一种新的装备配置优化模型

传统的装备配置优化问题一般采用确定性的数学规划方法解决,难以满足高技术条件下现代战争中需要对大量随机现象和模糊现象进行精确定量分析的实际要求。在分析了高技术条件下装备配置问题一般特性的基础上,根据机会约束规划和模糊机会约束规划的思想,提出了一种新的建立装备配置优化模型的思路和方法,并给出了基于随机模拟的遗传算法的实值算例,算例结果与实际情况基本相符,反映了模型的科学性与实用性。     

Estimating critical path and arc probabilities in stochastic activity networks

This article describes a new procedure for estimating parameters of a stochastic activity network of N arcs. The parameters include the probability that path m is the longest path, the probability that path m is the shortest path, the probability that arc i is on the longest path, and the probability that arc i is on the shortest path. The proposed procedure uses quasirandom points together with information on a cutset ? of the network to produce an upper bound of O[(log K)^N?|?|+1/K] on the absolute error of approximation, where K denotes the number of replications. This is a deterministic bound and is more favorable than the convergence rate of 1/K^1/2 that one obtains from the standard error for K independent replications using random sampling. It is also shown how series reduction can improve the convergence rate by reducing the exponent on log K. The technique is illustrated using a Monte Carlo sampling experiment for a network of 16 relevant arcs with a cutset of ? = 7 arcs. The illustration shows the superior performance of using quasirandom points with a cutset (plan A) and the even better performance of using quasirandom points with the cutset together with series reduction (plan B) with regard to mean square error. However, it also shows that computation time considerations favor plan A when K is small and plan B when K is large.     

Simulation of stochastic activity networks using path control variates

This article details several procedures for using path control variates to improve the accuracy of simulation-based point and confidence-interval estimators of the mean completion time of a stochastic activity network (SAN). Because each path control variate is the duration of the corresponding directed path in the network from the source to the sink, the vector of selected path controls has both a known mean and a known covariance matrix. This information is incorporated into estimation procedures for both normal and nonnormal responses. To evaluate the performance of these procedures experimentally, we examine the bias, variance, and mean square error of the controlled point estimators as well as the average half-length and coverage probability of the corresponding confidence-interval estimators for a set of SANs in which the following characteristics are systematically varied: (a) the size of the network (number of nodes and arcs); (b) the topology of the network; (c) the percentage of activities with exponentially distributed durations; and (d) the relative dominance of the critical path. The experimental results show that although large improvements in accuracy can be achieved with some of these procedures, the confidence-interval estimators for normal responses may suffer serious loss of coverage probability in some applications.     

基于混合智能算法的小型通信干扰装备分配优化

如何充分发挥小型通信干扰装备的作战效能是指挥员面临的棘手问题。本文将战术指标——干扰后的通信畅通区覆盖程度作为评估通信干扰装备分配优劣的指标,分别建立了单机和多部干扰时的通信干扰有效压制区和通信畅通区边界的计算模型,并给出了通信干扰有效压制区和通信畅通区面积的计算方法。构建了基于机会约束规划的空域频域通信干扰任务分配模型,并设计了混合蚁群算法和遗传算法的模型求解算法。最后进行了仿真实验,验证分析了模型和算法的合理性。研究成果为通信对抗战术计算和作战运用研究拓展了思路。     

A chance-constrained distribution problem

The transportation model with supplies (S_i) and demands (D_i) treated as bounded variables developed by Charnes and Klingman is extended to the case where the S_i and D_i are independently and uniformly distributed random variables. Chance constraints which require that demand at the jth destination will be satisfied with probability at least β_i and that stockout at the ith origin will occur with probability less than α_i are imposed. Conversion of the chance constraints to their linear equivalents results in a transportation problem with one more row and column than the original with some of the new arcs capacitated. The chance-constrained formulation is extended to the transshipment problem.     

Economic lot sizing with constant capacities and concave inventory costs

This article studies the classical single‐item economic lot‐sizing problem with constant capacities, fixed‐plus‐linear order costs, and concave inventory costs, where backlogging is allowed. We propose an O(T³) optimal algorithm for the problem, which improves upon the O(T⁴) running time of the famous algorithm developed by Florian and Klein (Manage Sci18 (1971) 12–20). Instead of using the standard dynamic programming approach by predetermining the minimal cost for every possible subplan, we develop a backward dynamic programming algorithm to obtain a more efficient implementation. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Probability density function of a stochastic linear programming problem

A stochastic linear programming problem under the “wait-and-see” situation is studied. After the conditions for the interchange of the order of integration and differentiation are surveyed, an explicit form of the probability density function of the stochastic linear programming problem is found. An example is also given to illustrate the result.     

