Abstract: This paper investigates the impact of service constraints on the retailer’s optimal ordering strategy under supply disruptions. Considering a single-period supply chain that consists of one supplier and one retailer, we first establish a non-binding profit function model and prove the existence of an optimal order quantity at which the retailer’s expected profit can achieve the optimal value. We then formulate the profit model with service constraints, i.e. fill rate and service level constraints, respectively. Through the analysis, we find that the expected value of the retailer’s profit is a convex function of the order quantity and there exists a unique order quantity that makes the retailer’s expected profit maximum under each service constraint. In numerical analysis we explain how the retailer can achieve the desired profit by changing the order quantity.
Keywords: Ordering strategy, supply disruption, service constraint, lagrange multiplier
