Analytic solution for the nucleolus of a three‐player cooperative game

The nucleolus solution for cooperative games in characteristic function form is usually computed numerically by solving a sequence of linear programing (LP) problems, or by solving a single, but very large‐scale, LP problem. This article proposes an algebraic method to compute the nucleolus solution analytically (i.e., in closed‐form) for a three‐player cooperative game in characteristic function form. We first consider cooperative games with empty core and derive a formula to compute the nucleolus solution. Next, we examine cooperative games with nonempty core and calculate the nucleolus solution analytically for five possible cases arising from the relationship among the value functions of different coalitions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

An integer decomposition algorithm for solving a two‐stage facility location problem with second‐stage activation costs

We study a stochastic scenario‐based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. Unlike typical facility location problems, fixed charges arise in the initial location of the facilities, and then in the activation of located facilities. The first‐stage variables in our problem are the traditional binary facility‐location variables, whereas the second‐stage variables involve a mix of binary facility‐activation variables and continuous flow variables. Benders decomposition is not applicable for these problems due to the presence of the second‐stage integer activation variables. Instead, we derive cutting planes tailored to the problem under investigation from recourse solution data. These cutting planes are derived by solving a series of specialized shortest path problems based on a modified residual graph from the recourse solution, and are tighter than the general cuts established by Laporte and Louveaux for two‐stage binary programming problems. We demonstrate the computational efficacy of our approach on a variety of randomly generated test problems. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

A partial characterization of the optimal ordering/rationing policy for a periodic review system with two demand classes and backordering

We consider a finite horizon periodic review, single product inventory system with a fixed setup cost and two stochastic demand classes that differ in their backordering costs. In each period, one must decide whether and how much to order, and how much demand of the lower class should be satisfied. We show that the optimal ordering policy can be characterized as a state dependent (s,S) policy, and the rationing structure is partially obtained based on the subconvexity of the cost function. We then propose a simple heuristic rationing policy, which is easy to implement and close to optimal for intensive numerical examples. We further study the case when the first demand class is deterministic and must be satisfied immediately. We show the optimality of the state dependent (s,S) ordering policy, and obtain additional rationing structural properties. Based on these properties, the optimal ordering and rationing policy for any state can be generated by finding the optimal policy of only a finite set of states, and for each state in this set, the optimal policy is obtained simply by choosing a policy from at most two alternatives. An efficient algorithm is then proposed. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

镜像法求解导体球外点电荷电场的代数解

用代数法求解了导体球外点电荷在空间产生的静电场。得到了能反映导体球中自由电荷性质的新解该结果既符合唯一性定理,又有明确的物理含义。     

具有时滞的二阶多点边值问题3个正解的存在性

研究具有时滞的二阶多点边值问题,应用Avery和Peterson推广的Leggett-Williams不动点定理,给出了该边值问题至少存在3个正解的充分条件。     

求解非线性规划的小生境遗传模拟退火算法

提出了用小生境遗传模拟退火算法求解带复杂约束的非线性规划问题。首先分析了遗传算法＂早熟＂收敛以及局部搜索能力弱的不足,由此引入小生境以增加种群多样性,并抑制＂早熟＂收敛现象,同时引入模拟退火算法以增强局部搜索能力,改进进化后期收敛速度慢的不足,最后结合典型非线性规划算例验证了混合算法的效率、精度和可靠性。     

重型鱼雷的机动搜索及机动搜索弹道架构

针对潜射重型鱼雷在技术性能上的大幅提高和智能化作战的需要,在提出并分析鱼雷机动搜索概念和机动搜索时机的基础上,研究了远程重型鱼雷实现机动搜索在弥补发射平台目标定位误差、鱼雷发射后目标的有意机动和适应点对域攻击战法转变等作战环节中的必要性,构建了重型鱼雷机动搜索弹道的技术框架.     

浅谈武警院校教学改革中互动式教学法的应用

互动式教学是武警院校教育改革中倡导的一种新型的教学模式,要正确应用互动式教学模式,就要注重互动双方的定位、互动问题的选取、互动方法的选择。     

Natural gas storage valuation and optimization: A real options application

In this article, we present an algorithm for the valuation and optimal operation of natural gas storage facilities. Real options theory is used to derive nonlinear partial‐integro‐differential equations (PIDEs), the solution of which give both valuation and optimal operating strategies for these facilities. The equations are designed to incorporate a wide class of spot price models that can exhibit the same time‐dependent, mean‐reverting dynamics, and price spikes as those observed in most energy markets. Particular attention is paid to the operational characteristics of real storage units. These characteristics include working gas capacities, variable deliverability and injection rates, and cycling limitations. We illustrate the model with a numerical example of a salt cavern storage facility that clearly shows how a gas storage facility is like a financial straddle with both put and call properties. Depending on the amount of gas in storage the relative influence of the put and call components vary. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Designing and pricing menus of extended warranty contracts

Extended warranties provide “piece of mind” to a consumer in that product failures which occur after the base warranty expires are rectified at little or no cost. They also provide an additional source of revenue for manufacturers or third‐party providers, such as retailers or insurance providers, and help cultivate consumer loyalty. In this article, we analyze a number of extended warranty contracts which differ in design, including restrictions on deferrals and renewals. With the use of dynamic programming, we compute the optimal strategy for a consumer with perfect information and determine the optimal pricing policy for the provider given the consumer's risk characterization. We also provide insight into when different contracts should be issued. Finally, we illustrate how profits can be dramatically increased by offering menus of warranty contracts, as opposed to stand alone contracts, with the use of integer programming. Surprisingly, risk‐taking consumers provide the greatest benefit to offering menus. These insights can help a company develop a comprehensive warranty planning strategy for given products or product lines. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009