A multi-period inventory-routing problem is considered where a vendor serves multiple geographically dispersed customers who receive units of a single product from a depot, with adequate supply, using a capacitated vehicle. The class of problems arising from the combination of routing and inventory management decisions is known as the inventory routing problem (IRP). In this category of problems, the inventory routing problem with backorders (IRPB) deals with determining inventory levels when backorders are allowed. The aim is to minimise the total cost for the planning period, comprising of holding cost, transportation and backorder penalty cost while ensuring that inventory level capacity constraints are not violated. An Integer Programming model is first developed to provide an accurate description of the problem and then a Genetic Algorithm (GA) with suitably designed genetic operators is employed in order to obtain near optimal solutions. Computational results are presented to demonstrate the effectiveness of the proposed procedure.