OPTIMUM SCHEDULE FOR PREVENTIVE MAINTENANCE: A GENERAL SOLUTION FOR A PARTIALLY SPECIFIED TIME-TO-FAILURE DISTRIBUTION

The classic problem of determining an optimum schedule for preventive maintenance when the time-to-failure (TTF) is random has been previously addressed in the literature under various distributional assumptions. However, no general solution that requires only partial distributional information (in the form of the first few moments) has been suggested. In this paper we develop solution procedures characterized by four features: (1) The solutions are general in the sense that only the first few moments of the TTF distribution need to be specified. (2) The optimal solution is given explicitly in terms of the decision variables, thus allowing simple sensitivity analysis. (3) When the TTF moments are unknown, a new two-moment (partial and complete) distributional fitting procedure, used in the solution routine, ensures a better representation for the underlying TTF distribution relative to three-moment or four-moment distributional fitting. (4) When the TTF observations are truncated, simple routines to calculate maximum likelihood estimates are developed. We demonstrate that the partiál distributional specification, required for the new solution procedures, does not detract meaningfully from the optimality of the solution.     

A mixed inventory model with variable lead time and random supplier capacity

In this paper, we have studied analytically the implication of a controllable lead-time and a random supplier capacity on the continuous review inventory policy, in which the order quantity, reorder point and lead-time are decision variables. Two models are considered: the normal lead-time demand and lead-time demand is distributed free. For both cases, after formulating the general model, some properties of the optimal ordering policy have been developed. Particularly, we have shown that the expected annual total cost is a unimodal function and quasi-convex in the order quantity. When the variable capacity distribution is exponential, we develop effective procedures for finding the optimal solutions. Furthermore, the effects of parameters are also performed.     

Coordinated Capacitated Lot‐Sizing Problem with Dynamic Demand: A Lagrangian Heuristic

Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed‐integer programming formulation and Lagrangian relaxation solution procedure for the single‐family coordinated capacitated lot‐sizing problem with dynamic demand. The problem extends both the multi‐item capacitated dynamic demand lot‐sizing problem and the uncapacitated coordinated dynamic demand lot‐sizing problem. We provide the results of computational experiments investigating the mathematical properties of the formulation and the performance of the Lagrangian procedures. The results indicate the superiority of the dual‐based heuristic over linear programming‐based approaches to the problem. The quality of the Lagrangian heuristic solution improved in most instances with increases in problem size. Heuristic solutions averaged 2.52% above optimal. The procedures were applied to an industry test problem yielding a 22.5% reduction in total costs.     

A Practical Two‐Step Method for Testing Moment Inequalities

This paper considers the problem of testing a finite number of moment inequalities. We propose a two‐step approach. In the first step, a confidence region for the moments is constructed. In the second step, this set is used to provide information about which moments are “negative.” A Bonferonni‐type correction is used to account for the fact that, with some probability, the moments may not lie in the confidence region. It is shown that the test controls size uniformly over a large class of distributions for the observed data. An important feature of the proposal is that it remains computationally feasible, even when the number of moments is large. The finite‐sample properties of the procedure are examined via a simulation study, which demonstrates, among other things, that the proposal remains competitive with existing procedures while being computationally more attractive.     

A near-optimal heuristic for the sequencing problem in multiple-batch flow-shops with small equal sublots

In this paper, we consider the lot-streaming problem of sequencing a set of batches, to be processed in equal sublots, in a flow-shop, so as to minimize makespan. A new heuristic procedure, called the bottleneck minimal idleness heuristic, is developed. Results of an experimental study are presented. It is shown that the proposed procedure generates solutions that are very close to the optimal solutions, and that the solutions generated are better than those obtained by using the fast insertion heuristic, considered to be a good heuristic for solving the flow-shop scheduling problem, when applied to the problem on hand.     

