Stochastic scheduling subject to machine breakdowns: The preemptive‐repeat model with discounted reward and other criteria

We consider the problem of scheduling a set of jobs on a single machine subject to random breakdowns. We focus on the preemptive‐repeat model, which addresses the situation where, if a machine breaks down during the processing of a job, the work done on the job prior to the breakdown is lost and the job will have to be started from the beginning again when the machine resumes its work. We allow that (i) the uptimes and downtimes of the machine follow general probability distributions, (ii) the breakdown process of the machine depends upon the job being processed, (iii) the processing times of the jobs are random variables following arbitrary distributions, and (iv) after a breakdown, the processing time of a job may either remain a same but unknown amount, or be resampled according to its probability distribution. We first derive the optimal policy for a class of problems under the criterion to maximize the expected discounted reward earned from completing all jobs. The result is then applied to further obtain the optimal policies for other due date‐related criteria. We also discuss a method to compute the moments and probability distributions of job completion times by using their Laplace transforms, which can convert a general stochastic scheduling problem to its deterministic equivalent. The weighted squared flowtime problem and the maintenance checkup and repair problem are analyzed as applications. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

A Territorial Conflict: Trade-offs and Strategies

We study a war scenario in which the winner occupies the loser’s territory. Attacking a territory increases the chance of winning, but also causes harm, which in turn decreases the territory’s value (i.e. the reward of winning). This paper highlights the effects of this trade-off on the equilibrium strategies of the warring states in a contest game with endogenous rewards. Providing both static and dynamic models, our analysis captures insights regarding strategic behavior in asymmetric contests with such conflict.     

Performance evaluation of a production/inventory system with periodic review and endogenous lead times

This paper considers a discrete time, single item production/inventory system with random period demands. Inventory levels are reviewed periodically and managed using a base‐stock policy. Replenishment orders are placed with the production system which is capacitated in the sense that there is a single server that sequentially processes the items one at a time with stochastic unit processing times. In this setting the variability in demand determines the arrival pattern of production orders at the queue, influencing supply lead times. In addition, the inventory behavior is impacted by the correlation between demand and lead times: a large demand size corresponds to a long lead time, depleting the inventory longer. The contribution of this paper is threefold. First, we present an exact procedure based on matrix‐analytic techniques for computing the replenishment lead time distribution given an arbitrary discrete demand distribution. Second, we numerically characterize the distribution of inventory levels, and various other performance measures such as fill rate, base‐stock levels and optimal safety stocks, taking the correlation between demand and lead times into account. Third, we develop an algorithm to fit the first two moments of the demand and service time distribution to a discrete phase‐type distribution with a minimal number of phases. This provides a practical tool to analyze the effect of demand variability, as measured by its coefficient of variation, on system performance. We also show that our model is more appropriate than some existing models of capacitated systems in discrete time. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Information disclosure with endogenous channel structure

This article investigates the firms' optimal quality information disclosure strategies in a supply chain, wherein the supplier may encroach into the retail channel to sell products directly to end consumers. We consider two disclosure formats, namely, retailer disclosure (R-C) and supplier disclosure (S-C), and examine the optimal disclosure format from each firm's perspective. We show that either firm prefers to delegate the disclosure option to its partner when the supplier cannot encroach. However, the threat of supplier encroachment dramatically alters the firm's preference of disclosure. The supplier may prefer the S-C format to the R-C format when the entry cost is low and the disclosure cost is high to achieve a higher quality information transparency. Meanwhile, the retailer may prefer the R-C format to the S-C format when the entry cost is intermediate to deter the possible encroachment of the supplier. In this sense, the firms' preferences of disclosure format can be aligned due to the threat of supplier encroachment. The consumer surplus is always higher under the S-C format while either disclosure format can lead to a higher social welfare. We also consider an alternative scenario under which the supplier encroaches after the product quality information is disclosed. An interesting observation appears that the supplier may encroach when the product quality is low but foregoes encroachment when the product quality gets higher.     

秦简中的军事法律制度

通过对睡虎地秦墓竹简的分析,指出秦朝已经建立了比较完善的军事法律制度:在军事训练方面有对基层军官、战马、驾车者的考核制度;在军事保障方面,利用法律手段保证军队的兵源、装备、军粮的供应;在军事奖赏方面则实行优厚的封爵制度;在军事纪律方面,对违反军事纪律者给予严厉的处罚。     

Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty

We propose a novel simulation‐based approach for solving two‐stage stochastic programs with recourse and endogenous (decision dependent) uncertainty. The proposed augmented nested sampling approach recasts the stochastic optimization problem as a simulation problem by treating the decision variables as random. The optimal decision is obtained via the mode of the augmented probability model. We illustrate our methodology on a newsvendor problem with stock‐dependent uncertain demand both in single and multi‐item (news‐stand) cases. We provide performance comparisons with Markov chain Monte Carlo and traditional Monte Carlo simulation‐based optimization schemes. Finally, we conclude with directions for future research.     

A bivariate optimal replacement policy for a cold standby repairable system with repair priority

In this article, an optimal replacement policy for a cold standby repairable system consisting of two dissimilar components with repair priority is studied. Assume that both Components 1 and 2, after repair, are not as good as new, and the main component (Component 1) has repair priority. Both the sequence of working times and that of the components'repair times are generated by geometric processes. We consider a bivariate replacement policy (T,N) in which the system is replaced when either cumulative working time of Component 1 reaches T, or the number of failures of Component 1 reaches N, whichever occurs first. The problem is to determine the optimal replacement policy (T,N)* such that the long run average loss per unit time (or simply the average loss rate) of the system is minimized. An explicit expression of this rate is derived, and then optimal policy (T,N)* can be numerically determined through a two‐dimensional‐search procedure. A numerical example is given to illustrate the model's applicability and procedure, and to illustrate some properties of the optimal solution. We also show that if replacements are made solely on the basis of the number of failures N, or solely on the basis of the cumulative working time T, the former class of policies performs better than the latter, albeit only under some mild conditions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Inducing coordination in supply chains through linear reward schemes

Decentralized decision‐making in supply chain management is quite common, and often inevitable, due to the magnitude of the chain, its geographical dispersion, and the number of agents that play a role in it. But, decentralized decision‐making is known to result in inefficient Nash equilibrium outcomes, and optimal outcomes that maximize the sum of the utilities of all agents need not be Nash equilibria. In this paper we demonstrate through several examples of supply chain models how linear reward/penalty schemes can be implemented so that a given optimal solution becomes a Nash equilibrium. The examples represent both vertical and horizontal coordination issues. The techniques we employ build on a general framework for the use of linear reward/penalty schemes to induce stability in given optimal solutions and should be useful to other multi‐agent operations management settings. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006