A shortfall modelling-based solution approach for stochastic cyclic inventory routing

This paper studies the cyclic inventory routing problem with stochastic demand. A geographically dispersed set of retailers with stochastic demand rates is replenished from a single depot using vehicles with limited capacity. For an infinite horizon, a fixed-partition policy is adopted that partitions the retailers into subsets that are always replenished together in the same route being cyclically repeated. The objective is to provide cost efficient buffering of the demand variability within a cyclic distribution plan by providing carefully calibrated safety stock levels at the retailers. In doing so, the vehicle capacity needs to be taken into account, since cumulative demand during a cycle of the retailers in a route may exceed this capacity. In that case, shortfall remains at the retailer inventories because they are not fully replenished, which affects the service level (and cost balance) in the consecutive cycle(s). An approximate method is presented for determining the safety stock levels and is integrated into a state-of-the-art metaheuristic solution approach for cyclic inventory routing. An illustrative example and experiments on benchmark instances show (i) the effect of the vehicle capacity on the cost balance in a route, (ii) the accuracy of the approximation, and (iii) the added value of taking demand variability and shortfall due to limited vehicle capacity into account during the route design.