COST-VOLUME-PROFIT ANALYSIS IN STOCHASTIC PROGRAMMING MODELS

This paper applies mathematical programming to cost-volume-profit (CVP) analysis under contribution margin uncertainty. Three CVP probabilistic chance-constraint models based on various safety-first criteria for decisions under uncertainty are presented and compared. It is shown that a break-even segment of the mean-standard deviation frontier is a set of optimal solutions for the proposed models. An operational parametric quadratic programming (QP) model is constructed, and the efficiency frontier is generated. The procedures for locating an optimal solution on the efficiency frontier are then presented. The recommended QP procedure offers both technical relief from the computational difficulties posed by the probabilistic constraints and a desired flexibility in generating and presenting the relevant information for decisions under uncertainty.     

不确定需求下二级供应链中的鲁棒定价问题

对由一个制造商和一个零售商组成的单一产品二级供应链,在市场潜在需求和价格敏感系数不确定的情况下,分析制造商和零售商的鲁棒定价决策。首先考虑了零售商掌握完全信息而制造商仅已知各参数区间的不对称信息情形,建立Stackelberg鲁棒博弈模型并对模型的均衡解进行探讨,进一步通过对解的分析和对比讨论了不对称信息下零售商的决策优势。然后研究了制造商和零售商都仅已知各参数区间的不完全信息情形,给出Stackelberg鲁棒博弈模型,求得其均衡解并与完全信息下的情形以及不对称信息下的情形进行比较,分别得到制造商和零售商在不完全信息下所获得的利润比在完全信息下所获得利润高的条件,并证明了制造商在不完全信息下所获得的利润比在不对称信息下获得的利润高,而零售商则刚好相反。最后给出算例分析,对所得到的解和结论做一些补充。     

Concepts,Theory, and Techniques ON THE USE OF THE GEOMETRIC MEAN IN LONG-TERM INVESTMENT

Application of the geometric mean to holding-period returns is discussed from a statistical theory standpoint. The population geometric mean is considered a parameter of the probability distribution of returns its relationship to moments of the distribution is discussed. The sample geometric mean and its relation to sample moments is assessed through its sampling distribution it is viewed as an estimator of the population geometric mean. For application to long-term investment where a geometric mean is maximized, the distributional properties of the geometric mean should be used. The terms statistic, approximation, and parameter are differentiated.     

A NOTE ON PROCEDURES FOR TESTING THE QUALITY OF A CLUSTERING OF A SET OF OBJECTS

Despite the increased application of cluster analysis in decision sciences, few attempts have been made to derive hypothesis-testing procedures for the evaluation of clustering solutions. In fact, the present paper shows that at least one such attempt failed to specify a meaningful sampling distribution for the test procedure. An alternative index based on the concept of point-biserial correlation is proposed as a possible recovery measure. The index is subsequently used to form the basis of a valid statistical test for the existence of cluster structure.     

A Note on Determining Optimal Selling Price and Lot Size Under All-Unit Quantity Discounts

A recent study conducted by Abad [1] described a method of determining the optimal price and lot size when the supplier offers all-unit quantity discounts. The author developed a procedure using centralized and decentralized approaches. According to the author's suggestion, further study is necessary to determine if the decentralized approach always provides an optimal solution. In the present study, an attempt is made to investigate the uniformity between the centralized and decentralized approaches and to verify whether the decentralized approach always yields optimal solutions.     

