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heuristic AND SPECIAL CASE ALGORITHMS FOR DISPERSION PROBLEMS

OPERATIONS RESEARCH 1994年第2期42卷 299-310页

作者： RAVI, SS ROSENKRANTZ, DJ TAYI, GK SUNY ALBANY FAC COMP SCI ALBANY NY 12222 USA

The dispersion problem arises in selecting facilities to maximize som, function of the distances between the facilities. The problem also arises in selecting nondominated solutions for multiobjective decision making. It is known to be NP-hard under two objectives: maximizing the minimum distance (MAX-MIN) between any pair of facilities and maximizing the average distance (MAX-AVG). We consider the question of obtaining near-optimal solutions. For MAX-MIN, we show that if the distances do not satisfy the triangle inequality, there is no polynomial-time relative approximation algorithm unless P = NP. When the distances satisfy the triangle inequality, we analyze an efficient heuristic and show that it provides a performance guarantee of two. We also prove that obtaining a performance guarantee of less than two is NP-hard. For MAX-AVG, we analyze an efficient heuristic and show that it provides a performance guarantee of four when the distances satisfy the triangle inequality. We also present a polynomial-time algorithm for the 1-dimensional MAX-AVG dispersion problem. Using that algorithm, we obtain a heuristic which provides an asymptotic performance guarantee of pi/2 for the 2-dimensional MAX-AVG dispersion problem.

关键词： analysis of algorithms: computational complexity facilities/equipment planning: discrete location programming: heuristic

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MINIMIZING VARIATION OF FLOW TIME IN SINGLE-MACHINE SYSTEMS

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MANAGEMENT SCIENCE 1981年第12期27卷 1453-1459页

作者： KANET, JJ University of Georgia

This paper addresses the problem of n jobs to be scheduled on a single machine in such a way that flow time variation is minimized. When the measure of variation is total absolute difference of completion times (TADC) the problem is shown to be quite simple. Sufficient conditions are shown for minimal TADC and a simple method for generating an optimal solution is provided.

关键词： production/scheduling: flow shop programming: heuristic

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