Adaptive stochastic lookahead policies for dynamic multi-period purchasing and inventory routing

We explore a problem faced by agri-food e-commerce platforms in purchasing different, perishable products and collecting them from multiple producers and delivering them to a single warehouse, aiming to maintain adequate inventory levels to meet current and future customer demand, while avoiding waste. Customer demand and suppliers' purchase prices and supply volumes are uncertain and revealed on a periodical basis. Every period, purchasing, inventory, and routing decisions are made to satisfy demand and to build inventory for future periods. For effective decisions integrating all three decision components and anticipating future developments, we propose a stochastic lookahead method that, in every period, samples future scenarios for demand, supply volumes, and prices. It then solves a two-stage stochastic program to obtain the decision for the current period. To make this approach computationally tractable, we reduce the routing decision in the two-stage program and use an approximate routing cost instead. Given the reduced decision, we then create the final decision via a conventional routing heuristic. We learn the routing cost approximation adaptively via repeated training simulations. In comprehensive experiments, we show that all three components, stochastic lookahead, routing cost approximation, and adaptive learning, are very effective individually, but especially in combination. We also provide a comprehensive analysis of the problem parameters and obtain valuable insights in problem and methodology.