Gary R. Reeves

A multiple criteria approach to data envelopment analysis

In this paper, we present a Multiple Criteria Data Envelopment Analysis (MCDEA) model which can be used to improve discriminating power of DEA methods and also effectively yield more reasonable input and output weights without a priori information about the weights. In the proposed model, several different efficiency measures, including classical DEA efficiency, are defined under the same constraints. Each measure serves as a criterion to be optimized. Efficiencies are then evaluated under the framework of multiple objective linear programming (MOLP). The method is illustrated through three examples in which data sets are taken from previous research on DEAs discriminating power and weight restriction.

A simplified interactive multiple objective linear programming procedure

Abstract Differences in decision making styles and decision settings have motivated the development of a variety of interactive approaches to assist decision makers (DMs) in determining preferred solutions to multiple criteria decision making problems. This paper presents a Simplified Interactive Multiple Objective Linear Programming (SIMOLP) procedure which is designed to appeal to a broad range of DMs because of its simplicity and flexibility. Specifically, at any stage in the interactive process, the procedure attempts to 1. (1) minimize the inputs required from the DMs; 2. (2) provide DMs with a representative set of decision alternatives while simultaneously limiting the number of alternatives considered; and 3. (3) allow DMs to change their minds about previously eliminated alternatives. The procedure is illustrated with both graphical and numerical examples and computational experience is discussed.

Minimum values over the efficient set in multiple objective decision making

Abstract In multiple objective decision making (MODM), it is often helpful to provide the decision maker (DM) with bounds on the values of each of the objectives. Ideal solutions are relatively easy to calculate and provide upper bounds on the value of each objective over the set of efficient solutions. Ideal solutions also provide lower bounds on the value of each objective over the ideal set. However, the lower bounds over the set of efficient solutions can be strictly less than the ideal lower bounds, but are, in general, more difficult to determine. Thus MODM procedures which utilize the ideal lower bound may overlook elements of the set of efficient solutions. This study explores the differences between the subset of the set of efficient solutions to a MODM problem bounded by its ideal solutions and the complete efficient set.

An Integrative Model-Based Approach to Hospital Layout

Abstract The issues of facility layout and bed allocation in health care settings are typically evaluated separately using very different model-based approaches. This paper describes a two-phase approach to the hospital layout problem that incorporates a number of considerations from typical layout models and methods used in determining bed allocations. The first phase involves a quadratic integer goal programming model that determines a configuration and recommended allocation of beds to hospital services. The detailed ramifications of the proposed layout are then evaluated in the second phase via a simulation model. The application of the optimization-simulation approach in a general purpose hospital is described. Handled by the Department of Health Systems.

Master production scheduling: A multiple-objective linear programming approach

This paper describes and discusses a mathematical model for developing a Master Production Schedule. The model considers multiple objectives and several typical constraints. The input parameters to the model are determined and an example is solved to illustrate the procedure.

A comparison of two interactive mcdm procedures

Abstract A number of interactive procedures exists for multiple criteria decision making ( mcdm ). Different procedures may be better suited for different types of decision makers, for different types of decision situations or for different stages in the decision making process. This paper compares the computational performance of, and specifically the quality of the solutions generated by, two similar, yet contrasting, interactive procedures, the simolp procedure of Reeves and Franz, and the Tchebycheff procedure of Steuer and Choo. Both procedures were easy to use and produced good quality solutions, although some differences in the performance of the two methods were observed.

An Interactive Procedure for Solving Multiple Objective Integer Linear Programming Problems

This research presents an interactive procedure for solving Multiple Objective Integer Linear Programming Problems (MOILP). The procedure uses preference information extracted during the interactive steps of the procedure to help the decision-maker (DM) find a preferred integer solution. The scenario considered here assumes that the DM cannot provide a quantitative specification of his (her) preferences in the form of a utility function. The demands imposed by the procedure upon the DM consist of requesting from him (her) the indication of the least preferred solution from a reduced set of candidate efficient solutions presented to him (her) for examination at each interaction. These candidate solutions are generated by the procedure utilizing a software package that solves single objective integer linear programming problems. In the last interaction, the DM is requested to select the most preferred solution from the reduced set that contains those solutions that are more attractive to him. A test problem is presented and solved following the indications of the procedure.

A military reserve manpower planning model

Abstract A multiple objective model for manpower planning in a company sized, 100 person, military reserve unit was developed and tested. The model involves five objectives and consists of over 1150 decision variables and 650 constraints over a 12 month planning horizon. US Army Reserve officers were used as subjects in an experiment in which model solutions were generated interactively using two different solution procedures. One procedure asked subjects to identify their most preferred solution from a set of candidate solutions at each stage of the interactive process, while the other procedure asked subjects to identify their least preferred solution. Scope and purpose This paper describes the development and testing of a multiple objective model for manpower planning in a company sized, 100 person, military reserve unit. US Army Reserve officers were used as subjects in an experiment in which model solutions were generated interactively using two different solution procedures. Participants found the model and solution procedures useful in helping to meet their manpower planning needs.

A zero-one goal programming model for capital budgeting in a property and liability insurance company

Abstract This paper presents a zero-one goal programming model for capital budgeting in a property and liability insurance company. The model structure allows for the inclusion of multiple goals, indivisible projects and a multiple period planning horizon. The model offers an advantage of being closer to reality than many previous models and, at the same time, is easy for decision makers to understand and use. Model solutions and sensitivity analyses are presented.

A generalized interactive goal programming procedure

Abstract This paper generalizes the interactive sequential goal programming (ISGP) procedure of Masud and Hwang [1]. A fundamental ISGP assumption concerning the preemptive relative importance of achieving adjusted goal target levels is shown to be unnecessarily restrictive and is relaxed. The modified procedure is illustrated with examples.