application of 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. This problem in its most general form is as follows: There are a number of agents and a number of tasks. Any ...

Abstract. Given n items and m knapsacks, the Generalized Assignment Problem (GAP) is to find the optimum assignment of each item to exactly one knapsack, without exceeding the capacity of any knapsack. This problem can also be described as the optimal assignment of n jobs to m capacitated agents. During the last three decades, many papers have been published on the GAP.

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 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].

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 ...

In this section we will focus on other models with multiple tasks per agent, starting with different versions of the generalized assignment problem. 3.1. The generalized assignment problemThe most basic version of the AP that allows an agent to be assigned to multiple tasks is the generalized assignment problem or GAP.

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 (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 generalized assignment problem is an assignment problem (15.7) with the complicating constraint that the jobs j assigned to each resource i satisfy . 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 is too slow, the ...

Abstract. Having reached the 50th (golden) anniversary of the publication of Kuhn's seminal article on the solution of the classic assignment problem, it seems useful to take a look at the variety of models to which it has given birth. This paper is a limited survey of what appear to be the most useful of the variations of the assignment ...

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 survey focuses on the real-life applications of the Generalized Assignment Problem (GAP) in scheduling, timetabling, telecommunication, facility location, transportation, production planning, etc. Abstract Given n items and m knapsacks, the Generalized Assignment Problem (GAP) is to find the optimum assignment of each item to exactly one knapsack, without exceeding the capacity of any ...

Within the education domain, this review classified the assignment problem into two: timetabling problem and allocation problem. Assignment problem refers to the analysis on how to assign objects to objects in the best possible way (optimal way) [ 2, 3 ]. The two components of assignment problem are the assignments and the objective function.

The well-known Generalized Assignment Problem (GAP) is to find the optimal assignment of n items (jobs) into m knapsacks (agents) where each of which with a fixed capacity availability. The GAP is a well-known combinatorial optimization problem with various real-life applications.

The above optimization problem can be expressed as a task assignment solution that minimizes the task offloading delay while maximizing the task offloading success rate, which is a generalized ...

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).

Worked example of assigning tasks to an unequal number of workers using the Hungarian method. 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 ...

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 ...

The generalized assignment problem (GAP) is a well-studied classical optimiza-tion problem that commonly appears in areas of application such as scheduling and load balancing. Using scheduling notation for convenience, consider a set of ... prominent application of this problem is the National Residency Matching Program (NRMP), a centralized ...

An Assignment Problem and Its Application in Education Domain: A Review and Potential Path. May 2018; Advances in Operations Research 2018 ... e general aim of assignment problem is t o optimize.

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 Bj for each bin j, and n items such that each item i has size si,j and yields profit pi,j when packed into bin j.

problems such as the linear network flow and shortest path problems to take the form of an assignment problem. The assignment problem finds many applications; the most obvious being that of matching such as the matching of operators and machines or delivery vehicles and deliveries. There are however numerous other interesting applications.

Multi-Agent Path Finding (MAPF), i.e., finding collision-free paths for multiple robots, plays a critical role in many applications. Sometimes, assigning a target to each agent also presents a challenge. The Combined Target-Assignment and Path-Finding (TAPF) problem, a variant of MAPF, requires one to simultaneously assign targets to agents and plan collision-free paths for agents.

Teaching and grading assignments will be explained, as well as preparation, teaching tips, problems and questions, quizzes and exams, weekly meetings, grading, appropriate office use and the Sexual Harassment Prevention EducationMailbox in 241 Schaeffer Hall All graduate students will have a mailbox in our main office. The faculty do as well.

The rapid development of online platforms has inspired a wide range of applications for timely resources allocations, such as the hotel booking, the cargo logistics, the cloud servers and so on. Motivated by such needs, we study the online versions of the famous generalized assignment problem (GAP) and the packing problem (also known as d-GAP ...