Computing equilibria via nonconvex programming

The problem of determining a vector that places a system in a state of equilibrium is studied with the aid of mathematical programming. The approach derives from the logical equivalence between the general equilibrium problem and the complementarity problem, the latter being explicitly concerned with finding a point in the set S = {x: < x, g(x)> = 0, g(x) ≦ 0, x ≧ 0}. An associated nonconvex program, min{? < x, g(x) > : g(x) ≦ 0, x ≧ 0}, is proposed whose solution set coincides with S. When the excess demand function g(x) meets certain separability conditions, equilibrium solutions are obtained by using an established branch and bound algorithm. Because the best upper bound is known at the outset, an independent check for convergence can be made at each iteration of the algorithm, thereby greatly increasing its efficiency. A number of examples drawn from economic and network theory are presented in order to demonstrate the computational aspects of the approach. The results appear promising for a wide range of problem sizes and types, with solutions occurring in a relatively small number of iterations.     

Appointment scheduling at a multidisciplinary outpatient clinic using stochastic programming

The purpose of this paper is to investigate the problem of constructing an appointment template for scheduling patients at a specific type of multidisciplinary outpatient clinic called an integrated practice unit (IPU). The focus is on developing and solving a stochastic optimization model for a back pain IPU in the face of random arrivals, an uncertain patient mix, and variable service times. The deterministic version of the problem is modeled as a mixed integer program with the objective of minimizing a weighted combination of clinic closing time (duration) and total patient waiting time (length of stay). A two‐stage stochastic program is then derived to account for the randomness and the sequential nature of the decisions. Although it was not possible to solve the two‐stage problem for even a limited number of scenarios, the wait‐and‐see (WS) problem was sufficiently tractable to provide a lower bound on the stochastic solution. The introduction of valid inequalities, limiting indices, and the use of special ordered sets helped to speed up the computations. A greedy heuristic was also developed to obtain solutions much more quickly. Out of practical considerations, it was necessary to develop appointment templates with time slots at fixed intervals, which are not available from the WS solution. The first to be derived was the expected value (EV) template that is used to find the expected value of the EV solution (EEV). This solution provides an upper bound on the objective function value of the two‐stage stochastic program. The average gap between the EEV and WS solutions was 18%. Results from extensive computational testing are presented for the EV template and for our adaptation of three other templates found in the literature. Depending on the relative importance of the two objective function metrics, the results demonstrate the trade‐off that exists between them. For the templates investigated, the “closing time” ranged from an average of 235 to 275 minutes for a 300‐minute session, while the corresponding “total patient time in clinic” ranged from 80 to 71 minutes.     

The Morale Maze: the German Army in Late 1918

The state of the German Army’s morale in 1918 is central to our understanding not only of the outcome of World War I, but also of the German Revolution and, indeed, through the pernicious ‘stab-in-the-back-myth’, on Weimar politics and the rise of the Nazis, too. This article presents new evidence from the German archives, blended with statistical analysis, to show that the morale of some units held up better than previously thought almost to the end, and thus to suggest three things. First, it proposes that some historians have placed too much reliance on English-language sources alone, such as British Army intelligence reports, which have various flaws as evidence. Second, it argues that, while historians have increasingly moved away from generalisations about German morale, this process has further to run. Third, it suggests that no single tipping point can be identified, and that morale alone does not provide a sufficient explanation for battlefield defeat. Indeed, much of the data can only be explained if the tactical realities of the war in late 1918 are clearly understood.     

In Search of the ‘X’ Factor: Morale and the Study of Strategy

A functional conceptualisation of morale is proposed, which focuses its meaning on motivation and the willingness to act rather than mood and group dynamics. Morale, it is argued, emerges from the subtle interrelationships of the many factors known to affect military means. It can be assessed both qualitatively and quantitatively, allowing the interaction between morale and policy to be explored in a manner that facilitates insight into the strategic process. A case study from the North African campaign of World War II is presented to explore in detail the relationship between morale and the art of war – strategy.     

Assessing Capabilities in International Politics: Biased Overestimation and the Case of the Imaginary ‘Missile Gap’

How states assess the capabilities of their adversaries and rivals is of paramount importance to the theory and practice of international relations. This paper presents a framework for understanding why states overestimate the capabilities of their adversaries. Three types of overestimation are presented, consisting of conscious/rational, erroneous and biased overestimation. In order to demonstrate the phenomenon of biased overestimation in international politics, the case of the ‘Missile Gap’ (1957–61) controversy in the United States is examined.     

The Persistent Military Security Dilemma between China and India

This paper evaluates to what extent the improving Sino-Indian relations coincide with a mitigation of military threat perceptions. A critical review of the demilitarisation of the border, the military strategies with respect to the Indian Ocean and nuclear arms programmes, reveals that the two countries are still locked in a military security dilemma. Distrust still results in military balancing. The outcome is a complex and multi-level military balance of power that might not bring about peace but enhances stability.     

Rubber match: a third Lebanon war

Israel and Hezbollah have applied the lessons learned from the 2006 Lebanon War and have been preparing for a future conflict with both sides aiming for a more decisive victory. With improved capabilities from 2006, future hostilities will be far more destructive. This article analyzes their performance in 2006 and the lessons they have drawn to predict what a future conflict is likely to look like. The article analyzes both parties in three categories: ground forces; rockets, missiles, and anti-armor weapons; and lastly, Israel's air and sea dominance and Hezbollah's efforts to counter that dominance. Finally, this article argues that, contrary to conventional wisdom, a large-scale conflict between Israel and Hezbollah is unlikely to become a larger regional conflict involving Syria and Iran.     

Reassessing private military and security company (PMSC) ‘competition‘ in civil war: lessons from Sierra Leone

ABSTRACT

This paper challenges recent claims that competitive market dynamics incentivize Private Military and Security Companies (PMSCs) to fully commit to providing effective services, thereby reducing the duration of civil war. Our assessment of a most-likely case scenario for this argument – Sierra Leone – reveals four critical problems. First, there is rarely direct competition, even if numerous companies are present. Second, the presence of multiple PMSCs usually represents a collaboration among subsidiaries providing distinct services, often under the same corporate umbrella. Third, data aggregation obfuscates the overlap of PMSC presence, inflating the amount of perceived competition. Finally, we raise concerns regarding how quantitative analyses can conflate conflict intensity with conflict termination.     

SHOULD MILITARY UNIFORMS CARRY THE UNION LABEL?

It is widely believed that the unionization of military labor leads to reduced discipline and lower combat capability. Case studies of the performance of existing military unions, however, generally suggest that unionization has a benign impact on the performance of the armed forces. In this paper, we offer a theoretical economic analysis of the likely impact of military unionization on volunteer militaries. Our analysis suggests that military unionization will unambiguously lead to larger, but less disciplined, armed forces, leaving the overall impact of unionization on defense capability ambiguous. Military unionization, however, will clearly enhance social welfare.