1. 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, 2012Wood 492 - Saba Vahid2

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, 2012Wood 492 - Saba Vahid3 Lab 1 Overview

4. 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, 2012Wood 492 - Saba Vahid4... 1 x CB1 + 0 x CB2 + …<= 2,000CB1<= 2,000... 2000 x CB1 + 0 x CB2 + …<= 02000 CB1<= 0

5. Sept 12-14, 2012Wood 492 - Saba Vahid5 Feasible Region Example 1 LP Intersection of two binding constraints. Binding constraints are the ones that have reached the value on their RHS.

6. Example: Lumber and Chip Production Sept 12-14, 2012Wood 492 - Saba Vahid6 TB 1 5000 m3 30% Pine 70% Fir $38/m3 TB2 8000 m3 50% Pine 50% 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

7. Next week More LP Modelling examples and concepts Sept 12-14, 2012Wood 492 - Saba Vahid7