Optimal switchover times between two activities utilizing the same resource

The “gold‐mining” decision problem is concerned with the efficient utilization of a delicate mining equipment working in a number of different mines. Richard Bellman was the first to consider this type of a problem. The solution found by Bellman for the finite‐horizon, continuous‐time version of the problem with two mines is not overly realistic since he assumed that fractional parts of the same mining equipment could be used in different mines and this fraction could change instantaneously. In this paper, we provide some extensions to this model in order to produce more operational and realistic solutions. Our first model is concerned with developing an operational policy where the equipment may be switched from one mine to the other at most once during a finite horizon. In the next extension we incorporate a cost component in the objective function and assume that the horizon length is not fixed but it is the second decision variable. Structural properties of the optimal solutions are obtained using nonlinear programming. Each model and its solution is illustrated with a numerical example. The models developed here may have potential applications in other areas including production of items requiring the same machine or choosing a sequence of activities requiring the same resource. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 186–203, 2002; DOI 10.1002/nav.10008     

微分对策界栅理论在舰艇作战能力评估中的应用

作战能力是表征战斗舰艇战术技术性能的一项重要指标,如何正确评价舰艇的作战能力一直是军事运筹研究的热点.利用定性微分对策的界栅理论研究了一类作战问题,通过构造捕获区面积和咽喉区域面积,并以此作为动态评估舰艇作战能力的衡量指标.研究结果可为综合评价舰艇作战能力提供一条新途径.     

基于博弈论的装备科研、购置、维修经费比例关系优化分析

通过不同时期国家战略部署、科研发展情况及经济承受能力对装备经费分配的影响分析,采用博弈的方法,建立了装备科研、购置和维修费之间的比例关系优化模型,给出了寻求纳什均衡点的迭代算法,并进行了仿真计算.仿真结果证明了该方法的可行性与正确性.     

Adjacency‐based local top‐down search method for finding maximal efficient faces in multiple objective linear programming

It is well‐known that the efficient set of a multiobjective linear programming (MOLP) problem can be represented as a union of the maximal efficient faces of the feasible region. In this paper, we propose a method for finding all maximal efficient faces for an MOLP. The new method is based on a condition that all efficient vertices (short for the efficient extreme points and rays) for the MOLP have been found and it relies on the adjacency, affine independence and convexity results of efficient sets. The method uses a local top‐down search strategy to determine maximal efficient faces incident to every efficient vertex for finding maximal efficient faces of an MOLP problem. To our knowledge, the proposed method is the first top‐down search method that uses the adjacency property of the efficient set to find all maximal efficient faces. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several MOLP problems with the code.     

The multiplicative representation for multiple objectives optimization with an application for arms procurement

Multiple Objectives Optimization is much seen in combination with linear functions and even with linear programming, together with an adding of the objectives by using weights. With distance functions, normalization instead of weights is used. It is also possible that together with an additive direct influence of the objectives on the utility function a mutual utility of the objectives exists under the form of a multiplicative representation. A critical comment is brought on some representations of this kind. A full‐multiplicative form may offer other opportunities, which will be discussed at length in an effort to exclude weights and normalization. This theoretical approach is followed by an application for arms procurement. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 327–340, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10014     

Resequencing with parallel queues to minimize the maximum number of items in the overflow area

This article treats an elementary optimization problem, where an inbound stream of successive items is to be resequenced with the help of multiple parallel queues in order to restore an intended target sequence. Whenever early items block the one item to be currently released into the target sequence, they are withdrawn from their queue and intermediately stored in an overflow area until their actual release is reached. We aim to minimize the maximum number of items simultaneously stored in the overflow area during the complete resequencing process. We met this problem in industry practice at a large German automobile producer, who has to resequence containers with car seats prior to the assembly process. We formalize the resulting resequencing problem and provide suited exact and heuristic solution algorithms. In our computational study, we also address managerial aspects such as how to properly avoid the negative effects of sequence alterations. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 401–415, 2016     

Determination of burn‐in parameters and residual life for highly reliable products

Today, many products are designed and manufactured to function for a long period of time before they fail. Determining product reliability is a great challenge to manufacturers of highly reliable products with only a relatively short period of time available for internal life testing. In particular, it may be difficult to determine optimal burn‐in parameters and characterize the residual life distribution. A promising alternative is to use data on a quality characteristic (QC) whose degradation over time can be related to product failure. Typically, product failure corresponds to the first passage time of the degradation path beyond a critical value. If degradation paths can be modeled properly, one can predict failure time and determine the life distribution without actually observing failures. In this paper, we first use a Wiener process to describe the continuous degradation path of the quality characteristic of the product. A Wiener process allows nonconstant variance and nonzero correlation among data collected at different time points. We propose a decision rule for classifying a unit as normal or weak, and give an economic model for determining the optimal termination time and other parameters of a burn‐in test. Next, we propose a method for assessing the product's lifetime distribution of the passed units. The proposed methodologies are all based only on the product's initial observed degradation data. Finally, an example of an electronic product, namely contact image scanner (CIS), is used to illustrate the proposed procedure. © 2002 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

The building evacuation problem with shared information

In this article, the Building Evacuation Problem with Shared Information (BEPSI) is formulated as a mixed integer linear program, where the objective is to determine the set of routes along which to send evacuees (supply) from multiple locations throughout a building (sources) to the exits (sinks) such that the total time until all evacuees reach the exits is minimized. The formulation explicitly incorporates the constraints of shared information in providing online instructions to evacuees, ensuring that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. Arc travel time and capacity, as well as supply at the nodes, are permitted to vary with time and capacity is assumed to be recaptured over time. The BEPSI is shown to be NP‐hard. An exact technique based on Benders decomposition is proposed for its solution. Computational results from numerical experiments on a real‐world network representing a four‐story building are given. Results of experiments employing Benders cuts generated in solving a given problem instance as initial cuts in addressing an updated problem instance are also provided. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Estimating failure time distribution and its parameters based on intermediate data from a Wiener degradation model

Instead of measuring a Wiener degradation or performance process at predetermined time points to track degradation or performance of a product for estimating its lifetime, we propose to obtain the first‐passage times of the process over certain nonfailure thresholds. Based on only these intermediate data, we obtain the uniformly minimum variance unbiased estimator and uniformly most accurate confidence interval for the mean lifetime. For estimating the lifetime distribution function, we propose a modified maximum likelihood estimator and a new estimator and prove that, by increasing the sample size of the intermediate data, these estimators and the above‐mentioned estimator of the mean lifetime can achieve the same levels of accuracy as the estimators assuming one has failure times. Thus, our method of using only intermediate data is useful for highly reliable products when their failure times are difficult to obtain. Furthermore, we show that the proposed new estimator of the lifetime distribution function is more accurate than the standard and modified maximum likelihood estimators. We also obtain approximate confidence intervals for the lifetime distribution function and its percentiles. Finally, we use light‐emitting diodes as an example to illustrate our method and demonstrate how to validate the Wiener assumption during the testing. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008