Using container inspection history to improve interdiction logistics for illicit nuclear materials

Strengthening the United States' ability to prevent adversaries from smuggling nuclear materials into the country is a vital and ongoing issue. The prospect of additional countries, such as Iran, obtaining the know‐how and equipment to produce these special nuclear materials in the near future underscores the need for efficient and effective inspection policies at ports and border crossings. In addition, the reduction of defense and homeland security budgets in recent years has made it increasingly important to accomplish the interdiction mission with fewer funds. Addressing these complications, in this article, we present a novel two‐port interdiction model. We propose using prior inspection data as a low‐cost way of increasing overall interdiction performance. We provide insights into two primary questions: first, how should a decision maker at a domestic port use detection data from the foreign port to improve the overall detection capability? Second, what are potential limitations to the usefulness of prior inspection data—is it possible that using prior data actually harms decision making at the domestic port? We find that a boundary curve policy (BCP) that takes into account both foreign and domestic inspection data can provide a significant improvement in detection probability. This BCP also proves to be surprisingly robust, even if adversaries are able to infiltrate shipments during transit. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 433‐448, 2013     

New results on rendezvous search on the interval

In a rendezvous search problem, two players are placed in a network and must try to meet each other in the least possible expected time. We look at rendezvous search on a discrete interval in which the players are initially placed using independent draws (usually assumed to be from the same distribution). Some optimal solutions are known if this distribution is uniform, and also for certain other special types of distribution. In this article, we present two new results. First, we characterize the complete set of solutions for the uniform case, showing that all optimal strategies must have two specific properties (namely, of being swept and strictly geodesic). Second, we relate search strategies on the interval to proper binary trees, and use this correspondence to derive a recurrence relation for solutions to the symmetric rendezvous problem for any initial distribution. This relation allows us to solve any such problem computationally by dynamic programming. Finally, some ideas for future research are discussed. © Wiley Periodicals, Inc. Naval Research Logistics 60: 454–467, 2013     

Asymptotic analysis of periodic policies for the inventory routing problem

In this article, a distribution system is studied where the sum of transportation and inventory costs is to be minimized. The inventory holding cost is assumed to be the same for all retailers. A fixed partition (FP) periodic policy is proposed with tight asymptotic worst‐case performance of 3/2 with respect to the best possible policy. This bound cannot be improved in the class of FP periodic policies. In partition‐based PB policies, the retailers are first partitioned into sets and then the sets are grouped in such a way that sets of retailers within a group are served together at selected times. A PB periodic, policy is presented with tight worst‐case asymptotic performance of with respect to the best possible policy. This latter performance improves the worst‐case asymptotic performance of of the previously best known policy for this problem. We also show that the proposed PB periodic policy has the best worst‐case asymptotic performance within the class of PB policies. Finally, practical heuristics inspired by the analyzed policies are designed and tested. The asymptotic worst–case performances of the heuristics are shown to be the same of those of the analyzed policies. Computational results show that the heuristics suggested are less than 6.4% on average from a lower bound on the optimal cost when 50 or more retailers are involved. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 00: 000–000, 2013