1. WOOD 492 MODELLING FOR DECISION SUPPORT Lecture 14 Sensitivity Analysis

2. Lab 4 review Harvest scheduling –3 stands with different ages and species –Different harvest regimes (based on the period of first cut, first cut can happen in any period) –Considering the total forest inventory (standing tree volume) –Even-flow restrictions –Beginning and ending inventory limits –Growth and yield volumes (how much trees grow in each period) objective : maximize the total harvest (over 8 decades) decision variable : total area (ha) in each stand to manage with each harvest regime Oct 5, 2012Wood 492 - Saba Vahid2 Lab 4 matrix

3. 100% rule in Sensitivity Analysis What would happen if we change the objective coefficients of two variables simultaneously? –For example, what would happen to the optimal solution if we change the price of fir-lumber and chips? Oct 5, 2012Wood 492 - Saba Vahid3 Change to $30 Change to $300

4. 100% rule in Sensitivity Analysis One was is to re-solve the LP Another way is to look at the sensitivity report Calculate the % change for each coefficient: –chips: change=$7, allowable decrease=191 → %change=7/191=3.6% –fir-lumber: change=$20, allowable increase=42.36 → %change=20/42.36=47.2% If sum of % changes ≤ 100% → the current optimal solution will stay optimal, otherwise we can’t be sure Oct 5, 2012Wood 492 - Saba Vahid4 Check the allowable increase or decrease for the objective coefficient

5. Using LPs for Forest Planning Forest resource management uses LPs in different ways, for example: –Allocating land to different purposes –Scheduling harvest to meet demand and supply constraints –Maximizing harvest revenues while maintaining environmental standards –Designing effective road networks to access forest stands while minimizing disturbance to natural habitat –Selecting the optimal investment projects that maximize the combined private and public welfare Oct 5, 2012Wood 492 - Saba Vahid5

6. Example: land Allocation An area of land, divided into three types Three land uses: Timber, Forage, and Recreation Maximum budget Costs and revenues for each land use option Some external requirements Objective: maximize net profits Oct 5, 2012Wood 492 - Saba Vahid6 Example 8

7. Next week Continue forest planning Midterm on Friday Oct 12 th Oct 5, 20127Wood 492 - Saba Vahid