Building A Rate Model LTL Service

One important point about the LTL rate tariff in Table 4.3 that is not immediately evident from looking at the numbers is that a shipper could actually benefit from over-declaring a shipment, or simply shipping more in an attempt to reduce the overall shipping cost. This stems from the tapering  

Origir Destir Minin Class iZIP lation ZIP lum Charge 94601 30303 203.59 (CA) (GA) LTL rate ( fcwt)  

Looking ahead, this type of quantity discount structure also appears in Chapter 5, where we discuss techniques for representing this all-unit-discount cost structure in mixed-integer programming models. 

We will consider the rate tariff table as a matrix R, whose constituent values Rij give the stated rate, in /cwt, for a shipment of class i corresponding to rate breakpoint . Let W be the shipment weight (lb), such that if w is the item weight (Ib/unit) and Q is the number of units shipped, then W = Q w. Thus, given a shipment weight W, we determine the appropriate rate breakpoint to be 

Applying the expressions developed earlier to the data presented in Example 4.6, we see that for an 8,500-lb shipment, the ap propriate rate breakpoint to consider in the LTL tariff given in Table 4.3 is / = 5, corresponding to the M5M rate, since Bj = 5,0001b and = 10,0001b. Thus, Rij = Rioo,5 = 68.20/cwt and = Rioo,6 = 55.92/cwt. Using expression (4.15), we obtain 

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