Integrated inventory model for three‐layer supply chains with stochastic demand

In this paper, we consider three‐stage inventory production system in three‐layer supply chain with equal‐sized shipments and incorporating raw material procurement. The vendor converts raw material, which is ordered from supplier, to finished product and delivers it to the buyer. We assume that the demand in buyer's side is stochastic and shortage is allowed. The objective is to minimise the expected total cost incurred by the vendor and the buyer. We derive expected total joint cost function and propose solution procedure to determine the optimal policy. Finally, we present numerical examples to illustrate the significance of cost reduction of the integrated model in comparison with independent model.