1. WOOD 492 MODELLING FOR DECISION SUPPORT Lecture 7 LP Formulation Examples

2. Last Class LP assumptions 2Wood 492 - Saba VahidSept 19, 2012

3. Review: converting equations to matrix form 1.Write the equation with the variables and the appropriate sign (=, ) –e.g. we have a problem with 4 variables (X1 to X4) and a constraint like the following: 15 X1 + X2 – X4 <= 100 2.Identify the coefficients for each variable 15 X1 + 1 X2 + 0 X3 – 1 X4 <= 100 3.Insert the coefficient in the row corresponding to the constraint and in the column representing each variable 3Wood 492 - Saba VahidSept 19, 2012 Variablex1X2X3x4 Constraint151

4. Example: US Steel Company Shipping iron ore from the mines, through the storage facilities to the steel plant These types of LP problems are called “transportation” problems 4Wood 492 - Saba VahidSept 19, 2012

5. Example: Cut-Fill areas What is our objective? –Minimize total iron ore transportation costs ($) per month What are our decision variables? –How much ore (tons) to transfer on each route (from mines to storage facilities and then to the plant) each month What are our constraints? –The monthly production capacity of mines (tons) –The monthly demand of the steel plant (tons) –The monthly capacity of the shipping routes (tons) Naming our variables (common in transportation problems): –M1S1: volume of ore (tons) transferred from M1 to S1 per month –S1P: volume of ore (tons) transferred from S1 to steel plant per month US Steel Example 5Wood 492 - Saba VahidSept 19, 2012

6. Lab 2 Preview Three sawmills Three timber harvesting areas One private log source Plan for the next 30 days Maximize profits Supply and demand constraints Sept 19, 2012Wood 492 - Saba Vahid6 Lab 2 preview

7. Next Class More formulation examples Review of the lab Quiz 7Wood 492 - Saba VahidSept 19, 2012