1. WOOD 492 MODELLING FOR DECISION SUPPORT Lecture 18 Branch and Bound Algorithm

2. Review the big M method Used with indicator variables to activate or eliminate a constraint –May be slightly different for each situation, so we have to check each constraint separately for the case of indicator=1 or 0 For the sawing pattern selection in lab 6 –An either/or constraint Total logs processed with SP1 <= M. SP1_indicator Total logs processed with SP2 <= M. (1-SP1_indicator) –Instead of using one indicator variable, we can use two (one for each SP) and then make sure the sum of the two indicator variables is =1. Total logs processed with SP1 <= M. SP1_indicator Total logs processed with SP2 <= M. SP2_indicator SP1_indicator + SP2_indicator =1 Oct 19, 2012Wood 492 - Saba Vahid2

3. Oct 17, 2012 Example 10: Mixed Integer programming (MIP) Sort yard location problem –Transportation and upgrade costs, sort yard capacities, mill demands and camp supplies are given –Objective is to upgrade the sort yards (up to 3) that would minimize costs while meeting the supply and demand constraints CAMP SUPPLY MILL DEMAND C1 C2 C3 M1 M2 M3 M4 Y1Y2Y3 SORTYARD LOCATIONS 300015002000 1500 2000 3Wood 492 - Saba Vahid LP matrix

4. Next Class IP solution approach Oct 19, 20124Wood 492 - Saba Vahid