production chain management chp 14
DESCRIPTION
Chapter 14 of Production Chain ManagementTRANSCRIPT
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Chapter 14 Supplement
Linear Programming Decision Analysis Tools and Techniques
Copyright 2011 John Wiley & Sons, Inc.
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Lecture OutlineModel FormulationGraphical Solution MethodLinear Programming Model SolutionSolving Linear Programming Problems with ExcelSensitivity Analysis
Copyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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Linear Programming (LP)A model consisting of linear relationships representing a firms objective and resource constraintsA mathematical modeling technique which determines a level of operational activity in order to achieve an objective, subject to restrictions called constraints
Copyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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Types of LPCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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Types of LPCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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Types of LPCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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LP Model FormulationDecision variablessymbols representing levels of activity of an operationObjective functionlinear relationship for the objective of an operationmost frequent business objective is to maximize profitmost frequent objective of individual operational units (such as a production or packaging department) is to minimize costConstraintlinear relationship representing a restriction on decision makingCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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LP Model FormulationMax/min z = c1x1 + c2x2 + ... + cnxn
subject to:a11x1 + a12x2 + ... + a1nxn (, =, ) b1a21x1 + a22x2 + ... + a2nxn (, =, ) b2: an1x1 + an2x2 + ... + annxn (, =, ) bn
xj = decision variablesbi = constraint levelscj = objective function coefficientsaij = constraint coefficientsCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*Constraints
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Highlands Craft StoreCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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Highlands Craft StoreCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*Maximize Z = $40 x1 + 50 x2
Subject tox1+2x240 hr(labor constraint)4x1+3x2120 lb(clay constraint)x1 , x20
Solution is x1 = 24 bowls x2 = 8 mugsRevenue = $1,360
Copyright 2011 John Wiley & Sons, Inc.
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Graphical Solution MethodPlot model constraint on a set of coordinates in a planeIdentify the feasible solution space on the graph where all constraints are satisfied simultaneouslyPlot objective function to find the point on boundary of this space that maximizes (or minimizes) value of objective function
Copyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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Graphical Solution MethodCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*4 x1 + 3 x2 120 lbx1 + 2 x2 40 hrArea common toboth constraints50 40 30 20 10 0 |10|60|50|20|30|40x1x2Objective function
Copyright 2011 John Wiley & Sons, Inc.
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Computing Optimal ValuesCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
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Extreme Corner PointsCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
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Objective FunctionCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*40 30 20 10 0
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Minimization ProblemCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
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Graphical SolutionCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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Simplex MethodMathematical procedure for solving LP problemsFollow a set of steps to reach optimal solutionSlack variables added to constraints to represent unused resources x1 + 2x2 + s1 = 40 hours of labor4x1 + 3x2 + s2 = 120 lb of claySurplus variables subtracted from constraints to represent excess above resource requirement. 2x1 + 4x2 16 is transformed into2x1 + 4x2 - s1 = 16Slack/surplus variables have a 0 coefficient in the objective functionZ = $40x1 + $50x2 + 0s1 + 0s2
Copyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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Copyright 2011 John Wiley & Sons, Inc.Supplement 14-*Solution Points With Slack Variables
Copyright 2011 John Wiley & Sons, Inc.
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Copyright 2011 John Wiley & Sons, Inc.Supplement 14-*Solution Points With Surplus Variables
Copyright 2011 John Wiley & Sons, Inc.
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Solving LP Problems with ExcelCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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Solving LP Problems with ExcelCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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LP SolutionCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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Sensitivity AnalysisCopyright 2011 John Wiley & Sons, Inc.Supplement 14-*
Copyright 2011 John Wiley & Sons, Inc.
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Copyright 2011 John Wiley & Sons, Inc.Supplement 14-*Sensitivity Range for Labor Hours
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Copyright 2011 John Wiley & Sons, Inc.Supplement 14-*Sensitivity Range for Profit for Bowls
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Copyright 2011 John Wiley & Sons, Inc.Supplement 14-*Copyright 2011 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in section 117 of the 1976 United States Copyright Act without express permission of the copyright owner is unlawful. Request for further information should be addressed to the Permission Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information herein.
Copyright 2011 John Wiley & Sons, Inc.
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