Generalizing Goal Programming

Abstract

The linear goal programming model assumes that the decision maker’s preference structure can be decomposed into an additive multiattribute value function. The model further assumes that each of the conditional single attribute value functions are linear or that they can each be adequately approximated by a linear function. This is shown graphically in Figure 3.1. As Figure 3.1 illustrates, the linear goal programming model uses a piecewise linear approximation for each of the single attribute value functions. The linear goal programming model uses one linear segment for each monotonically increasing or monotonically decreasing segment of the single attribute value function. This is the simplest piecewise linear approximation for these functions but it is also the least accurate. This chapter will discuss a procedure for obtaining more accurate piecewise linear approximations for the conditional single attribute value functions. In addition, the goal programming model will be generalized to accommodate multiplicative multiattribute value functions, which no longer require mutual preference independence.