Chapter 2: Shipping Costs to the Far East

Hosford International, Inc. of Erie, Pennsylvania is an international freight forwarding company that provides services to firms that export and import products worldwide. The company assists its clients in preparing documentation such as letters of credit, which spell out the terms of payment, as well as in arranging the scheduling and transportation of freight shipments using the most cost-efficient methods of shipment.

Actual shipping costs will, of course, vary according to such factors as the mode of transportation, the distance over which the cargo must be shipped, and the actual freight line chosen to transport the cargo. Approximately half of the overseas shipments of Hosford International's clients are transported by air, while the remainder is transported by ship.

In addition, some ocean freight lines base their shipping fees on how much space (out of a standard-sized full container) is taken up by the cargo. A full container's capacity is generally 1800 cubic feet, or in the language of the trade, 45 "measures," where one "measure" is equal to 40 cubic feet. One particular ocean freight shipping company, Maersk Line, has quoted the following costs as of March 1994 for shipping machinery from Baltimore to Hong Kong:

$332 per measure (i.e., per 40 cubic feet) of cargo, or

$4690 for a full container of 45 measures (i.e., 1800 cubic feet)

A company with a small volume of machinery to ship might choose to pay the per-measure cost, but a company with a much larger freight volume could lower its average shipping costs per measure by renting a full container. For example, the average shipping cost per measure of cargo remains fixed at $332 up to the point where the cargo load is 14.13 measures ($4690/$332), but begins to decline thereafter, reaching a minimum of $104.22 per measure at a full load of 45 measures. Thus, for all cargo loads ranging from 14.13 measures up to a full load of 45 measures, the average shipping cost per measure of cargo is given by the equation



where Y is the average shipping cost in dollars per measure and X is the volume of cargo in measures (or fractions of measures).



For all cargo volumes over 14.13 measures, up to a full load, average shipping costs decline, but at a diminishing rate. The rate at which average shipping costs decline as the volume of cargo increases is given by the derivative of the function Y with respect to cargo volume X:



Such patterns in freight shipping costs have practical implications for a company that is in the process of shipping a final product overseas. Knowing the rate at which average shipping costs decline with cargo volume will help in making better financial decisions. For more information on freight forwarding see www.forwarders.com.

 

What Would You Do?

1. Suppose that a shipping line charges the following rates for shipping freight from Baltimore to London, England:

• $261 per measure of cargo
• $5079 per full container of 45 measures

(a) Formulate a general guideline for when to choose the per-measure cost or the full container cost, and justify with calculations.
(b) Construct a function that reflects the average shipping cost per measure for this situation, and sketch its graph on the appropriate domain.
(c) At which shipment level is it more beneficial in terms of cost to increase the shipment size by one measure at 25 measures or at 35 measures? Explain your reasoning.

2. Suppose you have more than enough cargo to fill one full load, but not enough to fill two loads. How would you use the cost functions to decide whether to make one shipment first or ship all of your goods at the same time?