A multivariate utility function approach to stochastic capacity planning

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The problem being considered is the expansion of a single capacity when the installation cost is large and there are neither absolescence nor spatial effects on the expansion. Demand is assumed to follow an evolving process; in particular, the demand increments are normally distributed with linearly increasing mean and variance in time (i.e., a Wiener process). Selecting the optimum size and timing of capacity additions in the face of uncertain demand forecasts involves both the minimization of cost as well as the minimization of risk. For the situation where demand acts as a Wiener process, Kang and Park have derived the expectation of the “equivalent cost rate.” Using the standard deviation of the equivalent cost rate as a measure of the risk of expansion, Kang and Park then minimized an objective function that was a linear combination of cost and risk. The purpose of this paper is to extend this line of research. Using standard decision analysis procedures, a multiattribute utility function is constructed that reflects the decision maker's trade-off for cost and risk. A significant advantage of the utility function approach is that it allows for nonlinear trade-offs of cost and risk.