Integrated inventory-transportation problems with common carrier freight charges

Abstract

Inventory management models aim to find an optimal solution in terms of minimal costs by proposing decisions on delivery quantities using data on order quantity purchasing costs and holding costs. Goods have to be transported from the supplier to the customer and the transport (freight charge) cost can be included in various ways. Some production companies make use of a private carrier, offering transport services only for one or a few companies. Most companies make use of the services of a common carrier, which offers its transport service to whatever customer in need for transporting goods. A common carrier offers its transport services mostly in terms of less-than-truckload tariffs. Those tariffs depend on shipment sizes, but also on commodity class (representing ease of handling or risk of shipping) and on shipment distance. These additional costs make the integration of ordering and shipment decision problem more complex. In this paper, after the literature review, the optimal solutions are investigated for four different inventory model types with or without backlogging using various types of cost functions in combination with a number of freight charge models. For most combinations no analytical results are available but the optimal solutions can be easily found using spreadsheets based on our formulas. In this way the models are kept accessible to practitioners without the need for a complex software.