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
X-pod
BlueBerry
Available
Electronics
4 hours
3 hours
240 hours
Assembly
2 hours
1 hour
100 hours
Profit/unit
$7
$5
• How many units of each should be produced for the highest profit?
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
I personally would use
“x” and “y” instead…
Cost per unit * number
of units
• Third, model the constraints
• 4x1 + 3x2 <= 240
• 2x1 + 1x2 <= 100
• x1, x2 >= 0
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)