# lec3 - IE521 Advanced Optimization Lecture 3 Dr Zeliha Akca...

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IE521 Advanced Optimization Lecture 3 Dr. Zeliha Akc ¸a October 2011 1 / 14

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Reading I Bertsimas 1.5 I Bertsimas 2.1 - 2.4 2 / 14
Problem of the Week I A coal production company produces coal for 4 customers using 3 mines . I For each mine, the unit production cost, ash and sulfer contents are given as follows: Prod. Cost Cap. Ash Sulfur Mine 1 \$50 120 0.08 ton 0.05 ton Mine 2 \$55 100 0.06 ton 0.04 ton Mine 3 \$62 140 0.04 ton 0.03 ton I Demand of each customer: Customer 1 Customer 2 Customer 3 Customer 4 Demand 80 70 60 40 I Transportation cost from each mine to each customer: Customer 1 Customer 2 Customer 3 Customer 4 Mine 1 4 6 8 12 Mine 2 9 6 7 11 Mine 3 8 12 3 5 I Transported coal cannot include more than %6 ash and %3.5 sulfur. I How can the demand of each customer be satisﬁed with minimum cost? 3 / 14

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HW: LP Model I Decision variables? I Objective function? I Constraints? I Write the formulation and solve the model! 4 / 14
Recall: Deﬁnitions - 1 I If K i = 1 λ i x i = 0 is only satisﬁed with λ i = 0 , i = 1 , . . . , K , then x 1 , x 2 , ..., x K vectors are linearly independent . I Are x > 1 = ( 2 , 1 ) , x > 2 = ( 1 , 2 ) linearly independent?

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## This note was uploaded on 01/09/2012 for the course IE 521 taught by Professor Zelihaakça during the Fall '11 term at Fatih Üniversitesi.

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lec3 - IE521 Advanced Optimization Lecture 3 Dr Zeliha Akca...

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