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Toward an Efficient Resolution for a Single-machine Bi-objective Scheduling Problem with Rejection

Moghaddam Atefeh, Teghem Jacques, Tuyttens Daniel, Yalaoui Farouk, Amodeo Lionel

Foundations of Computing and Decision Sciences

2019

Vol. 44, No. 2

179--211

We consider a single-machine bi-objective scheduling problem with rejection. In this problem, it is possible to reject some jobs. Four algorithms are provided to solve this scheduling problem. The two objectives are the total weighted completion time and the total rejection cost. The aim is to determine the set of efficient solutions. Four heuristics are described; they are implicit enumeration algorithms forming a branching tree, each one having two versions according to the root of the tree corresponding either to acceptance or rejection of all the jobs. The algorithms are first illustrated by a didactic example. Then they are compared on a large set of instances of various dimension and their respective performances are analysed.

Collaborative paradigm for single-machine scheduling under just-in-time principles: total holding-tardiness cost problem

Varela M. L. R., Madureira A. M., Dantas J. D., Santos A. S., Putnik G. D., Trojanowska J., Machado J.

Management and Production Engineering Review

2018

Vol. 9, No. 1

90--103

The problem of sequencing jobs on a single machine to minimize total cost (earliness and tardiness) is nowadays not just important due to traditional concerns but also due to its importance in the context of Collaborative Networked Organizations and Virtual Enterprises, where precision about promptly responses to customers’ requests, along with other important requirements, assume a crucial role. In order to provide a contribution in this direction, in this paper the authors contribute with an applied constructive heuristics that tries to find appropriate solutions for single machine scheduling problems under different processing times and due dates, and without preemption allowed. In this paper, two different approaches for single-machine scheduling problems, based on external and internal performance measures are applied to the problem and a comparative analysis is performed. Computational results are presented for the problem under Just-in-Time and agile conditions on which each job has a due date, and the objective is to minimize the sum of holding costs for jobs completed before their due date and tardiness costs for jobs completed after their due date. Additional computational tests were developed based on different customer and enterprise oriented performance criteria, although preference is given to customer-oriented measures, namely the total number of tardy jobs and the maximum tardiness.