Business Administration, Management, and Operations Commons^™

Paints-R-Us Term Project, Tyler Campbell, Skye Gilbreth, Michael Oluwole, Elijah Raffo, Brad Unruh

Engineering and Technology Management Student Projects

This project will consider a linear product mix optimization problem for a fictional paint company, Paints-R-Us. Paints-R-Us is a wholesale paint manufacturer located in the Pacific Northwest. The Global Production Manager, Steve Brush, has been tasked with maximizing Paints-R-Us’s profit in the upcoming quarter. Steve Brush oversees the global production plan, and in collaboration with the production planners will develop a production plan which optimizes the profits that Paints-R-Us can create in the quarter accounting for the following criteria:

• Demand in the given quarter for each of the 5 paint types that Paints-R-Us produces • The warehousing storage capacity …

A Frequency Domain Step Size Estimation Procedure For Path Search Simulation Optimization Algorithms, Sheldon H. Jacobson, Lee W. Schruben

Research Reports from the Department of Operations

A frequency domain approach for step size estimation in path search simulation optimization algorithms is presented. The approach is based on Newton's method. Computational comparisons with stochastic approximation step sizes are included which indicate that the two methods can be effectively used together. The frequency domain approach can be used first to efficiently move into a neighborhood of the local optima; stochastic approximation can then improve the accuracy of the estimated optima. [Published circa 1998-1990.]

Heuristics: Rules Of Thumb For Logistics Decision Making, Ronald H. Ballou

Research Reports from the Department of Operations

A careful look is taken at the use of heuristics, or rules of thumb, in logistics decision making. These rules that guide computational procedures to find satisfactory solutions quickly are vital to solving many logistics problems. Heuristics are defined and appraised as a procedure in contrast with simulation and optimization methods. Examples are given of the use of heuristics in both strategic and operating problem types. How to develop heuristics is also discussed.

Some Observations On The Optimal Material Removal Rate In Unreliable Metal Cutting Processes, Anlong Li, Wenyaw Chan, Henry C. Co

Research Reports from the Department of Operations

This paper examines the foundation for economic analysis in unreliable metal cutting processes. We present some results on the machining parameter optimization problem, explaining the effect of the cutting speed on tool life and the rate of acceptance. [Published circa 1985-1988.]

Multinomial Approximating Models For Options With K State Variables, Bardia Kamrad, Peter H. Ritchken

Research Reports from the Department of Operations

Contingent claims whose values depend on multiple sources of uncertainty arise in many financial contracts and in the analysis of real projects. Unfortunately closed form solutions for these options are rare and numerical methods can be computationally expensive. This article extends the literature on multinomial approximating models. Specifically, new multinomial models are presented, that include as special cases existing models. The more general models are shown to be computationally more efficient.

Optimization Of A Multi-Product, Multi-Period Distribution Network With Fixed Costs, For Refined Petroleum Products, Cynthia Diane Leach

Research Reports from the Department of Operations

The distribution network for refined petroleum products is multicommodity in nature since multiple products must share the same transportation resources. To satisfactorily model this network in order to study strategic decisions requires modeling multiple time periods and the use of integer variables for fixed costs. Although the problem can be mathematically formulated as a mixed integer linear program the number of variables makes it difficult to solve using standard linear programming software for real world problems. In order to exploit the structure of the problem, which includes coupling constraints, coupling variables and embedded networks, a three-level decomposition algorithm using the …

A Systematic Approach To Countertrade Decision Making Analysis, Kil Ju Park

Research Reports from the Department of Operations

Countertrade literature to date has concentrated ondiscussing the motivations, reasons, and advantages of specificcountertrades and the negotiation contract requirements fortransactions between countries. However, developing ascience-based decision model for countertrade has drawn littleattention in the literature. Increasing importance ofcountertrade in the world market requires a systematic decision-making process in order to reduce the transaction negotiationtime and cost, and increase profitability of a country or aninternational company.This thesis attempts to improve the countertradenegotiation process by recognizing a hierarchy of objectives tobe met in 1) Picking the proper negotiation partner. 2)Selecting the proper quantities of the different goods to betraded. The first objective …

