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The document outlines a storage plan for minimizing total costs associated with shipping various types of gasoline to multiple storage tanks. It defines decision variables, an objective function to minimize costs, and constraints related to supply and demand for each gasoline type across different tanks. Additionally, it emphasizes the non-negativity requirement for the quantities shipped.

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Asim Awan
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11 views2 pages

Questions

The document outlines a storage plan for minimizing total costs associated with shipping various types of gasoline to multiple storage tanks. It defines decision variables, an objective function to minimize costs, and constraints related to supply and demand for each gasoline type across different tanks. Additionally, it emphasizes the non-negativity requirement for the quantities shipped.

Uploaded by

Asim Awan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Question 03:

We GOT GAS
Objective:

Minimizing total cost storage plan

Decision Variables:

x ij =Qty of gasoline shipped type ( i ) shipped ¿ storage tanks ( j )

Where:

i=Gasoline type= A , B , C , … , E

j=Storage tanks=1 ,2 , 3 , … ,8

Objective Function:

Min Z

¿ 1∗x 1 A +2∗x 2 A+ 2∗x 3 A +1∗x 4 A+ 4∗x 5 A+ 4∗x 6 A +5∗x 7 A +3∗x 8 A

+2∗x 1 B+ 3∗x 2 B+3∗x 3 B+3∗x 4 B+ 1∗x 5 B+ 4∗x 6 B+5∗x 7 B+2∗x 8 B

+3∗x 1 C+ 4∗x 2 C +1∗x 3C +2∗x 4 C+1∗x 5 C+ 4∗x 6C +5∗x 7 C +1∗x 8 C

+1∗x 1 D+1∗x 2 D+2∗x 3 D+2∗x 4 D+3∗x 5 D+4∗x 6 D+5∗x 7 D+2∗x 8 D

+1∗x 1E+1∗x 2E+1∗x 3E+1∗x 4E+1∗x 5E+1∗x 6E+5∗x 7E+5∗x 8 E

Constraints:

x 1 A+ x 2 A+ x 3 A+ x 4 A+ x 5 A + x 6 A+ x 7 A+ x 8 A=75000

x 1 B+ x 2 B+ x 3 B+ x 4 B+ x 5 B+ x 6 B+ x 7 B+ x 8 B=50 000

x 1 C+ x 2 C+ x 3C + x 4 C + x 5 C+ x 6 C+ x 7 C+ x 8 C=25 000

x 1 D+ x 2 D+ x 3 D+ x 4 D+ x 5 D+ x 6 D+ x 7 D+ x 8 D=8 0000

x 1E+ x 2E+ x 3E+ x 4E+ x 5E+ x 6E+ x 7E+ x 8 E=20 000


Demand:

x 1 A+ x 1 B+ x 1C + x 1 D+ x 1 E ≤25000

x 2 A+ x 2 B+ x 2C + x 2 D+ x 2 E ≤ 25 000

x 3 A+ x 3 B+ x 3 C+ x 3 D+ x 3 E ≤ 30 000

x 4 A+ x 4 B+ x 4 C + x 4 D+ x 4 E ≤ 60 000

x 5 A+ x 5 B+ x 5 C+ x 5 D+ x 5 E ≤80 000

x 6 A + x 6 B+ x 6C + x 6 D+ x 6 E ≤ 8 5000

x 7 A+ x 7 B+ x 7 C + x 7 D+ x 7 E ≤100 000

x 8 A+ x 8 B+ x 8 C + x 8 D+ x 8 E ≤50 000

Non-Negativity:

x ij ≥ 0

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