End-of-Life Inventory Management Problem: Results and Insights

TL;DR

This paper models and analyzes an end-of-life inventory management problem, introducing a dynamic programming approach and martingale theory to optimize decisions involving ordering, usage, and outside sourcing, with significant managerial insights.

Contribution

It formulates a novel optimal stopping problem with multiple decisions for end-of-life inventory management and provides analytical, structural, and numerical insights into optimal policies.

Findings

High potential loss if flexibility is not exploited

Optimal stopping times depend on demand and inventory dynamics

Numerical results demonstrate the value of the proposed approach

Abstract

We consider a manufacturer who manages the end-of-life phase and takes one of the three actions at each period: (1) place an order, (2) use existing inventory, (3) stop holding inventory and use an outside/alternative source. Two examples of this source are discounts for a new generation product and delegating operations. Demand is described by a non-homogeneous Poisson process, and the decision to stop holding inventory is described by a stopping time. After formulating this problem as an optimal stopping problem with additional decisions and presenting its dynamic programming algorithm, we use martingale theory to facilitate the calculation of the value function. Moreover, we show analytical results to understand the additional difficulties of the problem solved, as well as structural results on optimal stopping times. Furthermore, we devise an expandable taxonomy and categorize the models in the literature. Analytical insights from the models as well as an extensive numerical analysis show the value of our approach. The results indicate that the loss can be high in case the manufacturer does not exploit flexibility in placing orders or use an outside source. Several managerial insights are obtained through numerical analysis as well as structural results to facilitate decision-making during the end-of-life horizon.