P. Tyler and M. Kitson (1987) “Geographical Variations in Transport Costs of
Manufacturing Firms in Great Britain” Urban Studies Vol.24 pp.61-73
Appendix A: Variable Port-Terminal Handling Costs
For analytical simplicity, we have so far ignored the question of handling costs which
are proportional to the size of the shipment, and have assumed a fixed port handling
cost Si which is independent of the size of the shipment. However, the existence of
any such costs can be incorporated into the model quite easily. For a single type of
good or mix of goods being moved by the shipper, it may be the larger the individual
shipment, the greater the number of units of labour required to load and unload a
vehicle-vessel in the terminal or port. Also, handling these larger shipments may incur
greater land costs and the labour costs involving in inventory handling operations. In
this case, the effect of these terminal-port handling costs due to larger shipments will
be included in our framework via a space-handling coefficient term si .7 On the
variable Q. Once again, assuming that the demand for material remains constant over
a time period, the total annual space costs incurred in holding inventory can be
expressed as siQi /2 where si is the logistics space-cost coefficient defined as
(McCann 1996; 1998):
bulk
Si = 2 × —гт— ratio × [r Ri + w Li ]
i weight ii
and where:
r = annual rent per square meter of warehouse/factory space
w = annual unit wage of a warehouse/materials-handling worker
Ri = area required to store one cubic meter of inventory of a particular product
Li = number of units of labour required to handle one cubic metre of inventory of a
particular product.
Meanwhile, any variations in port-handling costs which are due solely to the
characteristics of product being handled, will be reflected in variations in the values
Si and Si , depending on whether these costs are independent or dependent of the size
of shipment, respectively. In general, products which are fragile, perishable and/or
bulky will have high values of Si and Si . In order to account for the effects of these
costs on the optimum shipment size problem, it is simply necessary to also incorporate
Si Qi /2 into equation (7) and then continue the optimisation procedure as described in
section 6.
7It may be that in some circumstances, newer, larger ships actually incur lower absolute levels of port-
handling costs than some smaller ships. In our model, this will tend to reduce the value of the parameter
Si such that in some circumstances it may be that it tends towards being zero or even negative.
However, as Garrod and Miklius (1985) point out, the role of the inventory capital costs will ensure that
the optimum ship size is not infinitely large.
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