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324 CHAPTER 7 TRANSPORTATION, ASSIGNMENT AND TRANSSHIPMENT PROBLEMS

Figure 7.13 Excel Solution for the Contois Carpets Problem

Objective Function Value = 5150.000

Variable Value Reduced Costs
EXCEL file
-------------- --------------- -----------------
Contois X15 600.000 0.000
X26 300.000 0.000
X37 400.000 0.000
X48 400.000 0.000
X56 200.000 0.000
X67 0.000 2.250
X78 0.000 0.000

We used Excel to solve the Contois Carpets problem. Figure 7.13 shows the
results: Contois Carpets should manufacture 600 square metres of carpet in
quarter 1, 300 square metres in quarter 2, 400 square metres in quarter 3
and 400 square metres in quarter 4. Note also that 200 square metres will be
carried over from quarter 1 to quarter 2. The total production and inventory cost
is E5150.

NOTES AND COMMENTS

1 Often the same problem can be modelled in where a gain or a loss occurs as an arc is
different ways. In this section we modelled the traversed. The amount entering the destination
Contois Carpets problem as a transshipment node may be greater or smaller than the amount
problem. It also can be modelled as a leaving the origin node. For instance, if cash is
transportation problem. In Problem 18 at the end of the commodity flowing across an arc, the cash
the chapter, we ask you to develop such a model. earns interest from one period to the next. Thus,
2 In the network model we developed for the the amount of cash entering the next period is
transshipment problem, the amount leaving the greater than the amount leaving the previous
starting node for an arc is always equal to the period by the amount of interest earned.
amount entering the ending node for that arc. An Networks with gains or losses are treated in more
extension of such a network model is the case advanced texts on network flow programming.

Summary

l In this chapter we introduced transportation, assignment and transshipment problems.
l All three types of problems belong to the special category of linear programmes called network flow
problems. The network model of a transportation problem consists of nodes representing a set of
origins and a set of destinations. In the basic model, an arc is used to represent the route from each
origin to each destination. Each origin has a supply and each destination has a demand. The problem
is to determine the optimal amount to ship from each origin to each destination.

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