A More General Rate Model for LTL Service

In their model, Kay and Warsing (2009) use publicly available data— from the CzarLite tables discussed earlier, and from various government and industry sources—to develop an LTL rate model that is scaled to economic conditions, using the PPI for LTL services provided by the U.S. Bureau of Labor Statistics, similar to what was done earlier in the chapter 

Technically, although this is not pointed out in Kay and Warsing (2009), the proper rate estimate is actually the maximum of the value generated by expression (4.22) and the minimum charge specified in the LTL rate tariff. 

Let us compare the LTL rate functions that result from the approach we built earlier, based on the tariff-specified Class 100 rates for the OAK-ATL lane, and the fimctional estimate from Kay and Warsing (2009). Based on assumptions from public data, Kay and Warsing (2009) computed the average density for a Class 100 shipment to be s = 9.721b/ft3. As we indicated earlier, the distance from Oakland to Atlanta is d = 2463 mi. Since s and d are given, we can restate expression (4.22) as 

Recall that this function gives the (circa 2000) LTL rate in units of /ton-mi. Thus, we must multiply by 2463 mi, the length of the shipment lane for which we are estimating the LTL rate, to obtain the rate in /ton, and then by l/20ton/cwt to obtain the rate in /cwt, making the result consistent with the rate function we generate from the LTL rate tariff tables. Finally, since = W/2000, we obtain 

Comparing tariff-based LTL rate estimate to Kay-Warsing estimation function. 

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