Stochastic Models of Peak-load Pricing

Abstract

So far, in setting out the classic peak-load model and its extensions, we have retained the assumption of that model, i.e. that demand is deter­ministic. Many public utilities face demands that have not only the strong periodic element of the peak-load model, but also an important random element. Stochastic demand creates various complications which typically are not considered in the deterministic case. It is neces­sary to decide whether demand is to be met, and what happens, by way of rationing, when demand is not met.¹ The analysis which follows is directed at answering these questions. In Section 5.1 we describe briefly some of the main contributions to the literature on peak-load pricing under uncertainty. In Section 5.2 we provide a general framework for analysing problems of stochastic demand, comparing the results with the deterministic solutions derived in Chapters 3 and 4. Section 5.3 is concerned with examining some major issues of the stochastic problem, namely dealing with excess demand and rationing. Section 5.4 presents a brief summary and conclusions of the arguments of this chapter.