Optimal patrol to uncover threats in time when detection is imperfect

Consider a patrol problem, where a patroller traverses a graph through edges to detect potential attacks at nodes. An attack takes a random amount of time to complete. The patroller takes one time unit to move to and inspect an adjacent node, and will detect an ongoing attack with some probability. If an attack completes before it is detected, a cost is incurred. The attack time distribution, the cost due to a successful attack, and the detection probability all depend on the attack node. The patroller seeks a patrol policy that minimizes the expected cost incurred when, and if, an attack eventually happens. We consider two cases. A random attacker chooses where to attack according to predetermined probabilities, while a strategic attacker chooses where to attack to incur the maximal expected cost. In each case, computing the optimal solution, although possible, quickly becomes intractable for problems of practical sizes. Our main contribution is to develop efficient index policies—based on Lagrangian relaxation methodology, and also on approximate dynamic programming—which typically achieve within 1% of optimality with computation time orders of magnitude less than what is required to compute the optimal policy for problems of practical sizes. © 2014 Wiley Periodicals, Inc. Naval Research Logistics, 61: 557–576, 2014     

Concave envelopes of monomial functions over rectangles

The construction of convex and concave envelopes of real‐valued functions has been of interest in mathematical programming for over 3 decades. Much of this interest stems from the fact that convex and concave envelopes can play important roles in algorithms for solving various discrete and continuous global optimization problems. In this article, we use a simplicial subdivision tool to present and validate the formula for the concave envelope of a monomial function over a rectangle. Potential algorithmic applications of this formula are briefly indicated. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

A fluid queueing model for link travel time moments

We analyze the moments of the random time required for a vehicle to traverse a transportation network link of arbitrary length when its speed is governed by a random environment. The problem is motivated by stochastic transportation network applications in which the estimation of travel time moments is of great importance. We analyze this random time in a transient and asymptotic sense by employing results from the field of fluid queues. The results are demonstrated on two example problems. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Two‐dimensional failure modeling with minimal repair

In this paper, we discuss two‐dimensional failure modeling for a system where degradation is due to age and usage. We extend the concept of minimal repair for the one‐dimensional case to the two‐dimensional case and characterize the failures over a two‐dimensional region under minimal repair. An application of this important result to a manufacturer's servicing costs for a two‐dimensional warranty policy is given and we compare the minimal repair strategy with the strategy of replacement of failure. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

From management crisis to crisis management? Japan’s post-2012 institutional reforms and Sino-Japanese crisis (In)stability

Since 2012, China’s assertion of its sovereignty claim to the contested Senkaku/Diaoyu Islands has significantly raised the risk of a potentially escalatory political-military crisis with Japan. As circumstances worsen, Japanese Prime Minister Shinzo Abe has championed major institutional reforms aimed at centralizing Japanese security policy decision-making and vastly improving crisis management. This article assesses these reforms’ significance for ameliorating Japan’s long-standing internal crisis management weaknesses, and enhancing its ability to communicate with Beijing promptly under challenging conditions. While significant issues remain, recent developments – especially the establishment of Japan’s first-ever National Security Council – demonstrate significant progress. Bilaterally, however, important firebreaks remain conspicuously absent.     

Size Still Matters: Explaining Sri Lanka’s Counterinsurgency Victory over the Tamil Tigers

The military effectiveness literature has largely dismissed the role of material preponderance in favor of strategic interaction theories. The study of counterinsurgency, in which incumbent victory is increasingly rare despite material superiority, has also turned to other strategic dynamics explanations like force employment, leadership, and insurgent/adversary attributes. Challenging these two trends, this paper contends that even in cases of counterinsurgency, material preponderance remains an essential—and at times the most important—factor in explaining battlefield outcomes and effectiveness. To test this, the paper turns to the case of the Sri Lankan state’s fight against the Tamil Tiger insurgency, a conflict which offers rich variation over time across six periods and over 25 years. Drawing on evidence from historical and journalistic accounts, interviews, memoirs, and field research, the paper demonstrates that material preponderance accounts for variation in military effectiveness and campaign outcomes (including military victory in the final campaign) better than strategic explanations. Additionally, a new quantitative data-set assembled on annual loss-exchange ratios demonstrates the superiority of materialist explanations above those of skill, human capital, and regime type.     

An inventory problem with obsolescence

A stochastic single product convex cost inventory problem is considered in which there is a probability, π_j, that the product will become obsolete in the future period j. In an interesting paper, Barankin and Denny essentially formulate the model, but do not describe some of its interesting and relevant ramifications. This paper is written not only to bring out some of these ramifications, but also to describe some computational results using this model. The computational results show that if obsolescence is a distinct possibility in the near future, it is quite important that the probabilities of obsolescence be incorporated into the model before computing the optimal policies.     

A finite algorithm for concave minimization over a polyhedron

We present a new algorithm for solving the problem of minimizing a nonseparable concave function over a polyhedron. The algorithm is of the branch-and-bound type. It finds a globally optimal extreme point solution for this problem in a finite number of steps. One of the major advantages of the algorithm is that the linear programming subproblems solved during the branch-and-bound search each have the same feasible region. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some preliminary computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several bilinear programming problems with the code.