5,123 research outputs found
The matching relaxation for a class of generalized set partitioning problems
This paper introduces a discrete relaxation for the class of combinatorial
optimization problems which can be described by a set partitioning formulation
under packing constraints. We present two combinatorial relaxations based on
computing maximum weighted matchings in suitable graphs. Besides providing dual
bounds, the relaxations are also used on a variable reduction technique and a
matheuristic. We show how that general method can be tailored to sample
applications, and also perform a successful computational evaluation with
benchmark instances of a problem in maritime logistics.Comment: 33 pages. A preliminary (4-page) version of this paper was presented
at CTW 2016 (Cologne-Twente Workshop on Graphs and Combinatorial
Optimization), with proceedings on Electronic Notes in Discrete Mathematic
Exact solutions to a class of stochastic generalized assignment problems
This paper deals with a stochastic Generalized Assignment Problem with recourse. Only a random subset of the given set of jobs will require to be actually processed. An assignment of each job to an agent is decided a priori, and once the demands are known, reassignments can be performed if there are overloaded agents. We construct a convex approximation of the objective function that is sharp at all feasible solutions. We then present three versions of an exact algorithm to solve this problem, based on branch and bound techniques, optimality cuts, and a special purpose lower bound. numerical results are reported.
Revisiting the Evolution and Application of Assignment Problem: A Brief Overview
The assignment problem (AP) is incredibly challenging that can model many real-life problems. This paper provides a limited review of the recent developments that have appeared in the literature, meaning of assignment problem as well as solving techniques and will provide a review on a lot of research studies on different types of assignment problem taking place in present day real life situation in order to capture the variations in different types of assignment techniques. Keywords: Assignment problem, Quadratic Assignment, Vehicle Routing, Exact Algorithm, Bound, Heuristic etc
Applications of network optimization
Includes bibliographical references (p. 41-48).Ravindra K. Ahuja ... [et al.]
Scheduling To Maximize Customer Satisfaction: A Project for the Shad Valley Program
This paper describes a project that was done for the Shad Valley Program, where it was required to assign students to seminars so as to maximize the satisfaction of the students with their assignments. We begin by describing the problem, its inputs and constraints. Two models are proposed to determine optimal assignments. The first model is based on the Capacitated Transportation Problem and a network formulation is proposed to solve it. The second model is a two phase model whose first phase involves solving a Bottleneck Capacitated Transportation Problem and the second phase solving a Capacitated Transportation Problem. A simple search algorithm is proposed that solves the second model. Implementation of these models is described and the results obtained are discussed. Extensions to the two models are also proposed
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