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A PRODUCTION AND INVENTORY APPLICATION 325

l The assignment model is a special case of the transportation model in which all supply and all
demand values are equal to 1. We represent each agent as an origin node and each task as a
destination node.
l The transshipment model is an extension of the transportation model to distribution problems
involving transfer points referred to as transshipment nodes. In this more general model, we allow arcs
between any pair of nodes. A variation of the transshipment problem allows for placing capacities on
the arcs. This variation, called the capacitated transshipment problem, is also known in the network
flow literature as the pure network problem.
l Each of these network flow problems can be modelled as a linear programme, and we solved each
using a general-purpose linear programming computer package.
l However, many practical applications of network flow models lead to large problems for which
general purpose linear programming codes are not efficient. The transportation Simplex method
was presented as an efficient special purpose solution procedure for solving transportation
problems. The procedure, and its extension to the transshipment problem, is hundreds of times
faster than the general purpose Simplex method for large transportation and transshipment
problems. The Hungarian method was presented as a special purpose solution procedure for
assignment problems.

WORKED EXAMPLE

n international aid organization routinely transports aid donations to different parts of the world. It is
A currently reviewing its transportation arrangements from its depots in Europe to its distribution centres in
Africa. The organization has three main European depots: Marseille, France; Portsmouth, UK; and Frankfurt,
Germany. Aid donations such as clothing and medicines are sent to these depots where volunteers pack them
into cases for transportation to the distribution centres. The organization estimates that the packing costs are
E2.95 per case in Marseille, E3.10 in Portsmouth and E3.05 in Frankfurt. For the next planning period, the
organization estimates that the Marseille depot can pack 400 cases per month, Portsmouth can pack 600
cases per month and Frankfurt 300 cases per month. There are three main regional distribution centres in
Africa: Capetown, Dar es Salaam and Nairobi. Each of the distribution centres in Africa has limited capacity to
receive the aid donations and then distribute them in their region so care must be taken not to send too many
cases to any one centre. The organization has calculated that each centre can cope with up to 400 cases each
month. The transportation costs vary depending which depot ships to which distribution centre and the costs
are shown below:

Cost per case E
From/To Capetown Dar es Salaam Nairobi
Marseille 1.45 1.60 1.40
Portsmouth 1.10 2.25 0.60
Frankfurt 1.20 1.20 1.80

The aid organization has asked for advice as to how it should organize its transportation of aid over
the coming months. In addition, the organization is keen to ensure that all the donations from Marseille
are used.

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