LTL Mode Building the Inventory Decision Model

In the academic literature, several authors have studied decision models that incorporate the explicit, discrete rate-discount structures like those of the LTL rate tariff we have explored earlier. In general, this approach involves the use of quantity breaks to represent the shipment weights at which the unit cost changes. Tersine and Barman (1991) provide a review of some earlier versions of this modeling work. More recently, Mutlu and C etinkaya (2010) extend previous work by ( etinkaya and Lee (2000) and Lee (1986), in which transportation cost is represented as a stepwise function by explicitly reflecting the lower per-unit rates for larger shipments. 

however, we note that, although Tyworth and Ruiz-Torres (2000) utilize a non-linear curve-fitting process to build the rate fimction, we will consider a computationally simpler linear regression approach. Since we wish to build an expression of the form 

Resulting power function estimate of LTL rates on OAK-ATL lane. 

Converting back to the form of expression (4.17) is also straightforward, requiring only that we compute which in this case gives 

This result gives the LTL rate as a function of shipment weight, and in terms of /cwt. Our goal, however, is to model the LTL rate as a function of the quantity shipped, stated in /unit. First, note that 

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