Commissioned Paper: Capacity Management, Investment, and Hedging: Review and Recent Developments

Abstract

T his paper reviews the literature on strategic capacity management concerned with determining the sizes, types, and timing of capacity investments and adjustments under uncertainty. Specific attention is given to recent developments to incorporate multiple decision makers, multiple capacity types, hedging, and risk aversion. Capacity is a measure of processing abilities and limitations and is represented as a vector of stocks of various processing resources, while investment is the change of capacity and includes expansion and contraction. After discussing general issues in capacity investment problems, the paper reviews models of capacity investment under uncertainty in three settings:The first reviews optimal capacity investment by single and multiple risk-neutral decision makers in a stationary environment where capacity remains constant. Allowing for multiple capacity types, the associated optimal capacity portfolio specifies the amounts and locations of safety capacity in a processing network. Its key feature is that it is unbalanced; i.e., regardless of how uncertainties are realized, one typically will never fully utilize all capacities. The second setting reviews the adjustment of capacity over time and the structure of optimal investment dynamics. The paper ends by reviewing how to incorporate risk aversion in capacity investment and contrasts hedging strategies involving financial versus operational means.

A Method for Staffing Large Call Centers Based on Stochastic Fluid Models

“…This particular kind of two-stage problem embodied in (5) is sometimes called a multi-dimensional newsvendor problem; see, e.g., the recent survey by Van Mieghem [22].…”

“…Those average cost values, along with their upper and lower 95% confidence intervals, are plotted in Figure 3, where the example under discussion is identified as our "variable demand scenario," to distinguish it from another case considered below. Also plotted in Figure 3 is the estimate of average daily cost (as a function of b) derived from our fluid approximation (22). There are three important conclusions to be drawn from Figure 3.…”

“…It is interesting to contrast the example just discussed with a "constant demand scenario" where Λ(·) is identically equal to the overall average value,λ = 100 that was identified earlier in (24). Figure 4 presents both the fluid-based performance estimate derived from (22) for that case, and the corresponding simulation results, again based on a sample of 1000 independent days for each b value. (In this case the 95% confidence intervals are so close to the simulation estimates of average daily cost, relative to the scale of the graph, that we have just omitted them.)…”

“…staffing decision is obtained by solving a variant of the newsvendor problem that has piecewise linear underage cost; in the system with two server pools there are two design variables resulting in a two-dimensional newsvendor problem; see Van Mieghem [22] for examples and further discussion of multi-dimensional newsvendor problems. The simulation results reported in Table 3 Table 3: Simulated average total costs for the two-class/two-pool system for various staffing levels.…”

Irreversible Capital Accumulation with Economic Impact

“…Otherwise, it is optimal to take minimal action so that the state process (X 0 , Y ) does not fall below the graph of G 0 , which amounts to reflecting it in G 0 in the positive y-direction. Irreversible capacity expansion models have attracted considerable interest and can be traced back to Manne [38] (see Van Mieghem [47] for a survey). More relevant to this paper models have been studied by several authors in the economics literature: see Dixit and Pindyck [17,Chapter 11] and references therein.…”