Manufacturing cell formation using similarity coefficients and pair-wise interchange: formulation and comparison

Many algorithms have been proposed to form manufacturing cells from component routeings. Most of these methods require specialized algorithms for implementation. Some others use well-known procedures such as integer programming. But these may be difficult for practising managers to comprehend. In this study we propose a simple method that can be implemented using spreadsheet software and an inexpensive layout package such as CRAFT. In addition, we also compare our procedure with many existing procedures using eight well-known problems from the literature. The results show that the proposed procedure compares well with the existing procedures using three evaluation measures. Therefore, this procedure may be useful to practitioners and researchers.     

A Unified Approach to Hedging Interest Rate Risk with Financial Futures*

There is abundant literature on the use of financial futures to reduce interest rate risk. While many applications have been developed and evaluated in the literature, little has been done to provide a simple, mathematical model unifying the disparate types of hedges. The purpose of this paper is to provide such a unifying framework. Under idealized conditions, an equation is developed giving a perfect hedge solution for arbitrary choice of planning horizon, existing or planned cash market position, and asset/liability mix. The paper is pedagogic in nature.     

A NOTE ON USER SOLUTION STRATEGY FOR MIXED-INTEGER LINEAR PROGRAMMING MODELS

Large-scale mixed-integer linear programming (MILP) models may easily prove extraordinarily difficult to solve, even with efficient commercially implemented MILP solution codes. Drawing on experience gained in solving and analyzing three intertemporal investment planning MILP models for electric power supply, this note offers several practical suggestions for reducing computer solution times for general production-allocation MILP models. Solution time reduction stems from judicious use of the powerful computational capabilities of existing commercial linear programming codes in conjunction with information known or to be learned by the practitioner about the model's structure.     

COST-VOLUME-PROFIT ANALYSIS IN STOCHASTIC PROGRAMMING MODELS

This paper applies mathematical programming to cost-volume-profit (CVP) analysis under contribution margin uncertainty. Three CVP probabilistic chance-constraint models based on various safety-first criteria for decisions under uncertainty are presented and compared. It is shown that a break-even segment of the mean-standard deviation frontier is a set of optimal solutions for the proposed models. An operational parametric quadratic programming (QP) model is constructed, and the efficiency frontier is generated. The procedures for locating an optimal solution on the efficiency frontier are then presented. The recommended QP procedure offers both technical relief from the computational difficulties posed by the probabilistic constraints and a desired flexibility in generating and presenting the relevant information for decisions under uncertainty.     

Review of Empirical Studies in Multiobjective Mathematical Programming: Subject Reflection of Nonlinear Utility and Learning

Multiple objective programming provides a means of aiding decision makers facing complex decisions where trade-offs among conflicting objectives must be reconciled. Interactive multiobjective programming provides a means for decision makers to learn what these trade-offs involve, while the mathematical program generates solutions that seek improvement of the implied utility of the decision maker. A variety of multiobjective programming techniques have been presented in the multicriteria decision-making literature. This study reviews published studies with human subjects where some of these techniques were applied. While all of the techniques have the ability to support decision makers under conditions of multiple objectives, a number of features in applying these systems have been tested by these studies. A general evolution of techniques is traced, starting with methods relying upon linear combinations of value, to more recent methods capable of reflecting nonlinear trade-offs of value. Support of nonlinear utility and enhancing decision-maker learning are considered.     

ASSESSMENT OF MULTIATTRIBUTED MEASURABLE VALUE AND UTILITY FUNCTIONS VIA MATHEMATICAL PROGRAMMING*

A major restriction on the use of decision analysis in practice is the frequent difficulty of determining a decision maker's multiattribute utility function. The assessment process can be complex and tedious and generally involves: (1) identifying relevant independence conditions, (2) assessing conditional utility functions, (3) assessing scaling constants, and (4) checking for consistency. Some of the assessment and modeling complexities encountered include an assessor's inability to respond in a quantitatively meaningful and consistent way to hypothetical gambles and an analyst's problem in selecting an appropriate functional form that accurately characterizes the conditional utility assessments. A simplified procedure that mitigates these difficulties is proposed. This procedure facilitates the determination of scaling constants by obtaining (via mathematical programming) a multiattributed measurable value function which is converted to a multiattributed utility function. The methodology can be developed advantageously to produce an interactive software package for use as an assessment aid.     

