Exact and approximate algorithms for the inventory routing problem

Abstract

In this thesis we develop exact and approximate algorithms for the inventory routing problem (IRP). The inventory routing problem is one of deciding an optimal delivery policy for a set of customers through a given planning period. Customers can hold inventory and do not need deliveries every day. Deliveries are carried out by a fleet of homogeneous vehicles that must be routed to travel a minimum distance while visiting all customers scheduled for that day. Decisions concern which customers to be visited and how much to deliver to each of them must be taken. A new formulation for the IRP is presented as a mixed integer programming model. This new approach allows split deliveries so customers can receive the inventory through more than one vehicle during the same day. It also seeks periodic solutions through a given planning period. Although throughout our research the planning period is fixed, all algorithms presented in this thesis can be applied to any length of the planning period. Special cases for this problem are also considered and optimal polynomial algorithms have been developed. We develop four constructive heuristics for the inventory routing problem. These heuristics are based on a schedule-first route-second approach. First, a decision is made on which customers to visit each day, and how much inventory they should receive on each delivery. Then, a vehicle routing problem is solved for each day to perform the deliveries to the customers. Several experiments are carried out to compare the performance of each heuristic. An iterated local search method is then applied to the best solution obtained with these heuristics. The local search is based on node interchange and aims to reduce the number of routes per day as well as the total distance travelled. Extensive computational tests are carried out to assess the effectiveness of this local search procedure.

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