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Abstract
Practical considerations often necessitate using approximated, rather than actual, freight rates in logistics models. This research analyzed the accuracy of five continuous freight rate functions used to model freight rates: (1) a constant, (2) a proportional, (3) an adjusted inverse, (4) an exponential, and (5) a logarithmic.
Two types of problems were considered in this randomized experiment: (1) freight rate function and (2) inventory-theoretic. First, the best-fit parameters for each freight rate function were determined in the freight rate function problems. Best-fit parameters minimized the mean square difference between actual and approximated freight rates for a given combination of route, class, and discount. Second, the mean of each parameter was used in its respective function to approximate freight rates. Third, a regression equation was developed to predict the parameter value for each function. Each predicted parameter value was used in its respective function to approximate freight rates. Actual less-than-truckload and truckload freight rates were obtained for 2,228 routes spanning the United States; for discounts of 20, 30, 40, and 50%; and for class 60, 65, 70, and 77.5.
In the inventory-theoretic problems, optimal order quantities and annual logistics costs were determined when using actual and approximated freight rates. Annual logistics cost included carrying, ordering, and transportation costs. Randomly generated variables in each inventory-theoretic problem included: route, class, discount, unit weight, annual requirements, carrying cost rate, unit value, and order cost.
This research found that the proportional function was the most accurate in the freight rate function problems, followed by the exponential, adjusted inverse, constant, and logarithmic functions, respectively. In the inventory-theoretic problems, the means of the annual logistics costs of the proportional and adjusted inverse functions never differed significantly from the mean optimal annual logistics cost determined with actual freight rates. In addition, a mean value of the parameter for the proportional function was determined. The proportional function using this mean value was accurate and produced estimates for annual logistics cost that did not differ significantly from actual logistics cost.
