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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 100 
The following 2 images present an expanded view for better clarity of the 
left and right halves of the preceding complete Excel model. The 1
st
image is the left side of the model and list all possible cutting 
combinations and the waste left-over from each. The 2
nd
image shown is 
the right side of the model with the green Decision Variables and the 
yellow 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 101 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 102 
Step 4 – List all Constraints
The light blue Constraint cells in the model the preceding image link to 
the light blue user-controlled inputs outside of the model in the following 
image. The user-controlled inputs represent the customer’s order as 
follows: 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 103 
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 104 
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: 
Note that the Decision Variables are Constrained to be integers because 
only whole numbers of garment rolls can be cut. The equality 
Constraints are the links between the number of garment rolls in the 
customer’s order and the model. Unconstrained variables are made 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 105 
nonnegative to ensure that there can be no negative numbers of rolls 
cut. 
There are still a few more Constraints not shown in the preceding image 
that are shown as follows by scrolling down the slider bar next to the 
Constraints: 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 106 
All equations on the Excel spreadsheet are linear (1
st
order) so we can 
use the Simplex LP (Linear Programming) Solver engine for this 
optimization problem. 
Step 3 shows the completed problem with Decision Variables that have 
been optimized by the Solver to maximize the Objective while staying 
within the problem’s Constraints. 
Answer Report
Part 1 
Note: 
 The Solver Result 
 How long Solver took to solve the problem 
 The Solver Engine that was used and the Solver Options settings 
 Where the Objective Cell was labeled in the Excel model for its 
name to appear as it does in Part 1 of the Answer Report 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 107 
Part 2 
 Note that the Variable Cells contain the Decision Variables 
 Note where the labels for each Decision Variable are placed in 
the Excel model so that the Decision Variable’s name will appear 
here in Part 2 of the Answer Report as it does 
 Note the type of variable  - Either Continuous or Integer (Integer, 
Binary, or Alldifferent) 
 Note the Before and After values of each Decision Variable 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 108 
Part 3 
 Note how each Constraint is labeled in the Excel model in order 
for the Constraint’s name to appear here in Part 3 of the Answer 
Report as it does 
 Note which Constraints are binding (had their limits hit) and which 
aren’t. 
 Note how much slack is still available in any Constraint that has 
not had its limit hit. 
 Note any Integer Constraints (Integer, Binary, Alldifferent) 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011 http://excelmasterseries.com/New_Manuals.php
Page 109 
Machine Selection Example
Selecting Machines to Optimally Fulfill an Order 
This Solver problem involves dividing a task among different machines 
to fulfill a customer order while minimizing total cost. Each machine 
varies in operating cost, production speed, and ability to perform 
different elements of the task. The correct combination of machines must 
be selected to fulfill individual customer orders and minimize the total 
cost of order fulfillment. 
The Problem
3 machines perform the same generic type of task; they all make 
bolts. Each machine varies in the variety of bolts that it can 
produce. Each machine also has a different operating cost and a 
different operating speed. The objective is to fulfill an individual 
customer order within a specified time limit while minimizing the 
total cost of fulfilling this order. 
500 minutes is the total time allowed to complete this entire order. 
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