Module B: Linear Programming

Linear Programming (LP) A mathematical technique designed to help operations managers plan and make decisions necessary to allocate resources Minimizing (cost) or maximizing (profit)

Elements of LP Problems Objective Function – what you want to maximize or minimize Profit or cost Constraints – things that restrict your ability to meet your objective Production capacity, labour time, amount of materials, money Alternative course of action Must be several ways to allocate resources, etc Can be expressed as a mathematical problem

Example LP Problem - Glickman Glickman Electronics Two products to manufacture: x-pod and BlueBerry How many units of each should be produced for the highest profit? X-pod BlueBerry Available Electronics 4 hours 3 hours 240 hours Assembly 2 hours 1 hour 100 hours Profit/unit $7 $5

Example LP model - Glickman First, declare variables Let x1 = Number of x-pods to be produced Let x2 = Number of BlueBerrys to be produced Second, present objective function Maximize Profit = $7x1 + $5x2 Third, model the constraints 4x1 + 3x2 <= 240 2x1 + 1x2 <= 100 x1, x2 >= 0 I personally would use “x” and “y” instead… Cost per unit * number of units Time to produce one unit * number of units cant be greater than time available Cant produce a negative number of units

LP Issues Graphing LP Problems with more than two/three variables Nope Just use excel to solve Do all problems have solutions? (ie no feasible region?) No May have to revisit constraints (ie add more resources, capacity, etc)