A Network Flow Algorithm for Solving Generalized Assignment Problem

Hu, Yang‐Gen; Liu, Qunpo

doi:10.1155/2021/5803092

Cited by 4 publications

(3 citation statements)

References 33 publications

(40 reference statements)

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“…The OTM-AP can be viewed as a scheduling problem [11], which has been solved by the shortest processing time first (SPT) algorithm [12]. Moreover, by applying the circular flow method, the OTM-AP can be solved in polynomial time [10,13]. In addition, a variation of the OTM-AP is to minimize the maximum processing time of the machines.…”

Section: Literature Reviewmentioning

confidence: 99%

Two Combinatorial Algorithms for the Constrained Assignment Problem with Bounds and Penalties

Hu,

Lichen,

Pan

2023

Mathematics

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In the paper, we consider a generalization of the classical assignment problem, which is called the constrained assignment problem with bounds and penalties (CA-BP). Specifically, given a set of machines and a set of independent jobs, each machine has a lower and upper bound on the number of jobs that can be executed, and each job must be either executed on some machine with a given processing time or rejected with a penalty that we must pay for. No job can be executed on more than one machine. We aim to find an assignment scheme for these jobs that satisfies the constraints mentioned above. The objective is to minimize the total processing time of executed jobs as well as the penalties from rejected jobs. The CA-BP is related to some practical applications such as edge computing, which involves selecting tasks and processing them on the edge servers of an internet network. As a result, a motivation of this study is to improve the efficiency of internet networks by limiting the lower bound of the number of objects processed by each edge server. Our main contribution is modifying the previous network flow algorithms to satisfy the lower capacity constraints, for which we design two exact combinatorial algorithms to solve the CA-BP. Our methodologies and results bring novel perspectives into other research areas related to the assignment problem.

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Section: Literature Reviewmentioning

confidence: 99%

Two Combinatorial Algorithms for the Constrained Assignment Problem with Bounds and Penalties

Hu,

Lichen,

Pan

2023

Mathematics

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“…Several methods have been proposed in the literature to answer such a question [12]. The most important ones include exact methods, heuristic methods, population search methods, and local search methods [11,[13][14][15]. Recently, the Bio-Inspired Hybrid approach seems to be quite promising [16].…”

Section: Literature Reviewmentioning

confidence: 99%

A New Approach to the Allocation of Multidimensional Resources in Production Processes

Wikarek

Sitek

2022

Applied Sciences

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Modern technologies in the field of automation, robotics and IT have significantly changed the face of modern production systems. In particular, the use of AVG, PLC, mobile robots, RFID, IoT, etc. results in modern production processes being characterized by, among others, shortened production cycles and supply chains, reduced production costs, increased product quality and reliability, etc. Moreover, the application of these technologies requires a new definition and methods of using production resources. Most often these are resources that are characterized by many functionalities, the so-called multidimensional resources, which can be configured, remotely controlled, updated, etc., and their use in many cases enables the self-optimization and self-organization of the production system. The article presents the problem of allocation and control of multidimensional resources in production processes. The proprietary formal model of the problem is proposed, as well as how to use it in both proactive and reactive modes. A procedure for reducing the size of the modeled problem is also proposed, the use of which enables a two-fold reduction in the number of constraints and even a fifty-fold reduction in the number of decision variables of the proposed model. This results in an almost hundredfold reduction in computation time for the considered data instances. An original hybrid approach is used to implement the model, which enables the integration of mathematical programming (MP) and programming in constrained logic (CLP). Model data and parameters have been saved as facts.

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“…Derigs [14] presented an optimization method for BAP with a shortest augmenting path method. Hu [15] transformed GAP into a minimum cost flow problem and presented an algorithm with complementary slack condition. Recently, several exact algorithms [16][17][18] have been developed for the GAP.…”

Section: Introductionmentioning

confidence: 99%

A Feasible Flow-based Algorithm for Solving Classic Assignment Problem with Bottleneck

Yongwen Hu, Lixun Wang, Zejian Zhang

2024

jes

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Classic assignment problem with bottleneck is a fundamental combinatorial optimization problem with numerous practical applications in diverse domains. In order to comprehensively explore the classic assignment problem with bottleneck and to develop efficient algorithm, a feasible flow-based algorithm is proposed for optimizing classic assignment problem with bottleneck. The bottleneck constraints are addressed by updating the bottleneck of the problem, and a feasible-flow approach is leveraged to efficiently identify optimal solutions within the network framework associated with such problems. To assess the effectiveness of our proposed algorithm, a comprehensive set of numerical experiments is carried out across various instances of classic assignment problem with bottleneck. Our numerical results demonstrate the superior performance of our algorithm, particularly when applied to problems with smaller cost scales, making it particularly suitable for addressing medium-sized to smaller-scale problems.

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A Network Flow Algorithm for Solving Generalized Assignment Problem

Abstract: The generalized assignment problem (GAP) is an open problem in which an integer k is given and one wants to assign k ′ agents to … Show more

Cited by 4 publications

References 33 publications

Two Combinatorial Algorithms for the Constrained Assignment Problem with Bounds and Penalties

Two Combinatorial Algorithms for the Constrained Assignment Problem with Bounds and Penalties

A New Approach to the Allocation of Multidimensional Resources in Production Processes

A Feasible Flow-based Algorithm for Solving Classic Assignment Problem with Bottleneck

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