Parallel-machine serial-batching scheduling with release times under the effects of position-dependent learning and time-dependent deterioration

This paper addresses a serial-batching scheduling problem where the jobs with arbitrary release times are scheduled on parallel machines with the objective to minimize the makespan. The effects of learning and deterioration are considered simultaneously, and each job’s actual processing time depends on the sum of previous jobs’ processing times and the position of the current job. Each machine can process up to c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ c $$\end{document} jobs in the manner of serial batch, i.e., one after another with a setup time for each batch. Structural properties are identified for the special cases of the studied problem. Based on these derived structural properties, we propose a novel hybrid SC-VNS algorithm to solve the studied problem, which combines Society and Civilization (SC) algorithm with Variable Neighborhood Search (VNS). Computational experiments are conducted to evaluate the performance of the proposed hybrid algorithm and some other well-known algorithms. The results demonstrate that the proposed hybrid SC-VNS algorithm performs quite better than the compared algorithms in terms of the solution quality and the required running time.