An energy-efficient scheduling approach for a two-stage hybrid flow shop with parallel batch machines

With the rise of energy costs and the deterioration of the environment, manufacturing companies face increasing production expenses. Reducing energy consumption while improving manufacturing efficiency has become a major challenge. This study addresses the scheduling problem of a two-stage hybrid flow shop with time-of-use (TOU) electricity pricing, which arises from a tempered glass production environment. In the first stage, parallel machines are subject to specific qualification requirements, while parallel batch processing machines are used in the second stage. The objectives are to minimize both the makespan (Cmax) and total energy consumption (TEC). To address this problem, a mixed-integer programming (MIP) model is developed. Furthermore, a constructive heuristic based on greedy local search and an adaptive multi-population cooperative evolutionary algorithm (AMCEA) are proposed, respectively. In AMCEA, subpopulations are formed based on reference vectors, and adaptive cooperative search facilitates information exchange. Two regional local search operators and two adjustment strategies based on TOU electricity pricing are designed to enhance the exploitation capability of the proposed algorithm. Experimental results demonstrate that the proposed algorithm outperforms state-of-the-art algorithms for the hybrid flow shop under TOU electricity pricing problem.