Optimal ordering quantity under stochastic time-dependent price and demand with a supply disruption: A solution based on the change of measure technique

Abstract

This paper presents a solution of a generalized newsvendor problem with supply disruption and dual sourcing, where the underlying product price and demand are correlated and evolve randomly over time. We contribute to the literature by employing a non-stationary model for demand, and proposing a novel solution methodology using the change of measure technique often applied for derivative pricing in the mathematical finance literature but not frequently considered in the management science and operations management literature. The application of this technique allows the non-linear expectation terms in the profit function, that are often computed numerically in the literature, to be determined analytically. This, in turn, leads to analytic solutions in special cases, and provides the foundations for a highly efficient numerical solution algorithm in general. A comparison against an alternative benchmark technique from the literature is provided to demonstrate the efficiency of our approach.