We consider a multi-period inventory-routing problem where a
vendor serves multiple geographically dispersed customers who receive units of a single product from a depot with adequate supply. The class of problems arising from the combination of distribution and inventory management decisions is perhaps the most striking example of this concept and is known as the inventory routing problem (IRP). In this category of problems, the inventory routing problem with backlogs (IRPwB) deals with determining inventory level, backlogging and vehicle routing decisions from a single depot to a set of n customers over a specific number of time periods, using a fleet of homogenous vehicles. The aim is to minimise the average daily cost for the planning period, while ensuring that inventory level capacity constraints are not violated. We first develop an Integer Programming model to provide an accurate description of the problem and in a second phase a Genetic Algorithm (GA) with suitably designed genetic operators, is employed in order to obtain near optimal solutions.