A logistics cost function with explicit transport costs

With a view to construct a new framework to assess the benefits of freight transport improvements, an Economic Order Quantity model with uncertain lead time demand is equipped with detailed transport costs. The problem is to minimise total logistics cost by choosing shipment size, vehicle size and reorder point subject to constraints on vehicle size and annual transport capacity. An analytical solution in all variables except the reorder point is derived, reducing the cost minimisation problem to a well-behaved problem in one dimension only. Different parts of transport costs influence the solution differently: Some act like ordering costs, some like holding costs and some have no influence on the solution. The solution exhibits economies of scale at all levels of optimal shipment size. Examples with real data show that model calibration for an entire population of firms is feasible at the firm level, and that the model produces reasonable results.