1. Module B: Linear Programming

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

3. 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

4. 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

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

6. 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)