Safety stock reduction by order splitting

In this article we consider an item for which a continuous review, reorder point, order quantity inventory control system is used. The amount of safety stock required depends upon, among other factors, the average value and variability of the length of the replenishment lead time. One way to reduce these quantities is to split orders among two or more vendors. In this article the random lead times are assumed to have Weibull distributions. This permits the development of analytic expressions for the reduction in the expected value and variability of total demand until the critical first (earliest) delivery received from a vendor. An expression is also obtained for the reorder point that provides a given probability of no stockout prior to the first delivery. Lower bounds are given on the order quantity so as to ensure that the probability of a stockout before any one of the later (second, third, etc.) deliveries is sufficiently small to be considered negligible. The analytic and tabular results can be used to estimate the benefits (reduced carrying costs and/or increased service level) of order splitting.     

Nonadjacent extreme point methods for solving linear programs

In this article we present some advanced basis or block-pivoting, relaxation, and feasible direction methods for solving linear programming problems. Preliminary computational results appear to indicate that the former two types of simplex-based procedures may hold promise for solving linear programming problems, unlike the third type of scheme which is shown to be computationally unattractive.     

Aggregating assignment constraints

This article shows how simple systems of linear equations with {0,1} variables can be aggregated into a single linear equation whose {0,1} solutions are identical to the solutions of the original system. Structures of the original systems are exploited to keep the aggregator's integer coefficients from becoming unnecessarily large. The results have potential application in integer programming and information theory, especially for problems that contain assignment-type constraints along with other constraints. Several unresolved questions of a number-theoretic nature are mentioned at the conclusion of the article.     

A linear programming model for design of communications networks with time varying probabilistic demands

In this paper marginal investment costs are assumed known for two kinds of equipment stocks employed to supply telecommunications services: trunks and switching facilities. A network hierarchy is defined which includes important cases occurring in the field and also appearing in the literature. A different use of the classical concept of the marginal capacity of an additional trunk at prescribed blocking probability leads to a linear programming supply model which can be used to compute the sizes of all the high usage trunk groups. The sizes of the remaining trunk groups are approximated by the linear programming models, but can be determined more accurately by alternate methods once all high usage group sizes are computed. The approach applies to larger scale networks than previously reported in the literature and permits direct application of the duality theory of linear programming and its sensitivity analyses to the study and design of switched probabilistic communications networks with multiple busy hours during the day. Numerical results are presented for two examples based on field data, one of which having been designed by the multi-hour engineering method.     

Information in two-stage programming under uncertainty

The random variables in two-stage programming under uncertainty are generally treated in a passive manner in that no information regarding the random variables or the process generating the random variables may be obtained. This paper develops the economics of information for the case in which the probability distributions are discrete. A multinomial process is assumed to generate the random variables, and the parameter vector of that process is assumed to be unknown. A Dirichlet prior distribution on the parameter vector is used, and the computation of the value of information thus involves a Dirichlet-multinomial distribution on the random variables. An example involving producing to meet uncertain demands is presented.     

援潜救生进度风险分析

失事潜艇的援救要求在潜艇失事后48h内展开,综合考虑援救任务耗时的随机性和模糊性,将计划评审技术PERT(project evalution and review technique)和模糊概率分析结合起来,用以评估援潜救生任务的进度风险。首先,给出了单独使用PERT技术计算援潜救生准备工作在48h内完成的概率的基本算法;然后,将模糊概率分析引入PERT技术,求出援潜救生任务的关键路线,给出基于模糊PERT分析的完工概率算法;最后,以深潜救生艇从我国北方某基地转运至目的地实施救援任务为例,计算援潜救生准备工作在48h内完成的概率。计算结果的对比表明:使用模糊PERT分析方法比单独使用PERT技术得出的数据更为可靠。     

保证率点值区间估计的Monte-Carlo方法

提出了一种根据实测样本系列对保证率点值进行区间估计的Ｍｏｎｔｅ─Ｃａｒｌｏ方法。对于具有正态分布或对数正态分布的样本,首先推出总体参数的分布,然后用Ｍｏｎｔｅ─Ｃａｒｌｏ法生成总体参数系列,据此求得相应的保证率点值系列,最后通过经验分布推得在给定置信度下保证率点值的区间估计,本文还给出了一个算例。     

Closure properties of the relevation transform*

Sufficient conditions under which the relevation of two probability distributions is (i) NBU, (ii) IFRA, (iii) IFR are derived. The result for case (iii) corrects an error in a previous article by Baxter.     

