Optimal empty vehicle redistribution for hub‐and‐spoke transportation systems

This article considers the empty vehicle redistribution problem in a hub‐and‐spoke transportation system, with random demands and stochastic transportation times. An event‐driven model is formulated, which yields the implicit optimal control policy. Based on the analytical results for two‐depot systems, a dynamic decomposition procedure is presented which produces a near‐optimal policy with linear computational complexity in terms of the number of spokes. The resulting policy has the same asymptotic behavior as that of the optimal policy. It is found that the threshold‐type control policy is not usually optimal in such systems. The results are illustrated through small‐scale numerical examples. Through simulation the robustness of the dynamic decomposition policy is tested using a variety of scenarios: more spokes, more vehicles, different combinations of distribution types for the empty vehicle travel times and loaded vehicle arrivals. This shows that the dynamic decomposition policy is significantly better than a heuristics policy in all scenarios and appears to be robust to the assumptions of the distribution types. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Dynamic evacuation routes for personnel on a naval ship

We propose a dynamic escape route system for emergency evacuation of a naval ship. The system employs signals that adapt to the causative contingency and the crew's physical distribution about the ship. A mixed‐integer nonlinear programming model, with underlying network structure, optimizes the evacuation process. The network's nodes represent compartments, closures (e.g., doors and hatches) and intersections, while arcs represent various types of passageways. The objective function integrates two potentially conflicting factors: average evacuation time and the watertight and airtight integrity of the ship after evacuation. A heuristic solves the model approximately using a sequence of mixed‐integer linear approximating problems. Using data for a Spanish frigate, with standard static routes specified by the ship's designers, computational tests show that the dynamic system can reduce average evacuation times, nearly 23%, and can improve a combined measure of ship integrity by up to 50%. In addition, plausible design changes to the frigate yield further, substantial improvements. Published 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008     

Design of follow‐up experiments for improving model discrimination and parameter estimation

One goal of experimentation is to identify which design parameters most significantly influence the mean performance of a system. Another goal is to obtain good parameter estimates for a response model that quantifies how the mean performance depends on influential parameters. Most experimental design techniques focus on one goal at a time. This paper proposes a new entropy‐based design criterion for follow‐up experiments that jointly identifies the important parameters and reduces the variance of parameter estimates. We simplify computations for the normal linear model by identifying an approximation that leads to a closed form solution. The criterion is applied to an example from the experimental design literature, to a known model and to a critical care facility simulation experiment. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

On the asymptotic optimality of algorithms for the flow shop problem with release dates

We consider the nonpermutation flow shop problem with release dates, with the objective of minimizing the sum of the weighted completion times on the final machine. Since the problem is NP‐hard, we focus on the analysis of the performance of several approximation algorithms, all of which are related to the classical Weighted Shortest Processing Time Among Available Jobs heuristic. In particular, we perform a probabilistic analysis and prove that two online heuristics and one offline heuristic are asymptotically optimal. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Irreducibility of joint inventory positions in an assemble‐to‐order system under (r,nQ) policies

In a typical assemble‐to‐order system, a customer order may request multiple items, and the order may not be filled if any of the requested items are out of stock. A key customer service measure when unfilled orders are backordered is the order‐based backorder level. To evaluate this crucial performance measure, a fundamental question is whether the stationary joint inventory positions follow an independent and uniform distribution. In this context, this is equivalent to the irreducibility of the Markov chain formed by the joint inventory positions. This article presents a necessary and sufficient condition for the irreducibility of such a Markov chain through a set of simultaneous Diophantine equations. This result also leads to sufficient conditions that are more general than those in the published reports. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

A standardized scan statistic for detecting spatial clusters with estimated parameters

The scan statistic based on likelihood ratios (LRs) have been widely discussed for detecting spatial clusters. When developing the scan statistic, it uses the maximum likelihood estimates of the incidence rates inside and outside candidate clusters to substitute the true values in the LR statistic. However, the parameter estimation has a significant impact on the sensitivity of the scan statistic, which favors the detection of clusters in areas with large population sizes. By presenting the effects of parameter estimation on Kulldorff's scan statistic, we suggest a standardized scan statistic for spatial cluster detection. Compared to the traditional scan statistic, the standardized scan statistic can account for the varying mean and variance of the LR statistic due to inhomogeneous background population sizes. Extensive simulations have been performed to compare the power of the two cluster detection methods with known or/and estimated parameters. The simulation results show that the standardization can help alleviate the effects of parameter estimation and improve the detection of localized clusters. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Newsvendor problems with sequentially revealed demand information

This article analyzes a capacity/inventory planning problem with a one‐time uncertain demand. There is a long procurement leadtime, but as some partial demand information is revealed, the firm is allowed to cancel some of the original capacity reservation at a certain fee or sell off some inventory at a lower price. The problem can be viewed as a generalization of the classic newsvendor problem and can be found in many applications. One key observation of the analysis is that the dynamic programming formulation of the problem is closely related to a recursion that arises in the study of a far more complex system, a series inventory system with stochastic demand over an infinite horizon. Using this equivalence, we characterize the optimal policy and assess the value of the additional demand information. We also extend the analysis to a richer model of information. Here, demand is driven by an underlying Markov process, representing economic conditions, weather, market competition, and other environmental factors. Interestingly, under this more general model, the connection to the series inventory system is different. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 2012