A Multifactory Integrated Production and Distribution Scheduling Problem with Parallel Machines and Immediate Shipments Solved by Improved Whale Optimization Algorithm

This paper discusses the integrated scheduling of production and distribution operations in a multifactory supply chain with make-to-order production system. For the production side of the supply chain, we considered distributed parallel-established factories with identical parallel machines available at each factory. We assumed that the factories could produce all customers’ orders with different production rates and costs. For the distribution side of the supply chain, we considered a limited number of homogeneous vehicles that immediately distribute the finalized orders to the customers. Then, a mixed-integer nonlinear programming model is developed to determine the detailed scheduling of production and distribution that minimizes the total costs of the supply chain including production, distribution, and late delivery costs. To solve the real-world scale problems, we developed a new whale optimization algorithm (WOA). Moreover, we conducted computational experiments by generating several test problems to evaluate the proposed algorithm. Statistical analysis showed that the proposed algorithm has better performance than traditional WOA for different scales of the problem. Moreover, it confirms the capability of the improved whale optimization algorithm (IWOA) to solve the medium-scale instances; however, the results indicate the better performance of genetic algorithm (GA) for the large-scale instances.