An Optimization Problem of Distributed Permutation Flowshop Scheduling with an Order Acceptance Strategy in Heterogeneous Factories

This paper addresses a distributed permutation flowshop scheduling problem with an order acceptance strategy in heterogeneous factories. Each order has a related revenue and due date, and several flowshop machines are operated in each factory, and they have a distinct sequence-dependent setup time. We select/reject production orders, assign the selected orders to the factories, and determine the permutation manufacturing sequence in each factory to maximize the total profit. To optimally solve the scheduling problem, we formulate the scheduling problem as a mixed integer linear programming model to find an optimal solution for small-sized experiments. Then, we propose two population-based algorithms, a genetic algorithm and particle swarm optimization for large-sized experiments. We proved that the proposed genetic algorithm effectively and efficiently solves the problem to guarantee a near optimal solution through computational experiments. Finally, we conduct a sensitivity analysis of the genetic algorithm to observe the relationship between order selection, revenue, and order tardiness cost.