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

models where transport cost is fixed with respect to bundle size”. This leads us to the
second type of shipment size optimisation models.

(b) Modelswithtransportcostsdefinedasvehicle-vesselmovementcosts

The simplest model in which the optimum size of a shipment is determined with
respect to haulage distance, in the case where transport costs are specified as vehicle-
vessel moving costs, is the case of a single vehicle-vessel. Subject to the constraint
that the calculated optimal value of Q, given as Q*, does not exceed the total capacity
of the vehicle, the shipment size problem can be defined (Bunn 1982; Bacon 1984;
1992; 1993) as determining the shipment size Q which minimises:

m_r  ^mt_tv.,₁ I÷¹Q^cι                                     ma

TL Ci = Q (Si + di Vi ) + 2                                                        (4)

where vi represents the cost of moving the particular vehicle-vessel through a distance
of one mile. In other words, every time the vehicle is moved through a particular
distance dithe total transport costs incurred are given as vid_i, as described by Fig.2.
Once again, taking the first-order conditions we have:

and:

Observation of (6) suggests that in the case of a single vehicle-vessel, the optimised
shipment size is a positive function of distance. However, this result cannot yet inform
us concerning the question of the relationship between the optimum vehicle-vessel
size and the haulage distance, because it is limited to the case of a single vehicle-
vessel. Nor can this model throw any light on the observed structure of transport costs.

(c) TheArgument

The key argument of this paper is that it is possible to combine models of type (a) with
models of type (b) in order to provide analytical solutions to the problems outlined in
sections 1 and 2. In order to do this we must be able to overcome the problem of
indeterminacy generally faced by models of type (a), and to allow models of type (b)
to be extended to incorporate a more general description of transport costs which
allows for the possibility of choices between multiple vehicle-vessels. The first stage
of this analytical problem is to overcome the problem of indeterminacy in models of
type (a) by describing transport rates in terms of vehicle hauling costs, as in models of
type (b). In section 4 this will be done initially in the case of one vehicle-vessel. Then
in section 5 this principle will be extended to the case where the logistics or transport
planner has multiple vehicle-vessels to choose from. In section 6, this more general

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