A Stochastic Inventory Model for a Random Yield Supply Chain with Wholesale-Price and Shortage Penalty Contracts

Abstract

This paper analyzes an infinite horizon, single-product, continuous-time inventory model with supply and demand risks to evaluate the impact of coordinating a production policy between a distributor and a supplier. We consider a wholesale-price contract and a shortage penalty contract as a coordination mechanisms in an inventory replenishment system. The demand process is described by a Brownian motion with drift, and this inventory model can be formulated as an impulse control problem with uncertain replenishment quantities. We show that under some assumptions, there exist optimal ordering and production policies. We also provide some numerical examples to investigate the effect of these coordination mechanisms on the expected costs and the optimal policies. The computational experiments reveal that (i) the production quantity in decentralized case is higher than that in the centralized case, (ii) the centralized approach strategy results in the lower joint total cost as compared with independent decision approaches, and (iii) the shortage penalty contract has a beneficial effect on the total cost to the entire supply chain in decentralized system.