Single-machine past-sequence-dependent setup times scheduling with resource allocation and learning effect

¹ College of Economics and Management, Nanjing Agricultural University, Nanjing 210095, P.R. China
² Laboratoire d’informatique, biologie intégrative et systèmes complexes (IBISC), EA 4526, Université d’Evry Val d’Essonne, 91020 Evry cedex, France.
feng.chu@ibisc.univ-evry.fr
³ School of Management, University of Science and Technology of China, Hefei, P.R. China
⁴ School of Management, Xi’an Jiaotong University, Xi’an, 710049 Shaanxi Province, P.R. China

Received: 20 May 2015
Accepted: 21 January 2016

Abstract

This paper addresses single-machine scheduling problem with resource allocation and learning effect in the background of past-sequence-dependent (p-s-d) setup times. In the proposed model of this paper, the actual job processing times are dependent on learning effect and the amount of resource allocated, and the setup times are proportional to the length of the already processed jobs. The resource function used here is a general convex one. The optimal job sequence and the optimal amount of resource allocated to each job are determined jointly for the objective function yielded by a combination of the total completion time, total absolute differences in completion times, and the total resource consumption. Besides, we also discuss some extension and special cases of this problem. It is shown that all the problems under study are polynomially solvable while the complexity results are different.