to-date orders, dollars, items, payment method, and very minimal demographics. All the customers receive the Division D catalog. The project is aimed at identifying the characteristics of would-be responders and the construction of a model that can predict which customers are most likely to respond to their Division D catalog solicitation. The outcome variable, “buying from division D”, is binary, while the predictor variables are either continuous or categorical. Logistic regression, CHAID, and CART approaches are employed. Since there are 163 variables involved, reducing the variables to a manageable size prior to model building is an essential and big step. Due to the dominant number of non-responders in our dataset and the limitation of the software Answer Tree 1.0, logistic regression contributes a lot in variable screening. The final logistic regression model can correctly predict 60.8% of the total wouldbe responders; the CHAID can correctly predict 54.09% of the would-be responders, and the CART algorithm in Answer Tree 1.0 can correctly predict 66.58% of the would-be responders. In terms of prediction, the CART outperforms the other two. Furthermore, the tree maps provide an intuitive understanding of why certain segments respond better than others. However, the 15-node CART tree can only provide 15 different estimated probabilities. The logistic regression model has unique predicted ability for every record.
Snehlata Bomma, Conjoint Bridging and Optimization Project, November 24, 2003 (David Curry, Jeffrey Camm, Uday Rao)
Political polling, whether of public opinion about issues, such as gun control, or direct preference polling for political candidates, has traditionally relied on very distinct survey methodology. Respondents are asked to select their preferred candidate in a mock election or to answer “yes or no” regarding a specific issue. However, most of the supercharged issues of today are multidimensional. Their complexity is “dumbed down” by standard methods, a disservice to political constituents most affected by polling results. This thesis suggests an alternative technique for assessing public opinion that deals well with complexity. The basic method, called conjoint analysis, has been employed in marketing and psychological research for several decades. However, recent developments in conjoint bridging designs and conjoint optimization enhance the applicability of the overall “technique package” to political polling, yielding many insights unavailable with today's standard approaches. In this thesis, we analyze results from an online survey that involves conjoint analysis. We test a theory of “conjoint bridging” that pools parameter estimates between two conjoint exercises. Respondents are asked to react to various hypothetical candidates for US president based on the candidate's positions on several dimensions of Homeland Security policy. Output from the conjoint analysis is then used in a conjoint optimization phase to find an “optimal position on Homeland Security”. Optimal means that even though individual voters weight attributes differently and prefer different levels, there is a single combination of levels that will please the most voters.
Xuming Yang, Framingham Heart Study Data Analysis -- A Case Study for GLM, GPLSIM and GAM, November 12, 2003 (Yan Yu, Jeffrey Camm, Norman Bruvold)
One of the most important techniques in statistics is regression analysis. Applications lie in a variety of fields, such as finance, marketing, and many medical fields. Linear regression can provide useful and interpretable descriptions in the linear relationship between response and predictor variables. The generalized linear models are powerful in fitting the linear relationship between variables when the response is from a general exponential family, for instance, binomial or Poisson. Unfortunately, in many applications, there is not always evidence of a generalized linear relationship. Other data-driven nonparametric modeling techniques, e.g., the generalized single-index models, generalized additive models, emerge as promising alternatives that offer the flexibility of fitting the curvature and yet retain the ease-of-interpretability. This project focuses on the application of several different modeling techniques -- generalized linear models (GLM), generalized partially linear single-index models (GPLSIM) and generalized additive models (GAM) -- on Framingham Heart Study data. The response variable of interest is a binary variable indicating the occurrence of coronary heart disease. The predictors are the patients' age, cholesterol level, systolic blood pressure, and their smoking status. The objective of this project is to apply and compare different models using Framingham Heart Study data to reveal the relationship between variables and to capture the curvature if any non-linearity exists. From this case study we conclude that the logistic or probit regression performs well to fit the linear relationship. When the nonlinear relationship exists, generalized additive models and generalized partially linear single index models are better in terms of capturing the non-linearity. GAM are very helpful for a visual inspection of non-linearity. GPLSIM fit the Framingham data best and retain ease-of-interpretability.
Neil D. Eisner, A Daily Replenishment Production Scheduling and Inventory Minimization Simulation, October 15, 2003 (Michael Fry, David Kelton, David Rogers)
General Cable Corporation is a $1.6 billion manufacturer of industrial and specialty cable products, spread over seven major product groups. Within a major product group, products are initially subdivided into families, termed by management ”product lines.” The Portable Cord major product group is manufactured exclusively at the company's facility in Lincoln, Rhode Island. While the firm is relatively early in its implementation of more modern manufacturing practices, several cells are currently in operation at the Lincoln plant, with each cell dedicated to the manufacture of a particular group of product lines. This study addresses demand planning and production scheduling for a single cell involved in the manufacture of product lines 40, 42, 43, 46, P5, and Q5. A well-known advantage of cellular manufacturing configurations is the enhanced capability for quick and more effective response to highly variable demand. The daily aggregate bookings for these product lines, aggregated across the company's five distribution centers, demonstrate extreme variability (i.e., a coefficient of variation of 79.16). Current demand planning is simplistic and leads to excessively high inventory carrying costs. Using a quarterly planning horizon, the mean plus 2.06 standard deviations (corresponding to a 98% service level) of the previous quarter's demand is calculated, and production is scheduled for the upcoming quarter at a fixed daily rate sufficient to equal last quarter's demand. A simulation model is developed using the most recent two years of historical booking data. We provide an estimate of the inventory levels the firm would need to carry if a daily replenishment production scheduling system were to be implemented, maintaining the same 98% service level to customers. The product lines under investigation exhibit strong commonality in both their manufacturing processes and in their bills of material. Manufacturing cycle times are on the order of magnitude of hours; therefore, the cell dedicated to a particular product line is capable of a one-day turnaround time in response to bookings. Additionally, the individual distribution centers demonstrate their own individual and unique characteristics. The mean demands at the distribution centers (RDC's) differ widely (all with similar high variability), implying that the relative contribution of each is very different with respect to meeting the overall service level goal. Neither shipping lead times, nor shipping frequency, are the same for any two RDC's. Another complicating factor is the occasional need to make a large shipment from the plant directly to a customer. This study first identifies the forecasting method which will drive the daily production schedule. The proposed process through which products are distributed, manufactured, and replenished is mapped in detail. A simulation model of this system is built using Arena® discrete event simulation software. Variants of the model are explored, such as the sequence of RDC fulfillment, the daily production control limits, and the pallet (lot) size |
