Capacity expansion under a service‐level constraint for uncertain demand with lead times

Abstract

For a service provider facing stochastic demand growth, expansion lead times and economies of scale complicate the expansion timing and sizing decisions. We formulate a model to minimize the infinite horizon expected discounted expansion cost under a service‐level constraint. The service level is defined as the proportion of demand over an expansion cycle that is satisfied by available capacity. For demand that follows a geometric Brownian motion process, we impose a stationary policy under which expansions are triggered by a fixed ratio of demand to the capacity position, i.e., the capacity that will be available when any current expansion project is completed, and each expansion increases capacity by the same proportion. The risk of capacity shortage during a cycle is estimated analytically using the value of an up‐and‐out partial barrier call option. A cutting plane procedure identifies the optimal values of the two expansion policy parameters simultaneously. Numerical instances illustrate that if demand grows slowly with low volatility and the expansion lead times are short, then it is optimal to delay the start of expansion beyond when demand exceeds the capacity position. Delays in initiating expansions are coupled with larger expansion sizes. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009

Stochastic comparisons of multivariate mixtures

“…In the context of production, when an expansion is desired due to a demand growth, significant lead times or delays exist between the time when the expansion decision is made and the time when the added capacity is actually available to satisfy the demand. For example, such a time includes the time needed for recruiting and training new personnel, and for increasing the inventory of the necessary raw materials (see [15] and references therein). In the applications that are studied in the above papers, the lead times are taken to be stochastic.…”

Specifying and Validating Probabilistic Inputs for Prescriptive Models of Decision Making over Time

“…It would be interesting to re-examine updated data concerning demand for capacity in the two then-nascent industries for which we found the GBM model to not fit well. Meanwhile, Marathe and Ryan (2009) employed formulas for pricing exotic options to evaluate the potential for shortage during the lead time required to add capacity, assuming GBM demand growth.…”

Capacity decision under preset service level and process flexibility

“…In many situations, the manufacturer may need to decide on the service level first and then invest in capacity accordingly. (For application of service level concept in manufacturing sector see Tarim and Kingsman, 2004;Farahani and Elahipanah, 2008;Marathe and Ryan, 2009;Jiang et al, 2017). Here, the service level is considered as the expected fraction of occasions where the demand is higher than production.…”