Paul H. Zipkin

A Combined Vehicle Routing and Inventory Allocation Problem

We address the combined problem of allocating a scarce resource among several locations, and planning deliveries using a fleet of vehicles. Demands are random, and holding and shortage costs must be considered in the decision along with transportation costs. We show how to extend some of the available methods for the deterministic vehicle routing problem to this case. Computational results using one such adaptation show that the algorithm is fast enough for practical work, and that substantial cost savings can be achieved with this approach.

An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion

This paper considers a single-item, periodic-review inventory model with uncertain demands. We assume a finite production capacity in each period. With stationary data, a convex one-period cost function and a continuous demand distribution, we show under a few additional unrestrictive assumptions that a modified basic-stock policy is optimal under the discounted cost criterion, both for finite and infinite planning horizons. In addition we characterize the optimal base-stock levels in several ways.

Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model

Clark and Scarf Clark, A., H. Scarf. 1960. Optimal policies for a multi-echelon inventory problem. Mgmt. Sci.6 475-490. characterize optimal policies in a two-echelon, two-location inventory model. We extend their result to the infinite-horizon case for both discounted and average costs. The computations required are far easier than for the finite horizon problem. Further simplification is achieved for normal demands. We also consider the more interesting case of multiple locations at the lower echelon. We show that, under certain conditions, this problem can be closely approximated by a model with one such location. A rather simple computation thus yields both a near-optimal policy and a good approximation of the cost of the system.

Inventory control in a fluctuating demand environment

We present an inventory model, where the demand rate varies with an underlying state-of-the-world variable. This variable can represent economic fluctuations, or stages in the product life-cycle, for example. We derive some basic characteristics of optimal policies and develop algorithms for computing them. In addition, we show that certain monotonicity patterns in the problem data are reflected in the optimal policies.

Estimating the performance of multi-level inventory systems

B. Deuermeyer and L. B. Schwarz have developed a very simple approximation of a complex multi-echelon system. Here we propose several refinements of their technique, leading to models nearly as simple and considerably more robust. Our analysis suggests guidelines for the design of large-scale logistics systems, differing markedly from those of earlier studies.

Models for design and control of stochastic, multi-item batch production systems

We propose an approach to modeling a production facility that makes many products in large, discrete batches, when demands and the production process are stochastic. This approach combines standard inventory and queueing submodels into classical optimization problems. The models developed in this paper to illustrate the approach represent the production facility by a single-server queueing system or by a network of queues; other systems can also be handled within the approach. The models optimize the approximate operating cost of a given facility over certain simple, plausible control policies; furthermore, the models are tractable enough to be used routinely for design studies.

Supply Chain Operations: Assemble-to-Order Systems

Publisher Summary An assemble-to-order (or ATO) system includes several components and several products. The time to acquire or produce a component is substantial. A product is assembled only in response to demand. This chapter reviews the research on ATO systems. It discusses the modeling issues and analytical methods, and summarizes the managerial insights gained from the research. An assembly system has just one product, and a distribution system has just one component. The key issue in an assembly system is the coordination of the components, while the key issue in a distribution system is the allocation of the component among the products. An ATO system combines the elements of assembly and distribution, and resolves both coordination and allocation issues. This makes the ATO systems difficult to analyze, design, and manage. The chapter also discusses one-period models, multi-period models, discrete-time models, and continuous-time models.

Computing optimal lot sizes in the economic lot scheduling problem

This paper treats a version of the Economic Lot Scheduling Problem (ELSP) in which items may be produced several times in different amounts during a cycle. We show how to compute the optimal lot sizes and cycle length, given the sequence of items in a cycle. This requires solving a parametric quadratic program, plus a few EOQ calculations. Our procedure is designed to be used along with a heuristic for selecting the sequence of items in a cycle, such as the one proposed in 1987 by G. Dobson. The two algorithms together comprise a simple, plausible heuristic for the ELSP as a whole.

A Queueing Model to Analyze the Value of Centralized Inventory Information

Competitive pressures and technological improvements are leading many firms to consider centralized information systems to manage inventories and schedule production. We propose a simple model to explore the potential benefits of such coordination. The model represents two products competing for a single production facility. Simple Markovian behavior is assumed throughout. The key step in the analysis is the explicit solution of a queueing model with a novel priority discipline: Serve a customer from the class having the largest number of customers in the system.

Analysis and Comparison of Queues with Different Levels of Delay Information

Information about delays can enhance service quality in many industries. Delay information can take many forms, with different degrees of precision. Different levels of information have different effects on customers and therefore on the overall system. To explore these effects, we consider a queue with balking under three levels of delay information: no information, partial information (the system occupancy), and full information (the exact waiting time). We assume Poisson arrivals, independent exponential service times, and a single server. Customers decide whether to stay or balk based on their expected waiting costs, conditional on the information provided. We show how to compute the key performance measures in the three systems, obtaining closed-form solutions for special cases. We then compare the three systems. We identify some important cases where more accurate delay information improves performance. In other cases, however, information can actually hurt the provider or the customers.