Inventory control under substitutable demand: A stochastic game application

Substitutable product inventory problem is analyzed using the concepts of stochastic game theory. It is assumed that there are two substitutable products that are sold by different retailers and the demand for each product is random. Game theoretic nature of this problem is the result of substitution between products. Since retailers compete for the substitutable demand, ordering decision of each retailer depends on the ordering decision of the other retailer. Under the discounted payoff criterion, this problem is formulated as a two‐person nonzero‐sum stochastic game. In the case of linear ordering cost, it is shown that there exists a Nash equilibrium characterized by a pair of stationary base stock strategies for the infinite horizon problem. This is the unique Nash equilibrium within the class of stationary base stock strategies. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 359–375, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10018     

Detection of a Markovian target with optimization of the search efforts under generalized linear constraints

This paper deals with search for a target following a Markovian movement or a conditionally deterministic motion. The problem is to allocate the search efforts, when search resources renew with generalized linear constraints. The model obtained is extended to resource mixing management. New optimality equations of de Guenin's style are obtained. Practically, the problem is solved by using an algorithm derived from the FAB method. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 117–142, 2002; DOI 10.1002/nav.10009     

Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine

This paper tackles the general single machine scheduling problem, where jobs have different release and due dates and the objective is to minimize the weighted number of late jobs. The notion of master sequence is first introduced, i.e., a sequence that contains at least an optimal sequence of jobs on time. This master sequence is used to derive an original mixed‐integer linear programming formulation. By relaxing some constraints, a Lagrangean relaxation algorithm is designed which gives both lower and upper bounds. The special case where jobs have equal weights is analyzed. Computational results are presented and, although the duality gap becomes larger with the number of jobs, it is possible to solve problems of more than 100 jobs. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 50: 2003     

Discrete‐time analysis of MAP/PH/1 multiclass general preemptive priority queue

We use the matrix‐geometric method to study the MAP/PH/1 general preemptive priority queue with a multiple class of jobs. A procedure for obtaining the block matrices representing the transition matrix P is presented. We show that the special upper triangular structure of the matrix R obtained by Miller [Computation of steady‐state probabilities for M/M/1 priority queues, Oper Res 29(5) (1981), 945–958] can be extended to an upper triangular block structure. Moreover, the subblock matrices of matrix R also have such a structure. With this special structure, we develop a procedure to compute the matrix R. After obtaining the stationary distribution of the system, we study two primary performance indices, namely, the distributions of the number of jobs of each type in the system and their waiting times. Although most of our analysis is carried out for the case of K = 3, the developed approach is general enough to study the other cases (K ≥ 4). © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 662–682, 2003.     

Scheduling patients in an ambulatory surgical center

This paper presents a deterministic approach to schedule patients in an ambulatory surgical center (ASC) such that the number of postanesthesia care unit nurses at the center is minimized. We formulate the patient scheduling problem as new variants of the no‐wait, two‐stage process shop scheduling problem and present computational complexity results for the new scheduling models. Also, we develop a tabu search‐based heuristic algorithm to solve the patient scheduling problem. Our algorithm is shown to be very effective in finding near optimal schedules on a set of real data from a university hospital's ASC. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

脉冲等离子体推力器工作过程一维磁流体动力学数值模拟

通过耦合脉冲等离子体推力器(PPT)工作过程中电场、磁场、流场之间的相互作用,描述了电容器放电、推进剂烧蚀、等离子体加速流动等过程,建立了基于磁流体动力学(MHD)的一维非定常数学模型,对PPT的工作过程进行数值模拟。对数值模拟结果作了相应分析,并将部分模拟结果与实验数据进行了比较。结果表明,模型正确反映了推力器放电过程、推进剂烧蚀质量与表面温度的变化趋势。     

A branch‐and‐cut algorithm for the quay crane scheduling problem in a container terminal

The quay crane scheduling problem consists of determining a sequence of unloading and loading movements for cranes assigned to a vessel in order to minimize the vessel completion time as well as the crane idle times. Idle times originate from interferences between cranes since these roll on the same rails and a minimum safety distance must be maintained between them. The productivity of container terminals is often measured in terms of the time necessary to load and unload vessels by quay cranes, which are the most important and expensive equipment used in ports. We formulate the quay crane scheduling problem as a vehicle routing problem with side constraints, including precedence relationships between vertices. For small size instances our formulation can be solved by CPLEX. For larger ones we have developed a branch‐and‐cut algorithm incorporating several families of valid inequalities, which exploit the precedence constraints between vertices. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

高空风场条件风速概率分布与正态分布差异分析

在飞行器多学科优化设计中,高空风场是有重要影响的不确定性因素,需要准确获取其统计特性。高空风场条件风速的概率分布是特定的,为了便于将高空风场概率模型用于不确定性设计,减少计算量,提出了高空风场条件风速概率分布与正态分布差异的分析方法,给出了将高空风场条件风速概率分布简化为正态分布的适用条件。数值仿真结果表明:在纬度为24.3°N～42.2°N范围内,不同地区高空风场条件风速概率密度与正态分布概率密度的差异在海拔2～30 km范围内呈喇叭形分布,在海拔15 km附近,高空风场条件风速概率密度与正态分布概率密度最接近,高空风场条件风速的概率分布可近似假设为正态分布。综合以上工作,给出了在飞行器不确定性设计中考虑条件风速不确定性时,生成随机样本方法的选择建议。     

Optimizing usage and maintenance decisions for k‐out‐of‐n systems of moving assets

We consider an integrated usage and maintenance optimization problem for a k‐out‐of‐n system pertaining to a moving asset. The k‐out‐of‐n systems are commonly utilized in practice to increase availability, where n denotes the total number of parallel and identical units and k the number of units required to be active for a functional system. Moving assets such as aircraft, ships, and submarines are subject to different operating modes. Operating modes can dictate not only the number of system units that are needed to be active, but also where the moving asset physically is, and under which environmental conditions it operates. We use the intrinsic age concept to model the degradation process. The intrinsic age is analogous to an intrinsic clock which ticks on a different pace in different operating modes. In our problem setting, the number of active units, degradation rates of active and standby units, maintenance costs, and type of economic dependencies are functions of operating modes. In each operating mode, the decision maker should decide on the set of units to activate (usage decision) and the set of units to maintain (maintenance decision). Since the degradation rate differs for active and standby units, the units to be maintained depend on the units that have been activated, and vice versa. In order to minimize maintenance costs, usage and maintenance decisions should be jointly optimized. We formulate this problem as a Markov decision process and provide some structural properties of the optimal policy. Moreover, we assess the performance of usage policies that are commonly implemented for maritime systems. We show that the cost increase resulting from these policies is up to 27% for realistic settings. Our numerical experiments demonstrate the cases in which joint usage and maintenance optimization is more valuable. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 418–434, 2017