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     

The case for demilitarising Lesotho

ABSTRACT

The Kingdom of Lesotho spends around five per cent of its annual budget – some 700 million Maloti ($US52.6 million) in 2017 – on the Lesotho Defence Force (LDF). Lesotho’s geographical position means that the LDF has no meaningful role regarding its primary function of defending the country from external aggression and it hardly engages in its secondary functions. In addition, the LDF has a long history of interference with democratic processes and engaging in human rights abuse. The financial resources currently allocated to the LDF could do far more for security, widely defined, if they were allocated to a number of other government expenditure categories.     

Piracy,state capacity and root causes

By comparing the Somali experience of piracy with the emerging situation in the Gulf of Guinea, I show that increases in the enforcement aspects of state capacity in the Gulf of Guinea states are necessary but not sufficient tools to combat the emergence, growth, and institutionalisation of piracy. Such tools would require state-building measures that would minimise the incentives of individuals to join piracy organisations and they would have to effectively deal with youth unemployment, income inequality, and environmental degradation.     

Book reviews

John Lawrence Tone, The Fatal Knot: The Guerrilla War in Navarre and the Defeat of Napoleon in Spain. Chapel Hill and London; The University of North Carolina Press 1994. Pp.vii + 239, 1 map, biblio., index. $34.95 (cloth). ISBN 0–8078–2169–1.

Robert Holland (ed), Emergencies and Disorder in the European Empires after 1945. London: Frank Cass, 1994. Pp.x + 256; index. £32 (cloth); £15 (paper). ISBN 0–7146–4516–8 and 4109 X

Deborah L. Norden, Military Rebellion in Argentina: Between Coups and Consolidation. Lincoln, NE: University of Nebraska Press, 1996. Pp.242, index, $35/$17.50 (paper). ISBN 0–8032–8369–5.

William M. Minter, Apartheid's Contras: An Inquiry into the Roots of War in Angola and Mozambique. London and Atlantic Highlands, NJ: Zed Books Ltd; Johannesburg: Witwatersrand University Press, 1994. Pp. xii +308, 3 maps, biblio., index. $69.95/£39.95 (cloth); $29.95/£16.95(paper). ISBN 1–85649–266–4 and 266–4.     

Comparison between constant‐stress and step‐stress accelerated life tests under Time Constraint

By running life tests at higher stress levels than normal operating conditions, accelerated life testing (ALT) quickly yields information on the lifetime distribution of a test unit. The lifetime at the design stress is then estimated through extrapolation using a regression model. In constant‐stress testing, a unit is tested at a fixed stress level until failure or the termination time point of test, whereas step‐stress testing allows the experimenter to gradually increase the stress levels at some prefixed time points during the test. In this work, the optimal k‐level constant‐stress and step‐stress ALTs are compared for the exponential failure data under complete sampling and Type‐I censoring. The objective is to quantify the advantage of using the step‐stress testing relative to the constant‐stress one. Assuming a log‐linear life–stress relationship with the cumulative exposure model for the effect of changing stress in step‐stress testing, the optimal design points are determined under C/D/A‐optimality criteria. The efficiency of step‐stress testing to constant‐stress one is then discussed in terms of the ratio of optimal objective functions based on the information matrix. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 00: 000–000, 2013