Methods for Characterizing Variability and Uncertainty: Comparison of Bootstrap Simulation and Likelihood-Based Approaches

Variability arises due to differences in the value of a quantity among different members of a population. Uncertainty arises due to lack of knowledge regarding the true value of a quantity for a given member of a population. We describe and evaluate two methods for quantifying both variability and uncertainty. These methods, bootstrap simulation and a likelihood-based method, are applied to three datasets. The datasets include a synthetic sample of 19 values from a Lognormal distribution, a sample of nine values obtained from measurements of the PCB concentration in leafy produce, and a sample of five values for the partitioning of chromium in the flue gas desulfurization system of coal-fired power plants. For each of these datasets, we employ the two methods to characterize uncertainty in the arithmetic mean and standard deviation, cumulative distribution functions based upon fitted parametric distributions, the 95th percentile of variability, and the 63rd percentile of uncertainty for the 81st percentile of variability. The latter is intended to show that it is possible to describe any point within the uncertain frequency distribution by specifying an uncertainty percentile and a variability percentile. Using the bootstrap method, we compare results based upon use of the method of matching moments and the method of maximum likelihood for fitting distributions to data. Our results indicate that with only 5–19 data points as in the datasets we have evaluated, there is substantial uncertainty based upon random sampling error. Both the boostrap and likelihood-based approaches yield comparable uncertainty estimates in most cases.     

静态市场下考虑重复购买的价格和质保期联合决策

本文研究静态市场下的以质保期和价格为决策变量的最优控制决策问题。考虑了初次购买和重复购买两个过程以及重复购买过程是否受价格影响两种情况。模型中的生产成本考虑了产品生产过程中的学习效应, 质保成本使用了免费维修质保策略并假设产品两次故障之间的时间服从韦伯分布。在完整建模的基础上, 应用最大化原理对基本模型进行了求解, 之后本文给出了一种基本模型的具体应用场景, 并运用Lingo11软件进行了数值试验。最后对主要研究结论进行了应用讨论。     

Locating social service centres using interactive graphics

The paper explores the feasibility of using interactive graphic based solution procedures in location problems with discrete choices. It compares solutions generated through interactive graphics with those generated through optimization for a problem context where service centres had to be located in rural India. The comparison demonstrates the feasibility of generating near optimal solutions for problems with a certain dimensionality. Broad features of the graphic software are described. The paper also highlights other advantages and limitations of the interactive graphic procedure.     

On statistical bounds of heuristic solutions to location problems

Combinatorial optimization problems such as locating facilities frequently rely on heuristics to minimize the objective function. The optimum is often sought iteratively; a criterion is therefore necessary to be able to decide when the procedure attains such an optimum. Pre-setting the number of iterations is dominant in OR applications, however, the fact that the quality of the solution cannot be ascertained by pre-setting the number of iterations makes it less preferable. A small and, almost dormant, branch of the literature suggests usage of statistical principles to estimate the minimum and its bounds as a tool to decide upon the stopping criteria and also to evaluate the quality of the solution. In the current work we have examined the functioning of statistical bounds obtained from four different estimators using simulated annealing. P-median test problems taken from Beasley’s OR-library were used for the sake of testing. Our findings show that the Weibull estimator and 2nd order Jackknife estimators are preferable and the requirement of sample size to be about 10. It should be noted that reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality; we have therefore provided a simple statistic for checking the quality. The work finally concludes with an illustration of applying statistical bounds to the problem of locating 70 post distribution centers in a region in Sweden.     

Assembly Line Balancing with Resource Dependent Task Times*

Paced assembly lines are widely used in repetitive manufacturing applications. Most previous research on the design of paced lines has assumed that each task along the line can be performed by only one worker (or a fixed number of workers). In many cases, however, task duration times may be reduced by increasing the number of workers or changing the equipment assigned to work stations. Thus, the problem becomes one of assigning resource alternatives (e.g., workers and/or equipment) and tasks to work stations to minimize total cost for a desired production rate. For this problem, we present three procedures. The first formulates the problem as a shortest path problem and guarantees optimality. The second and third are heuristic adaptations of the shortest path procedure that are capable of solving large problems. The procedures are compared in terms of solution quality and computation time on a set of 128 randomly generated problems for which optimal solutions could be found. Our simulation results indicate that the choice of procedure depends on problem complexity and resource costs.     

