Optimal ordering policy for complementary components with partial backordering and emergency replenishment under spectral risk measure

Abstract

A firm (assembler) faces random demand for a final product which is made up of multiple complementary components. Before demand is realized, the firm purchases the components via a regular channel. After demand realization, unsatisfied demand is allowed to be partially backordered in case of component shortages, where the firm is assumed to have an option to purchase the components via an emergency channel with a relatively higher unit cost. The firm needs to adopt an appropriate ordering policy to maximize the spectral risk measure of its profit. We formulate and transform the newsvendor problem into a concise optimization problem which can be further decomposed into two sub-problems. We provide optimality properties and show that the objective function of each sub-problem is separable, which enables us to determine the optimal order quantity of each component independently. We show that the optimal order quantity of each component decreases in the firm's level of risk-aversion. Numerical experiments are conducted to illustrate the effectiveness of our solution method and examine the impacts of lost sales and risk attitude on the optimal solutions.