Bottleneck Assignment Problem

Bottleneck Assignment Problem-5
However, we can solve it without the integrality constraints (i.e., drop the last constraint), using standard methods for solving continuous linear programs.

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Using the isolation lemma, a minimum weight perfect matching in a graph can be found with probability at least ½. Suppose that a taxi firm has three taxis (the agents) available, and three customers (the tasks) wishing to be picked up as soon as possible.

The firm prides itself on speedy pickups, so for each taxi the "cost" of picking up a particular customer will depend on the time taken for the taxi to reach the pickup point.

Other algorithms include adaptations of the primal simplex algorithm, and the auction algorithm.

The assignment problem is a special case of the transportation problem, which is a special case of the minimum cost flow problem, which in turn is a special case of a linear program.

A common variant consists of finding a minimum-weight perfect matching.

Bottleneck Assignment Problem

It is a specialization of the maximum weight matching problem for bipartite graphs.

Without loss of generality we can assume that the cycle ends at vertex i1, so the last fractional variable in the cycle is .

So the number of edges in the cycle is 2m - it must be even since the graph is bipartite.

The solution to the assignment problem will be whichever combination of taxis and customers results in the least total cost.

However, the assignment problem can be made rather more flexible than it first appears.


Comments Bottleneck Assignment Problem

  • Solving linear bottleneck assignment problems via strong.

    Operations Research Letters 12 1992 179-180 September 1992 North-Holland Solving linear bottleneck assignment problems via strong spanning trees Ronald D. Armstrong and Zhiying Jin Graduate School of Management, Rutgers Unit'ersity, Newark, NJ 07102, USA Received August 1991 Revised February 1992 An efficient algorithm for solving the n n linear bottleneck assignment problem is described.…

  • Asymptotic Moments of the Bottleneck Assignment Problem

    One of the most important variants of the standard linear assignment problem is the bottleneck assignment problem. In this paper we give a method by which one can nd all of the asymptotic moments of a random bottleneck assignment problem in which costs independent and identically distributed are chosen from a wide…

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    Abstract. The FORTRAN implementation of an efficient algorithm which solves the Bottleneck Assignment Problem is given. Computational results are presented, showing the proposed method to be generally superior to the best known algorithms.…

  • Linear bottleneck assignment problem - Wikipedia

    In combinatorial optimization, a field within mathematics, the linear bottleneck assignment problem LBAP is similar to the linear assignment problem. In plain words the problem is stated as follows There are a number of agents and a number of tasks.…

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  • Chapter 6 Other types of linear assignment problems

    Chapter 6. OtherTypes of Linear Assignment Problems 6.2 Bottleneck assignment problem 6.2.1 Background Linear bottleneck assignment problems were introduced by Fulkerson, Glicksberg, and Gross 292 and occur, e.g. in connection with assigning jobs to parallel machines so as to minimize the latest completion time. Let n jobs and n machines.…

  • Technical Note—An Improved Algorithm for the Bottleneck.

    Gross has proposed an algorithm for the bottleneck assignment problem. This note reports a test of it against a “threshold” algorithm, and finds that the latter is superior computationally.…

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