Optimal Decision And Detection In The Decentralized Case, Moula Cherikh

Research Reports from the Department of Operations

This dissertation addresses the problem of optimal decentralized detection or decision-making about some binary states of the world. In the centralized case, the solutions are well known and easily obtained using the classical theory of statistical hypothesis testing. The decentralized case has an additional degree of complexity due to the interrelationships and the dependence between the decision-makers. As formulated here, the model has applications to any problem in which stochastically independent observations are abstracted to inform a central decision-maker, or are used to determine a team action. Examples include: a strategic defense system, a battery of medical tests, or an …

Valid Inequalities For Constrained Assignment Problems, Sunil Dhamankar, Daniel Solow

Research Reports from the Department of Operations

Recently, valid inequalities derived from polytopal structure of the constraints are playing an important role in solving difficult combinatorial problems. These inequalities strengthen the LP relaxation of the problems and improve the lower bounds substantially. It is expected that in an branch-and-cut type algorithm stronger lower bounds will reduce size of the search tree and will minimize computational effort. In this paper , we consider an Assignment Problem with a single Knapsack Constraint (APKC). We present efficient procedures to identify valid inequalities for the APKC from the LP optimal solution. These inequalities can be strengthened by including additional variables for …

An Improved Counterexample To The Rudimentary Primal Algorithm, Robert Haas, Kamlesh Mathur, Harvey M. Salkin

Research Reports from the Department of Operations

The rudimentary primal algorithm (RPA) is a simple and convenient algorithm to solve all-integer integer programs; its considerably more complex alternative is the "simplified primal algorithm" (SPA) of Young [3] and Glover [1]. The RPA has not been demonstrated to converge, however; Mathis [3] and Salkin [4] have in fact presented counterexamples for which it cycles indefinitely with period six. The counterexamples depend critically, though, on a rigid choice of the "optimal" pivot columns; Mathis' example converges if alternative columns are selected, and we observe here that Salkin's converges quickly too. The issue thus remained open whether the RPA might …

An Efficient Resource Directive Algorithm For Multicommodity Network Flow Problems, Chandrashekhar Madhukar Khot

Research Reports from the Department of Operations

Resource directive algorithms for multicommodity network flow problems are decomposition schemes that work by transforming the problem into one of finding the best possible allocation of capacities to the competing commodities. The transformed problem has a piecewise linear convex master program, with single commodity network flow subproblems, which can be solved fast. Resource directive algorithms presented in the literature have attempted to exploit the convexity of the objective. However, the best resource directive algorithm available, the subgradient algorithm, remains heuristic in nature. On the other hand, optimizing algorithms are usually computationally effective variants of the revised simplex algorithm; are roughly …

Unification Of Single Objective Mathematical Programming Problems, Gregory Pollock, Arnold Reisman

Research Reports from the Department of Operations

This paper attempts to unify a broad, though not exhaustive, arena of mathematical programming. The approach involves the development of a general mathematical problem formulation, which is shown to reduce, in a deductive manner, to each of the major subfields of mathematical programming. Furthermore, a taxonomy is provided for classifying each of the special cases. Lastly, the premier algorithms for solving each of the cases are indicated and referenced.

Resource Requirements For Scheduling With Different Processor Sizes - Part Ii, Hamilton Emmons, Venkateswara Reddy Dondeti

Research Reports from the Department of Operations

Given a start time s, duration p, and the minimal processor capacity required Rj, for each of n jobs (j=1,...,n), we wish to find the optimal mix of processors, available in r≥2 different sizes, with capacities C1

A Mean Value Analysis Model For Job Shop-Like Systems, Henry C. Co, Gang Li

Research Reports from the Department of Operations

The purpose of this paper is to present a mean-value analysis model for determining some congestion measures of job shop-like systems such as the flexible manufacturing system (FMS).

Scheduling To A Common Due Date On Parallel Uniform Processors, Hamilton Emmons

Research Reports from the Department of Operations

We consider scheduling a set of jobs on parallel processors, when all jobs have a common due date and earliness and lateness are penalized at different cost rates. For identical processors, the secondary criteria of minimizing makespan and machine occupancy are addressed. The extension to different, uniform processors is also solved.

Resource Requirements For Scheduling With Different Processor Sizes - Part I, Venkateswara Reddy Dondeti, Hamilton Emmons

Research Reports from the Department of Operations

Given a start time sj, duration pj, and the minimal processor capacity required rj, for each of n jobs (j=1,...,n), we wish to find the optimal mix of processors, available in two different sizes, required to complete all jobs on schedule. A job with a smaller size requirement can be done by a bigger processor, but not vice versa. We present algorithms for solving this problem under two different objectives: (a) Minimize the total number of processors, and, given that, minimize the number of bigger processors: (b) Minimize the total costs of the processors.

