A multifaceted heuristic for the orienteering problem

The orienteering problem involves the selection of a path between an origin and a destination which maximizes total score subject to a time restriction. In previous work we presented an effective heuristic for this NP-hard problem that outperformed other heuristics from the literature. In this article we describe and test a significantly improved procedure. The new procedure is based on four concepts—center of gravity, randomness, subgravity, and learning. These concepts combine to yield a procedure which is much faster and which results in more nearly optimal solutions than previous procedures.     

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     

Heuristic scheduling of resource-constrained projects with cash flows

Resource-constrained project scheduling with cash flows occurs in many settings, ranging from research and development to commercial and residential construction. Although efforts have been made to develop efficient optimal procedures to maximize the net present value of cash flows for resource-constrained projects, the inherent intractability of the problem has led to the development of a variety of heuristic methods to aid in the development of near-optimal schedules for large projects. This research focuses on the use of insights gained from the solution of a relaxed optimization model in developing heuristic procedures to schedule projects with multiple constrained resources. It is shown that a heuristic procedure with embedded priority rules that uses information from the revised solution of a relaxed optimization model increases project net present value. The heuristic procedure and nine different embedded priority rules are tested in a variety of project environments that account for different network structures, levels of resource constrainedness, and cash-flow parameters. Extensive testing with problems ranging in size from 21 to 1000 activities shows that the new heuristic procedures dominate heuristics using information from the critical path method (CPM), and in most cases outperform heuristics from previous research. The best performing heuristic rules classify activities into priority and secondary queues according to whether they lead to immediate progress payments, thus front loading the project schedule. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 365–381, 1997     

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     

不同流量的复杂保障网络抗毁性仿真分析

通过引入流量强度指数和流量分布指数,建立了不同网络流量下的复杂保障网络级联失效抗毁性模型。基于该模型比较分析了无标度网络、随机网络和复杂保障网络在不同流量强度和流量分布下对单个节点的随机失效和故意攻击的抗毁性。结果表明:复杂保障网络的抗毁性随着流量强度的增加急剧下降。此外,流量分布对复杂保障网络的抗毁性也有显著影响。