Teaching Notes on Linear Programming

Teaching Notes on Linear Programming - 311 OPERATION...

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311 O PERATION  M ANAGEMENT I NFORMATION   AND  O PERATIONS  M ANAGEMENT M ARSHALL  S CHOOL   OF  B USINESS T EACHING  N OTES   ON  L INEAR  P ROGRAMMING 1. Introduction: The objective of this class is to present the linear programming model and a software (Excel) tool for  solving these problems.  This note also contains several examples that illustrate the broad domain of  applications in which the tool is useful. General Structure of Optimization Problem : What is an optimization problem? Loosely speaking, you have an optimization problem when you are trying to maximize (profits, cash on  hand, market share) or minimize (inventory levels, project completion time, costs) an   objective .   To  accomplish this you have to make some   decisions   (choose among alternative investment options,  determine production quantities, allocate money to alternate advertising outlets, etc).  However, there are  constraints  or restrictions on your decision choices (your ability to borrow and cash on hand constraints  the amount you can invest, your advertising budget constrains the amount you can allocate to different  advertising channels, machine capacities restrict the amount that you can produce).   Thus the key elements of an optimization problem are: (1) Objective, (2) Decision Variables and (3)  Constraints (or Restrictions) on the options available.  And the structure of an optimization problem is as  follows: Objective:   Maximize (or Minimize) an Objective  Subject to:  Constraints on the decision choices. A constraint is a restriction on the set of feasible (allowable) decisions.  We will study several problems in  which: Spending can not exceed budget Production can not exceed capacity Sales can not exceed demand P AGE  1   
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311 OPERATIONS MANAGEMENT We concentrate on Linear Programming that is a special case of constrained optimization.   The objective  of linear programming is to allocate limited resources to competing demands in an optimal way, that is, in  a way that either maximizes the profits or minimizes the costs.  Every linear programming problem has a  linear  objective function to either be maximized or minimized, and linear  constraints.   Graphically, a linear objective function (of two variables) or linear constraints are functions that can be  represented by straight lines.  In general, a linear function is a function in which each of the variables  appears as a separate term (together with a coefficient).  In a linear function two variables do not multiply,  or divide each other.  Linear functions have the following structure:  n n x a x a x a + + + ... 2
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This note was uploaded on 05/08/2008 for the course BUAD 311 taught by Professor Vaitsos during the Spring '07 term at USC.

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Teaching Notes on Linear Programming - 311 OPERATION...

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