Integrated production and delivery scheduling for multi-factory supply chain with stage-dependent inventory holding cost

This paper will introduce a new scheduling problem in the supply chain. This is an integrated scheduling and transportation problem where stage-dependent holding cost is taken into consideration. This supply chain consists of a number of serial factories joined together. The objective is minimizing the whole system's criteria which are the sum of the transportation cost and stage-dependent holding costs. Transporting and delivering a number of jobs in the form of batches are also allowed. In scheduling systems with delivery, a job can be delivered when its processing is completed. The processed job should remain in the system until its batch's completion time. On the other hand, on receiving at a factory, jobs should wait until their process has started. These would impose the WIP inventory cost. The other holding cost imposed on the system is finished-goods holding cost which is incurred on the jobs that are delivered to the customer before their due dates. Thus, the objective of this study is to find a schedule with trade-off among holding costs and delivery cost. A time-indexed formulation of the problem is also presented. Computational studies are performed to check the performance of the proposed models.