Article
An algorithm for the bottleneck generalized assignment problem
Fuqua School of Business, Duke University, Durham, NC 27706 USA
Computers & Operations Research (Impact Factor: 1.86). 05/1993; 20(4):355362. DOI: 10.1016/03050548(93)90079X Source: dx.doi.org
ABSTRACT
We discuss a bottleneck (or minimax) version of the generalized assignment problem, known as the task bottleneck generalized assignment problem (TBGAP). TBGAP involves the assignment of a number of jobs to a number of agents such that each job is performed by a unique agent, and capacity limitations on the agents are not exceeded. The objective is to minimize the maximum of the costs of the assignments that are made. We present an algorithm for solving TBGAP. The TBGAP algorithm is illustrated by an example and computational experience is reported. The algorithm is seen to be effective in solving TBGAP problems to optimality.

 "The weights μ i 's in various cost minimizing transportation problems can be used as earlier (Mazzola and Neebe, 1993; Sherali, 1982). "
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ABSTRACT: A nonconvex optimization problem involving minimization of the sum of max and min concave functions over a transportation polytope is studied in this paper. Based upon solving at most (g+1)(< p) cost minimizing transportation problems with m sources and n destinations, a polynomial time algorithm is proposed which minimizes the concave objective function where, p is the number of pairwise disjoint entries in the m× n time matrix {t ij } sorted decreasingly and T g is the minimum value of the max concave function. An exact global minimizer is obtained in a finite number of iterations. A numerical illustration and computational experience on the proposed algorithm is also included. 
 ") and Mazzola (Mazzola, 1993). There are many more problems where it becomes necessary to study a TMTP wherein the products are shipped to the destinations in two stages. "
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ABSTRACT: A Two Stage Interval Time Minimizing Transportation Problem, where total availability of a homogeneous product at various sources is known to lie in a specified interval, is studied in the present paper. In the first stage, the sources ship all of their onhand material to the demand points, while a secondstage delivery covers the demand that is not fulfilled in the first shipment. In each stage, the objective is to minimize the shipment time, and the overall goal is to find a solution that minimizes the sum of the first and second stage shipment times. A polynomial time algorithm is proposed to solve the problem to optimality, where at various steps of the algorithm lexicographic optimal solutions of restricted versions of a related standard time minimizing transportation problem are examined and finally the global optimal solution is determined. 
Article: Heuristics for the generalised assignment problem: Simulated annealing and tabu search approaches
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ABSTRACT: The generalised assignment problem (GAP) is the problem of finding a minimum cost assignment of a set of jobs to a set of agents. Each job is assigned to exactly one agent. The total demands of all jobs assigned to any agent can not exceed the total resources available to that agent. A review of exact and heuristic methods is presented. A λgeneration mechanism is introduced. Different search strategies and parameter settings are investigated for the λgeneration descent, hybrid simulated annealing/tabu search and tabu search heuristic methods. The developed methods incorporate a number of features that have proven useful for obtaining optimal and near optimal solutions. The effectiveness of our approaches is established by comparing their performance in terms of solution quality and computional requirement to other specialized branchandbound tree search, simulated annealing and set partitioning heuristics on a set of standard problems from the literature.
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