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     

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     

A branch and bound algorithm for computing optimal replacement policies in consecutive k‐out‐of‐n‐systems

This paper presents a branch and bound algorithm for computing optimal replacement policies in a discrete‐time, infinite‐horizon, dynamic programming model of a binary coherent system with n statistically independent components, and then specializes the algorithm to consecutive k‐out‐of‐n systems. The objective is to minimize the long‐run expected average undiscounted cost per period. (Costs arise when the system fails and when failed components are replaced.) An earlier paper established the optimality of following a critical component policy (CCP), i.e., a policy specified by a critical component set and the rule: Replace a component if and only if it is failed and in the critical component set. Computing an optimal CCP is a optimization problem with n binary variables and a nonlinear objective function. Our branch and bound algorithm for solving this problem has memory storage requirement O(n) for consecutive k‐out‐of‐n systems. Extensive computational experiments on such systems involving over 350,000 test problems with n ranging from 10 to 150 find this algorithm to be effective when n ≤ 40 or k is near n. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 288–302, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10017     

A Bayesian analysis on the effect of multiple supply options in a quick response environment

In the apparel industry, vendors often suffer from high mismatches in supply and demand. To cope with this problem, they procure the same style product from different suppliers with different manufacturing costs. Especially in the quick response environment, which allows vendors to monitor trends in customer demand and search for available suppliers through the electronic market, they have additional opportunities to improve their decision‐making. In this paper, we propose an analytical profit maximization model and develop efficient decision tools to help both the middle and lower level managers pursuing this strategy. Furthermore, we have shown how significantly the vendors' potential competitive edge can be improved by exploiting multiple supply options, even at the expense of high premium procurement costs for late orders. The effect is critical, especially in a highly competitive market, and it has important implications for the top managers. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

The cost impact of using simple forecasting techniques in a supply chain

In this paper we consider an inventory model in which the retailer does not know the exact distribution of demand and thus must use some observed demand data to forecast demand. We present an extension of the basic newsvendor model that allows us to quantify the value of the observed demand data and the impact of suboptimal forecasting on the expected costs at the retailer. We demonstrate the approach through an example in which the retailer employs a commonly used forecasting technique, exponential smoothing. The model is also used to quantify the value of information and information sharing for a decoupled supply chain in which both the retailer and the manufacturer must forecast demand. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 388–411, 2003