Quantity discount pricing for container transportation services by shipping lines

Because transportation services provided by container lines to forwarders cannot be stored, they can be considered to be newsvendor‐type products. This paper discusses a method used to optimize container lines’ freight tariffs in order to maximize their expected profit by considering changes in order quantities made by forwarders responding to the price schemes suggested by the container lines. The container line freight tariff can be characterized by price‐break points, discounted freight rates, and penalties for unsold space. An analytic model has been designed that addresses all‐unit quantity discount schemes with single or multiple price‐break points. Some properties regarding the optimal solution are suggested and a procedure to find the optimal freight tariff is provided. Numerical examples are provided that illustrate the solution procedure and various numerical experiments have been done in order to analyze the effectiveness of the quantity discount scheme employing a penalty.