Parallel-batching scheduling with nonlinear processing times on a single and unrelated parallel machines
Parallel-batching processing and job deterioration are universal in the real industry. Scholars have deeply investigated the problem of parallel-batching scheduling and the problem of scheduling with deteriorating jobs separately. However, the situations where both parallel-batching processing and job deterioration exist simultaneously were seldom considered. This paper studies the parallel-batching scheduling problem with nonlinear processing times on a single machine, and proposes several structural properties and an optimal algorithm to solve it. Based on the above properties and optimal algorithm for the single machine setting, we further study the problem of parallel-batching scheduling with nonlinear processing times under the unrelated parallel machine setting. Since the unrelated parallel machines scheduling problem is NP-hard, a hybrid SFLA-VNS algorithm combining Shuffle Frog Leap Algorithm (SFLA) with Variable Neighborhood Search Algorithm (VNS) is proposed. Computational experiments and comparison are finally conducted to demonstrate the effectiveness of the proposed algorithm.
KeywordsParallel-batching Scheduling Nonlinear processing times Meta-heuristic algorithm
This work is supported by the National Natural Science Foundation of China (Nos. 71231004, 71871080, 71601065, 71690235, 71501058, 71601060, 71801071), and Innovative Research Groups of the National Natural Science Foundation of China (71521001), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), Anhui Province Natural Science Foundation (No. 1608085QG167), the Project of Key Research Institute of Humanities and Social Science in University of Anhui Province (No. SK2017A0055), the Philosophy and Social Science Cultivation Project of Hefei University of Technology (No. JS2017AJRW0031), the Fundamental Research Funds for the Central Universities (JZ2018HGBZ0129), Base of Introducing Talents of Discipline to Universities for Optimization and Decision-making in the Manufacturing Process of Complex Product (111 project), the Project of Key Research Institute of Humanities and Social Science in University of Anhui Province, Open Research Fund Program of Key Laboratory of Process Optimization and Intelligent Decision-making (Hefei University of Technology), Ministry of Education. Panos M. Pardalos is partially supported by the project of Distinguished International Professor by the Chinese Ministry of Education (MS2014HFGY026).