Integrated production and delivery withmultiple factories and multiple customers

This paper considers coordinated scheduling of production and delivery with multiple factories and multiple customers. Due to the variation of cost, the production and delivery costs of a job are dependent on the factory to which it is assigned. Our problem is to find a schedule that minimises the makespan or the total completion time, subject to the constraint that the total cost does not exceed a given threshold. We first describe a linear programming algorithm to solve the preemptive case. The result of the linear program serves as a lower bound of the nonpreemptive case and suggests heuristics to solve the nonpreemptive case. We also show that minimising the total completion time subject to a given threshold of the cost is NP-complete. Computational experiments are conducted and the results show that the heuristics perform very well in practice.