Minimal Resources For Fixed Job Schedules With Defferent Processor Size Requirements And A Hierarchical Structure, Venkateswara Reddy Dondeti

Research Reports from the Department of Operations

In resource allocation and scheduling problems, we frequently come across situations wherein the tasks, although similar in nature, require resources of different capacities. An example is the assignment of airplanes to different flights. In this case, the basic task is the same, but depending on the expected load of a flight, we would assign a plane of larger or smaller capacity to that flight. The essential feature of this type of problem is that not only the tasks require resources of different capacities, but also a resource with a higher capacity can, if necessary, undertake a task which requires a …

A Sequential Linear Programming Approach For Solving The Linear Complementarity Problem, Syamal Roy

Research Reports from the Department of Operations

This research is concerned with the linear complementarity problem (LCP). In the first part of this research, we develop an algorithm which finds a solution to the LCP or detects that none exists when the given matrix M is either a P-matrix, or M is nonsingular and its inverse is nonpositive. Our approach is to solve an equivalent constrained optimization problem, the feasible region of which is the same as that defined by the linearity constraints of the LCP. The algorithm starts with a solution to the linearity constraints, if one exists, and solves a sequence of linear programming subproblems. …

Decision Support System For Capacity Planning And Operational Design, Mahesh Chandra Pati

Research Reports from the Department of Operations

The purpose of this dissertation was to provide a decision support system to address the capacity planning and operational design issues of a multi-product, multi-family, multi-stage serial flow production line. The existing algorithms find production schedules either for a single-product case or for a multi-product, single-family manufacturing system of only one stage. The latter problem is an NP-complete problem. The model developed in this thesis is called the Manufacturing Analysis System (MAS). MAS determines a feasible schedule that will minimize the total setup and inventory holding costs, which should be close to the optimal schedule. The Extended Basic Period (EBP) …

Multivariate Quality Control : An Hypothesis Testing And Optimization Approach To Effective Use And Measure Of Performance, Joel K. Jolayemi

Research Reports from the Department of Operations

There are many good techniques, whose developments are based on sound statistical and economic considerations, available for use in the design of Univariate Quality Control (UQC). Despite their familiarities and popularities in UQC, many of these techniques have not been adopted for use in Multivariate Quality Control (MQC). In this dissertation, we have classified the various design techniques used for Shewhart's plan into two parts, viz: 1) the hypothesis testing approach, and 2) the optimization approach. A few good design techniques in the two categories above have been thoroughly modified and extended for the design of MQC plans. Under the …

Improving And Expanding The Role Of D-Optimality In Experimental Designs With Emphasis On Response Surfaces, Chin-Kyooh Lee

Research Reports from the Department of Operations

When an experimenter performs experiments, the most important consideration is the experimental design. However, if the experimental cost is low, the experimental design is not a problem because the experimenter is at liberty to choose any design he wants. But if the cost is high and the number of experiments is restricted, then the experimental design becomes critical. Classical experimental designs are the best designs and they have unique properties. But they cannot be used when the experimenter is confronted with special problems such as a restriction on the number of experiments, restricted experimental runs, augmentation of designs, or special …

A New Approach For Determining When The Linear Complementarity Problem Has No Solution, Venky Venkateswaran

Research Reports from the Department of Operations

For the Linear Complementarity Problem (LCP) we have developed a finite descent algorithm that is capable of obtaining an optimal solution when the given matrix is a P-matrix. Conventional finite descent algorithms for solving geometric optimization problems move only from the current point to a geometrically adjacent one while traversing the feasible region. Here, we develop an algorithm that may 'jump' over infeasible regions during its operation. In a sense analogous to the methods of combinatorial optimization, the proposed algorithm exploits a 'nearness' structure that is defined not with respect to physical adjacency but with respect to the objective function …

A Mean-Lower Partial Moment Analysis Of Hedge Portfolios, Wen-Kuei Chen

Research Reports from the Department of Operations

If the continuous trading assumption is met, then the Black-Scholes (BS) model is appropriate for option valuation. However, in this case, since the market is complete, the claims are redundant and offer no economic benefits. Trading and monitoring costs may prevent the continuous trading assumption from being met. In incomplete markets, shareholders benefit by trading options since they can alter their risk exposures in ways that could not be done without options. On the other hand, portfolio strategies based on meshing options for future periods are likely to be more relevant for individuals and institutions that use options as a …

