Optimal Vehicle Size, Haulage Length, and the Structure of Transport Costs

In order for the optimum vehicle-vessel size to increase with the haulage distance,
equation (12) must be positive. In other words:

a Ib [( Si + adi )J°
[⁽Si + adi)] ²[ⁱ⁽ci^{+ b}di)⁺ si]    ^[1 (^ci^{+ bd}i)^{+ s}iI

i.e.

a[I(ci+bdi)+si]>Ib[(Si+adi)]

which rearranges to give:

a    ISi

b   I ci+ si

The relationship between the optimised shipment size and the haulage distance
depends on the extent of the static economies of scale inherent in vehicle-vessel
shipment capacity. In order to understand the general conditions under which the
optimised vehicle-vessel size will increase or fall with the haulage distance, we can
once again discuss the two cases of significant economies of scale in vehicle-vessel
movement costs relative to carrying capacity, and the case of constant returns to scale
in this relationship.

If we experience significant static economies of vehicle-vessel movement costs
relative to carrying capacity, where a is highly positive and b is equal or close to zero
as in the Type (b) example outlined above, larger shipments will incur less than
proportionately increased fuel-time costs per shipment. In other words, as the
geographical haulage distance increases, the shipper can reduce the fuel-time costs per
unit of cargo shipped both by increasing the size of an individual shipment and by
reducing the shipment frequency. What is important here is that it is not the
geographical haulage distance which is important, but the economic batch-distance
travelled per unit of cargo hauled, where the batch distance is defined as the
geographical distance multiplied by the shipment frequency. Therefore, assuming that
the chosen vehicle-vessels are always at full load Q_i capacity, such that Q_i= Q_i^* , we
can see that the optimum size of a vehicle-vessel will increase with respect to haulage
distance if there are static economies of scale in vehicle-vessel movement costs
relative to vessel carrying capacities.

On the other hand, if vehicle-vessel movement costs experience more or less
constant returns to shipment size, i.e. a is equal or close to zero and b is highly
positive, as represented by the Type (a) model outlined above, bulk shipments will
incur fuel-time and stock inventory costs directly proportional to the shipment size.
Under these conditions, over any given geographical haulage distance the only
advantage in having bulk shipments is the reduction in total port-handling costs,
which are a multiple of the number of shipments per time period. However, as the
geographical haulage distance increases, the total fuel-time inventory costs will also
increase, for any given shipment size. The result of this is that the optimised shipment
size actually falls, and the optimised shipment frequency actually increases, in order to

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