Operations & Supply Chain Management

Polling system models are extensively used to model a large variety of computer and communication networks as well as production and service systems in which multiple customer classes or a number of distinct items compete for the capacity of a common server or production facility. In this paper we describe an efficient approximation method for the steady state distributions of the queue sizes and waiting times. This method is highly accurate as demonstrated by an extensive numerical study.

In many industries, managers face the problem of selling a given stock of items by a deadline. We investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm's objective is to maximize expected revenues. Examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry, which markets space such as seats on airline flights, cabins on vacation cruises, and rooms in hotels that become worthless if not sold by a specific time.

We show for the general dynamic lot sizing model how minimal forecast horizons may be detected by a slight adaptation of an earlier 0(n log n) or 0(n) forward solution method for the model. A detailed numerical study indicates that minimal forecast horizons tend to be small, that is, include a small number of orders.

We address the Joint Replenishment Problem (JRP) where, in the presence of joint setup costs, dynamic lot sizing schedules need to be determined for m items over a planning horizon of N periods, with general time-varying cost and demand parameters. We develop a new, so-called, partitioning heuristic for this problem, which partitions the complete horizon of N periods into several relatively small intervals, specifies an associated joint replenishment problem for each of these, and solves them via a new, efficient branch-and-bound method.

Most models of multilevel production and distribution systems assume unlimited production capacity at each site. When capacity limits are introduced, an ineffective policy may lead to increasingly large order backlogs: The stability of the system becomes an issue. In this paper, we examine the stability of a multi-echelon system in which each node has limited production capacity and operates under a base-stock policy.

In this paper we develop a model for a capacitated production/distribution network of general (but acyclic) topology with a general bill of materials, as considered in MRP (Material Requirement Planning) or DRP (Distribution Requirement Planning) systems. This model assumes stationary, deterministic demand rates and a standard stationary cost structure; it is a generalization of the uncapacitated model treated in the seminal papers of Maxwell and Muckstadt (1985) and Roundy (1986).

We analyze a class of stochastic and dynamic vehicle routing problems in which demands arrive randomly over time and the objective is minimizing waiting time. In our previous analysis ([5] and [6]) on this problem, we needed to assume uniformly distributed demand locations and Poisson arrivals. In this paper, using quite different techniques, we are able to extend our results to the more realistic case where demand locations have an arbitrary distribution and arrivals follow a general renewal process.

In 1991, D. J. Bertsimas and G. van Ryzin introduced and analyzed a model for stochastic and dynamic vehicle routing in which a single, uncapacitated vehicle traveling at a constant velocity in a Euclidian region must service demands whose time of arrival, location and on-site service are stochastic. The objective is to find a policy to service demands over an infinite horizon that minimizes the expected system time (wait plus service) of the demands. This paper extends our analysis in several directions.

We investigate optimal production controls for a tandem two-machine system with an internal buffer and unreliable machines. First, numerical methods are used to generate optimal policies for specific examples. Then, based on diese numerical results, an approximate suboptimal control policy is developed that divides the state space into distinct regions and uses only simple hedging-point policies in each region. Algorithms to obtain hedging points are provided.