Operations & Supply Chain Management

We analyze a general model of dynamic vehicle dispatching systems in which congestion is the primary measure of performance. In the model, a finite collection of tours are dynamically dispatched to deliver loads that arrive randomly over time. A load waits in queue until it is assigned to a tour. This representation, which is analogous to classical set-covering models, can be used to study a variety of dynamic routing and load consolidation problems.

We describe effective time partitioning heuristics for dynamic lot-sizing problems in multiitem and multilocation production/distribution systems. In a time-partitioning heuristic, the complete horizon of (say) N periods, is partitioned into smaller intervals. An instance of the problem is solved, to optimality, on each of these intervals, and the resulting solution coalesced into a solution for the complete horizon. The intervals are selected to be of a size which permits the use of exact and effective solution methods (e.g., branch-and-bound methods).

In this chapter, we provide a survey of analytical models which can be used to assess the benefits and costs associated with delayed product differentiation in a large variety of settings.

This paper addresses the simultaneous determination of pricing and inventory replenishment strategies in the face of demand uncertainty. More specifically, we analyze the following single item, periodic review model. Demands in consecutive periods are independent, but their distributions depend on the item's price in accordance with general stochastic demand functions. The price charged in any given period can be specified dynamically as a function of the state of the system. A replenishment order may be placed at the beginning of some or all of the periods. Stockouts are fully backlogged.

The bottleneck in a production-inventory network is commonly taken to be the facility that most limits flow through the network and thus the most highly utilized facility. A further connotation of "bottleneck," however, is the facility that most constrains system-wide performance or the facility at which additional resources would have the greatest impact.

This paper describes a family of discrete-review policies for scheduling open multiclass queueing networks. Each of the policies in the family is derived from what we call a dynamic reward function: such a function associates with each queue length vector q and each job class k a positive value rk(q), which is treated as a reward rate for time devoted to processing class k jobs. Assuming that each station has a traffic intensity parameter less than one, all policies in the family considered are shown to be stable.

Contemporary management theories such as Just-in-Time and Total Quality Management emphasize variance reduction as a critical step in improving system performance. But little is said about how such efforts should be directed. Suppose a manager has only limited resources for variance reduction efforts. How should she allocate them among a set of competing activities? Which activity should receive highest priority?

In this paper we develop policies for scheduling dynamically arriving jobs to a broad class of parallel-processing queueing systems. We show that in heavy traffic the policies asymptotically minimize a measure of the expected system backlog, which we call system work. Our results yield succinct, closed-form expressions for optimal system work in heavy traffic.