Scheduling a Make-To-Stock Queue: Index Policies and Hedging Points

Abstract

A single machine produces several different classes of items in a make-to-stock mode. We consider the problem of scheduling the machine to regulate finished goods inventory, minimizing holding and backorder or holding and lost sales costs. Demands are Poisson, service times are exponentially distributed, and there are no delays or costs associated with switching products. A scheduling policy dictates whether the machine is idle or busy, and specifies the job class to serve in the latter case. Since the optimal solution can only be numerically computed for problems with several products, our goal is to develop effective policies that are computationally tractable for a large number of products. We develop index policies to decide which class to produce, including Whittle's "restless bandit" index, which possesses a certain asymptotic optimality. Several idleness policies are derived, and the best policy is obtained from a heavy traffic diffusion approximation. Nine sample problems are considered in a numerical study, and the average suboptimality of the best policy is less than 3%.

On the Benefits of Pooling in Production-Inventory Systems

“…In particular, TC s = 1 s , and an optimal base-stock level is given by s * = s wheres = ln / ln ; see also Veatch and Wein (1996). For a distributed system, operating under the best base-stock policy is not known to be optimal (among all possible control policies).…”

“…Zipkin (2000) offers a comprehensive discussion of various types of supply systems including those that induce constant, exogenous and sequential, and load-dependent lead times. Treatments of multiclass production-inventory systems include Wein (1992), Zipkin (1995), Veatch and Wein (1996), Ha (1997), de Véricourt et al (2000ade Véricourt et al ( , 2001de Véricourt et al ( , 2002, Bertsimas and Paschilidis (2001), and . Despite the large body of work on pooling, the issue has, to our knowledge, not been fully explored in a production-inventory framework, which captures dependencies between production and inventory systems.…”

The influence of demand variability on the performance of a make-to-stock queue

“…In particular, let F N be the cumulative distribution function of N , then the optimal base-stock level S Ã is given by (see [15] for example)…”

Managing Response Time in a Call-Routing Problem with Service Failure

“…Ha [13] or Veatch and Wein [32]). Let v(n) be the standard MDP "cost-to-go" function in state n, then v is a mapping from N C+1 to + , where N and + are the sets of integers and non-negative real numbers respectively.…”