A Corporate R&D Strategic Planning And Budgeting Model, Gregory Richard Madey

Research Reports from the Department of Operations

This thesis describes an R&D decision support model that was developed and subsequently tested for use within a division of an aerospace firm. The model is used for R&D project evaluation, selection and budgeting. The model uses multiattribute utility theory to describe the preference structure of the organization's decision makers. Data defining the projects is obtained from the firm's decision support system. Mathematical programming techniques are used to select a portfolio of R&D projects that maximizes the expected utility of the firm. Several multiobjective mathematical programming approaches for maximizing expected utility are formulated and evaluated. These include (1) minimization of …

Applications Of Integer Programming To Radio Frequency Management, Koichi Nishimura

Research Reports from the Department of Operations

The management of the radio communication environment has become increasingly complex as communication requirements have evolved. Various types of interference could seriously degrade the performance of a communications network. In a Naval fleet radio communication scenario, a particular type of interference, referred to as intermodulation interference, is important and amenable to mathematical study. In this problem scenario, the primary objective is to find an overall assignment of frequencies to each communication net such that potential intermodulation interference is minimized, while satisfying other communication requirements. In order to determine the potential level of intermodulation interference for each candidate set of frequencies …

Duality, Finite Improvement And Efficiently Solved Problems, J. Franco, Daniel Solow, Hamilton Emmons

Research Reports from the Department of Operations

We generalize the concept of duality, known for Linear Programming, to other optimization problems and introduce finite improvement algorithms as a class of algorithms which includes the simplex method. The concept of finite improvement is interesting because such algorithms can work on non-convex problems such as the Linear Complementarity problem. Our goal is to find the relationship between finite improvement, duality and optimization problems which can be considered tractable. The study of these concepts naturally includes consideration of complementary problems (CO-NP) and data-independent and data-dependent neighborhoods. We find that the class of optimization problems with duals is the same as …

Principles For Evaluating And Selection Of Alternative Systems, Chung-Ung Lee

Research Reports from the Department of Operations

The Multi Attribute Decision Making (MADM) problem arises in the selection of the most appropriate alternative from a set of very complex alternatives, such as, plans, projects, actions, tactics, strategies, products, etc. MADM methods are based on the multi-dimensionality of decision attributes. The significant advantage of the MADM method is that they avoid the rather arbitrary transformation of decision attribute values into unique monetary units. Moreover, these methods are capable of taking into account intangible attributes. But MADM methods may suffer from the degree of uncertainty, both in decision attribute values and in the weighting vector. The existence of many …

Functional Approximation Approach To Multistate Control Problems, Prasert Shusang

Research Reports from the Department of Operations

An iterative method for solving multistate dynamic control problems is presented. The algorithm differs from most decomposition methods currently used in the deterministic optimization of control systems. The method is described as a functional approximation of the recursive equation in dynamic programming. The basic concept is directly dependent on the Sensitivity Theorem in nonlinear programming. The method, referred to as Functional Approximation approach to multistate Control Problem (FACP) is shown to be efficient in case study for operation of multireservoir system. It results in a marked reduction in computer storage and thus directly increases the power of multistate dynamic programming …

Quality Control And Servicing : A Decision Framework, Charles S. Tapiero, Hau L. Lee

Research Reports from the Department of Operations

It has been widely recognized that quality control and the repair services provided by a firm are important strategic tools for the sales of the firm's product. This paper considers the relationship between these two important decision variables of the firm: quality control and service capacities. For both the cases of degenerate and non-degenerate probability distributions of defective items, analytical results for the determination of optimal quality control inspection policy and optimum service capacities are obtained. The sufficient conditions derived provide a powerful means to determine the optimal strategies under different scenarios. For the non-degenerate case, bounds for the optimal …

A Finite Improvement Algorithm For The Linear Complementarity Problem, Konstantinos Paparrizos

Research Reports from the Department of Operations

This research is concerned with the development of a computationally efficient improvement algorithm for the linear complementarity problem (LCP). Our approach to finding a solution to the LCP is to solve the equivalent constrained optimization problem (COP) of maximizing the sum of the minimum of each complementary pair of variables subject to the constraints that each such minimum is nonpositive. An optimal solution with objective function value of zero yields a solution of the LCP. The algorithm, descent in nature, is similar to the simplex method in the sense that it moves between basic points of an associated system of …