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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 120
Individual ratings from each salesperson are as follows:
A rating of 5 indicates maximum desirability. The lowest desirability
rating is a 1.
Use this information to determine the optimal assignment of sales
territories among the salespeople that will maximize cumulative
satisfaction among the entire sales force.
Problem Solving Steps
Step 1 – Determine the Objective
In this case, the objective is to maximize cumulative satisfaction among
the 4 salespeople. The Objective cell will contain the sum of the
satisfaction ratings that each salesperson had previously rated his or her
newly-assigned territory.
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 121
Step 2 – Determine the Decision Variables
We are trying to determine which territory to assign to each salesperson
in order to maximize cumulative satisfaction. The Decision Variables will
be binary variables having the values of only 1 or 0, which will indicate
whether or not a specific sales territory will be assigned to specific
salesperson.
The Decision Variables will be forced to be binary by using numerical
Constraints, not the built-in Binary Integer Constraint.
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 122
Step 3 – Build the Excel Equations That Combine
the Objective With All Decision Variables
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 123
Note that the green Decision Variables (cells C14 to F17) were forced to
be binary by Constraining their row totals (light blue cells G14 to G17)
and column totals (light blue cells C19 to F19) to 1. We did not in this
apply the built-in Binary Integer Constraint because of this.
How To Display Only the Satisfaction Rating Associated With Each
Salesperson’s Assigned Territory
Note the If-Then-Else statements in each of the cells in the preceding
image.
As shown above, Cell C25 contains:  =IF(C14=1,C5,” “). This If-Then-
Else statement translates to: If Cell C14 contains “1,” then copy the
contents of Cell C5 into Cell C25, else leave Cell C25 blank.
In this case, the If-Then-Else statements place the salesperson’s
desirability rating of that territory (Cell C5) into Cell C25 only if Solver
has assigned that territory to the salesperson (if Solver has assigned a
“1” in Cell C14).
If-Then-Else statements are some of the most useful tools in Excel. If
you create Excel models often, you should definitely master the If-Then-
Else statement.
The yellow Objective cell displays the combined level of employee
satisfaction and will be maximized. The Decision Variable cells are
binary and display whether or not the particular territory will be assign
the respective salesperson.
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 124
Step 4 – List all Constraints
Once again note that no Binary Constraint was used because the
Decision Variables were forced to be binary by setting row and column
totals to 1 using the Constraints in the preceding image.
These Constraints could be varied to allow more than 1 salesperson to
be assigned to any of the territories, or allow each salesperson to be
assigned more than 1 territory. Try varying the Constraints on the
downloadable Excel workbook containing this and all other examples in
this manual.
Step 5 – Test the Excel spreadsheet
Test the Excel spreadsheet completely before adding information to the
Solver dialogue box. Make sure that any changes to Decision Variables
produce the correct results in the Objective cell.
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 125
Step 6 – Insert All Data into the Solver Dialogue
Box
Input the Objective cell, Decision Variable cell, and all Constraints into
the Solver dialogue box as follows:
The Integer Constraints ensure that only a whole number of salespeople
occupy each territory. The equality Constraints ensure that every
salesperson gets assigned 1 unique territory. These equality Constraints
also ensure that the Decision Variables are binary.