An inventory routing problem with soft time windows

Inventory routing problem (IRP) which is a problem integrated with inventory control and vehicle routing is a typical NP-hard problem, and also is the key of inventory and distribution coordinated optimization in the vendor managed inventory (VMI). An IRP of petrol secondary delivery system on the background of petroleum and petrochemical enterprise is investigated. Given a set of homogeneous vehicles with capacity constraint, which can be used for fuel distribution from one depot to a set of petrol stations that have deterministic fuel consumption, to minimize the total cost of the system, a mixed integer linear programming model of the inventory routing problem with soft time window (IRPSTW) is established. The model is solved by Lingo software. Simulations are done on an example. Based on solutions with different weight coefficients, we analyse the impact on the total cost by vehicle assignment cost and travel cost. The results of this paper provide a theoretical basis to solve the petrol secondary distribution problem of multiple terminal stations.