Capacity Expansion when Demand Is a Birth-Death Random Process

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Abstract
When demand is assumed to be a birth-death process, and capacity expansion costs are assumed to occur instantaneously at the time of expansion, it is shown that an “equivalent” deterministic-demand problem can readily be generated. The derived problem is equivalent in the sense that its solution by ordinary deterministic capacity expansion methods would also yield the solution of the stochastic problem. It is shown that the “equivalent deterministic demand” is always greater than the “expected demand,” where the latter is defined by the expected time to first reach various levels of demand, and is not the expected number of customers. In addition to general formulas for the discrete-customer case, equations are also derived for the “equivalent deterministic demand” when demand is based on a diffusion process.

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