Optimal strategies for problems of simultaneous attack against an area defense with impact-point prediction

An area to be defended consists of separated point targets. These targets are subject to an attack in which the offensive weapons are assumed to arrive simultaneously. The defense has area defenders, each of which is capable of intercepting any attacker'. Furthermore, the defense has impact-point prediction, i.e., it has knowledge of each attacker's intended target prior to allocation of the area interceptors. For a given attack, the defense wishes to allocate its interceptors against attackers so as to maximize the expected total survival value of the targets. In its first move, the offense seeks an attack allocation which will minimize expected total surviving value against best defense. We develop an algorithm to determine optimal attack and defense strategies and the optimal value of this sequential min-max problem. Branch-and-bound techniques are used to obtain integer solutions, and illustrative computational results are provided.     

Bounds and properties of the expected value of sample information for a project-selection problem

In this article we extend the work of Mehrez and Stulman [5] on the expected value of perfect information (EVPI) to the expected value of sample information (EVSI) for a class of economic problems dealing with the decision to reject or accept an investment project. It is shown that shifting the mean of the underlying a priori distribution of X, the project's monetary value from zero in either direction will decrease the associated EVSI of Y, the random sampled information. A theorem is then presented which gives an upper bound on the EVSI over all distributions of Y, as well as the structure of the posterior mean E[X|Y] for which this upper bound is achieved. Finally, the case where E[X|Y] is linear in Y is discussed and its performance compared with that of the optimal case.     

Optimal production ramp-up in the smartphone manufacturing industry

Motivated by challenges in the smartphone manufacturing industry, we develop a dynamic production ramp-up model that can be applied to economically satisfy nonstationary demand for short-life-cycle products by high-tech companies. Due to shorter life cycles and more rapid evolution of smartphones, production ramp-up has been increasingly critical to the success of a new smartphone. In the production ramp-up, the key challenge is to match the increasing capacity to nonstationary demand. The high-tech smartphone manufacturers are urged to jointly consider the effect of increasing capacity and decreasing demand. We study the production planning problem using a high-dimensional Markov decision process (MDP) model to characterize the production ramp-up. To address the curse of dimensionality, we refine Monte Carlo tree search (MCTS) algorithm and theoretically analyze its convergence and computational complexity. In a real case study, we find that the MDP model achieves revenue improvement by stopping producing the existing product earlier than the benchmark policy. In synthetic instances, we validate that the proposed MCTS algorithm saves computation time without loss of solution quality compared with traditional value iteration algorithm. As part of the Lenovo production solution, our MDP model enables high-tech smartphone manufacturers to better plan the production ramp-up.     

Modeling the performance of a scanning radio communications sensor

A model which allows the prediction of long-term average report rates against an array of radio emitters by a scanning sensor is presented. The model is based on Markov renewal theory.     

A decomposition procedure for convex quadratic programs

This article deals with the solution of convex quadratic programs by iteratively solving a master problem and a subproblem as proposed previously by Sacher. The approach has the advantage that the subproblems are linear programs so that advantage can be taken of existing schemes for solving large linear problems. At each step in solving the master problem, a closed-form solution can be specified so that the procedure is well suited for solving large quadratic programs and can take advantage of the constraint structure.     

Multiple criteria decision making in the USSR: A survey

A brief historical overview of the development of multiple criteria decision making (MCDM) in the USSR during the last fifteen years is presented. Soviet MCDM research is reviewed. Several applications of MCDM methodology in the USSR are described. Long-term trends in the research and application of MCDM in the Soviet Union are discussed.     

Continuous sampling plans for markov-dependent production processes

This article discusses the behavior of three continuous sampling plans: continuous sampling plan 1 (CSP 1) and continuous sampling plan 2 (CSP 2) developed by Dodge [5] and Dodge and Torrey [7], and multilevel continuous sampling plan 2 (MLP 2) developed by Lieberman and Solomon [11], when the quality of successive units in a continuous production process follows a two-state time-homogeneous Markov chain. We first derive the average outgoing quality (AOQ) expressions of these plans. Exact procedures for determining the average outgoing quality limit (AOQL) can be obtained only for CSP 1. For CSP 2 and MLP 2 plans, iterative procedures have been used to obtain the AOQL contours. For these plans, it is assumed that the serial correlation coefficient between the two consecutive random variables of the Markov chain is known. In addition, estimation procedures for the coefficient are given. We show that if the serial correlation coefficient of the Markov chain is positive (negative), the AOQL is increased (decreased) as compared to the case when the successive units in the production process follows a Bernoulli pattern. Let r denote the number of production units examined in succession which are found to be of good quality and k denote the inverse of the sampling fraction employed when quality is good. Then if r and k are sufficiently small, it is observed from the graph that, for small departures of the serial correlation coefficient from zero, the AOQL values do not differ significantly for each of the three plans; whereas for sufficiently large values of r and k, the AOQL values differ significantly. Various aspects of these plans, such as their operating characteristics 2 (OC 2) and the serial correlation coefficient, are discussed.     

Optimal strategies for problems of simultaneous attack against an area defense without impact-point prediction

An area to be defended consists of separated point targets. These targets are subject to an attack in which the offensive weapons are assumed to arrive simultaneously. The defense has area defenders, each of which is capable of intercepting any attacker. The defense has no impact-point prediction; that is, it has no knowledge of any attacker's destination prior to allocation of area interceptors. For a given attack, the defense wishes to allocate its interceptors to maximize the total expected survival value of the targets. For a given attack size, the offense seeks a strategy to minimize total expected surviving value against best defense. We determine an optimal defensive strategy directly and develop an algorithm to determine an optimal attack and the optimal value of the min-max problem. A dynamic programming technique is used to obtain integer solutions, and illustrative computational results are provided.