Bargaining with nuclear weapons: Thomas Schelling's ‘general’ concept of stability

This article identifies a consistent approach to stability across a wide range of conflict situations at the heart of Thomas Schelling's strategic theory. It finds that there are two main aspects of this ‘general’ concept of stability. The first is the ability to strike a bargain at a mutually acceptable resting place as seen in the Korean War stalemate. The second is the ability to maintain a strategic bargain over the long term as in the stability of the balance of terror. This article finds that crucial assumptions which underpin Schelling's general concept, such as the existence of restraints on the degree of competition and the idea that nuclear weapons assist the bargaining process, hold up better in some cases than in others. Stability consequently seems more possible in a conventional conflict or crisis when nuclear weapons are a background influence than in a war where the nuclear threshold has already been crossed.     

Non-lethal weapons and the long tail of warfare

This paper examines whether non-lethal weapons (NLWs) enhance the capability of the US armed forces to conduct irregular warfare (IW) operations. With expectations that the operational environment will only continue to become more complex in the future, NLWs may reduce the level of violence received, as well as dispensed, by US forces while performing tasks in the IW spectrum. We argue that NLWs increase the ability of US forces to address the long tail of warfare and their deployment should be increased in the near term.     

Economic lot scheduling of fully loaded processes with external setups

Without restricting the class of permissible schedules, we derive optimal schedules for economic lot scheduling problems that are fully loaded, have external setups, and have only two products. The fully loaded condition accurately represents certain types of bottlenecks. We show that the optimal schedule must have the Wagner-Whitin property. We also develop a measure of aggregate inventory, derive an optimal steady-state aggregate inventory policy, and provide conditions under which the aggregate inventory level of an optimal schedule must approach a steady state. By restricting the class of permissible schedules to rotation cycle schedules, we extend these results to more than two products.     

Estimating travel distances by the weighted lp norm

Empirical distance functions are used to estimate actual travel distances in a transportation network, to verify the accuracy of road mileage data, and to formulate continuous location models. In this article we consider the problem of fitting the weighted l_p norm to a given network. Mathematical properties are derived for two fitting criteria found in the literature. These properties are used to develop an accurate and efficient methodology to solve for the best-fitting parameter values. The directional bias of the l_p norm is analyzed for its effect on the range of search for the optimal p value. Concepts and methodology are applied to a case study of the road system in Southern Ontario. In conclusion, a general framework for other types of distance functions is briefly discussed.     

A localization property for facility-location problems with arbitrary norms

In an earlier article we showed that, for facilities-location problems characterized by generalized distance norms and any even number of existing facilities, the optimal location of the new facility is at the intersection of the lines joining the pairs of facilities if these lines intersect at a single point. In this article we extend this concept to show that, for a more general class of problems, the optimal location is one of a set of points which is specified by the existing facilities.     

Optimal control of entry to an M/Ek/1 queue serving several classes of customers

The individual and social optimum control policies for entry to an M/M//1 queue serving several classes of customers have been shown to be control-limit policies. The technique of policy iteration provides the social optimum policy for such a queue in a straightforward manner. In this article, the problem of finding the optimal control policy for the M/E_k/1 system is solved, thereby expanding the potential applicability of the solutions developed. The Markovian nature of the queueing system is preserved by considering the service as having k sequential phases, each with independent, identically distributed, exponential service times, through which a customer must pass to be serviced. The optimal policy derived by policy iteration for such a system is likely to be difficult to use because it requires knowledge of the number of phases rather than customers in the system when an arrival occurs. To circumvent this difficulty, a heuristic is used to find a good usable (implementable) solution. In addition, a mixed-integer program is developed which yields the optimal implementable solution when solved.