基于改进遗传算法的置换装配线调度问题研究

企业的置换装配线调度问题（Permutation Assembly-line Scheduling Problem,PASP）是一类典型的NP-hard型生产调度问题,是现代集成制造系统CIMS极为关心的问题。该问题可以具体描述为n个工件要在m台机器上加工,每个工件需要经过m道工序,每道工序要求不同的机器,这n个工件通过m台机器的顺序相同,它们在每台机器上的加工顺序也相同,问题的主要目标是找到n个工件在每台机器上的最优加工顺序,使得最大完工时间最小。由于PASP问题的NP-hard性质,本文使用遗传算法对其进行求解。尽管遗传算法常用以求解调度问题,但其选择与交叉机制易导致局部最优及收敛慢。因此,本文提出基于区块挖掘与重组的改进遗传算法用于求解置换装配线调度问题。首先通过关联规则挖掘出不同的优秀基因,然后将具有较优结果的基因组合为优势区块,产生具优势的人工解,并引入高收敛性的局部搜索方法,提高搜索到最优解的机会与收敛效率。本文以OR-Library中Taillard标准测试例来验证改进遗传算法的求解质量与效率,结果证明：本文所提算法与其它求解调度问题的现有5种知名算法相比,不仅收敛速度较快,同时求解质量优于它们。     

A Methodology for More Efficient Tail Area Sampling with Discrete Probability Distributions

Monte Carlo Method is commonly used to observe the overall distribution and to determine the lower or upper bound value in statistical approach when direct analytical calculation is unavailable. However, this method would not be efficient if the tail area of a distribution is concerned. A new method, entitled Two-Step Tail Area Sampling, is developed, which uses the assumption of discrete probability distribution and samples only the tail area without distorting the overall distribution. This method uses a two-step sampling procedure. First, sampling at points separated by large intervals is done and second, sampling at points separated by small intervals is done with some check points determined at first-step sampling. Comparison with Monte Carlo Method shows that the results obtained from the new method converge to analytic value faster than Monte Carlo Method if the numbers of calculation of both methods are the same. This new method is applied to DNBR (Departure from Nucleate Boiling Ratio) prediction problem in design of the pressurized light water nuclear reactor.     

The price-setting newsvendor with service and loss constraints

Current performance measurement systems consider not only financial measures, like costs and profits, but also non-financial indicators with respect to customer service, quality and flexibility. Using the newsvendor model, we analyse the respective influence of these possibly conflicting performance measures on important operations and marketing decisions, for instance the order quantity and the selling price of a product. As in the classical newsvendor model for price-independent as well as price-dependent demand distribution, the objective of the firm is to maximise expected profit. In this paper, we also consider a service constraint—a lower bound for the level of product availability—and a loss constraint—an upper bound for the probability of a loss occurring. For both models, we provide conditions for the existence of solutions. We then analyse the influence of demand variability using a set of conditions specifying the quantiles of the predetermined performance measures: a higher variability of demand implies a smaller admissible region of the decision variables. In the price-independent case, the optimal solution has a control-limit structure: the optimal order quantity is thus given either by the classical newsvendor solution or by the control-limits corresponding to the constraints. In the price-setting model with multiplicative demand, this structure is used to check whether small admissible prices are determined by the service constraint or by the loss constraint. Using these structural results, a procedure is developed to more easily enable the computation of the optimal values of the order quantity, selling price and expected profit.     

Impact of investing in quality improvement on (Q,r, L) model involving the imperfect production process

This paper investigates the impact of quality improvement on the modified lot size reorder point models involving variable lead time and partial backorders. The formulated models include the imperfect production process and an investing option of improving the process quality. The objective is simultaneously optimizing the lot size, reorder point, process quality level and lead time. We first assume that the lead time demand follows a normal distribution, then relax this assumption to consider the distribution-free case where only the mean and standard deviation of lead time demand are known. An algorithm procedure of finding the optimal solution is developed, and two numerical examples are given to illustrate the results.