Modeling and solving the multi-period inventory routing problem with constant demand rates

The inventory routing problem (IRP) is one of the challenging optimization problems in supply chain logistics. It combines inventory control and vehicle routing optimization. The main purpose of the IRP is to determine optimal delivery times and quantities to be delivered to customers, as well as optimal vehicle routes to distribute these quantities. The IRP is an underlying logistical optimization problem for supply chains implementing vendor-managed inventory (VMI) policies, in which the supplier takes responsibility for the management of the customers' inventory. In this paper, we consider a multi-period inventory routing problem assuming constant demand rates (MP-CIRP). The proposed model is formulated as a linear mixed-integer program and solved with a Lagrangian relaxation method. The solution obtained by the Lagrangian relaxation method is then used to generate a close to optimal feasible solution of the MP-CIRP by solving a series of assignment problems. The numerical experiments carried out so far show that the proposed Lagrangian relaxation approach nds quite good solutions for the MP-CIRP and in reasonable computation times.