The value of integration of full container load, less than container load and air freight shipments in vendor–managed inventory systems

We address a long–haul transportation problem of delivering a set of products from a producer to a customer, where Full Container Load (FCL) shipments on one side and Less than Container Load (LCL) or Air Freight shipments on the other side are integrated. A Vendor-Managed Inventory (VMI) approach is used: a decision- maker has to find a periodic shipping policy that minimizes the sum of transportation cost and inventory cost, both at the producer and at the customer. This problem is defined at the tactical level implying that the initial inventory levels at the producer and at the customer are not data, but decision variables. For this problem we formulate a Mixed Integer Linear Programming model and prove its computational complexity. Furthermore, we introduce the concept of Value of Integration of FCL and LCL/Air Freight shipments and prove performance bounds to show that the integration of FCL and LCL/Air Freight shipments can lead to significant cost savings, both in the worst case and on average. Systematic computational experiments are finally carried out.