Scheduling with centralized and decentralized batching policies in concurrent open shops

This article considers batch scheduling with centralized and decentralized decisions. The context of our study is concurrent open shop scheduling where the jobs are to be processed on a set of independent dedicated machines, which process designated operations of the jobs in batches. The batching policy across the machines can be centralized or decentralized. We study such scheduling problems with the objectives of minimizing the maximum lateness, weighted number of tardy jobs, and total weighted completion time, when the job sequence is determined in advance. We present polynomial time dynamic programming algorithms for some cases of these problems and pseudo‐polynomial time algorithms for some problems that are NP‐hard in the ordinary sense. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 58: 17–27, 2011     

Using stochastic programming to solve an outpatient appointment scheduling problem with random service and arrival times

We study a stochastic outpatient appointment scheduling problem (SOASP) in which we need to design a schedule and an adaptive rescheduling (i.e., resequencing or declining) policy for a set of patients. Each patient has a known type and associated probability distributions of random service duration and random arrival time. Finding a provably optimal solution to this problem requires solving a multistage stochastic mixed‐integer program (MSMIP) with a schedule optimization problem solved at each stage, determining the optimal rescheduling policy over the various random service durations and arrival times. In recognition that this MSMIP is intractable, we first consider a two‐stage model (TSM) that relaxes the nonanticipativity constraints of MSMIP and so yields a lower bound. Second, we derive a set of valid inequalities to strengthen and improve the solvability of the TSM formulation. Third, we obtain an upper bound for the MSMIP by solving the TSM under the feasible (and easily implementable) appointment order (AO) policy, which requires that patients are served in the order of their scheduled appointments, independent of their actual arrival times. Fourth, we propose a Monte Carlo approach to evaluate the relative gap between the MSMIP upper and lower bounds. Finally, in a series of numerical experiments, we show that these two bounds are very close in a wide range of SOASP instances, demonstrating the near‐optimality of the AO policy. We also identify parameter settings that result in a large gap in between these two bounds. Accordingly, we propose an alternative policy based on neighbor‐swapping. We demonstrate that this alternative policy leads to a much tighter upper bound and significantly shrinks the gap.     

Emergency transshipment in decentralized dealer networks: When to send and accept transshipment requests

While there has been significant previous literature on inventory transshipment, most research has focused on the dealers' demand filling decision (when to fill transshipment requests from other dealers), ignoring the requesting decision (when to send transshipment requests to other dealers). In this paper we develop optimal inventory transshipment policies that incorporate both types of decisions. We consider a decentralized system in which the dealers are independent of the manufacturer and of each other. We first study a network consisting of a very large number of dealers. We prove that the optimal inventory and transshipment decisions for an individual dealer are controlled by threshold rationing and requesting levels. Then, in order to study the impact of transshipment among independent dealers in a smaller dealer network, we consider a decentralized two‐dealer network and use a game theoretic approach to characterize the equilibrium inventory strategies of the individual dealers. An extensive numerical study highlights the impact of the requesting decision on the dealers' equilibrium behavior in a decentralized setting. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Optimal maintenance policies for serial,multi‐machine systems with non‐instantaneous repairs

We study optimal age‐replacement policies for machines in series with non‐instantaneous repair times by formulating two nonlinear programs: one that minimizes total cost‐rate subject to a steady‐state throughput requirement and another that maximizes steady‐state throughput subject to a cost‐rate budget constraint. Under reasonable assumptions, the single‐machine cost‐optimal and throughput‐optimal solutions are unique and orderable, and the multi‐machine optimal solutions have appealing structure. Furthermore, we establish equivalence between the two formulations and provide an illustrative numerical example. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

A stochastic model for burn‐in procedures in accelerated environment

Burn‐in procedure is a manufacturing technique that is intended to eliminate early failures of system or product. Burning‐in a component or system means to subject it to a period of use prior to being used in field. Generally, burn‐in is considered expensive and so the length of burn‐in is typically limited. Thus, burn‐in is most often accomplished in an accelerated environment in order to shorten the burn‐in process. A new failure rate model for an accelerated burn‐in procedure, which incorporates the accelerated ageing process induced by the accelerated environmental stress, is proposed. Under a more general assumption on the shape of failure rate function of products, which includes the traditional bathtub‐shaped failure rate function as a special case, upper bounds for optimal burn‐in time will be derived. A numerical example will also be given for illustration. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Relaxed sequencing games have a nonempty core

