WOOD 492 MODELLING FOR DECISION SUPPORT Lecture 7 LP Formulation Examples

Last Class LP assumptions 2Wood Saba VahidSept 19, 2012

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 <= Identify the coefficients for each variable 15 X1 + 1 X2 + 0 X3 – 1 X4 <= Insert the coefficient in the row corresponding to the constraint and in the column representing each variable 3Wood Saba VahidSept 19, 2012 Variablex1X2X3x4 Constraint151

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 Saba VahidSept 19, 2012

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 Saba VahidSept 19, 2012

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 Saba Vahid6 Lab 2 preview

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