MELJUN CORTES - Operations Management 6th-a Lecture (MANAGEMENT SYSTEM)

8/9/2019 MELJUN CORTES - Operations Management 6th-a Lecture (MANAGEMENT SYSTEM)

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MELJUN CORTES,MBA,MPA,BSCS,ACSMELJUN CORTES,

MBA,MPA,BSCS,ACS

Operations Management

MELJUNELJUN

MELJUN CORTES,BSCS,ACS

Department of ICT

Faculty of Information

Technology


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MBA,MPA,BSCS,ACS

H

APTER

6s

LinearProgramming

MELJUNELJUN


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MBA,MPA,BSCS,ACS

Used to obtain optimal solutions toproblems that involve restrictions or

limitations, such as:

Materials Budgets

Labor

Machine time

Linear ProgrammingLinear Programming


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MBA,MPA,BSCS,ACS

Linear programming(LP) techniquesconsist of a sequence of steps that will lead

to an optimal solution to problems, in cases

where an optimum exists

Linear ProgrammingLinear Programming


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MBA,MPA,BSCS,ACS

Objective: the goal of an LP model is maximization orminimization

Decision variables: amounts of either inputs oroutputs

Feasible solution space: the set of all feasiblecombinations of decision variables as defined by the

constraints

Constraints: limitations that restrict the availablealternatives

Parameters: numerical values

Linear Programming ModelLinear Programming Model


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MBA,MPA,BSCS,ACS

Linearity: the impact of decision variables islinear in constraints and objective function

Divisibility: noninteger values of decision

variables are acceptable Certainty: values of parameters are known and

constant

Nonnegativity: negative values of decisionvariables are unacceptable

Linear Programming AssumptionsLinear Programming Assumptions


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MELJUN CORTES,MBA,MPA,BSCS,ACSMELJUN CORTES,MBA,MPA,BSCS,ACS

1. Set up objective function and constraintsin mathematical format

2. Plot the constraints

3. Identify the feasible solution space

4. Plot the objective function

5. Determine the optimum solution

Graphical Linear ProgrammingGraphical Linear Programming


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Objective - profitMaximize Z=60X

1+ 50X

2

Subject to

Assembly 4X1+ 10X

2


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Assembly Constraint

4X1 +10X2 = 100

0

2

4

6

8

10

12

0 2 4 6 8 10 12 14 16 18 20 22 24

Product X1

Produ

ctX2

Linear Programming ExampleLinear Programming Example

CO S SCS CSMELJUN CORTES

MBA MPA BSCS ACS


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Add Inspection Constraint

2X1 + 1X2 = 22

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18 20 22 24

Product X1

Produc

tX2

MELJUN CORTES MBA MPA BSCS ACSMELJUN CORTES

MBA MPA BSCS ACS


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Add Storage Constraint

3X1 + 3X2 = 39

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18 20 22 24

Product X1

Produc

tX2

AssemblyStorage

Inspection

Feasible solution space



MBA MPA BSCS ACS


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Add Profit Lines

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18 20 22 24

Product X1

Pro

ductX2

Z=300

Z=900

Z=600



MBA MPA BSCS ACS


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The intersection of inspection and storage Solve two equations in two unknowns

2X1 + 1X2 = 22

3X1 + 3X2 = 39

X1 = 9

X2 = 4Z = $740

SolutionSolution


MBA MPA BSCS ACS


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Redundant constraint: a constraint that doesnot form a unique boundary of the feasible

solution space

Binding constraint: a constraint that forms theoptimal corner point of the feasible solutionspace

ConstraintsConstraints


MBA MPA BSCS ACS


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Surplus: when the optimal values of decisionvariables are substituted into a greater than or equalto constraint and the resulting value exceeds theright side value

Slack: when the optimal values of decision variablesare substituted into a less than or equal to constraintand the resulting value is less than the right sidevalue

Slack and SurplusSlack and Surplus


MBA MPA BSCS ACS


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Simplex: a linear-programming algorithmthat can solve problems having more than

two decision variables

Simplex MethodSimplex Method


MBA MPA BSCS ACS


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Figure 6S.15

MS Excel Worksheet forMS Excel Worksheet forMicrocomputer ProblemMicrocomputer Problem

Biet tin gi chua, vao day coi di http://www.freewebtown.com/gaigoisaigon/


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Range of optimality: the range of values forwhich the solution quantities of the decision

variables remains the same

Range of feasibility: the range of values forthe fight-hand side of a constraint over which

the shadow price remains the same

Shadow prices: negative values indicatinghow much a one-unit decrease in the original

amount of a constraint would decrease the

final value of the objective function

Sensitivity AnalysisSensitivity Analysis



MELJUN CORTES - Operations Management 6th-a Lecture (MANAGEMENT SYSTEM)

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