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Zahra_Mohaghegh_Jan22_module 3_EMSE102-202

Zahra_Mohaghegh_Jan22_module 3_EMSE102-202 - Engineering...

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Engineering Management & Systems Engineering The George Washington University EMSE 102 EMSE 102 - - 202 202 Survey of Operations Research Methods Survey of Operations Research Methods Zahra Mohaghegh [email protected] Post-Doctoral Research Associate Center For Risk and Reliability University of Maryland January22, 2008 Module_3
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Engineering Management & Systems Engineering The George Washington University Chapter (3) Chapter (3) Introduction to Linear Programming: Modeling Practices CREDITS: PARTS OF THIS LECTURE HAVE BEEN DEVELOPED BY PROFESSORS ABELEDO AND CAMPOS-NONEZ
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Engineering Management & Systems Engineering The George Washington University Linear Programming Models Linear Programming Models The Diet Problem Shift Scheduling Blending Problems: Oil Blending
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Engineering Management & Systems Engineering The George Washington University Diet Problem: Low Cost Satisfying Diet Diet Problem: Low Cost Satisfying Diet We want to buy the week’s food. We want to guarantee that 100% of the recommended vitamin intakes are covered at a minimum cost. cost / packet name code $2.49 turkey T $1.99 spaghetti S $1.99 meat loaf ML $1.89 macaroni MC $2.89 ham H $2.29 fish F $2.59 chicken CK $3.19 beef B
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Engineering Management & Systems Engineering The George Washington University Vitamin Contents Vitamin Contents The percentage of the daily requirements contained in each package 10 15 20 60 Turkey 15 25 50 25 Spaghetti 15 15 30 70 Meat Loaf 15 15 35 15 Macaroni 10 35 40 40 Ham 10 15 10 8 Fish 20 20 0 8 Chicken 15 10 20 60 Beef B2 B1 C A
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Engineering Management & Systems Engineering The George Washington University Formulate! Formulate! Quantities under our control? Quantities not under our control? Objective? Constraints?
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Engineering Management & Systems Engineering The George Washington University Decision Variables Decision Variables We need to decide how many packets of frozen food of each type to buy. We can define a variable for each type of food as follows here i =B,CK,F,H,MC,ML,S, and T. x i = Number of packages if frozen food of type i
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Engineering Management & Systems Engineering The George Washington University Formulation Formulation The objective is easy to write, since the cost of the diet is the sum of the costs of individual packages: min 3 . 19 x B + 2 . 59 x CK + 2 . 29 x F + 2 . 89 x H + 1 . 89 x MC + 1 . 99 x ML + 1 . 99 x S + 2 . 49 x T
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Engineering Management & Systems Engineering The George Washington University How much Vitamin A is being consumed? How much Vitamin A is being consumed? Given the variables x i , we can compute the Vitamin A contents of the diet as obtained by multiplying the percentage of the daily requirements contained in each package and their quantity. To cover 7 days, we need to satisfy 60 x B + 8 x CK + 8 x F + 40 x H + 15 x MC + 70 x ML + 25 x S + 60 x T 60 x B + 8 x CK + 8 x F + 40 x H + 15 x MC + 70 x ML + 25 x S + 60 x T 700
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Engineering Management & Systems Engineering The George Washington University
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