Stochastic call center staffing with uncertain arrival,service and abandonment rates: A Bayesian perspective

In this article, we introduce staffing strategies for the Erlang‐A queuing system in call center operations with uncertain arrival, service, and abandonment rates. In doing so, we model the system rates using gamma distributions that create randomness in operating characteristics used in the optimization formulation. We divide the day into discrete time intervals where a simulation based stochastic programming method is used to determine staffing levels. More specifically, we develop a model to select the optimal number of agents required for a given time interval by minimizing an expected cost function, which consists of agent and abandonment (opportunity) costs, while considering the service quality requirements such as the delay probability. The objective function as well as the constraints in our formulation are random variables. The novelty of our approach is to introduce a solution method for the staffing of an operation where all three system rates (arrival, service, and abandonment) are random variables. We illustrate the use of the proposed model using both real and simulated call center data. In addition, we provide solution comparisons across different formulations, consider a dynamic extension, and discuss sensitivity implications of changing constraint upper bounds as well as prior hyper‐parameters. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 460–478, 2016     

A simulated annealing approach to the cyclic staff-scheduling problem

This article presents the application of a simulated annealing heuristic to an NP-complete cyclic staff-scheduling problem. The new heuristic is compared to branch-and-bound integer programming algorithms, as well as construction and linear programming-based heuristics. It is designed for use in a continuously operating scheduling environment with the objective of minimizing the number of employees necessary to satisfy forecast demand. The results indicate that the simulated annealing-based method tends to dominate the branch-and-bound algorithms and the other heuristics in terms of solution quality. Moreover, the annealing algorithm exhibited rapid convergence to a low-cost solution. The simulated annealing heuristic is executed in a single program and does not require mathematical programming software. © 1993 John Wiley & Sons, Inc.     

Stochastic linear fractional programming with the ratio of independent Cauchy variates

In this article is studied a stochastic linear fractional programming problem, in which the parameters of both the numerator and the denominator are assumed to be mutually independent Cauchy variates. The deterministic equivalent of the problem is obtained and is shown to be a linear fractional program. A numerical example is also added for illustration.     

Arrival and departure state distributions in the general bulk‐service queue

In this paper, we give an explicit relation between steady‐state probability distributions of the buffer occupancy at customer entrance and departure epochs, for the classical single‐server system G/G^[N]/1 with batch services and for the finite capacity case. The method relies on level‐crossing arguments. For the particular case of Poisson input, we also express the loss probability in terms of state probabilities at departure epochs, yielding probabilities observed by arriving customers. This work provides the “bulk queue” version of a result established by Burke, who stated the equality between probabilities at arrival and departure epochs for systems with “unit jumps.” © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 107–118, 1999     

Optimal path finding in direction,location, and time dependent environments

This article examines optimal path finding problems where cost function and constraints are direction, location, and time dependent. Recent advancements in sensor and data‐processing technology facilitate the collection of detailed real‐time information about the environment surrounding a ground vehicle, an airplane, or a naval vessel. We present a navigation model that makes use of such information. We relax a number of assumptions from existing literature on path‐finding problems and create an accurate, yet tractable, model suitable for implementation for a large class of problems. We present a dynamic programming model which integrates our earlier results for direction‐dependent, time and space homogeneous environment, and consequently, improves its accuracy, efficiency, and run‐time. The proposed path finding model also addresses limited information about the surrounding environment, control‐feasibility of the considered paths, such as sharpest feasible turns a vehicle can make, and computational demands of a time‐dependent environment. To demonstrate the applicability and performance of our path‐finding algorithm, computational experiments for a short‐range ship routing in dynamic wave‐field problem are presented. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012