A generalized inspection game

The paper addresses the problem of a patrol trying to stop smugglers who are attempting to ship a cargo of perishable contraband across a strait in one of M time units. The situation was modeled as a two-person zero-sum game of exhaustion by Thomas and Nisgav and this article extends their results. The game has many characteristics in common with the Inspection Game in Owen's book on Game Theory; this Inspection Game is generalized and the relations between the two games are discussed.     

Dependence in target element detections induced by the environment

When modeling the detection of targets in a simulation of combat, the detection process is frequently represented as a series of independent detections of individual elements of the target. This assumption ignores the effect of a common but unknown field environment within which the detections take place. In this article, multivariate survival distributions are developed for target element detections which occur in an unknown dynamic environment. A proportional hazards representation is adopted, which uses a random variable multiplying the detection rate to account for the effect of the environment. Several special cases are examined which are useful for modeling target unit detections.     

Safety stock reduction by order splitting

In this article we consider an item for which a continuous review, reorder point, order quantity inventory control system is used. The amount of safety stock required depends upon, among other factors, the average value and variability of the length of the replenishment lead time. One way to reduce these quantities is to split orders among two or more vendors. In this article the random lead times are assumed to have Weibull distributions. This permits the development of analytic expressions for the reduction in the expected value and variability of total demand until the critical first (earliest) delivery received from a vendor. An expression is also obtained for the reorder point that provides a given probability of no stockout prior to the first delivery. Lower bounds are given on the order quantity so as to ensure that the probability of a stockout before any one of the later (second, third, etc.) deliveries is sufficiently small to be considered negligible. The analytic and tabular results can be used to estimate the benefits (reduced carrying costs and/or increased service level) of order splitting.     

Assessment of machine tool reliability using a proportional hazards model

In this article we present a proportional hazards model for describing machine tool failures. The model enables us to describe the effect of aging as well as the effect of the machining environment on tool life. We discuss inference for the model and show that computable results can be obtained in a fully Bayesian analysis by using approximation techniques. We illustrate the usefulness of our model by applying it to some actual data on machine tool failures.     

Service levels in distribution systems with random customer order size

An approximate method for measuring the service levels of the warehouse-retailer system operating under (s, S) policy is presented. All the retailers are identical and the demand process at each retailer follows a stationary stuttering Poisson process. This type of demand process allows customer orders to be for a random number of units, which gives rise to the undershoot quantity at both the warehouse and retailer levels. Exact analyses of the distribution of the undershoot quantity and the number of orders place by a retailer during the warehouse reordering lead time are derived. By using this distribution together with probability approximation and other heuristic approaches, we model the behavior of the warehouse level. Based on the results of the warehouse level and on an existing framework from previous work, the service level at the retailer level is estimated. Results of the approximate method are then compared with those of simulation. © 1995 John Wiley & Sons, Inc.     

A bayesian approach to environmental stress screening

The article presents a Bayesian analysis for the environmental stress screening problem. The decision problem of deriving optimal stress screen durations is solved. Given a screen duration, the optimal stress level can also be determined. Indicators of the quality of a screen of any duration are derived. A statistical model is presented which allows a posterior density for the rate of early failures of the production process to be calculated. This enables the user to update his opinion about the quality of the process. © 1994 John Wiley & Sons, Inc.     

A two-machine repair model with variable repair rate

A two-unit cold standby production system with one repairman is considered. After inspection of a failed unit the repairman chooses either a slow or a fast repair rate to carry out the corresponding amount of work. At system breakdown the repairman has an additional opportunity to switch to the fast rate. If there are no fixed costs associated with system breakdowns, then the policy which minimizes longrun average costs is shown to be a two-dimensional control limit rule. If fixed costs are incurred every time the system breaks down, then the optimal policy is not necessarily of control limit type. This is illustrated by a counterexample. Furthermore, we present several performance measures for this maintenance system controlled by a two-dimensional control limit rule. © 1993 John Wiley & Sons, Inc.     

Scheduling semiconductor test operations: Minimizing maximum lateness and number of tardy jobs on a single machine

We examine a class of single-machine scheduling problems with sequence-dependent setup times that arise in the context of semiconductor test operations. We present heuristics for the problems of minimizing maximum lateness with dynamic arrivals and minimizing number of tardy jobs. We exploit special problem structure to derive worst-case error bounds. The special problem structure also enables us to derive dynamic programming procedures for the problems where all jobs are available simultaneously.     

Multi-item service constrained (s,S) policies for spare parts logistics systems

Many organizations providing service support for products or families of products must allocate inventory investment among the parts (or, identically, items) that make up those products or families. The allocation decision is crucial in today's competitive environment in which rapid response and low levels of inventory are both required for providing competitive levels of customer service in marketing a firm's products. This is particularly important in high-tech industries, such as computers, military equipment, and consumer appliances. Such rapid response typically implies regional and local distribution points for final products and for spare parts for repairs. In this article we fix attention on a given product or product family at a single location. This single-location problem is the basic building block of multi-echelon inventory systems based on level-by-level decomposition, and our modeling approach is developed with this application in mind. The product consists of field-replaceable units (i.e., parts), which are to be stocked as spares for field service repair. We assume that each part will be stocked at each location according to an (s, S) stocking policy. Moreover, we distinguish two classes of demand at each location: customer (or emergency) demand and normal replenishment demand from lower levels in the multiechelon system. The basic problem of interest is to determine the appropriate policies (s_i S_i) for each part i in the product under consideration. We formulate an approximate cost function and service level constraint, and we present a greedy heuristic algorithm for solving the resulting approximate constrained optimization problem. We present experimental results showing that the heuristics developed have good cost performance relative to optimal. We also discuss extensions to the multiproduct component commonality problem.     

Stochastic analysis of a single server retrial queue with general retrial times

Retrial queueing systems are widely used in teletraffic theory and computer and communication networks. Although there has been a rapid growth in the literature on retrial queueing systems, the research on retrial queues with nonexponential retrial times is very limited. This paper is concerned with the analytical treatment of an M/G/1 retrial queue with general retrial times. Our queueing model is different from most single server retrial queueing models in several respectives. First, customers who find the server busy are queued in the orbit in accordance with an FCFS (first‐come‐first‐served) discipline and only the customer at the head of the queue is allowed for access to the server. Besides, a retrial time begins (if applicable) only when the server completes a service rather upon a service attempt failure. We carry out an extensive analysis of the queue, including a necessary and sufficient condition for the system to be stable, the steady state distribution of the server state and the orbit length, the waiting time distribution, the busy period, and other related quantities. Finally, we study the joint distribution of the server state and the orbit length in non‐stationary regime. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 561–581, 1999