Approximation algorithms for minimizing total weighted completion time of orders on identical machines in parallel

We consider the problem of scheduling orders on identical machines in parallel. Each order consists of one or more individual jobs. A job that belongs to an order can be processed by any one of the machines. Multiple machines can process the jobs of an order concurrently. No setup is required if a machine switches over from one job to another. Each order is released at time zero and has a positive weight. Preemptions are not allowed. The completion time of an order is the time at which all jobs of that order have been completed. The objective is to minimize the total weighted completion time of the orders. The problem is NP‐hard for any fixed number (≥2) of machines. Because of this, we focus our attention on two classes of heuristics, which we refer to as sequential two‐phase heuristics and dynamic two‐phase heuristics. We perform a worst case analysis as well as an empirical analysis of nine heuristics. Our analyses enable us to rank these heuristics according to their effectiveness, taking solution quality as well as running time into account. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

AN ENDOGENOUS GROWTH MODEL OF CAPITAL AND ARMS ACCUMULATION

This paper attempts to examine the effect of an anticipated foreign military threat on the steady‐state growth rate and the transitional behavior of the economy. The modeling strategy follows the Sandler and Hartley (1995 Sandler, T. and Hartley, K. 1995. The Economics of Defense, Cambridge: Cambridge University Press.  [Google Scholar]) and Dunne et al. (2005 Dunne, J.P., Smith, R.P. and Willenbockel, D. 2005. Models of military expenditure and growth: a critical review. Defence and Peace Economics, 16: 449–461. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) viewpoints to emphasize the role of national defense in affecting growth from the perspective of both the demand and the supply sides. We thus combine the public capital version of endogenous growth with a framework of competitive arms accumulation. It is found that the key factor determining the steady state and the transitional effects of a rise in the foreign military threat on the home weapon–capital ratio, the consumption–capital ratio, and the rate of economic growth, is the degree of relative risk aversion.     

TERRORIST THREATS AND TRANSITIONAL DYNAMICS IN AN OVERLAPPING GENERATIONS MODEL

Previous research has shown that the duration of a civil war is in part a function of how it ends: in government victory, rebel victory, or negotiated settlement. We present a model of how protagonists in a civil war choose to stop fighting. Hypotheses derived from this theory relate the duration of a civil war to its outcome as well as characteristics of the civil war and the civil war nation. Findings from a competing risk model reveal that the effects of predictors on duration vary according to whether the conflict ended in government victory, rebel victory, or negotiated settlement.     

Country survey IX: Spain

From the early 1980s Spain embarked on a wide‐ranging process of military reform, from organisational changes to defence industrial policies. Investment in military equipment was set to grow, policies were drawn up to foster the domestic defence industrial base, defence R&D rocketed, and Spain joined a myriad of international arms development programmes. Yet, by 1991 the process of reform had run out of steam. Expenditure planning proved unreliable, and firms suffered from sharp cutbacks in procurement expenditure. The model of defence industrial growth sketched in the mid‐1980s had floundered. The Spanish case provides an example of how the quest to maximise defence procurement from domestic sources can fall victim to industrial and budgetary constraints. Spanish defence producers are now becoming increasingly intertwined with foreign defence companies.     

THE DEFENCE SPENDING–EXTERNAL DEBT NEXUS IN ETHIOPIA

The aim of this paper is to examine the impact of defence spending and income on the evolution of Ethiopia’s external debt over the period 1970–2005. Using the bounds test approach to cointegration and Granger causality tests, we find a long run and a causal relationship between external debt, defence spending and income. Defence spending had a positive and a significant impact on the stock of external debt while income had a negative and a statistically significant impact on external debt. Our findings suggest that an increase in defence spending contributes to the accumulation of Ethiopia’s external debt, while an increase in economic growth helps Ethiopia to reduce its external debt.     

TIME-VARYING CHARACTERISTICS OF SOUTH KOREA-UNITED STATES AND JAPAN-UNITED STATES MILITARY ALLIANCES UNDER CHINESE THREAT: A PUBLIC GOOD APPROACH

This paper investigates the nature of two military alliances under Chinese threat. The findings are as follows: First, South Korea does not consider China a significant threat while Japan and the United States have recognized China as a serious threat since the 1990s and the 2000s, respectively. Second, the relationship between South Korea and the United States is a true military alliance for all time periods, but the nature of the alliance has changed since the 1970s. Third, although Japan began to form an alliance relationship with the United States in the 1990s, Japan is considered a more significant ally by the United States. This paper implies that, should China provoke a military confrontation, it might be difficult to deduce a common solution among the three countries because of the different response to military threats from China.     

DOES MILITARY EXPENDITURE MATTER FOR INFLATION AND ECONOMIC GROWTH?

This paper sets up a monetary endogenous growth model, and uses it to explain the ambiguous linkage between the military burden and the inflation rate observed in existing empirical studies. It is found that an expansion in the military burden has an ambiguous effect on the inflation rate depending upon the relative extent of two conflicting forces. More specifically, if the increase in the marginal benefit from holding money exceeds (falls short of) the increase in the marginal product of private capital, the inflation rate will rise (fall) in response. Moreover, it is found that an increase in the military burden will stimulate the balanced growth rate, confirming Benoit’s famous empirical findings.     

CHINA AND THE U.S. BEYOND THE KOREAN PENINSULA

China-U.S. cooperation over the most difficult security problem in Northeast Asia—the North Korean nuclear issue—in essence projects its bigger power game amid the tectonic shifts of Asian geopolitics. The nuclear issue affords a test case to gauge the future posture of China and the United States in East Asia and their partnership in that conflict-prone region. Approaches to resolving this issue must take into account the geopolitical realignment of Asia, Washington's reorientation of relations with its Asian allies, and China's rise as an influential regional player and the subsequent regional response. However, the long-standing mistrust between China and the United States is contributing to a lack of substantial progress in Korean nonproliferation efforts. The declared nuclear test by Pyongyang further put the denuclearization cooperation between China and the Unites States on the line. China-U.S. cooperation in denuclearizing Pyongyang may either produce lasting stability for the region or create ‘‘collateral damage,’’ with the North Korean issue paling in comparison.