# An algorithm for the bottleneck generalized assignment problem

**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.

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**ABSTRACT:**A non-convex 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.Annals of Operations Research 01/2006; 143(1):265-275. DOI:10.1007/s10479-006-7387-9 · 1.10 Impact Factor - [Show abstract] [Hide abstract]

**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 on-hand material to the demand points, while a second-stage 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-generation mechanism is introduced. Different search strategies and parameter settings are investigated for the-generation 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 branch-and-bound tree search, simulated annealing and set partitioning heuristics on a set of standard problems from the literature.Das verallgemeinerte Zuordnungsproblem (GAP) besteht darin, eine Menge von Auftrgen einer Menge von Agenten kostenminimal zuzuordnen. Jeder Auftrag wird genau einem Agenten zugeordnet; die Summe der Anforderungen der einem Agenten zugeordneten Auftrge ist durch die diesem zur Verfgung stehenden Ressourcen begrenzt. Die Arbeit gibt eine bersicht ber exakte und heuristische Lsungsverfahren zum GAP. Es wird ein-Generierungs-Mechanismus beschrieben, wobei verschiedene Suchstrategien (ein Hybridverfahren aus Simulated Annealing und Tabu Search sowie reine Tabu Search-Verfahren) sowie Parameterkonstellationen untersucht werden. Die entwickelten Methoden beinhalten eine Anzahl von Eigenschaften, die sich fr die Erzielung von optimalen Lsungen sowie guten Nherungen als geeignet erwiesen haben. Die Effektivitt der Anstze wird ber den Vergleich hinsichtlich Lsungsqualitt und Berechnungsanforderungen mit anderen speziellen Verfahren wie Branch und Bound, Simulated Annealing sowie Partitionierungs-Heuristiken bei Anwendung auf Standardprobleme aus der Literatur gezeigt.Operations Research-Spektrum 01/1995; 17(4):211-225. DOI:10.1007/BF01720977 · 1.09 Impact Factor