Single-machine slack due-window assignment scheduling with multiple maintenance activities and position-and-resource-dependent processing times

Abstract

This paper studies the slack due-window assignment method for single-machine scheduling problems with position-and resource-dependent processing times, for which the actual processing time is a continuous bivariate non-increasing convex function involving position and resource allocation. Only the slack due-window assignment method will be used. Two linear combination problems concerning position-dependent effects and resource allocation will be studied, in which the machine requires multiple maintenance activities. We present the optimal properties or design optimal algorithms to minimise the combination of the makespan, the total completion time and the total absolute deviation of completion time and to minimise the combination of the total costs of tardiness, the slack due date, the earliness cost, and the resource amount. Finally, we also consider the bi-criteria scheduling problem with nonmaintenance activities to minimise the combination of the total resource allocation cost, the weighted number of tardy jobs, and slack due-window assignment costs. A pseudo-polynomial time algorithm is designed to solve the bi-criteria scheduling problem.

Keywords:

• Scheduling
• single machine
• resource allocation
• slack due-window assignment

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 11991022, 11971443], the Chongqing Municipal Science and Technology Commission of Natural Science Fund Projects [cstc2018jcyjAX0631], Key Research Fund Projects of Chongqing Graduate Education and Teaching Reform [yjg182019], and in part by the Ministry of Science and Technology of Taiwan [MOST 109-2410-H-035-019; MOST 105-2221-E-035-053-MY3].

Notes on contributors

Xin-Gong Zhang

Xin-Gong Zhang is a professor in the School of Mathematical Science, Chongqing Normal University, China. He received the BS degree from Henan University, the master degree from Zhengzhou University, the PhD degree from University of Shanghai for Science and Technology in 2011, respectively. His teaching and research interests are theory of scheduling, combinatorial optimization, and supply chain.

Dan-Yu Bai

Dan-Yu Bai is a professor in the College of Management, Dalian Maritime University, China. He received the BS degree from Normal College of Shenyang University, the master degree from Liaoning University, the PhD degree from Northeastern University, china, in 2011, respectively. His teaching and research interests include logistics and supply chain,

Win-Chin Lin

Win-Chin Lin is a professor in the Department of Statistics, Feng Chia University, Taiwan. He received a doctoral degree from the department of Statistics, Iowa State University, USA in 1998. His teaching and research interests include intelligent optimization method and logistics and supply chain management.

Shuenn-Ren Cheng

Shuenn-Ren Cheng received the BS degree in Statistics from Tung Hui University, Taiwan, the MBA degree from the New York St. John University, the PhD degree from Manuel Quezon University, respectively. He is a Professor of the Cheng-Shiu University. His areas of research include applied statistics and finance.

Chin-Chia Wu

Chin-Chia Wu is a Professor in the Department of Statistics, Feng Chia University, Taiwan. He received a doctoral degree from the Graduate Institute of Management, School of Management, National Taiwan University of Science and Technology, Taiwan in 1997. His teaching and research interests include applied statistics and operations research.