Decisions With More One Goal

Decisions With More Than One Goal Public and not-for-profit organizations are frequently faced with the problem of conflicting goals. Returning to our hospital example (section 1.1), suppose that there is a Shortage of funds, necessitating cutbacks. Some proposals may call for a large reduction of staff and a small reduction in beds; other proposals may call for a large reduction in beds and a small reduction in staff. The hospital management is likely to have to make a trade off between these two attributes. In much analysis, profit-making organizations are considered to have profit or wealth maximization as their sole objective. As explained in chapter 1, we do not disagree with profit being a goal, but, rather, question how operational it is. A profitmaking organization may well find it more practical to select between alternatives, using several attributes such as direct cash flow impli-cations, product profile, market position, management time where this is not costed), the balance sheet appearance and so on. These attributes will then have to be combined in a manner that, in the opinion of the directors and managers, will maximize the wealth of the firm. In selecting between alternatives, managers will be faced with trade-off problems in much the same way as the hospital management. Should, for instance, management decide to develop a product which is economic on management time, improves the product profile and market position, and improves the balance sheet, but has a small cash flow directly attributable to it, or develop a rival product with a higher cash flow but which makes a lesser contribution to the other attributes? To some, the cash flows should measure the effect of all attributes; to most, we feel, the problem is better understood and analysed in this disaggregated form. After all, hospital management could equally claim that it wishes to maximize a single goal of 'social benefit' - it too is in a sense disaggregating its goals in order to address widely differing aspects of the problem. Let us take a decision with two attributes - say hospital beds and staff, or cash flow and balance sheet appearance, or profit and safety - which we shall call a, and a,. Suppose that various alternatives denoted by D, to D,2 can be mapped, as in Figure. Of the various decision that can be taken in Figure, only D6 to D11 need be considered. For all other decisions, there is an alternative that has one or both attributes with a higher score and none with a worse score. Thus Du has a higher a, and the same a, as D12. There is no trade-off to be made between the two options; the rational decision maker would choose Di as it is better or as good as D12 in all attributes. In comparing Di and D12, we say that Di is dominant or 'Pareto optimal' (after the Italian economist who formulated the principle). Thus D4 dominates D,, and D, dominates Da. No alternatives are dominant from Do through to Di, and for this reason Do to Du is known as the efficient set or Pareto optimal set. In selecting between the members of this set, difficult trade-offs are unavoidable: Ds, for instance, has a higher a, score than D, but a lower a, score - which is preferable? In order to choose the most attractive option we need to formulate a more discerning decision rule than Pareto optimalism. Ideally, we would like our decision rule to select the best option, be easy to understand, simple to administer and, as previously mentioned, require as few judgements as possible from the decision maker. These preconditions have given rise to a host of algorithms designed to aid the decision maker in his choice. In this chapter we shall look at some of the basic solutions offered, reserving a discussion of more sophisticated techniques to the next chapter. One simple approach suggested by Simon (1969) (see section 2.2.2) is to use constraints. In Figure the decision maker indicates that any solution below either a', and a', is unacceptable; thus E,, Ez and Es to E, are ruled out. Within the acceptable area, we can further rule out Ey and Es, as they are not in the Pareto optimal set. Our choice is therefore narrowed to E3, E6, or Ey. To distinguish between these elements some form of trade-off will need to be determined. The manager may subscribe to one of three statements : 1. I do not mind about the price of the machine so long as it comes within my budget, but I will always prefer more reliable to less reliable machines? 2. I am very keen to keep costs as low as possible but the machine must be of a certain level of reliability. 3. Thave to balance reliability and cost?' With statement 1, it seems likely that the manager would select Es, the most reliable of the options that came within his budget. By similar reasoning, a manager who supports statement 2 is likely to choose E7. The third statement does not allow us to select between Es, E, and Ey. We can, in this case, either say that the method has gone as far as it can and the manager must make the choice; or we can ask him to make more detailed statements concerning his preferences. In pursuing the latter course, we would need to ask such questions as 'At the a', level of cost, how much reliability would you be willing to sacrifice in order to save IX of initial cost?' In effect, we would be constructing an indifference curve, having first narrowed our choice (see Koutsoyiannis, 1979, for an analysis of indifference curves). The benefits of the constraints approach lie in its simplicity. The disadvantages are that (a) there is no guarantee that the method will significantly narrow the choice, for it is possible that the constraints may be set such that the whole of the Pareto optimal set is included; (b) it may not help the decision maker, as intuition may have told him that the choice was between E3, B6 and Er; and (c) he or she may not accept the idea of a constraint, the view that 'all levels of reliability have a potentially acceptable price' would effectively negate the whole approach in this example. A variation on the constraints approach that is sometimes suggested is lexicographic ordering (Keeney and Raiffa (1976), p. 77). This method has the disadvantage of asking questions which are less likely to reflect the 'winner' decision maker's preferences, but the advantage of producing a single'. The decision maker is asked to order the attributes according to importance. The best option is simply the one with the highest score for the section examines various ways in which this conversion process may be achieved.