The equivalence of general set-covering and implicit integer programming formulations for shift scheduling

In a recent article we demonstrated that implicit optimal modeling for shift scheduling (P2) has inherent size and execution time advantages over the general set-covering formulation for shift scheduling (P1) [11, 13]. We postulated that the absence of extraordinary overlap (EO) was a requirement for the equivalence of P1 and P2. We have defined EO as the condition in which the earliest and latest starts for a break in one shift are earlier and later than the earliest and latest starts for a break in any other shift(s). In this article, we prove that our earlier postulate was accurate. Additionally, we discuss research extensions and note other scheduling problems for which implicit modeling may be appropriate. © 1996 John Wiley & Sons, Inc.     

Optimal control of continuous-time terminal-value birth-and-death processes and airline overbooking

Consider a continuous-time airline overbooking problem that relates to a single-leg flight and a single service class with a stationary fare. Passengers may cancel their reservations at any time and receive a full refund. Therefore fares can be thought of as being paid at flight time. At that time, the airline bumps passengers in excess of flight capacity and pays a penalty for so doing. The wflight-time revenue, that is, fares received less bumping penalties paid, is quasiconcave in the number of reservations at that time. We model the reservations process as a continuous-time terminal-value birth-and-death process. A more general model than is necessary for an airline reservations system is considered, in which the airline controls both the reservation acceptance (birth) and the cancellation (death) rates. In current practice airlines do not control cancellation rates (though other industries do exercise such control, e.g., hotels) and control reservation acceptance rates by declining reservation requests. The more general model might be applied to other targeting applications, such as steering a vehicle through space toward a target location. For the general model a piecewise-constant booking-limit policy is optimal; that is, at all times the airline accepts reservation requests up to a booking limit if the current number of reservations is less than that booking limit, and declines reservation requests otherwise. When the airline is allowed to decline all reservation requests, as is the case in practice, the booking-limit optimal policy defined by using the greatest optimal booking limit at all times is piecewise constant. Moreover, these booking limits fall toward flight time. © 1996 John Wiley & Sons, Inc.     

Scheduling to minimize release-time resource consumption and tardiness penalties

We consider the problem of scheduling a set of jobs with a common due-date on a single-machine where the release time of a job is related to the amount of resource consumed. The objective is to minimize the total resource consumption and the total tardiness. While the problem is strongly NP-hard in general, we discuss two different special cases for which special properties are identified and used to develop efficient pseudo-polynomial time algorithms. © 1995 John Wiley & Sons, Inc.     

How Is a Man to Decide? Unjust Combatants,Duress and McMahan’s Killing in War

Jeff McMahan’s much-discussed work Killing in War is an important part of the revisionist school of just war studies. This paper avoids discussion of McMahan’s use of human rights and examines the practical consequences of his argument about duress on soldiers to fight an unjust war. These arguments are found to be wanting and to be impractical ones that do not fit battlefield realities. The importance of the Law of Armed Conflict and the legal equality of combatants that is part of it is emphasised and accepted as the most practical way of regulating battlefield behaviour and saving lives. It is concluded that attempts to tell soldiers what to do when they may be fighting an unjust war add to their burdens and are misplaced.     

An exact branch‐and‐price algorithm for multitasking scheduling on unrelated parallel machines

We consider the multitasking scheduling problem on unrelated parallel machines to minimize the total weighted completion time. In this problem, each machine processes a set of jobs, while the processing of a selected job on a machine may be interrupted by other available jobs scheduled on the same machine but unfinished. To solve this problem, we propose an exact branch‐and‐price algorithm, where the master problem at each search node is solved by a novel column generation scheme, called in‐out column generation, to maintain the stability of the dual variables. We use a greedy heuristic to obtain a set of initial columns to start the in‐out column generation, and a hybrid strategy combining a genetic algorithm and an exact dynamic programming algorithm to solve the pricing subproblems approximately and exactly, respectively. Using randomly generated data, we conduct numerical studies to evaluate the performance of the proposed solution approach. We also examine the effects of multitasking on the scheduling outcomes, with which the decision maker can justify making investments to adopt or avoid multitasking.     

Stochastic production capacity: A bane or a boon for quick response supply chains?

The quick response (QR) system that can cope with demand volatility by shortening lead time has been well studied in the literature. Much of the existing literature assumes implicitly or explicitly that the manufacturers under QR can always meet the demand because the production capacity is always sufficient. However, when the order comes with a short lead time under QR, availability of the manufacturer's production capacity is not guaranteed. This motivates us to explore QR in supply chains with stochastic production capacity. Specifically, we study QR in a two-echelon supply chain with Bayesian demand information updating. We consider the situation where the manufacturer's production capacity under QR is uncertain. We first explore how stochastic production capacity affects supply chain decisions and QR implementation. We then incorporate the manufacturer's ability to expand capacity into the model. We explore how the manufacturer determines the optimal capacity expansion decision, and the value of such an ability to the supply chain and its agents. Finally, we extend the model to the two-stage two-ordering case and derive the optimal ordering policy by dynamic programming. We compare the single-ordering and two-ordering cases to generate additional managerial insights about how ordering flexibility affects QR when production capacity is stochastic. We also explore the transparent supply chain and find that our main results still hold.     

Beyond the Double Game: Lessons from Pakistan’s Approach to Islamist Militancy

States commonly take one of three approaches to militant groups on their soil: collaboration; benign neglect; or belligerence. All three approaches are present in Pakistan, where some groups also move back and forth among these categories. I employ the term “coopetition” to capture this fluidity. The dynamic nature of militancy in Pakistan makes the country an excellent laboratory for exploring a state’s assessment of the utility an Islamist militant group offers, and the threat it poses relative to other threats informs the state’s treatment of that group. In this article, I put forward a typology that situates Islamist militants in Pakistan in one of the above four categories. I also illustrate how a group’s identity, objectives, and alliances inform assessments of its utility and threat relative to other threats. In addition to enhancing our understanding of militant–state dynamics, this taxonomy builds on and helps to unify earlier typologies of Pakistani militancy.     

From the sea to outer space: The command of space as the foundation of spacepower theory

Colin Gray once lamented the absence of a ‘Mahan for the final frontier’ and spacepower theory in strategic studies. This article proposes the command of space as the fundamental concept of spacepower theory, and that Mahan himself has much to offer in the endeavour of spacepower theory-making than has hitherto been realised. The theory is advanced by tempering versions of the ‘command of space’, stressing its educational intent, and explaining the nuanced sub-concepts of space control and denial through understanding some precedents set by seapower theory. In the process, aspects of Mahanian and Corbettian seapower theory are unified.