A hard knapsack problem

In this article we develop a class of general knapsack problems which are hard for branch and bound algorithms. The number of alternate optimal solutions for these problems grows exponentially with problem parameters. In addition the LP bound is shown to be ineffective. Computational tests indicate that these problems are truly difficult for even very small problems. Implications for the testing of algorithms using randomly generated problems is discussed.     

A duality model for a generalized minmax program

We consider a generalized minmax programming problem, and establish, under certain weaker convexity assumptions, the Fritz John sufficient optimality conditions for such a problem. A dual program is introduced and using those optimality conditions duality theorems are proved relating the dual and the primal. Duality for the generalized fractional programming problem is considered as an application of the results proved.     

Acceptance sampling,imperfect production,and the optimality of zero defects

Acceptance sampling is often used to monitor the quality of raw materials and components when product testing is destructive, time-consuming, or expensive. In this paper we consider the effect of a buyer-imposed acceptance sampling policy on the optimal batch size and optimal quality level delivered by an expected cost minimizing supplier. We define quality as the supplier's process capability, i.e., the probability that a unit conforms to all product specifications, and we assume that unit cost is an increasing function of the quality level. We also assume that the supplier faces a known and constant “pass-through” cost, i.e., a fixed cost per defective unit passed on to the buyer. We show that the acceptance sampling plan has a significant impact on the supplier's optimal quality level, and we derive the conditions under which zero defects (100% conformance) is the policy that minimizes the supplier's expected annual cost. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 515–530, 1997     

Parallel machine scheduling: A probabilistic analysis

The minimum makespan of the general parallel machine scheduling problem with m machines and n jobs is studied. As for a number of other important combinatorial problems, the theory of empirical processes proves to be a very elegant and powerful tool for the probabilistic analysis of the solution value. It is used in this paper to derive a scheduling constant θ such that, for random processing times, the minimum makespan almost surely grows as θn when n goes to infinity. Moreover, a thorough probabilistic analysis is performed on the difference between the minimum makespan and θn. Explicit expressions for the scheduling constant are given for an arbitrary number of unrelated machines with identically distributed processing times (with an increasing failure rate), and for an arbitrary number of uniform machines and generally distributed processing times. © 1996 John Wiley & Sons, Inc.     

Nuclear opportunism: A theory of how states use nuclear weapons in international politics

How do states use nuclear weapons to achieve their goals in international politics? Nuclear weapons can influence state decisions about a range of strategic choices relating to military aggression, the scope of foreign policy objectives, and relations with allies. The article offers a theory to explain why emerging nuclear powers use nuclear weapons to facilitate different foreign policies: becoming more or less aggressive; providing additional support to allies or proxies, seeking independence from allies; or expanding the state’s goals in international politics. I argue that a state’s choices depend on the presence of severe territorial threats or an ongoing war, the presence of allies that provide for the state’s security, and whether the state is increasing in relative power. The conclusion discusses implications of the argument for our understanding of nuclear weapons and the history of proliferation, and nonproliferation policy today.     

More military base closure? Considering the alternatives*

Despite multiple base closing rounds, the United States Department of Defense still has excess base capacity, and thus President Trump and high-level Defense Department officials are calling for more base closure through the Base Realignment and Closure (BRAC) process. However, another BRAC may not be the optimal solution, because simple base closure is not an efficient way to reduce surplus base capacity. Thus, Defense Department officials should consider other methods to reduce surplus capacity, including reduction in base size, leasing excess base property, or transferring it to another government agency for a variety of alternative uses. The surplus capacity issue also offers an opportunity to DOD to reassess base utilization, to update base requirements with current and future force structure. While BRAC focuses on American military bases, the process and alternatives also have international applications.     

The one‐warehouse multiretailer problem with an order‐up‐to level inventory policy

We consider a two‐level system in which a warehouse manages the inventories of multiple retailers. Each retailer employs an order‐up‐to level inventory policy over T periods and faces an external demand which is dynamic and known. A retailer's inventory should be raised to its maximum limit when replenished. The problem is to jointly decide on replenishment times and quantities of warehouse and retailers so as to minimize the total costs in the system. Unlike the case in the single level lot‐sizing problem, we cannot assume that the initial inventory will be zero without loss of generality. We propose a strong mixed integer program formulation for the problem with zero and nonzero initial inventories at the warehouse. The strong formulation for the zero initial inventory case has only T binary variables and represents the convex hull of the feasible region of the problem when there is only one retailer. Computational results with a state‐of‐the art solver reveal that our formulations are very effective in solving large‐size instances to optimality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Multi‐item capacitated lot‐sizing problems with setup times and pricing decisions

We study a multi‐item capacitated lot‐sizing problem with setup times and pricing (CLSTP) over a finite and discrete planning horizon. In this class of problems, the demand for each independent item in each time period is affected by pricing decisions. The corresponding demands are then satisfied through production in a single capacitated facility or from inventory, and the goal is to set prices and determine a production plan that maximizes total profit. In contrast with many traditional lot‐sizing problems with fixed demands, we cannot, without loss of generality, restrict ourselves to instances without initial inventories, which greatly complicates the analysis of the CLSTP. We develop two alternative Dantzig–Wolfe decomposition formulations of the problem, and propose to solve their relaxations using column generation and the overall problem using branch‐and‐price. The associated pricing problem is studied under both dynamic and static pricing strategies. Through a computational study, we analyze both the efficacy of our algorithms and the benefits of allowing item prices to vary over time. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

基于STEP的AI—ESTATE数据类型转换方法

针对ATML标准中诊断信息描述一致性问题,提出了基于STEP的AI—ESTATE数据类型转换方法。首先介绍了ATML中诊断信息的描述标准,其次分析了AI—ESTATE信息描述的转换方法,然后应用STEP28针对CEM存在的数据类型进行了EXPRESS-XML匹配结构和功能结构一致性研究,最后建立了CEM典型数据类型的XML标准化描述。