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     

Scheduling patients in an ambulatory surgical center

This paper presents a deterministic approach to schedule patients in an ambulatory surgical center (ASC) such that the number of postanesthesia care unit nurses at the center is minimized. We formulate the patient scheduling problem as new variants of the no‐wait, two‐stage process shop scheduling problem and present computational complexity results for the new scheduling models. Also, we develop a tabu search‐based heuristic algorithm to solve the patient scheduling problem. Our algorithm is shown to be very effective in finding near optimal schedules on a set of real data from a university hospital's ASC. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine

This paper tackles the general single machine scheduling problem, where jobs have different release and due dates and the objective is to minimize the weighted number of late jobs. The notion of master sequence is first introduced, i.e., a sequence that contains at least an optimal sequence of jobs on time. This master sequence is used to derive an original mixed‐integer linear programming formulation. By relaxing some constraints, a Lagrangean relaxation algorithm is designed which gives both lower and upper bounds. The special case where jobs have equal weights is analyzed. Computational results are presented and, although the duality gap becomes larger with the number of jobs, it is possible to solve problems of more than 100 jobs. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 50: 2003     

On efficiency of multistage channel with bargaining over wholesale prices

This article considers a multistage channel with deterministic price‐sensitive demand. Two systems for pricing decisions, that is, the bargaining system and the leader‐follower system, are compared. We characterize the necessary and sufficient conditions on the power structure, under which the solution of the bargaining system Pareto dominates that of the leader‐follower system. Also, under such conditions, we give a tight upper bound of channel efficiency of the bargaining system, which converges to 100% channel efficiency as the number of stages increases to infinity. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 449–459, 2016     

Inventory control under substitutable demand: A stochastic game application

Substitutable product inventory problem is analyzed using the concepts of stochastic game theory. It is assumed that there are two substitutable products that are sold by different retailers and the demand for each product is random. Game theoretic nature of this problem is the result of substitution between products. Since retailers compete for the substitutable demand, ordering decision of each retailer depends on the ordering decision of the other retailer. Under the discounted payoff criterion, this problem is formulated as a two‐person nonzero‐sum stochastic game. In the case of linear ordering cost, it is shown that there exists a Nash equilibrium characterized by a pair of stationary base stock strategies for the infinite horizon problem. This is the unique Nash equilibrium within the class of stationary base stock strategies. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 359–375, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10018     

Detection of a Markovian target with optimization of the search efforts under generalized linear constraints

This paper deals with search for a target following a Markovian movement or a conditionally deterministic motion. The problem is to allocate the search efforts, when search resources renew with generalized linear constraints. The model obtained is extended to resource mixing management. New optimality equations of de Guenin's style are obtained. Practically, the problem is solved by using an algorithm derived from the FAB method. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 117–142, 2002; DOI 10.1002/nav.10009     

A nested benders decomposition approach for telecommunication network planning

Despite its ability to result in more effective network plans, the telecommunication network planning problem with signal‐to‐interference ratio constraints gained less attention than the power‐based one because of its complexity. In this article, we provide an exact solution method for this class of problems that combines combinatorial Benders decomposition, classical Benders decomposition, and valid cuts in a nested way. Combinatorial Benders decomposition is first applied, leading to a binary master problem and a mixed integer subproblem. The subproblem is then decomposed using classical Benders decomposition. The algorithm is enhanced using valid cuts that are generated at the classical Benders subproblem and are added to the combinatorial Benders master problem. The valid cuts proved efficient in reducing the number of times the combinatorial Benders master problem is solved and in reducing the overall computational time. More than 120 instances of the W‐CDMA network planning problem ranging from 20 demand points and 10 base stations to 140 demand points and 30 base stations are solved to optimality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Discrete‐time analysis of MAP/PH/1 multiclass general preemptive priority queue

We use the matrix‐geometric method to study the MAP/PH/1 general preemptive priority queue with a multiple class of jobs. A procedure for obtaining the block matrices representing the transition matrix P is presented. We show that the special upper triangular structure of the matrix R obtained by Miller [Computation of steady‐state probabilities for M/M/1 priority queues, Oper Res 29(5) (1981), 945–958] can be extended to an upper triangular block structure. Moreover, the subblock matrices of matrix R also have such a structure. With this special structure, we develop a procedure to compute the matrix R. After obtaining the stationary distribution of the system, we study two primary performance indices, namely, the distributions of the number of jobs of each type in the system and their waiting times. Although most of our analysis is carried out for the case of K = 3, the developed approach is general enough to study the other cases (K ≥ 4). © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 662–682, 2003.     

Optimal production and maintenance policy for imperfect production systems

A joint optimization of the production run length and preventive maintenance (PM) policy is studied for a deteriorating production system where the in‐control period follows a general probability distribution with non‐decreasing failure rate. In the literature, the sufficient conditions for the optimality of the equal‐interval PM schedule is explored to derive an optimal production run length and an optimal number of PM actions. Nevertheless, an exhaustive search may arise. In this study, based on the assumption that the conditions for the optimality of the equal‐interval PM schedule hold, we derive some structural properties for the optimal production/PM policy, which increases the efficiency of the solution procedure. These analyses have implications for the practical application of the production/PM model to be more available in practice. A numerical example of gamma shift distribution with non‐decreasing failure rates is used to illustrate the solution procedure, leading to some insight into the management process. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Bin‐packing problem with concave costs of bin utilization

We consider a generalized one‐dimensional bin‐packing model where the cost of a bin is a nondecreasing concave function of the utilization of the bin. Four popular heuristics from the literature of the classical bin‐packing problem are studied: First Fit (FF), Best Fit (BF), First Fit Decreasing (FFD), and Best Fit Decreasing (BFD). We analyze their worst‐case performances when they are applied to our model. The absolute worst‐case performance ratio of FF and BF is shown to be exactly 2, and that of FFD and BFD is shown to be exactly 1.5. Computational experiments are also conducted to test the performance of these heuristics. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006