Reconfiguring the Supply Network Using Current Performance Data

Reconfiguration of the supply chain network from time to time is essential for businesses to retain their competitive edge. This paper presents a methodology for reconfiguration of an existing supply chain network. The methodology is characterized by two decision levels. In the first level, the current network performance is evaluated and efficient practices are identified. In the next level, a model that incorporates efficient practices is developed to reconfigure the network. This integrated methodology allows for decision maker (DM) input throughout the process. The methodology has been implemented and tested in the reconfiguration of an outbound petroleum supply chain network for CountryMark Cooperative, Inc. In this case study, Data Envelopment Analysis (DEA) is used to analyze current operations and an integer programming (IP) model that incorporates efficiency metrics is developed for selection of distribution facilities and allocation of resources to the facilities. Use of this methodology can lead to improved operations and reduced operating expenses.     

PORTFOLIO MODELING IN MULTIPLE-CRITERIA SITUATIONS UNDER UNCERTAINTY: COMMENT

In a recent issue of Decision Sciences, Muhlemann, Lockett, and Gear [8] developed a multiple-objective, stochastic linear programming formulation of the multiperiod portfolio selection problem under uncertainty. The purpose of this note is to offer some extensions to their multicriteria approach which is otherwise viewed as an excellent attempt at modeling realistic aspects of the portfolio selection problem. Further, integer goal programming combined with simulation is suggested as an alternate approach for solving the dynamic multiple-objective problem.     

Concepts,Theory, and Techniques PRINCIPLES OF MULTIOBJECTIVE OPTIMIZATION*

This paper attempts to isolate and analyze the principal ideas of multiobjective optimization. We do this without casting aspersions on single-objective optimization or championing any one multiobjective technique. We examine each fundamental idea for strengths and weaknesses and subject two—efficiency and utility—to extended consideration. Some general recommendations are made in light of this analysis. Besides the simple advice to retain single-objective optimization as a possible approach, we suggest that three broad classes of multiobjective techniques are very promising in terms of reliably, and believably, achieving a most preferred solution. These are: (1) partial generation of the efficient set, a rubric we use to unify a wide spectrum of both interactive and analytic methods; (2) explicit utility maximization, a much-overlooked approach combining multiattribute decision theory and mathematical programming; and (3) interactive implicit utility maximization, the popular class of methods introduced by Geoffrion, Dyer, and Feinberg [24] and extended significantly by others.     

The wireless network jamming problem

In adversarial environments, disabling the communication capabilities of the enemy is a high priority. We introduce the problem of determining the optimal number and locations for a set of jamming devices in order to neutralize a wireless communication network. This problem is known as the wireless network jamming problem. We develop several mathematical programming formulations based on covering the communication nodes and limiting the connectivity index of the nodes. Two case studies are presented comparing the formulations with the addition of various percentile constraints. Finally, directions of further research are addressed.     

Designing Distribution Systems to Support Vendor Strategies in Supply Chain Management*

The interactions among a firm's distribution strategy, market share, and distribution costs are an important consideration in the design of supply chain networks. However, these interactions are largely ignored by existing distribution system design methodologies, which assume demand is constant regardless of the firm's distribution strategy. This paper describes a multidisciplinary framework that considers these interactions in the design of “profit maximizing” distribution networks. The framework employs two major decision support methodologies: (1) binary logit models for estimating market share considering various demand-influencing parameters such as product price and distribution service, and (2) a mixed-integer programming (MIP) model for finding optimal distribution network designs. We applied the framework to an actual design problem facing a national distributor of industrial chemical products. The test results verify the framework's large-scale capability and the potential benefit of the integrated solution methodology.     

Notes and Communications A NON-DUAL APPROACH TO SENSITIVITY ANALYSIS—THE RIGHT-HAND-SIDE CASE

Linear programming and sensitivity analysis in linear programming have long been integral parts of business school curricula, both at the undergraduate and graduate levels. Most business school students are required to take an introductory course in management science emphasizing linear programming and sensitivity analysis. This note is educational and presents a non-dual approach to restoring the optimal solution to a linear program when changes in the right-hand-side vector render the current solution infeasible and thus nonoptimal.     

Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees

Multiattribute decision making (MADM) with multiple formats of information, which is called heterogeneous MADM for short, is very complex and interesting in applications. The purpose of this paper is to extend the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) for solving heterogeneous MADM problems which involve intuitionistic fuzzy (IF) sets (IFSs), trapezoidal fuzzy numbers (TrFNs), intervals and real numbers. In this method, DM's preference is given through pair-wise comparisons of alternatives with hesitation degrees which are represented as IFSs. The IF consistency and inconsistency indices are defined on the basis of pair-wise comparisons of alternatives. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) unknown a priori. Based on the defined IF consistency and inconsistency indices, we construct a new fuzzy mathematical programming model, which is solved by the developed method of fuzzy mathematical programming with IFSs. Once the FIS and the attribute weights are obtained, we can calculate the distances of all alternatives to the FIS, which are used to determine the ranking order of the alternatives. A supplier selection example is presented to demonstrate the validity and applicability of the proposed method.     

