Optimizing Shipment Size with Variable Transit Time and Random Transportation Capacity in Outsourcing Transportation Service

It is considered that Random transportation capacity of the third party logistics provider and variable transit time, and study analytically the implication of a controlled transit time and a random transportation capacity on the optimal shipping strategy. After formulating the general model, the optimal shipment size and transit time between a origin and a destination have been developed to achieve the logistics cost minimization. Particularly, we have shown that the expected total cost is a unimodal function and quasi-convex in the shipment size. A numerical example is given to demonstrate the effectiveness of the proposed model and perform the sensitivity analysis. Some useful observations are made from the sensitivity analysis.