Maximizing the survival probability in a cash flow inventory problem with a joint service level constraint

Abstract

This paper investigates a multi-period stochastic cash flow inventory problem with the aim of maximizing the long-term survival probability, which may be the objective of some retailers especially in periods of economic distress. Demand in each period is stochastic and can be non-stationary. In order to avoid too many lost sales under this objective, we introduce a joint chance constraint requiring the probability of no stockouts during the planning horizon to be higher than a specified service level. We develop a scenario-based model and a sample average approximation (SAA) model to solve the problem. A statistical upper bound on the survival probability based on SAA is provided and we discuss upper and lower bounds for the problem based on stochastic dynamic programming. We also propose a rolling horizon approach with service rate updating to test the out-of-sample performance of the two stochastic models and solve problems with long planning horizons. We test the two methods in large numerical tests and find that the rolling horizon approach together with the stochastic models can solve realistically sized problems in reasonable time.