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312 CHAPTER 7 TRANSPORTATION, ASSIGNMENT AND TRANSSHIPMENT PROBLEMS

Table 7.26 Estimated Project Completion Time (Days) for the Fowle Assignment
Problem with a Dummy Client
Client
Dummy client
Project Leader 1 2 3 D
Terry 10 15 9 0
Karl 9 18 5 0
Mustafa 6 14 3 0
Helen 8 16 6 0

What project completion time estimates should we show in this new dummy
column? The dummy client assignment will not actually take place, which means
that a zero project completion time for all project leaders seems logical. Table 7.26
shows the Fowle assignment problem with a dummy client, labelled D.
Note that if we had considered the case of four new clients and only three project
leaders, we would have had to add a dummy row (dummy project leader) in order to
apply the Hungarian method. The client receiving the dummy leader would not
actually be assigned a project leader immediately and would have to wait until one
becomes available. To obtain a problem form compatible with the solution algo-
rithm, adding several dummy rows or dummy columns, but never both, may be
necessary.
Maximization Objective To illustrate how maximization assignment problems can
be handled, let us consider the problem facing management of Salisbury Discounts
which has just leased a new store and is attempting to determine where various
departments should be located within the store. The store manager has four
locations that have not yet been assigned a department and is considering five
departments that might occupy the four locations. The departments under
consideration are shoes, toys, auto parts, housewares and DVDs. After a careful
study of the layout of the remainder of the store, the store manager has made
estimates of the expected daily profit for each department in each location. These
estimates are presented in Table 7.27.
This assignment problem requires a maximization objective. However, the prob-
lem also involves more rows than columns. So, we must first add a dummy column,
corresponding to a dummy or fictitious location, in order to apply the Hungarian

Table 7.27 Estimated Daily Profit (E1000s) for Each Department-Location
Combination

Location
Department 1 2 3 4
Shoe 10 6 12 8
Toy 15 18 5 11
Auto parts 17 10 13 16
Housewares 14 12 13 10
DVDs 14 16 6 12

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