Mixed integer and heuristics model for the inventory routing problem in fuel delivery

This paper presents solution approaches for the multi-product multi-period Inventory Routing Problem (IRP) in fuel delivery. A homogeneous fleet of vehicles with compartments is used for fuel distribution from one depot to a set of petrol stations that have deterministic fuel consumption. The IRP consists of two mutually dependent sub-problems, those of inventory and routing, in a Vendor Management Inventory (VMI) environment in which suppliers determine the quantities and time periods of the deliveries. For solving the IRP, we propose a Mixed Integer Programming (MIP) model and a heuristic approach with and without fleet size costs, to observe the impact of these costs on the solutions that are obtained. The heuristics model is based on constructive heuristics with two Variable Neighborhood Descent (VND) search types: a local intra-period search and a large inter-period neighborhood search. Both of these approaches were tested on numerical examples for which the results, together with the performances of the proposed models, are presented. A combination of good computational time and good quality solutions suggests the use of the proposed heuristics on problems with realistic dimensions where the MIP model cannot find an optimal solution in a reasonable amount of time.