Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

atch as it travels from origin to destination or, alternatively, as
engaging in a production run.. Job lots are usually discussed in the
operations research literature; 20 however, batch production functions
are reported in Smith. 21 Also, the linchaul process seems to provide
an example of the type of production for which volume of output (i.e.,
the aggregate output produced during one production run) should be dis-
tinguished from the rate of output. 22 A given volume linehaul movement
(e.g., 100,000 ton-miles) can occur at a variety of rates (e.g., dif-
ferent sized locomotives will pull the same cargo tonnage at different
speeds). It would be interesting to investigate the behavior of mar-
ginal costs when volume is varied at a given rate and vice versa. That
is, what effect does increasing length of haul have on costs given the
rate of output? And, in transporting a given amount of cargo a given
distance, what effect on costs results from varying the rate of output? 23
Once the linehaul process function has been obtained, one may in-
vestigate the various productivity relationships, isoquants, and re-
turns to scale. It is also possible to obtain cost curves for tHe
linehaul process. However, due to the complexity of the linehaul pro-
cess function, it may not be possible to obtain the functional form of
the expansion path and to derive therefrom functional forms for the
cost curves. Cost curves may be obtained from the process function
by holding input(s) constant at various levels and varying the other
input(s), calculating the total cost of each iteration. (In the cases
worked out below, there are ultimately only two inputs: one represent-;
ing the cargo vehicles and the other representing the motive vehicle.
Labor, fuel, etc. vary in known ways with these two inputs.) The
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