Continuous accumulation games on discrete locations

In an accumulation game, a HIDER attempts to accumulate a certain number of objects or a certain quantity of material before a certain time, and a SEEKER attempts to prevent this. In a continuous accumulation game the HIDER can pile material either at locations $1, 2, …, n, or over a region in space. The HIDER will win (payoff 1) it if accumulates N units of material before a given time, and the goal of the SEEKER will win (payoff 0) otherwise. We assume the HIDER can place continuous material such as fuel at discrete locations i = 1, 2, …, n, and the game is played in discrete time. At each time k > 0 the HIDER acquires h units of material and can distribute it among all of the locations. At the same time, k, the SEEKER can search a certain number s < n of the locations, and will confiscate (or destroy) all material found. After explicitly describing what we mean by a continuous accumulation game on discrete locations, we prove a theorem that gives a condition under which the HIDER can always win by using a uniform distribution at each stage of the game. When this condition does not hold, special cases and examples show that the resulting game becomes complicated even when played only for a single stage. We reduce the single stage game to an optimization problem, and also obtain some partial results on its solution. We also consider accumulation games where the locations are arranged in either a circle or in a line segment and the SEEKER must search a series of adjacent locations. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 60–77, 2002; DOI 10.1002/nav.1048     

Interactive optimization methodology for fleet scheduling

This article addresses the problem of scheduling the United States Navy's Atlantic Fleet to satisfy overseas strategic requirements. An integer programming formulation is developed but results in a model with prohibitive size. This fact and the qualitative nature of additional secondary objectives and constraints suggest an interactive optimization approach. A system that solves a natural relaxation of the integer program within an interactive environment is discussed.     

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     

On the use of standard tables to obtain Dodge-Romig LTPD sampling inspection plans

Procedures are described which yield single and double sample Dodge-Romig [1] lot tolerance percent defective (LTPD) rectifying inspection plans. For the determination of such plans only a desk calculator and standard tables of the discrete probability distributions are required. Some advantages gained by using these procedures rather than the Dodge-Romig table include: (a) The Consumer's Risk is not limited to 0.10. (b) More choices of LTPD are available. (c) Smaller average total inspection is achieved by using a plan designed for specific “process average” and lot size rather than a compromise plan designed to cover intervals on these two parameters.     

A dynamic inventory system with recycling

This paper deals with a periodic review inventory system in which a constant proportion of stock issued to meet demand each period feeds back into the inventory after a fixed number of periods. Various applications of the model are discussed, including blood bank management and the control of reparable item inventories. We assume that on hand inventory is subject to proportional decay. Demands in successive periods are assumed to be independent identically distributed random variables. The functional equation defining an optimal policy is formulated and a myopic base stock approximation is developed. This myopic policy is shown to be optimal for the case where the feedback delay is equal to one period. Both cost and ordering decision comparisons for optimal and myopic policies are carried out numerically for a delay time of two periods over a wide range of input parameter values.     

Test selection for a mass screeening program

Periodic mass screening is the scheduled application of a test to all members of a population to provide early detection of a randomly occurring defect or disease. This paper considers periodic mass screening with particular reference to the imperfect capacity of the test to detect an existing defect and the associated problem of selecting the kind of test to use. Alternative kinds of tests differ with respect to their reliability characteristics and their cost per application. Two kinds of imperfect test reliability are considered. In the first case, the probability that the test will detect an existing defect is constant over all values of elapsed time since the incidence of the defect. In the second case, the test will detect the defect if, and only if, the lapsed time since incidence exceeds a critical threshold T which characterizes the test. The cost of delayed detection is an arbitrary increasing function (the “disutility function”) of the duration of the delay. Expressions for the long-run expected disutility per unit time are derived for the above two cases along with results concerning the best choice of type of test (where the decision rules make reference to characteristics of the disutility function).     

Remarks on a univariate shock model with some bivariate generalizations

In a 1973 paper J. D. Esary, A. W. Marshall, and F. Proschan [5] considered a shock model giving rise to various nonparametric classes of life distributions of interest in reliability theory. A number of authors have extended these results in a variety of directions. In this paper, alternative proofs of the increasing failure rate (IFR) and decreasing mean residual life (DMRL) results are given which do not make use of the theory of total positivity. Some bivariate extensions are then obtained using a shock model similar to that originally used by H. W. Block, A. S. Paulson, and R. C. Kohberger [2] to unify various bivariate exponential distributions.     

Signaling resolve,democratization, and the first battle of Fallujah

Perceptions and efforts to signal resolve can play an important role in counterinsurgency. The Coalition offensive against Fallujah in April 2004 demonstrates the limitations of relying on military force to signal resolve. The offensive catalyzed insurgent violence in Iraq and generated popular support for the insurgency. The Coalition prematurely halted the offensive because the Iraqi Governing Council (IGC) could not maintain support for the Coalition in the face of popular outrage. Given the importance of democratizing Iraq and establishing a sovereign government, the objections of the IGC could not be ignored. Without Iraqi political support, military force ultimately signaled weakness instead of resolve.