A survey of algorithms for the generalized assignment problem

Abstract

This paper surveys algorithms for the well-known problem of finding the minimum cost assignment of jobs to agents so that each job is assigned exactly once and agents are not overloaded. All approaches seem to be based on branch and bound with bounds supplied through heuristics and through relaxations of the primal problem formulation. From the survey one can select building blocks for the design of one's own tailor-made algorithm. The survey also reveals that although just about any mathematical programming technique was tried on this problem, there is still a lack of a representative set of test problems on which competing enumeration algorithms can be compared, as well as a shortage of effective heuristics.

Good Laboratory Practice for optimization research

“…• Assignment Problems - (Cattrysse and Van Wassenhove, 1992, Loiola et al, 2007, Pentico, 2007 • Bioinformatics - (B lazewicz et al, 2005(B lazewicz et al, , Lukasiak et al, 2010 • Forecasting - Fildes (1979Fildes ( , 1985, Fildes et al (2008), Ghobbar and Friend (2003), Trapero et al (2015) • Job Shop Scheduling - (B lazewicz et al, 1996, Brucker et al, 2007, Cheng et al, 1999a,b, Kiran and Smith, 1984 • Knapsack Problem - (Lin, 1998, Lust and Teghem, 2012, Pisinger, 2007, Salkin and Kluyver, 1975, Wilbaut et al, 2008 • Personnel Scheduling - (Ernst et al, 2004, Miller, 1976 • Sports Scheduling - (Kendall et al, 2010, Rasmussen andTrick, 2008) • Traveling Salesman Problem - (Bellmore and Nemhauser, 1968, Burkard et al, 1998, Cook, 2011, Lust and Teghem, 2010 • Vehicle Routing - (Archetti and Speranza, 2008, Braysy et al, 2004, Braysy and Gendreau, 2005a,b, Cordeau et al, 2002, Doerner and Schmid, 2010, Gendreau et al, 2008, Jaillet and Wagner, 2008, Laporte, 2009, Vidal et al, 2013 Of course, there are many other areas which also come under the optimization research radar. Indeed, it is difficult to think of a discipline/sector that either does not currently use optimization research, or could benefit from some form of optimization.…”

The generalized assignment problem with minimum quantities

“…A comprehensive introduction to the problem can be found in [1]. A survey of algorithms for GAP is given in [2]. For a survey on different variants of assignment problems studied in literature, we refer to [4].…”

“…The generalized assignment problem (cf., for example, [1,2]) is a classical generalization of both the (multiple) knapsack problem and the bin packing problem. In the classical version of GAP, one is given m bins, a capacity B j for each bin j, and n items such that each item i has size s i,j and yields profit p i,j when packed into bin j.…”

“…Applications of GAP include fixed charge location problems, grouping and loading for flexible manufacturing systems, vehicle routing, scheduling projects, allocating storage space, scheduling payments on accounts, designing communication networks, assigning software development tasks to programmers, assigning jobs to computers in networks, scheduling variable length TV commercials, and assigning ships to overhaul facilities. For details on these applications, we refer to [2] and the references therein.…”

Designing Difficult Office Space Allocation Problem Instances with Mathematical Programming

“…subject to additional constraints. OSA is related to the multiple knapsack [15] and generalised assignment problems [6]. In OSA, the primary goal is to maximise the space utilisation by reducing the misuse of rooms.…”