Bounded flexibility in days‐on and days‐off scheduling

This article presents a flexible days‐on and days‐off scheduling problem and develops an exact branch and price (B&P) algorithm to find solutions. The main objective is to minimize the size of the total workforce required to cover time‐varying demand over a planning horizon that may extend up to 12 weeks. A new aspect of the problem is the general restriction that the number of consecutive days on and the number of consecutive days off must each fall within a predefined range. Moreover, the total assignment of working days in the planning horizon cannot exceed some maximum value. In the B&P framework, the master problem is stated as a set covering‐type problem whose columns are generated iteratively by solving one of three different subproblems. The first is an implicit model, the second is a resource constrained shortest path problem, and the third is a dynamic program. Computational experiments using both real‐word and randomly generated data show that workforce reductions up to 66% are possible with highly flexible days‐on and days‐off patterns. When evaluating the performance of the three subproblems, it was found that each yielded equivalent solutions but the dynamic program proved to be significantly more efficient. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 678–701, 2013     

United Nations Security Council reform and the dilemmas of African continental integration

This article analyses the disunity among African states in terms of United Nations Security Council (UNSC) reform, and attributes it to the contest between South Africa and Nigeria. These two countries have been locked in a hegemonic contest for continental domination. To this end, the article notes that African unity, not in terms of protocol but on the basis of principles and cooperation, is sacrosanct in order for the African Union to make a significant contribution to the reform of the UNSC. It is asserted that the contest between South Africa and Nigeria has been symbolised by the continental leadership aspirations of the heads of state of both countries, and recommends that it be tamed through forging diplomatic and strategic partnerships between the ruling parties of these two countries. The influence of external actors on the African countries, particularly that of France, is underscored as a contributing factor in stalling the debate on the UNSC reform. It recommends that South Africa use its strategic partnership within the association of Brazil, Russia, India, China and South Africa (BRICS), particularly Russia and China as permanent members of the UNSC, to influence the realisation of the reform debate.     

A best practice for assessment in counterinsurgency

In September 2011, the Commander of the International Security Assistance Force (ISAF) in Afghanistan directed the Afghan Assessment Group to redesign the way in which ISAF was assessing the status of the war, and to be ‘revolutionary’ in so doing. The resulting assessment paradigm was novel, non-doctrinal, and effectively addressed the unique complexities of the counterinsurgency in Afghanistan and the needs of the ISAF Commander. It had a two-tier structure consisting of both strategic and campaign assessments. The former focused on answering a set of strategic questions in narrative, analytic form to address the strategic environment, while the latter used a set of standards and accompanying narrative responses to gauge accomplishment of campaign tasks. Both tiers captured the current state of the war while maintaining an eye on future challenges and opportunities. The two assessments and their associated processes were designed to stimulate discussions leading directly to decisions by senior leaders on actions they could take, direct, or request. While any assessment paradigm will have advantages and disadvantages, an examination of the pros and cons of this assessment paradigm makes clear that it should be considered a ‘best practice’ in the field of counterinsurgency assessment.     

Challenges of measuring progress in Afghanistan using violence trends: the effects of aggregation,military operations,seasonality, weather,and other causal factors

Measuring nationwide progress of counterinsurgency operations in Afghanistan using violence trends is difficult due to several factors: aggregation of data to the national level may obfuscate disparate local trends; the observed seasonality in violence makes comparisons difficult and may obscure progress; and short-term spikes or troughs – attributable to weather, military operations and tempo, or holiday periods – heavily influence simple averaging schemes. Despite these challenges, proper understanding of violence statistics is critical to estimating the effectiveness of military forces added during a surge or redeployed as part of transition. This article explores methods for analyzing observed violence trends to identify causal factors, to provide a comparable baseline, and to inform assessments at appropriate levels of aggregation. One methodology for seasonal adjustment of violence data is discussed and shown to provide a logical baseline for examining trends. An ordinary least squares regression model is developed and implemented using time-series violence data.     

Optimality conditions for the bilevel programming problem

The bilevel programming problem (BLPP) is a sequence of two optimization problems where the constraint region of the first is determined implicitly by the solution to the second. In this article it is first shown that the linear BLPP is equivalent to maximizing a linear function over a feasible region comprised of connected faces and edges of the original polyhedral constraint set. The solution is shown to occur at a vertex of that set. Next, under assumptions of differentiability, first-order necessary optimality conditions are developed for the more general BLPP, and a potentially equivalent mathematical program is formulated. Finally, the relationship between the solution to this problem and Pareto optimality is discussed and a number of examples given.     

Optimal empty vehicle redistribution for hub‐and‐spoke transportation systems

This article considers the empty vehicle redistribution problem in a hub‐and‐spoke transportation system, with random demands and stochastic transportation times. An event‐driven model is formulated, which yields the implicit optimal control policy. Based on the analytical results for two‐depot systems, a dynamic decomposition procedure is presented which produces a near‐optimal policy with linear computational complexity in terms of the number of spokes. The resulting policy has the same asymptotic behavior as that of the optimal policy. It is found that the threshold‐type control policy is not usually optimal in such systems. The results are illustrated through small‐scale numerical examples. Through simulation the robustness of the dynamic decomposition policy is tested using a variety of scenarios: more spokes, more vehicles, different combinations of distribution types for the empty vehicle travel times and loaded vehicle arrivals. This shows that the dynamic decomposition policy is significantly better than a heuristics policy in all scenarios and appears to be robust to the assumptions of the distribution types. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008