Assignment problem

About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.

The Assignment Problem with Seniority and Job Priority Constraints

Abstract: Consider an assignment problem in which persons are qualified for some but usually not all of the jobs. Moreover, assume persons belong to given seniority classes and jobs have given priority levels. Seniority constraints impose that the solution be such that no unassigned person can be given a job unless an assigned person with the same or higher seniority becomes unassigned. Priority constraints specify that the solution must be such that no unassigned job can become assigned without a job with the same or higher priority becoming unassigned. It is shown that: (i) adding such constraints does not reduce and may even increase the number of assigned persons in the optimal solution; (ii) using a greedy heuristic for constrained assignment (as often done in practice) may reduce the number of assigned persons by half, and (iii) an optimal solution to the assignment problem with both types of constraints can be obtained by solving a classical assignment problem with adequately modified coefficients.

Optimal task assignment in homogeneous networks

Abstract: This paper considers the problem of assigning the tasks of a distributed application to the processors of a distributed system such that the sum of execution and communication costs is minimized. Previous work has shown this problem to be tractable for a system of two processors or a linear array of N processors, and for distributed programs of serial parallel structures. Here we focus on the assignment problem on a homogeneous network, which is composed of N functionally-identical processors, each with its own memory. Some processors in the network may have unique resources, such as data files or certain peripheral devices. Certain tasks may have to use these unique resources; they are called attached tasks. The tasks of a distributed program should therefore be assigned so as to make use of specific resources located at certain processors in the network while minimizing the amount of interprocessor communication. The assignment problem in such a homogeneous network is known to be NP-hard even for N=3, thus making it intractable for a network with a medium to large number of processors. We therefore focus on task assignment in general array networks, such as linear arrays, meshes, hypercubes, and trees. We first develop a modeling technique that transforms the assignment problem in an array or tree into a minimum-cut maximum-flow problem. The assignment problem is then solved for a general array or tree network in polynomial time.

Solving quadratic assignment problems using convex quadratic programming relaxations

Abstract: We describe a branch-and-bound algorithm for the quadratic assignment problem (QAP) that uses a convex quadratic programming (QP) relaxation to obtain a bound at each node. The QP subproblems are approximately solved using the Frank-Wolfe algorithm, which in this case requires the solution of a linear assignment problem on each iteration. Our branching strategy makes extensive use of dual information associated with the QP subproblems. We obtain state-of-the-art computational results on large benchmark QAPs