How to allocate funds within the army

Abstract

An interactive decision support system is proposed to aid decision making in material procurement in the Finnish Defence Forces. The system provides the decision maker with graphical information on the difference between a desired level of effectiveness and the level which will be attained in any particular resource allocation. As criteria for the allocations, we use weights for each military province, indicating the effectiveness resulting from any of their particular defense plan. Our solution procedure for the problem consists of three components: generating and screening alternatives, for which an algorithm is proposed; multiple-objective reference point optimization among selected alternatives, employing minimization of a scalarizing function; and display of alternative solutions in numerical and graphical form. Our system is a prototype which has been introduced to the military authorities responsible for resource allocation.

Introduction

Already as early as in 1940 there appeared an article in American Political Science Review where the author, V.O. Key, was concerned about the inefficiency of the budgeting procedure in the public sector. His statement was that it is too much focused on requesting for more resources, and finding supporting arguments. Key (1940) suggested that instead of only asking for more funds, the authorities should concentrate on the underlying reasons why a certain amount of money should be allocated to project A instead of project B. We consider this relevant also in today's Finland, more than 60 years later.

This study falls into the category of multiple criteria decision making (MCDM) or multi-criteria decision analysis (MCDA), if preferred. To be more specific, it deals with multiple criteria decision support (MCDS). During the last few decades, MCDM research, with its great variety of viewpoints, has seen remarkable growth and become one of the most important areas in management science (MS) and operations research (OR) all over the world (see, e.g., Fishburn and Lavalle, 1999). Steuer et al. (1995) have made a bibliographic survey of refereed journal articles published on MCDM between 1987 and 1992. They studied altogether 1216 articles which came from 52 different countries. About half of the articles (1087) were written in the USA, but there were 26 countries which published at least 12 articles. As pointed out by Korhonen et al. (1992), the research has recently shifted towards interactive decision support systems (DSS) (see also Shin and Ravindran, 1991; Vincke, 1992; Fishburn and Lavalle, 1999). A comprehensive survey of the methodology and applications of multiobjective optimization is given by Miettinen (1994), whilst the essence of decision support systems is described by Brännback (1996).

Due to improved computational facilities and the development of software, the procedures are more often also implemented in practice. However, according to White (1990), there is still a scarcity of real applications with actual data and real decision makers which have been applied and implemented into an interactive decision support system. And this seems to be the case even today (see, e.g., Pidd and Dunning-Lewis, 2001). Hannele Wallenius (1991) has studied a number of such problems, specially dealing with public policy and Kuula (1993) has studied such methods for strategic management. Nevertheless, the question: “Why are so many models built and so few used?” still remains valid and the answers are open (see, e.g., David, 2001). Our contribution to this field is to propose an interactive decision support system that has the status of a prototype. Our model has been proved to function, although the information employed in the experiments is not completely real.

This paper deals with a relatively complicated problem compared to those discussed in literature. When using the classification of MCDM problems, which is used by Korhonen et al. (1992), our problem has the nature of being discrete with a large number of explicitly defined and a priori known alternatives, the number of criteria is reasonable, and they are explicitly defined with known values.

The main contribution of our study is to show that by combining different procedures, and finding an appropriate method for each subproblem, a feasible decision support system can be constructed for our purpose. We use a new approach to the problem, and point out that there are far too many solutions to be evaluated without a computer-based support system.

After the initial work – gathering the information – we use a solution procedure with three stages: The first stage is to generate and screen the alternatives; we propose an algorithm for this. The next step is an interactive multiple-objective reference point optimization procedure among selected alternatives. Here we employ Wierzbicki (1980) method of minimizing a scalarizing function. The third stage is to display the candidate solutions in numerical and graphical form for decision maker's (DM) evaluation. This is done by using an advanced form of pie-presentation.

We have constructed a prototype system of this procedure and tested it with synthetic data. This numerical example is reported in Section 6. The system has also been introduced to the military authorities responsible for resource allocation. They found the system to be useful and to compel the decision maker to understand the procedure more thoroughly which is one of the main benefits of DSS (see, e.g., Zeleny, 1982; von Winterfeldt and Edwards, 1986). The reactions of the officers will be discussed in more detail in the concluding section of this report.