Parallel machine scheduling with job family, release time, and mold availability constraints: model and two solution approaches

This paper investigates a new problem in an identical parallel machine environment called parallel machine scheduling with job family, release time, and mold availability constraints (PMS-JRM), which is highly challenging from the computational perspective as it extends the basic NP-hard problem Pm||& sum;Cj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_m||\sum C_j$$\end{document}. The mold availability notion, first introduced in this paper, represents the availability relationship between jobs and machines. The PMS-JRM model originates from the imaging data collaborative processing in a low-earth-orbit satellite constellation under a time-varying communication network, and it can represent other multi-resource collaborative scheduling problems with discontinuous communication. An integer programming model was proposed to formulate the PMS-JRM. Due to its NP-hardness, two highly efficient heuristic solution approaches were proposed, namely a greedy algorithm with a hybrid first come first serve (HFCFS) dispatching rule (GA-HFCFS) and a Memetic Algorithm with Heterogeneous swap and Key job insertion operators (MA-HK). Extensive experiments were conducted on a set of test cases with various scales, and the results showed that GA-HFCFS outperforms three classical dispatching rules available in the literature. Taking the results of GA-HFCFS as initial solutions, MA-HK achieves optimal solutions for all small-scale cases while providing superior solutions within the same running time compared to two other competitors for large-scale cases. In particular, MA-HK yields better solutions in less running time than the state-of-the-art CPLEX solver. Additional experiments were conducted to highlight the critical ingredients of MA-HK.