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308 CHAPTER 7 TRANSPORTATION, ASSIGNMENT AND TRANSSHIPMENT PROBLEMS

MANAGEMENT SCIENCE IN ACTION

Heery International
eery International contracts with the State of the product of these coefficients with the assignment
H Tennessee and others for a variety of construc- variables.
tion projects including higher education facilities, With more construction projects than managers,
hotels and park facilities. At any particular time, it was necessary to consider a variation of the stand-
Heery typically has more than 100 ongoing projects. ard assignment problem involving multiple assign-
Each of these projects must be assigned a single ments. Of the two sets of constraints, one set
manager. With seven managers available, it means enforces the requirement that each project receive
that more than 700 ¼ 7(100) assignments are pos- one and only one manager. The other set of con-
sible. Assisted by an outside consultant, Heery Inter- straints limits the number of assignments each
national has developed a mathematical model for manager can accept by placing an upper bound
assigning construction managers to projects. on the total intensity that is acceptable over all
The assignment problem developed by Heery projects assigned.
uses 0/1 decision variables for each manager/proj- Heery International has implemented this assign-
ect pair, just as in the assignment problem dis- ment model with considerable success. According
cussed previously. The goal in assigning managers to Emory F. Redden, a Heery vice president, ‘The
is to balance the workload among managers and, at optimization model . . . has been very helpful for
the same time, to minimize travel cost from the assigning managers to projects . . . . We have been
manager’s home to the construction site. Thus, an satisfied with the assignments chosen at the Nash-
objective function coefficient for each possible ville office. . . . We look forward to using the model
assignment was developed that combined project in our Atlanta office and elsewhere in the Heery
intensity (a function of the size of the project budget) organization’.
with the travel distance from the manager’s home to
Based on Larry J. LeBlanc, Dale Randels, Jr., and T.K. Swann, ‘Heery
the construction site. The objective function calls for International’s Spreadsheet Optimization Model for Assigning Managers to
minimizing the sum over all possible assignments of Construction Projects’, Interfaces (November/December 2000): 95–106.

completed for three clients. Fowle’s assignment alternatives and estimated project
completion times in days are restated in Table 7.24.
The Hungarian method involves what is called matrix reduction. Subtracting and
adding appropriate values in the matrix yields an optimal solution to the assignment
problem. Three major steps are associated with the procedure. Step 1 involves row
and column reduction.

Step 1. Reduce the initial matrix by subtracting the smallest element in each row
from every element in that row. Then, using this row-reduced matrix,
subtract the smallest element in each column from every element in that
column.
So, we first reduce the matrix in Table 7.24 by subtracting the minimum value in
each row from each element in the row. With the minimum values of 9 for row 1, 5
for row 2 and 3 for row 3, the row-reduced matrix becomes:

1 2 3
Terry 1 6 0
Karl 4 13 0
Mustafa 3 11 0

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