On the risk-averse procurement strategy under unreliable supply

Abstract

This study investigates an effective procurement/inventory strategy for a risk-averse retailer facing unreliable supply and stochastic demand. By using an increasing and concave utility function to describe risk aversion, we construct a basic newsvendor (single-period) model and its multi-period extension. Both models are found to have unique solutions, as the optimized expected utility is strictly concave in initial inventory level. As a result, there is a unique optimal order quantity for the effective control of supply risk. For the single-period model, the optimal order quantity is derived in its analytical form. We then show by numerical analysis that the value of the optimized expected utility is a function of the initial inventory level when the retailer is risk-averse, becomes less sensitive to initial inventory level when the degree of risk aversion decreases, and is insensitive for the risk-neutral case. This finding suggests that in our setting the inventory holding matters only when the retailer is risk-averse. For the multi-period model, we propose a solution procedure using backward induction since a direct extension of the single-period solution is impossible. We also conduct a sensitivity analysis of demand and supply with the aim of giving some managerial suggestions for demand risk control and supplier selection