Logistics scheduling to minimize the sum of total weighted inventory cost and transport cost

This paper studies the logistics scheduling problem in the context of a three-stage supply chain comprising a supplier, a manufacturer, and a customer. The supplier supplies raw materials (jobs) to the manufacturer, which processes them into finished products (processed jobs) and transports them to the customer. We analyze the problem using a batching and scheduling model involving both batch supply and batch delivery. The objective is to minimize the sum of the total weighted inventory cost and transport cost. The inventory cost is related to the job flow time, which is the time between the arrival of a job to the manufacturer and the time it is finished processing and leaves the manufacturer. The transport cost is related to the number of batches created. Four cases associated with batch supply and batch delivery, depending on the relative strengths of the arrival cost, inventory cost, and delivery cost are discussed in this paper. We show that all the cases are NP-hard when the number of batches has a constant upper bound, and give a fully polynomial-time approximation scheme for each case.