An exact analysis of a joint production‐inventory problem in two‐echelon inventory systems

We consider a two‐echelon inventory system with a manufacturer operating from a warehouse supplying multiple distribution centers (DCs) that satisfy the demand originating from multiple sources. The manufacturer has a finite production capacity and production times are stochastic. Demand from each source follows an independent Poisson process. We assume that the transportation times between the warehouse and DCs may be positive which may require keeping inventory at both the warehouse and DCs. Inventory in both echelons is managed using the base‐stock policy. Each demand source can procure the product from one or more DCs, each incurring a different fulfilment cost. The objective is to determine the optimal base‐stock levels at the warehouse and DCs as well as the assignment of the demand sources to the DCs so that the sum of inventory holding, backlog, and transportation costs is minimized. We obtain a simple equation for finding the optimal base‐stock level at each DC and an upper bound for the optimal base‐stock level at the warehouse. We demonstrate several managerial insights including that the demand from each source is optimally fulfilled entirely from a single distribution center, and as the system's utilization approaches 1, the optimal base‐stock level increases in the transportation time at a rate equal to the demand rate arriving at the DC. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Approximation methods for the analysis of a multicomponent,multiproduct assemble‐to‐order system

In this article, we consider the performance evaluation of a multicomponent, multiproduct assemble‐to‐order (ATO) system. Each component is managed independently using a base‐stock policy at a supply facility with limited production capacity and an infinite buffer. The arrivals of demands follow a multivariate Poisson process and unfilled demands are backlogged. Because exact analysis of the proposed system is not feasible, we propose two approximation methods which provide upper and lower bounds for various performance measures such as fill rate, average waiting time, and average number of backorders of the proposed system. Our computational experiments demonstrate the effectiveness of the two approximation methods under various system settings. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Exponential size neighborhoods for makespan minimization scheduling

We investigate the quality of local search heuristics for the scheduling problem of minimizing the makespan on identical parallel machines. We study exponential size neighborhoods (whose size grows exponentially with the input length) that can be searched in polynomial time, and we derive worst‐case approximation guarantees for the local optima of such neighborhoods. The so‐called split neighborhood splits a feasible schedule into two layers, and then recombines the two layers by finding a perfect matching. We show that the makespan of every local optimum for split is at most a factor of 2 away from the globally optimal makespan. We then combine the split neighborhood with two neighborhoods from the literature. The combination of split with the jump neighborhood only marginally improves the approximation guarantee, whereas the combination with the lexicographic‐jump neighborhood decreases the approximation guarantee from 2 to 3/2. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

On the optimal detection of an underwater intruder in a channel using unmanned underwater vehicles

Given a number of patrollers that are required to detect an intruder in a channel, the channel patrol problem consists of determining the periodic trajectories that the patrollers must trace out so as to maximized the probability of detection of the intruder. We formulate this problem as an optimal control problem. We assume that the patrollers' sensors are imperfect and that their motions are subject to turn‐rate constraints, and that the intruder travels straight down a channel with constant speed. Using discretization of time and space, we approximate the optimal control problem with a large‐scale nonlinear programming problem which we solve to obtain an approximately stationary solution and a corresponding optimized trajectory for each patroller. In numerical tests for one, two, and three underwater patrollers, an underwater intruder, different trajectory constraints, several intruder speeds and other specific parameter choices, we obtain new insight—not easily obtained using simply geometric calculations—into efficient patrol trajectory design under certain conditions for multiple patrollers in a narrow channel where interaction between the patrollers is unavoidable due to their limited turn rate.© 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011