A sequential partial information bomber-defender shooting problem

A bomber carrying homogenous weapons sequentially engages ground targets capable of retaliation. Upon reaching a target, the bomber may fire a weapon at it. If the target survives the direct fire, it can either return fire or choose to hold fire (play dead). If the former occurs, the bomber is immediately made aware that the target is alive. If no return fire is seen, the true status of the target is unknown to the bomber. After the current engagement, the bomber, if still alive, can either re-engage the same target or move on to the next target in the sequence. The bomber seeks to maximize the expected cumulative damage it can inflict on the targets. We solve the perfect and partial information problems, where a target always fires back and sometimes fires back respectively using stochastic dynamic programming. The perfect information scenario yields an appealing threshold based bombing policy. Indeed, the marginal future reward is the threshold at which the control policy switches and furthermore, the threshold is monotonic decreasing with the number of weapons left with the bomber and monotonic nondecreasing with the number of targets left in the mission. For the partial information scenario, we show via a counterexample that the marginal future reward is not the threshold at which the control switches. In light of the negative result, we provide an appealing threshold based heuristic instead. Finally, we address the partial information game, where the target can choose to fire back and establish the Nash equilibrium strategies for a representative two target scenario.     

A forward network simplex algorithm for solving multiperiod network flow problems

An optimization model which is frequently used to assist decision makers in the areas of resource scheduling, planning, and distribution is the minimum cost multiperiod network flow problem. This model describes network structure decision-making problems over time. Such problems arise in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, as well as in many others. Although existing network solution techniques are efficient, there are still limitations to the size of problems that can be solved. To date, only a few researchers have taken the multiperiod structure into consideration in devising efficient solution methods. Standard network codes are usually used because of their availability and perceived efficiency. In this paper we discuss the development, implementation, and computational testing of a new technique, the forward network simplex method, for solving linear, minimum cost, multiperiod network flow problems. The forward network simplex method is a forward algorithm which exploits the natural decomposition of multiperiod network problems by limiting its pivoting activity. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for a large number of special structure models. Here we describe the specialization of the forward simplex method of Aronson, Morton, and Thompson to solving multiperiod network network flow problems. Computational results indicate that both the solution time and pivot count are linear in the number of periods. For standard network optimization codes, which do not exploit the multiperiod structure, the pivot count is linear in the number of periods; however, the solution time is quadratic.     

A new approach for dealing with the startup problem in discrete event simulation

This article proposes a practical, data-based statistical procedure which can be used to reduce or remove bias owing to artificial startup conditions in simulations aimed at estimating steady-state means. We discuss results of experiments designed to choose good parameter values for this procedure, and present results of extensive testing of the procedure on a variety of stochastic models for which partial analytical results are available. The article closes with two illustrations of the application of the procedure to more complex statistical problems which are more representative of the kinds of purposes for which real-world steady-state simulation studies might be undertaken.