Shortest path interdiction problem with arc improvement recourse: A multiobjective approach

We consider the shortest path interdiction problem involving two agents, a leader and a follower, playing a Stackelberg game. The leader seeks to maximize the follower's minimum costs by interdicting certain arcs, thus increasing the travel time of those arcs. The follower may improve the network after the interdiction by lowering the costs of some arcs, subject to a cardinality budget restriction on arc improvements. The leader and the follower are both aware of all problem data, with the exception that the leader is unaware of the follower's improvement budget. The effectiveness of an interdiction action is given by the length of a shortest path after arc costs are adjusted by both the interdiction and improvement. We propose a multiobjective optimization model for this problem, with each objective corresponding to a different possible improvement budget value. We provide mathematical optimization techniques to generate a complete set of strategies that are Pareto‐optimal. Additionally, for the special case of series‐parallel graphs, we provide a dynamic‐programming algorithm for generating all Pareto‐optimal solutions.     

Violence in context: Mapping the strategies and operational art of irregular warfare

The malaise that the United States, and the West, have experienced in recent campaigns stems in large part from unclear thinking about war, its political essence, and the strategies needed to join the two. Instead, analysis and response are predicated on entrenched theoretical concepts with limited practical utility. The inadequacy of understanding has spawned new, and not so new, terms to capture unanticipated trends, starting with the re-discovery of “insurgency” and “counterinsurgency” and leading to discussion of “hybrid threats” and “gray-zone” operations. New terminology can help, but the change must go deeper. Challenging analytical orthodoxy, this article sets out a unifying approach for the study of political violence, or more accurately: violent politics. It provides a conceptual foundation that helps to make sense of recent shifts in warfare. In effect, it offers sorely needed theoretical insights into the nature of strategy and guides the process of responding to nontraditional threats.     

On scheduling with ready-times,due-dates and vacations

A single machine sequencing problem is considered in which there are ready-time and due-date constraints on jobs and vacation constraints on the machine. Each vacation has fixed starting and finish time and no preemption is allowed for the jobs. The objective is to minimize maximum lateness. An intriguing feature of this formulation is that it allows sequencing in disconnected time windows. A relaxation of the problem is obtained by modeling the vacations as a set of jobs with flexible ready-times and artificial due-dates and a branch and bound algorithm is developed for the problem. In the algorithm, the search is not only guided by the bounds but also by a careful manipulation of the artificial due-dates. Consequently; while searching in the relaxed solution space, solutions of the original problem are implicitly enumerated. Computational results indicate that the algorithm can satisfactorily solve problems with multiple vacations.     

When is greedy module assembly optimal?

Many coherent systems are configurations of identically structured modules, each consisting of a number of different components. The objective is to assemble the modules out of a collection of available components, and to install the modules in the system in a way that maximizes reliability. The greedy assembly rule builds one module out of the best available components, another out of the best remaining components, and so on. This article shows that greedy assembly is optimal whenever the modules have a series structure, no matter what the structure of the system in which the modules will be used might be, provided that the modules, once assembled, are installed in the system in an optimal way. The article also demonstrates that series modules are unique in this regard.     

The frequency assignment problem: A solution via nonlinear programming

This paper gives a mathematical programming model for the problem of assigning frequencies to nodes in a communications network. The objective is to select a frequency assignment which minimizes both cochannel and adjacent-channel interference. In addition, a design engineer has the option to designate key links in which the avoidance of jamming due to self interference is given a higher priority. The model has a nonconvex quadratic objective function, generalized upper-bounding constraints, and binary decision variables. We developed a special heuristic algorithm and software for this model and tested it on five test problems which were modifications of a real-world problem. Even though most of the test problems had over 600 binary variables, we were able to obtain a near optimum in less than 12 seconds of CPU time on a CDC Cyber-875.     

The value of information sharing in a two‐stage supply chain with production capacity constraints

We consider a simple two‐stage supply chain with a single retailer facing i.i.d. demand and a single manufacturer with finite production capacity. We analyze the value of information sharing between the retailer and the manufacturer over a finite time horizon. In our model, the manufacturer receives demand information from the retailer even during time periods in which the retailer does not order. To analyze the impact of information sharing, we consider the following three strategies: (1) the retailer does not share demand information with the manufacturer; (2) the retailer does share demand information with the manufacturer and the manufacturer uses the optimal policy to schedule production; (3) the retailer shares demand information with the manufacturer and the manufacturer uses a greedy policy to schedule production. These strategies allow us to study the impact of information sharing on the manufacturer as a function of the production capacity, and the frequency and timing in which demand information is shared. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

New product introduction against a predator: A bilevel mixed‐integer programming approach

We consider a scenario with two firms determining which products to develop and introduce to the market. In this problem, there exists a finite set of potential products and market segments. Each market segment has a preference list of products and will buy its most preferred product among those available. The firms play a Stackelberg game in which the leader firm first introduces a set of products, and the follower responds with its own set of products. The leader's goal is to maximize its profit subject to a product introduction budget, assuming that the follower will attempt to minimize the leader's profit using a budget of its own. We formulate this problem as a multistage integer program amenable to decomposition techniques. Using this formulation, we develop three variations of an exact mathematical programming method for solving the multistage problem, along with a family of heuristic procedures for estimating the follower solution. The efficacy of our approaches is demonstrated on randomly generated test instances. This article contributes to the operations research literature a multistage algorithm that directly addresses difficulties posed by degeneracy, and contributes to the product variety literature an exact optimization algorithm for a novel competitive product introduction problem. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009