多目标物流网络优化模型的研究

针对物流网络规划中需要考虑多个目标的问题,以配流中心存储容量及使用率为约束,建立了基于总费用及最大单程距离(费用)最小的双目标数学模型,给出了优化模型的求解方法,为决策者提供多种可供选择的优化方案。     

Understanding the Elusive Black Box of Dynamic Capabilities

A major challenge for managers in turbulent environments is to make sound decisions quickly. Dynamic capabilities have been proposed as a means for addressing turbulent environments by helping managers extend, modify, and reconfigure existing operational capabilities into new ones that better match the environment. However, because dynamic capabilities have been viewed as an elusive black box, it is difficult for managers to make sound decisions in turbulent environments if they cannot effectively measure dynamic capabilities. Therefore, we first seek to propose a measurable model of dynamic capabilities by conceptualizing, operationalizing, and measuring dynamic capabilities. Specifically, drawing upon the dynamic capabilities literature, we identify a set of capabilities—sensing the environment, learning, coordinating, and integrating—that help reconfigure existing operational capabilities into new ones that better match the environment. Second, we propose a structural model where dynamic capabilities influence performance by reconfiguring existing operational capabilities in the context of new product development (NPD). Data from 180 NPD units support both the measurable model of dynamic capabilities and also the structural model by which dynamic capabilities influence performance in NPD by reconfiguring operational capabilities, particularly in higher levels of environmental turbulence. The study's implications for managerial decision making in turbulent environments by capturing the elusive black box of dynamic capabilities are discussed.     

Mathematical programming: Turing completeness and applications to software analysis

Mathematical programming is Turing complete, and can be used as a general-purpose declarative language. We present a new constructive proof of this fact, and showcase its usefulness by discussing an application to finding the hardest input of any given program running on a Minsky Register Machine. We also discuss an application of mathematical programming to software verification obtained by relaxing one of the properties of Turing complete languages.     

A simulated annealing algorithm for designing cellular manufacturing systems with productivity consideration

In this paper, we propose a productivity model for solving the machine-part grouping problem in cellular manufacturing (CM) systems. First, a non-linear 0-1 integer programming model is developed to identify machine groups and part families simultaneously. This model aims to maximize the system productivity defined as the ratio of total output to the total material handling cost. Second, an efficient simulated annealing (SA) algorithm is developed to solve large-scale problems. This algorithm provides several advantages over the existing algorithms. It forms part families and machine cells simultaneously. It also considers production volume, sales price, and maximum number of machines in each cell and total material handling cost. The proposed SA also has the ability to determine the optimum number of manufacturing cells. The performance of the developed models is tested on eight problems of different size and complexity selected from the literature. The results show the superiority of the SA algorithm over the mathematical programming model in both productivity and computational time.     

EDUCATION

The power of an integer programming approach—and more particularly a 0,1 programming approach—to resource allocation problems is not widely appreciated. Recent developments in mathematical programming and in problem formulation enable decision makers to deal explicitly with the special conditions which characterize real world problems in capital budgeting, scheduling, and facilities planning. In this paper, somewhat tutorial in nature, we seek to demonstrate formulation and solution of an equipment selection resource allocation problem with several special conditions. The problem can be solved on any reasonably equipped computer system. Sensitivity studies are also performed and discussed.     

Exact and heuristic approaches for the automated design of medical trainees rotation schedules

This article addresses the problem of designing rotation schedules for the training of medical students in a healthcare institution in Colombia. Rotations are carried out along the course of a six months time period during which students rotate through different services both during one or multiple fortnightly periods. The hospital receives trainees from different universities that present heterogeneous requirements, and must accomplish different rotations constraints even in those cases when they come from the same university. Two different approaches are proposed to tackle the problem. First, a mathematical programming model is considered. Secondly, a metaheuristic approach based on Variable Neighborhood Search is adapted to solve the problem in an efficient manner. In both cases the objective function is proposed to be either a linear or a quadratic function that seeks a stable allocation of personnel to the services all along the considered time horizon. The proposed techniques are implemented as a part of a basic spreadsheet that helps personnel in charge generate, validate and fix the proposed plans as needed. The effectiveness of the methodology is tested through ex-post analysis, comparing it against schedules generated by the personnel in charge at the hospital, and over simulated data. The results indicate that the applied metaheuristic is competitive against specialized optimization software and facilitates the work of optimization for the health professionals in charge, reducing the planning tasks from several days to minutes.