the generalised assignment problem

Generalized assignment problem. In applied mathematics, the maximum generalized assignment problem is a problem in combinatorial optimization. This problem is a generalization of the assignment problem in which both tasks and agents have a size. Moreover, the size of each task might vary from one agent to the other.

The generalized assignment problem (GAP) seeks the minimum cost assignment of n tasks to m agents such that each task is assigned to precisely one agent subject to capacity restrictions on the agents. The formulation of the problem is: where \ ( c_ {ij} \) is the cost of assigning task j to agent i , \ ( a_ {ij} \) is the capacity used when ...

The multi-resource generalized assignment problem (MRGAP), in which more than one resource constraint is considered for each agent, is a natural generalization of GAP and has many practical applications, e.g., in distributed computer systems and in the trucking industry [3, 4, 8]. For

8 1 The Generalized Assignment Problem 1.1.2 Special Cases and Extensions The GAP is a fundamental problem in combinatorial optimization and, given its structural simplicity and significance, it appears in restricted or generalized form in several different situations. Two obvious special cases appear when there is only one server, in which case

The generalized assignment problem (GAP) asks to assign n clients to m servers in such a way that the assignment cost is minimized, provided that all clients are assigned to a server and that the capacity of each server is not exceeded. It is a problem that appears, by itself or as a subproblem, in a very high number of practical applications and has therefore been intensively studied.

The generalized assignment problem is an assignment problem (15.7) with the complicating constraint that the jobs j assigned to each resource i satisfy ∑ j α i j x i j ≤ β i. Let's suppose that an LP relaxation of the problem is to be solved at each node of the search tree to obtain bounds. If solving this LP with a general-purpose solver ...

The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: The problem instance has a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment.

13-2 Lecture 13: Generalized Assignment Problem Theorem 1 For any bipartite graph G(U[V;E), any bfs of the above LP is integral. Also any feasible fractional solution can be turned to an integral solution of no more cost. Now back to the GAP, suppose xis an optimal solution with cost C to the LP presented. So we have a total of P n j=1 x

The generalized assignment problem (GAP) is the problem of determining an assignment of J jobs to M capacity constrained machines, such that each job is assigned to exactly one machine, while total costs are minimized. It has applications in e.g. routing (Fisher and Jaikumar. 1981),

The classical generalized assignment problem (GAP) may be stated as finding a minimum-cost assignment of tasks to agents such that each task is assigned to exactly one agent and such that each agent's resource capacity is honored. This NP-hard problem has applications that include job scheduling, routing, loading for flexible manufacturing ...

The generalized assignment problem was studied by Ross and Soland ( 1975 ) and later by Chalmet and Gelders (1976) and more recently by Fisher et al. (1986). Despite its wide applicability, it is difficult to find studies that address the multi-resource version of this problem. Perhaps this is partially due to the difficulty of solving the problem.

1 Generalized Assignment Problem In this lecture, we consider a generalized assignment problem. There are mmachines and njobs. Each job must be assigned to some machine. If job j2[n] is assigned to machine i2[m], it requires processing time p ij and incurs cost c ij. Moreover, there is a common budget Tsuch that the total

The generalized assignment problem (GAP) determines the minimum cost assignment of n jobs to m agents such that each job is assigned to exactly one agent, subject to an agent's capacity ...

generalized assignment problem (GAP). In GAP, a set of items has to be optimally assigned to a set of bins without exceeding the capacity of any singular bin. In the strategic variant of the problem we study, values for assigningitems to bins are the private information of bidders and the mechanism should provide bidders

We consider generalized assignment problems with different objective functions: min-sum, max-sum, min-max, max-min. We review transformations, bounds, approximation algorithms and exact algorithms. The results of extensive computational experiments are given. Download to read the full chapter text.

the generalized assignment problems (GAP). GAP is a generic form of linear sum assignment problem (LSAP) and is more challenging to solve owing to the presence of both equality and inequality constraints. We propose a novel deep unsupervised learning (DUL) approach to solve GAP in a time-efficient manner.

Keywords: Generalized Assignment Problem; Local ratio; Approximation algorithms 1. Introduction We study the following maximization version of the Generalized Assignment Problem: Instance: A pair (B,S) where B is a set of M bins (knapsacks) and S is a set of N items. Each bin C j ∈ B has capacity c(j), and for each item i and bin C j we are ...

The classical generalized assignment problem (GAP) may be stated as finding a minimum-cost assignment of tasks to agents such that each task is assigned to exactly one agent and such that each agent's resource capacity is honored. This NP-hard problem has applications that include job scheduling, routing, loading for flexible manufacturing ...

The generalized assignment problem (GAP) and its special cases multiple knapsack1 and bin packing2 capture several fundamental optimization problems and have many practical applications in computer science, operations research, and related disciplines. The (offline) GAP is defined as follows: Definition 1(Generalized Assignment Problem).

Foulds and Wilson' describe a problem of allocating milk-producing farms to collection depots in order to minimise total collection cost. The model used was a variation of the Generalised Assignment Problem (GAP). The generalised assignment problem can be described using the terminology of Martello and Toth2 as follows. Given n items and m ...

TLDR. A truthful-in-expectation, (1-1/e)-approximation mechanism for a strategic variant of the generalized assignment problem (GAP), which improves upon the existing optimization algorithms for GAP in terms of simplicity and runtime while the approximation ratio closely matches the best approximation ratio known for G AP when all inputs are ...

10 Concluding Remarks. In this chapter we have described the state of the art in solving the Generalized Assignment Problem, as well as many extensions thereof. The approach we have taken is to generalize the GAP to a much larger class of Convex Assignment Problems, show that many of the extensions of the GAP proposed in the literature are ...

Section snippets Background. This study proposes a set of Operations Research (OR) analytics for the Generalized Quadratic Assignment Problem (GQAP) which is a well-defined strong NP-hard combinatorial optimization problem (Lee and Ma, 2004). The GQAP addresses the critical task of allocating n equipment units to m production centers or locations, which has direct implications for various real ...

The generalized assignment problem (GAP) has been studied by numerous researchers over the past 30 years or so. Simply stated, one must find a minimum-cost assignment of tasks to agents such that each task is assigned to exactly one agent and such that each agent's resource capacity is honoured. The problem is known to be NP-hard. In this paper, we study the elastic generalized assignment ...