Two-Agent Single Machine Order Acceptance Scheduling Problem to Maximize Net Revenue

Jiaji Li,Huangen Chen,Amit Kumar Bhardwaj,Yuanyuan Liu,Yuvraj Gajpal,Shangce Gao

doi:10.1155/2021/6627081

Abstract

The paper considers two-agent order acceptance scheduling problems with different scheduling criteria. Two agents have a set of jobs to be processed by a single machine. The processing time and due date of each job are known in advance. In the order accepting scheduling problem, jobs are allowed to be rejected. The objective of the problem is to maximize the net revenue while keeping the weighted number of tardy jobs for the second agent within a predetermined value. A mixed-integer linear programming (MILP) formulation is provided to obtain the optimal solution. The problem is considered as an NP-hard problem. Therefore, MILP can be used to solve small problem instances optimally. To solve the problem instances with realistic size, heuristic and metaheuristic algorithms have been proposed. A heuristic method is used to determine and secure a quick solution while the metaheuristic based on particle swarm optimization (PSO) is designed to obtain the near-optimal solution. A numerical experiment is piloted and conducted on the benchmark instances that could be obtained from the literature. The performances of the proposed algorithms are tested through numerical experiments. The proposed PSO can obtain the solution within 0.1% of the optimal solution for problem instances up to 60 jobs. The performance of the proposed PSO is found to be significantly better than the performance of the heuristic.

Highlights

Order acceptance scheduling has been studied by researchers for the last few decades
E objectives of the order acceptance scheduling problem and multiagent scheduling problem are similar. Both refer to the construction of the settings for more explicitly specified conditions. e paper of Reisi-Nafchi and Moslehi [4] depicts a more practical application portraying the combination of the order acceptance with multiagent scheduling problems
Inspired by the work of Reisi-Nafchi and Moslehi [4], this paper extends their study, highlighting the following three perspectives: (1) propose a new variant of the twoagent order acceptance scheduling problem; (2) propose a mathematical model for the new variant of the problem; and (3) design algorithms that can be used to solve both versions of the problem. is paper focuses on two problems named as lateness penalty problem (LPP) and the tardiness penalty problem (TPP). e LPP problem is proposed by ReisiNafchi and Moslehi [4]; the TPP problem has been introduced in this paper, for the very first time

Summary

Introduction

Order acceptance scheduling has been studied by researchers for the last few decades. E paper of Reisi-Nafchi and Moslehi [4] depicts a more practical application portraying the combination of the order acceptance with multiagent scheduling problems In their research, they formulated a mathematical model for their problem and proposed a hybrid genetic algorithm to solve this problem. E LPP problem is proposed by ReisiNafchi and Moslehi [4]; the TPP problem has been introduced in this paper, for the very first time Both problems are the two-agent single machine order acceptance scheduling problems but their objective functions are different. E service provider can be considered as an agent A and all other users combined can be considered as an agent B. e objective of the cloud-computing service provider is to maximize the net revenue from all the accepted jobs, while the weighted number of tardy jobs from all other users is kept within a predefined limit set by the management.

Literature Review

Problem Formulation

Findings

Proposed Algorithms