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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 190 
Supplier Shipping/Purchasing Cost 
Minimize the Total Cost of Purchasing and 
Shipping From Multiple Suppliers 
This is very similar to a previous Solver problem in this manual called 
Shipping Cost Reduction except that now there is variation in the 
purchase price of the product. Product is being purchased and then 
shipped from multiple sources to multiple destinations. Shipping rates for 
each source/destination are different, as are purchase prices from each 
source. Each destination requires a different amount of product and the 
sources all have different amounts of product available. The Objective is 
to minimize the total cost of purchasing and shipping.  
The Problem
4 factories within 1 company obtain the same raw material Product 
A from 4 different outside suppliers. Each of the 4 suppliers 
provides a different per unit purchase price for Product A. Per unit 
shipping costs also vary greatly between each of the 4 suppliers 
and each of the 4 factories. Each of the 4 factories requires a 
different amount of Product A and each of the 4 suppliers has a 
different amount of Product A available. Determine the optimal 
amounts of Product A to purchase and ship between each supplier 
and each factory in order to minimize total purchase and shipping 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 191 
Specific information about the purchase price from each supplier 
and the shipping cost between each supplier and each factory is as 
Problem Solving Steps 
Step 1 – Determine the Objective 
In this case, the objective is to minimize the total cost of purchasing and 
shipping Product A. The cell that calculates this total cost is the 
Objective Cell. 
Step 2 – Determine the Decision Variables
We are trying to determine how many units of Product A to purchase 
from each supplier and ship to each factory in order to minimize the total 
cost. The Decision Variables are the numbers of units of Product A 
purchased from each supplier that will be shipped to each factory. 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 192 
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
Page 193 
The green Decision Variables (C20 to F23) shown in a previous image 
are number of units of Product A purchased from each supplier for each 
factory. The light blue Constraint cells (G20 to G23) on the right side of 
the model display the total number of units shipped to each factory.  
The light blue Constraint cells (C25 to F25) on the bottom of the model 
display the total number of units shipped from each supplier. Placing the 
Constraint cells here provides an efficient method to ensure that each 
factory receives the number of units it needs and that each supplier does 
not attempt to ship more units than they have available. 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 194 
The total number of units shipped from each supplier and the number of 
units shipped from each supplier to each factory are used to used to 
calculate total purchase and shipping costs from all suppliers. These 
calculations once again are shown as follows: 
The total cost of purchasing from all suppliers and the total cost of 
shipping from all suppliers is shown in the preceding image. These 2 
costs are added together to create the Total Cost, which is shown in the 
yellow Objective cell G38. 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 195 
Step 4 – List all Constraints
These light blue cells are user-controlled inputs and connect with the 
light blue Constraint cells in the Excel model. These user-controlled 
inputs determine how large each factory’s order is and how many units 
each supplier has available to ship. 
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Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 196 
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. 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 197 
Step 6 – Insert All Data into the Solver Dialogue 
Input the Objective cell, Decision Variable cell, and all Constraints into 
the Solver dialogue box as follows: 
Note that the Integer Constraint must be applied to Decision Variables to 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 198 
ensure that only whole numbers of units are shipped. Inequality 
Constraints are used to limit the factories’ order sizes and the suppliers’ 
product availability. 
We have to scroll the slider in the Constraints window down to see the 
rest of the Constraints. Here is the view of Constraints at the bottom of 
the list: 
Step-By-Step Optimization With Excel Solver              The Excel Statistical Master 
Copyright ©2011
Page 199 
All equations on the Excel spreadsheet are linear (1
order) so we can 
use the Simplex LP (Linear Programming) method for this optimization 
Step 3 shows the completed problem with Decision Variables that have 
been optimized by the Solver to minimize the Objective while staying 
within the problem’s Constraints. 
Answer Report
Part 1 
 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 
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