We study sequencing situations with a fixed initial order and linear cost functions. Cost savings can be obtained by rearranging jobs. Next to finding an optimal order, an additional issue is formed by the division of these savings. Cooperative game theory studies this issue. A common assumption states that cooperation between players is restricted to groups that are connected according to the initial order. The value of disconnected groups is defined additively over their connected components. In this paper we allow players in disconnected coalitions to switch places as long as they do not hurt the players not in the coalition under consideration. The resulting games are called relaxed sequencing games. Although they have been studied before, no general results on stable profit divisions have been derived so far. In this paper we prove that relaxed sequencing games have a nonempty core, i.e., they all have stable profit divisions. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Approximation algorithms for minimizing total weighted completion time of orders on identical machines in parallel

We consider the problem of scheduling orders on identical machines in parallel. Each order consists of one or more individual jobs. A job that belongs to an order can be processed by any one of the machines. Multiple machines can process the jobs of an order concurrently. No setup is required if a machine switches over from one job to another. Each order is released at time zero and has a positive weight. Preemptions are not allowed. The completion time of an order is the time at which all jobs of that order have been completed. The objective is to minimize the total weighted completion time of the orders. The problem is NP‐hard for any fixed number (≥2) of machines. Because of this, we focus our attention on two classes of heuristics, which we refer to as sequential two‐phase heuristics and dynamic two‐phase heuristics. We perform a worst case analysis as well as an empirical analysis of nine heuristics. Our analyses enable us to rank these heuristics according to their effectiveness, taking solution quality as well as running time into account. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Maximizing project cash availability

Consider a project during the life cycle of which there are cash payouts and in‐flows. To better meet his financial commitments, the project owner would like to meet all deadlines without running out of cash. We show that the cash availability objective is similar to the total weighted flowtime used to measure work‐in‐progress performance in the scheduling and inventory control literatures. In this article we provide several specialized solution methods for the problem of minimizing total weighted flowtime in an arbitrary acyclic project network, subject to activity release times and due dates, where the activity weights may be positive or negative and represent cash in‐ and out‐flows. We describe the structure of an optimal solution and provide several efficient algorithms and their complexity based on mincost and maxflow formulations. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Transient analysis of Markov models of fault‐tolerant systems with deferred repair using split regenerative randomization

The (standard) randomization method is an attractive alternative for the transient analysis of continuous time Markov models. The main advantages of the method are numerical stability, well‐controlled computation error, and ability to specify the computation error in advance. However, the fact that the method can be computationally very expensive limits its applicability. In this paper, we develop a new method called split regenerative randomization, which, having the same good properties as standard randomization, can be significantly more efficient. The method covers reliability‐like models with a particular but quite general structure and requires the selection of a subset of states and a regenerative state satisfying some conditions. For a class of continuous time Markov models, model class C₂, including typical failure/repair reliability‐like models with exponential failure and repair time distributions and deferred repair, natural selections are available for both the subset of states and the regenerative state and, for those natural selections, theoretical results are available assessing the efficiency of the method in terms of “visible” model characteristics. Those results can be used to anticipate when the method can be expected to be competitive. We illustrate the application of the method using a large class C₂ model and show that for models in that class the method can indeed be significantly more efficient than previously available randomization‐based methods. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

基于蚁群算法的试验流程优化研究

水中兵器的海上试验涉及许多人员、兵力、被试产品、测量设备等,试验周期长、消耗大,因此如何缩短试验周期是亟待研究解决的问题.文中首先将试验流程优化问题转化为车间调度问题,建立了相应的数学模型,再应用蚁群算法转移规则得到中间结果并进行排队以对各种资源约束进行处理.最后将结果利用局部搜索算法优化后作为蚁群算法信息素更新的基础.实例计算结果表明,该方法优化效果良好.