Parallel Machine Scheduling Problem with Machine Rental Cost and Shared Service Cost

With the rapid development of industrial internet, blockchain, and other new-generation information technology, the shared manufacturing model provides a new way to address the problems of low resource utilization of the traditional manufacturing industry and serious duplication of construction through the mechanism of collaborative resource sharing. Concurrently, to meet the requirements of sustainable development, manufacturing enterprises need to balance economic efficiency with production efficiency in their production practices. This study investigates an identical parallel machine offline scheduling problem with rental costs and shared service costs of shared machines. In machine renting, manufacturers with a certain number of identical parallel machines will incur fixed rental costs, unit variable rental costs, and shared service costs when renting the shared machines. The objective is to minimize the sum of the makespan and total sharing costs. To address this problem, an integer linear programming model is established, and several properties of the optimal solution are provided. A heuristic algorithm based on the number of rented machines is designed. Finally, numerical simulation experiments are conducted to compare the proposed heuristic algorithm with a genetic algorithm and the longest processing time (LPT) rule. The results demonstrate the effectiveness of the proposed heuristic algorithm in terms of calculation accuracy and efficiency. Additionally, the experimental findings reveal that the renting and scheduling results of the machines are influenced by various factors, such as the manufacturer’s production conditions, the characteristics of the jobs to be processed, production objectives, rental costs, and shared service costs.