Dylan F. Jones

GOAL PROGRAMMING FOR DECISION MAKING: AN OVERVIEW OF THE CURRENT STATE-OF-THE-ART

There have been significant advances in the theory of goal programming (GP) in recent years, particularly in the area of intelligent modelling and solution analysis. The intention of this paper is to provide an overview of these developments, to detail and assess the current state-of-the-art in the subject, and to highlight areas which seem promising for future research. Modelling techniques such as detection and restoration of pareto efficiency, normalisation, redundancy checking, and non-standard utility function modelling are overviewed. The connection between GP and other multi-objective-programming techniques as well as a utility interpretation of GP are examined. The rationality of ranking Multi-Criteria Decision Making techniques, and of placing GP in such a ranking, is discussed.

Multi-objective meta-heuristics: An overview of the current state-of-the-art

Abstract This paper gives an overview of meta-heuristics methods utilized within the paradigm of multi-objective programming. This is an area of research that has undergone substantial expansion and development in the past decade. A literature review for this period is presented and analyzed. Analysis of the types of multi-objective techniques and meta-heuristics is undertaken and reasons for their use hypothesized. The strengths and weaknesses of meta-heuristic methods as applied to multi-objective programmes are discussed. Finally, a summary is given together with suggestions for future research.

A review of Goal Programming and its applications

This paper presents a review of the current literature on the branch of multi-criteria decision modelling known as Goal Programming (GP). The result of our indepth investigations of the two main GP methods, lexicographic and weighted GP together with their distinct application areas is reported. Some guidelines to the scope of GP as an application tool are given and methods of determining which problem areas are best suited to the different GP approaches are proposed. The correlation between the method of assigning weights and priorities and the standard of the results is also ascertained.

Combining simulation and goal programming for healthcare planning in a medical assessment unit

This paper describes a detailed simulation model for healthcare planning in a medical assessment unit (MAU) of a general hospital belonging to the national health service (NHS), UK. The MAU is established to improve the quality of care given to acute medical patients on admission, and to provide the organisational means of rapid assessment and investigation in order to avoid unnecessary admissions. The simulation model enables different scenarios to be tested to eliminate bottlenecks in order to achieve optimal clinical workflow. The link between goal programming (GP) and simulation for efficient resource planning is explored. A GP model is developed for trade-off analysis of the results obtained from the simulation. The implications of MAU management preferences to various objectives are presented.

Goal Programming in the Period 1990–2000

This chapter presents a bibliography of goal programming for the period 1990–2000. Goal programming is introduced and the main variants are defined. An analysis of applications by field is given. A survey of advances in various goal programming extension areas is conducted. The integration and combination of goal programming with other solution, analysis, and modelling techniques is examined. Conclusions are drawn and suggestions for future research directions are made. A list of over 280 references is presented.

An integrated queuing and multi-objective bed allocation model with application to a hospital in China

In this paper, a multi-objective decision aiding model is introduced for allocation of beds in a hospital. The model is based on queuing theory and goal programming (GP). Queuing theory is used to obtain some essential characteristics of access to various departments (or specialities) within the hospital. Results from the queuing models are used to construct a multi-objective decision aiding model within a GP framework, taking account of targets and objectives related to customer service and profits from the hospital manager and all department heads. The paper describes an application of the model, dealing with a public hospital in China that had serious problems with loss of potential patients in some departments and a waste of hospital beds in others. The performance of the model and implications for hospital management are presented.

Detecting IIS in infeasible linear programmes using techniques from goal programming

This paper presents ideas from goal programming (GP) used as an accompaniment to linear programming (LP) for the analysis of LP infeasibility. A new algorithm (GPIIS) for the detection of irreducibly inconsistent systems (IIS) of constraints is presented using this approach. The structure necessary for implementing such a procedure into a commercial LP solver is outlined. Results for a selection of infeasible LP problems are given, and conclusions drawn.

Extensions of Pareto efficiency analysis to integer goal programming

This paper focuses on the design, development and implementation of new Pareto efficiency detection and restoration techniques for integer goal programming. The design of the algorithms and their implementation issues within (an otherwise continuous) goal programming system are detailed. The differences between continuous and integer goal programming regarding Pareto efficiency detection and restoration analysis are described. The integer Pareto efficiency techniques have been applied to a selection of problems from different industrial contexts in order to assess their computational performance. Finally, Pareto restoration and detection techniques are applied to an integer goal programming problem to illustrate the methodology.

A distance-metric methodology for the derivation of weights from a pairwise comparison matrix

A variety of approaches exist for the determination of a weighting scheme from a pairwise comparison matrix describing a scale-relation between objectives or alternatives. The most common context for such an algorithm is that of the analytic hierarchy process (AHP), although uses in other areas of the field of multicriteria decision making (MCDM) can also be found. Typically, the eigenvalue method is the standard method employed in the AHP to determine weights, as in the ExpertChoice software. However, another class of techniques are the distance-metric-based approaches, which are frequently proposed as alternatives to the eigenvalue method. This paper evaluates such distance-metric-based approaches comparing their effectiveness, using the eigenvalue method as a benchmark. A common framework is introduced to establish an efficient frontier for method comparison.

WEIGHTED ADDITIVE MODELS FOR SOLVING FUZZY GOAL PROGRAMMING PROBLEMS

Weighted additive models are well known for dealing with multiple criteria decision making problems. Fuzzy goal programming is a branch of multiple criteria decision making which has been applied to solve real life problems. Several weighted additive models are introduced to handle fuzzy goal programming problems. These models are based on two approaches in fuzzy goal programming namely goal programming and fuzzy programming techniques. However, some of these models are not able to solve all kinds of fuzzy goal programming problems and some of them that appear in current literature suffer from a lack of precision in their formulations. This paper focuses on weighed additive models for fuzzy goal programming. It explains the oversights within some of them and proposes the necessary corrections. A new improved weighted additive model for solving fuzzy goal programming problems is introduced. The relationships between the new model and some of the existing models are discussed and proved. A numerical example is given to demonstrate the validity and strengths of the new model.