New results on a Ruckle problem in discrete games of ambush

This article deals with a two‐person zero‐sum game in which player I chooses in integer interval [1, N] two integer intervals consisting of p and q points where p + q < N, and player II chooses an integer point in [1, N]. The payoff to player I equals 1 if the point chosen by player II is at least in one of the intervals chosen by player II and 0 otherwise. This paper complements the results obtained by Ruckle, Baston and Bostock, Lee, Garnaev, and Zoroa, Zoroa and Fernández‐Sáez. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 98–106, 2001     

A single‐period inventory placement problem for a serial supply chain

This article addresses the inventory placement problem in a serial supply chain facing a stochastic demand for a single planning period. All customer demand is served from stage 1, where the product is stored in its final form. If the demand exceeds the supply at stage 1, then stage 1 is resupplied from stocks held at the upstream stages 2 through N, where the product may be stored in finished form or as raw materials or subassemblies. All stocking decisions are made before the demand occurs. The demand is nonnegative and continuous with a known probability distribution, and the purchasing, holding, shipping, processing, and shortage costs are proportional. There are no fixed costs. All unsatisfied demand is lost. The objective is to select the stock quantities that should be placed different stages so as to maximize the expected profit. Under reasonable cost assumptions, this leads to a convex constrained optimization problem. We characterize the properties of the optimal solution and propose an effective algorithm for its computation. For the case of normal demands, the calculations can be done on a spreadsheet. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:506–517, 2001     

General multiprocessor task scheduling

Most papers in the scheduling field assume that a job can be processed by only one machine at a time. Namely, they use a one‐job‐on‐one‐machine model. In many industry settings, this may not be an adequate model. Motivated by human resource planning, diagnosable microprocessor systems, berth allocation, and manufacturing systems that may require several resources simultaneously to process a job, we study the problem with a one‐job‐on‐multiple‐machine model. In our model, there are several alternatives that can be used to process a job. In each alternative, several machines need to process simultaneously the job assigned. Our purpose is to select an alternative for each job and then to schedule jobs to minimize the completion time of all jobs. In this paper, we provide a pseudopolynomial algorithm to solve optimally the two‐machine problem, and a combination of a fully polynomial scheme and a heuristic to solve the three‐machine problem. We then extend the results to a general m‐machine problem. Our algorithms also provide an effective lower bounding scheme which lays the foundation for solving optimally the general m‐machine problem. Furthermore, our algorithms can also be applied to solve a special case of the three‐machine problem in pseudopolynomial time. Both pseudopolynomial algorithms (for two‐machine and three‐machine problems) are much more efficient than those in the literature. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 57–74, 1999     

An (s,S) model for inventory with exponential lifetimes and renewal demands

Inventory control of products with finite lifetimes is important in many modern business organizations. It has been an important and difficult research subject. Here, we study the (s, S) continuous review model for items with an exponential random lifetime and a general renewal demand process through a Markov process. We derive a fundamental rate conservation theorem and show that all the other system performance measures can be obtained easily through the expected reorder cycle length. This leads to a simple expression for the total expected long run cost rate function in terms of the expected reorder cycle length. Subsequently, we derive formulas for computing the expected cycle lengths for the general renewal demand as well as for a large class of demands characterized by the phase type interdemand time distribution. We show analytically when the cost as a function of the reorder level is monotone, concave, or convex. We also show analytically that, depending on the behavior of the expected reorder cycle, the cost as a function of the order‐up level is either monotone increasing or unimodal. These analytical properties enable us to understand the problem and make the subsequent numerical optimization much easier. Numerical studies confirm and illustrate some of the analytical properties. The results also demonstrate the impact of various parameters on the optimal policy and the cost. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 39–56, 1999     

An optimal procedure for the coordinated replenishment dynamic lot‐sizing problem with quantity discounts

We consider in this paper the coordinated replenishment dynamic lot‐sizing problem when quantity discounts are offered. In addition to the coordination required due to the presence of major and minor setup costs, a separate element of coordination made possible by the offer of quantity discounts needs to be considered as well. The mathematical programming formulation for the incremental discount version of the extended problem and a tighter reformulation of the problem based on variable redefinition are provided. These then serve as the basis for the development of a primal‐dual based approach that yields a strong lower bound for our problem. This lower bound is then used in a branch and bound scheme to find an optimal solution to the problem. Computational results for this optimal solution procedure are reported in the paper. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 686–695, 2000     

Inventory competition with yield reliability improvement

This article studies the inventory competition under yield uncertainty. Two firms with random yield compete for substitutable demand: If one firm suffers a stockout, which can be caused by yield failure, its unsatisfied customers may switch to its competitor. We first study the case in which two competing firms decide order quantities based on the exogenous reliability levels. The results from the traditional inventory competition are generalized to the case with yield uncertainty and we find that quantity and reliability can be complementary instruments in the competition. Furthermore, we allow the firms to endogenously improve their yield reliability before competing in quantity. We show that the reliability game is submodular under some assumptions. The results indicate that the competition in quantity can discourage the reliability improvement. With an extensive numerical study, we also demonstrate the robustness of our analytical results in more general settings. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 107–126, 2015     

An exact algorithm for the batch sequencing problem in a two-machine flow shop with limited buffer

This paper deals with the problem of makespan minimization in a flow shop with two machines when the input buffer of the second machine can only host a limited number of parts. Here we analyze the problem in the context of batch processing, i.e., when identical parts must be processed consecutively. We propose an exact branch-and-bound algorithm, in which the bounds exploit the batching nature of the problem. Extensive computational results show the effectiveness of the approach, and allow us to compare it with a previous heuristic approach. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 141–164, 1998     

The impact of exponential smoothing forecasts on the bullwhip effect

An important phenomenon often observed in supply chain management, known as the bullwhip effect, implies that demand variability increases as one moves up the supply chain, i.e., as one moves away from customer demand. In this paper we quantify this effect for simple, two‐stage, supply chains consisting of a single retailer and a single manufacturer. We demonstrate that the use of an exponential smoothing forecast by the retailer can cause the bullwhip effect and contrast these results with the increase in variability due to the use of a moving average forecast. We consider two types of demand processes, a correlated demand process and a demand process with a linear trend. We then discuss several important managerial insights that can be drawn from this research. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 269–286, 2000     

On the orbit characteristics of the M/G/ 1 retrial queue

In teletraffic applications of retrial queues only the service zone is observable. Another part of a retrial queue, the orbit, which represents the delay before repeated attempts to get service, cannot be observed. Thus, it is very important to get general results about behavior of the orbit. We investigate two characteristics of the orbit, namely, the orbit busy period and the orbit idle period, which seem to be very useful from this point of view. © 1996 John Wiley & Sons, Inc.