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Shawn Kenny, Ph.D., P.Eng.

 Assistant Professor 

Faculty of Engineering and Applied ScienceMemorial University o f Newfoundland

spkenny@engr.mun.ca

ENGI 5708 Design of Civil

Engineering Systems

Lecture 15: Use of Microsoft Excel Solver forLinear Programming Models

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2 ENGI 5708 Civil Engineering Systems – Lecture 15© 2008 S. Kenny, Ph.D., P.Eng.

Mid-Term Quiz Update

Monday March 3

1100-1150am Material Coverage

Up to and including Lecture 10

Closed book quiz

Quiz Policy

Student Use of Electronic Devices in Classes• http://www.engr.mun.ca/policies/elec_devices.php

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3 ENGI 5708 Civil Engineering Systems – Lecture 15© 2008 S. Kenny, Ph.D., P.Eng.

Lecture 15 Objective

to introduce Microsoft Excel Solver andexamine how a linear programmingtransportation model can be solved

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How to Install Solver Utility

Go to Tools menu

 Add-Ins• Check Solver Add-in• Press OK

If Solver is not on the Add-Ins menu Reinstall data analysis pack

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Example 15-01

Solve Example 4-02 using Microsoft ExcelSolver 

Maximize Objective Function

Constraint Equations

1 22 3z x x= +

1 22 10x x hr day+ ≤ Production time

2

1 22 10x x m day+ ≤ Space available

1 4x units day≤ Demand variety A

Ref: Beasley (2007)

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Example 15-01 (cont.)

Objective Function 1 22 3z x x= +

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Example 15-01 (cont.)

Production Time Constraint Equation

10hr day≤1 2

2x x+

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Example 15-01 (cont.)

Go toTools

Solver 

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Example 15-01

(cont.) Go to Tools

Solver 

• Options

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Example 15-01

(cont.) Solve

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Example

15-01 (cont.) Solution and

Reporting

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Example 15-01 (cont.)

Microsoft Solver – Answer Report

Lists target cell and adjustable cells

• Original and final values

Constraints

• Information about the constraints

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Example 15-01 (cont.)

 Answer Report

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Example 15-01 (cont.)

Microsoft Solver – Sensitivity Report

Solution sensitivity

• Small changes in the formula in the Set Target Cell box in theSolver Parameters dialog box or the constraints

No report for models with integer constraints

For linear models• Reduced costs• Shadow prices

• Objective coefficient (with allowable increase and decrease)• Constraint right-hand side ranges.

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Example 15-01 (cont.)

Sensitivity Report

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Example 15-01

(cont.) Non-negativity

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Example 15-02

SolveExample 5-03

( ) 1 2 3 4$,000 3 9 6 12dayZ x x x= + + +)1 2 3 440 15 40 15 330   tx x x x week+ + + ≥

( )1 2 3 414 35 14 35 225   tx x x x week+ + + ≥

( )1 2, 5   daysx x week≤ ( )3 4, 2   daysx x week≤

Ref: ReVelle et al. (2004)

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Example 15-02 (cont.)

 Answer Report

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Example 15-02 (cont.)

Sensitivity Report

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References

Beasley (2007).http://people.brunel.ac.uk/~mastjjb/jeb/or/class2q.html

ReVelle, C.S., E.E. Whitlatch, Jr. and J.R.

Wright (2004). Civil and EnvironmentalSystems Engineering 2nd Edition, Pearson

Prentice Hall ISBN 0-13-047822-9