Heuristic approaches for the inventory-routing problem with backlogging

We study an inventory-routing problem in which multiperiod inventory holding, backlogging, and vehicle routing decisions are to be taken for a set of customers who receive units of a single item from a depot with infinite supply. We consider a case in which the demand at each customer is deterministic and relatively small compared to the vehicle capacity, and the customers are located closely such that a consolidated shipping strategy is appropriate. We develop constructive and improvement heuristics to obtain an approximate solution for this NP-hard problem and demonstrate their effectiveness through computational experiments.