1 - Chap 04

Chapter 4 - Linear Programming: Computer Solution

Excel Solver

2 - Chap 04

Computer Solution

• Early linear programming used lengthy manual mathematical solution (Linear Algebra and Matrix Algebra) procedure called the Simplex Method.

• Steps of the Simplex Method have been programmed in software packages designed for linear programming problems.

• Many such packages available currently.• Used extensively in business and government.• Text focuses on Excel Spreadsheets.

3 - Chap 04

Excel Spreadsheets

Excel Spreadsheet for Beaver Creek Pottery Company Example

4 - Chap 04

Excel Spreadsheets Excel Spreadsheet for Beaver Creek Pottery Company Example

Excel Model

5 - Chap 04

When formulating a linear programming problem on an Excel spread sheet:•Parameters are called Data Cells.• Decision variables are called Variable Cells.•Right hand sides are part of the Constraints.•The objective function is called the Target Cell.

6 - Chap 04

Excel Spreadsheets “Solver” Parameter ScreenLocation of the Objective function valueOptimization Type

Location of the Decision Variables

Location of Constraints

Press “Add” to add constraintsChoose Simplex LP

Check the box of non-negativity

7 - Chap 04

Excel Spreadsheets Adding Model Constraints

8 - Chap 04

Check the box if integer constraint is not required

9 - Chap 04

Excel Spreadsheets Solution Screen

10 - Chap 04

Excel Spreadsheets Answer Report

11 - Chap 04

Example Problem: Airplane Parts

Problem Statement • Two airplane parts: no.1 and no.2.• Three manufacturing stages: stamping, drilling, finishing.• Decision variables: x1 (number of part no.1 to produce)

x2 (number of part no.2 to produce)• Model: maximize Z = $650x1 + 910x2

subject to

4x1 + 7.5x2 105 (stamping,hr)

6.2x1 + 4.9x2 90 (drilling, hr)

9.1x1 + 4.1x2 110 (finishing, hr)

x1,x2 0

12 - Chap 04

Example Problem: Airplane Parts Excel Spreadsheet Solution

13 - Chap 04

Example Problem: Airplane Parts Excel Spreadsheet Solution

Excel Solver Exercise

14 - Chap 04

Use Solver to solve the following LPP model with 6 decision variables and 7 functional constraints. Minimize Z = 18x1 + 22x2 + 10x3 + 12x4 + 10x5 + 9x6

subject toConstraint 1 2x2 + 2x3 + 2x4 + 5x5 + 3x6 200Constraint 2 270x5 + 8x6 300Constraint 3 6x1 + 4x2 + 2x3 + 3x4+ x5 50Constraint 4 20x1 + 48x2 + 12x3 + 8x4+ 30x5 4000Constraint 5 3x1 + 4x2 + 5x3 + 6x4 + 7x5 + 2x6 200Constraint 6 5x1 + 2x2 + 3x3 + 4x4 120Constraint 7 90x1 + 110x2 + 100x3 + 90x4 + 75x5 + 35x6 4200Non-negative All xj 0 Integer All xj are integers

Excel Solver Exercise: Excel Spreadsheet

15 - Chap 04