Simultaneous Capacity and Production Management of Short-Life-Cycle, Produce-to-Stock Goods Under Stochastic Demand

Abstract

This paper derives the optimal simultaneous capacity and production plan for a shortlife-cycle, produce-to-stock good under stochastic demand. Capacity can be reduced as well as added, at exogenously set unit prices. In both cases studied, with and without carryover of unsold units, a target interval policy is optimal: There is a (usually different) target interval for each period such that capacity should be changed as little as possible to bring the level available into that interval. Our contribution in the case of no carry-over, is a detailed characterization of the target intervals, assuming demands increase stochastically at the beginning of the life cycle and decrease thereafter. In the case of carry-over, we establish the general result and show that capacity and inventory are economic substitutes: The target intervals decrease in the initial stock level and the optimal unconstrained base stock level decreases in the capacity level. In both cases, optimal service rates are not necessarily constant over time. A numerical example illustrates the results.Capacity management, Production management, Capacity expansion, Capacity contraction, Finite lifetime, Stochastic demand, Nonstationary

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

“…An exception is , who consider stochastic upper-bounds, i.e., capacity uncertainty, in addition to demand uncertainty. Inventory papers that also consider capacity investment decisions include Angelus and Porteus (2002), Bradley and Glynn (2002), Van Mieghem and Rudi (2002), and will be discussed in the remaining sections. Networks where multiple agents control their own productive capacity require gametheoretic models as §4.3 will discuss.…”

“…Sophisticated stochastic control theory ultimately shows that the control is "bang-bang": Either carry out construction at maximal speed or do nothing and wait, similar to an ISD policy. Angelus and Porteus (2002) consider expansion followed by contraction through a single product's life cycle. The driving stochastic process, X, represents demand, which is first stochastically increasing over a known interval of time, after which it is stochastically decreasing.…”

“…Like Angelus and Porteus (2002), they consider a single product's life cycle, but assume a multiresource production process with lumpy capacity in a costminimization context. They show that the sequence in which resources are expanded in the first up-part of the cycle is the reverse of that in which they are contracted in the down part.…”

Optimal Capacity Conversion for Product Transitions Under High Service Requirements

“…The joint capacity and production problem is therefore more challenging. In simpler single-product, single-capacity settings of Angelus and Porteus (2002) and Bradley and Glynn (2002), capacity and production policies for minimizing a cost can be specified using thresholds. In this paper, we study a two-product, two-capacity, multi-period capacity problem with stochastic and time-varying demand under high service requirements, where service level requirements are exogenously imposed.…”

The Impact of Capacity Flexibility in a Rental Operation on the Financial Performance

“…So and Tang [18] considered a problem of managing congestion in two types of service systems and investigated a policy that dynamically adjusts operating capacity according to the system state using queueing models. Angelus and Porteus [1] studied the issue of determining capacity size and production planning in a produce-to-stock facility. Under instantaneous capacity additions and reductions, they showed that a target interval policy is optimal for capacity management, provided that demands stochastically increase up to a peak and then decrease, Inventory management with product returns is the other important area of research relevant to this problem.…”