Cal Poly Pomona IE 416 - Assignment #2 (3 pages)

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Assignment #2



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Assignment #2

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Pages:
3
School:
California State Polytechnic University, Pomona
Course:
Ie 416 - Operations Research I
Operations Research I Documents
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Patrick Reinagel IE 416 1 14 2019 Assignment 2 Pg 63 3 Chemical A B C Production Cost Times to Run Production Process Production Process 1 3 1 1 Production Process 2 1 1 0 4 1 P1 P2 Demand 10 5 3 Decision Variables 1 P1 Number of times to run Production Process 1 2 P1 Number of times to run Production Process 2 O F Zmin 4 P1 1 P2 S T 1 3 P1 P2 10 A must meet demand of at least 10 units each day 2 P1 P2 5 B must meet demand of at least 5 units each day 3 P1 3 C must meet demand of at least 3 units each day All variables 0 Equation Z 4P1 1P2 0 3P1 1P2 e1 a1 10 1P1 1P2 e2 a2 5 1P1 e3 a3 3 Matrix By Ms Siswanto below Patrick Reinagel IE 416 1 14 2019 First Simplex Tableau This should be updated as explained below but it is not expected from you Z 1 0 0 0 P1 4 3 1 1 P2 1 1 1 0 e1 0 1 0 0 e2 0 0 1 0 e3 0 0 0 1 a1 0 1 0 0 a2 0 0 1 0 a3 0 0 0 1 RHS 0 10 5 3 We should consider Big M method to handle artificial variables make sure they will not appear as BV in final solution and then apply modified Simplex method for minimization I did not cover these methods in class so they are not expected in exam Just for your general information I have added below how we use these methods Big M method Add Mai to OF then the standard form will look like Z 4P1 1P2 Ma1 Ma2 Ma3 0 Multiply each constraint that has ai and add to OF above we will have Z 5M 4 P1 2M 1 P2 Me1 Me2 Me3 18M Then new first Simplex tableau will be as Modified Simplex method for minimization There are two possible modifications I select the one that selects the most positive coefficient of OF for entering variable This will lead to selecting P1 Ratio testing will lead to select the last row Then perform ero until this iteration is over We will get the following tableau The next tableau will be Patrick Reinagel IE 416 1 14 2019


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