1. Operations Management
Module B – Linear Programming
PowerPoint presentation to accompany
Heizer/Render
Principles of Operations Management, 6e
Operations Management, 8e
© 2006 Prentice Hall, Inc.

2. Linear Programming (LP)
A mathematical technique to help plan and make decisions relative to the trade-offs necessary to allocate resources
Will find the minimum or maximum value of the objective
Guarantees the optimal solution to the model formulated

3. Another Definition for LP
A model consisting of linear relationships
representing a firm’s objective and resource constraints
LP is a mathematical modeling technique used to determine a level of operational activity in order to achieve an objective, subject to restrictions called constraints

4. Example LP Applications
Scheduling school buses to minimize total distance traveled
Allocating police patrol units to high crime areas in order to minimize response time to 911 calls
Scheduling tellers at banks so that needs are met during each hour of the day while minimizing the total cost of labor

5. Example LP Applications
Selecting the product mix in a factory to make best use of machine- and labor-hours available while maximizing the firm’s profit
Picking blends of raw materials in feed mills to produce finished feed combinations at minimum costs
Determining the distribution system that will minimize total shipping cost

6. Example LP Applications
Developing a production schedule that will satisfy future demands for a firm’s product and at the same time minimize total production and inventory costs
Allocating space for a tenant mix in a new shopping mall so as to maximize revenues to the leasing company

7. Requirements of an LP Problem
LP problems seek to maximize or minimize some quantity (usually profit or cost) expressed as an objective function
The presence of restrictions, or constraints, limits the degree to which we can pursue our objective

8. Requirements of an LP Problem
There must be alternative courses of action to choose from
The objective and constraints in linear programming problems must be expressed in terms of linear equations or inequalities

9. Common Elements to LP Decision variables Objective Function (OF)
Should completely describe the decisions to be made by the decision maker (DM)
Objective Function (OF)
DM wants to maximize or minimize some function of the decision variables
Constraints
Restrictions on resources such as time, money, labor, etc.

10. LP Assumptions OF and constraints must be linear Proportionality
Contribution of each decision variable is proportional to the value of the decision variable
Additivity
Contribution of any variable is independent of values of other decision variables

11. LP Assumptions, cont’d. Divisibility Certainty
Allow both integer and non-integer (real) numbers
Certainty
All coefficients are known with certainty
We are dealing with a deterministic world