A multi-objective inventory routing problem with back-order and lateral trans-shipments

Motivated by real needs, we consider a multi-objective, multi-period inventory routing problem in a distribution system involving a supplier and several retailers, where each retailer’s demand can be fulfilled directly by a supplier and indirectly by other retailers through lateral trans-shipments. Back-order is allowed and a penalty cost is charged. The model aims to minimize total transportation and inventory costs as well as total number of required vehicles over a given planning horizon. The problem is formulated as a bi-objective mixed integer linear programming model and Pareto-optimal solutions are generated via the reservation Level driven Tchebycheff Procedure (RLTP). By using of RLTP, the decision maker is allowed to participate in the solution process more actively in an interactive manner, and can directly control objective values through the use of reservation levels and reduction of objective space. To demonstrate the usefulness of the proposed model a randomly generated test problem is also provided. The numerical results indicate that allowing lateral trans-shipments between retailers could lead to reduction of total costs.