Evaluating approximate solution models for the stochastic periodic inventory routing problem

Abstract This paper considers the stochastic periodic inventory routing problem (SPIRP) when the variability of the retailers’ demands are vague. Two solution approaches to minimize transportation and inventory costs, while guaranteeing that each retailer's demand is satisfied up to a pre-set service level, are investigated and compared. The first approach uses a safety stock-based deterministic model, where extra amounts of stock are kept at the retailers on top of the cycle inventory to cope with their demands’ variability. The second approach uses the sample average approximation (SAA). The key question that this paper addresses is how to set the parameters of the safety-stock based model so that it can generate good quality solutions (compared to the SAA benchmark) while it is also effective in terms of computation time and estimated costs. To address this question we compare the performance of two versions of the safety-stock based approach and of the benchmark SAA, for a set of appropriately generated instances. We develop an experimental design to generate relevant instances, use simulation to evaluate the behaviour of the models in different cases, and verify their effects on a selected set of performance indicators.