Multi-Objective Decisions

Multi-Objective Decisions Under Uncertainty In section before we looked at the problem of evaluating alternatives when the attributes or consequences of proposed options were known with certainty. We now extend this analysis to examine options where the outcome is uncertain. The first example that we take is of a firm that wishes to value investments on the basis of short-term discounted cash flows, market share and balance sheet appearance the justification for such an approach is given in chapter 1). We describe uncertainty by use of a subjective probability distribution; the estimates are summarized in Table. The model we develop can also be used to analyse predominantly non-financial decisions. In Table (b), we look at the problem examined in chapter 1 - the location of a hospital unit. Here we look at a mixture of objectives that are affected by the decision namely: cost, deaths due to travelling time and recovery rates. The problem is, as always, to devise a decision rule that will use this information to score each option and thereby determine an order of prefer-ence. All the elements required to address these problems have already been analysed, and this section represents a bringing together of different strands. There are two points to make before looking more closely at the options in Table. First, we should emphasize that the choice processes that we describe are in essence theoretical. That their main purpose is to illustrate the different issues facing a decision maker. Whatever practical procedure a decision maker may adopt to interpret these issues, some position either explicit or implied will have been taken on each of the elements of the problem that we describe here. At one extreme, in practice, choice may be made by tossing a coin, thereby ignoring all the information; at the other extreme, an explicit analysis of the problem may be made in a manner close to the methods outlined here (see French (1989), for such case studies). A middle path is likely to prevail whereby a committee (formal or informal) will meet and 'discuss the issues'. Points will be made by various members of the committee that raise subjects in this chapter, though in less precise form. Thus it might be observed as regards Table (a) that Option 1 has a better balance sheet position. We can see that Option 1 has, in fact, first order stochastic dominance as regards this attribute. Another comment regarding Table (b) might be that Option 1 is not acceptable due to increased deaths from travelling time'. Such a statement implies that not only is there stochastic dominance of Option 2 over Option 1 in this respect, but also that the weighting given to this attribute should be such that the better recovery rate and the possibly better savings are outweighed. Another possibility is that discussion becomes confused and a decision is taken on an inadequate appreciation of the problem. This can always happen, but it is more likely to happen if the members of the committee do not appreciate the elements of the problem. A theoretical appeciation brings all the elements to the fore and shows how they are related. A second point is that we focus, as we have done throughout this chapter, solely on the problem of evaluation and selection. That is, we assume that the decision maker has been able to formulate the problem, as in Table. We should not underestimate the considerable task that this undertaking represents. The relevant attributes have to be determined, estimates have to be made of the possible levels of each attribute that options are likely to attain, and subjective probabilities have to be assigned to the levels. Table (a) Table (b) We now turn to the problems presented in Table 3.15(a) and (b). In the first of each of the options the attribute probabilities are regarded as occurring independently. In the second option the events are related in that there is for instance a 60 per cent chance of an £80,000 improvement in short-term cash flows, an improvement in market share and no change in the balance sheet occuring together. After a number of questions, preferences may be described as being independent. Physical interdependency, we should note, is quite different from preference independence. We may now draw up an additive multi-attribute or multi-objective utility model as follows: