WOOD 492 MODELLING FOR DECISION SUPPORT

Lecture 4-5

LP Formulation Example and Excel Solver

2

Last Class

• Introduction to Simplex Algorithm

• Solving LPs with the Excel Solver

Sept 12-14, 2012 Wood 492 - Saba Vahid

Wood 492 - Saba Vahid 3

Thursday Lab

• Harvest optimization from multiple blocks for log sales• Logs categorized by size and quality• Different distribution of logs in each block• Demand caps for each log quality group• Maximum harvest volumes enforced

Sept 12-14, 2012

Lab 1 Overview

Wood 492 - Saba Vahid 4

Sign RHS

<= 0CB1 Vol UB 2,000

Matrix format vs. Mathematical format

• each column represents a variable (basic decision variable or secondary ones)

• Each Row represents a constraint and is named accordingly• You should be able to write each row of the LP Matrix as a

constraint, using the “columns” as variables.

Sept 12-14, 2012

CB1 Vol UB 1

CB 1 CB 2 CB 3 SED_10 SED_15 . . .. . .

Sign RHS

<= 2,000

1 x CB1 + 0 x CB2 + … <= 2,000 CB1<= 2,000

CB 1 CB 2 CB 3 SED_10 SED_15 . . .. . .

2000 x CB1 + 0 x CB2 + … <= 0 2000 CB1<= 0

Wood 492 - Saba Vahid 5Sept 12-14, 2012

0

10

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50

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0 20 40 60 80

hu

tch

es p

rod

uce

d (

x2)

desks produced (x1)

wood

panel

f inish

Prof it

Feasible Region

Example 1 LP

Intersection of two binding constraints. Binding constraints are the ones that have reached the value on their RHS.

Wood 492 - Saba Vahid 6

Example: Lumber and Chip Production

Sept 12-14, 2012

TB 15000 m330% Pine70% Fir

$38/m3

TB28000 m350% Pine50% Fir

$40/m3

Mill Yard

Pine Logs (m3)

Fir Logs (m3)

0.275

0.235

Pine lumber (MBF)$245/MBF

Fir lumber (MBF)$280/MBF

Mill

Chips (bdu)$43/bdu

0.76

0.78

Lumber & Chip LP

Wood 492 - Saba Vahid 7

Next week

• More LP Modelling examples and concepts

Sept 12-14, 2012