Joint cyclic production and delivery scheduling in a two-stage supply chain

We study an integrated production and distribution scheduling model in a two-stage supply chain consisting of one or more suppliers, a warehouse, and a customer. Each supplier produces a different product at a constant rate. There is a setup time and a setup cost per production run for each supplier. Completed products are first delivered from the suppliers to the warehouse and are then sent from the warehouse to the customer. The customer's demand for each product is constant over time. The problem is to find jointly a cyclic production schedule for each supplier, a cyclic delivery schedule from each supplier to the warehouse, and a cyclic delivery schedule from the warehouse to the customer so that the customer demand for each product is satisfied without backlog at the least total production, inventory and distribution cost. We consider two production and delivery scheduling policies. We derive either an exact or a heuristic solution algorithm for the problem under each policy. Heuristics are evaluated computationally. We also evaluate the value of the warehouse by comparing our model with a model that does not have the warehouse in the supply chain (i.e. the products are delivered directly from the suppliers to the customer). Various managerial insights based on an extensive set of computational tests are reported, including how the value of warehouse and the delivery frequency from the suppliers to the warehouse are influenced by various problem parameters including production rates of the suppliers, unit inventory costs, delivery costs, and the warehouse location.