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The document outlines the decision variables and constraints for a manufacturing problem. The goal is to minimize total costs by determining the optimal number of tools to produce through regular hours, overtime hours, and subcontracting. The costs are calculated based on the number of units of each tool produced at different stages. The constraints include meeting production needs for each stage, limiting materials used to available quantities, fulfilling sales contracts, and not exceeding available staff hours for each operation.

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41 views3 pages

Ques

The document outlines the decision variables and constraints for a manufacturing problem. The goal is to minimize total costs by determining the optimal number of tools to produce through regular hours, overtime hours, and subcontracting. The costs are calculated based on the number of units of each tool produced at different stages. The constraints include meeting production needs for each stage, limiting materials used to available quantities, fulfilling sales contracts, and not exceeding available staff hours for each operation.

Uploaded by

ebrahim
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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DECISION VARIABLES:

The variables in this problem would be the number of each kind of tools manufactured
from regular and overtime hours and subcontracted

Let the number of units undergoing stage 1, stage 2 and subcontracted be:

Regular Overtime
Units
Stage 1 Stage 2 Stage 1 Stage 2 Subcontracted
Trowel R1T R 2T O1t O 2t S1T

Hoe R1H R2H O1H O2H S1H

Rake R1R R2R O1R O2R S1R

Shovel R1S R 2S O1S O 2S S1S

OBJECTIVE:

The main objective is to minimize the overall cost.

Cost of regular stage 1 production:

This cost can be calculated by summing up the cost of each tool. Cost of each tool can
be calculated by the product of the number of units multiplied by the cost of tool for
stage 1.

CR1  6 R1T  10 R1H  8 R1R  10 R1S

Cost of regular stage 2 production:

This cost can be calculated in the similar manner as above:

CR 2  3R 2T  5R 2 H  4 R 2 R  5R 2 S

Cost of overtime stage 1 production:

CO1  6.2O1T  10.7O1H  8.6O1R  10.75O1S

Cost of overtime stage 2 production:

CO 2  3.1O 2T  5.4O 2 H  4.3O 2 R  5.5O2 S

Cost of Subcontracted units - stage 1

CS 1  7.2S1T  12S1H  9.6S1R  12S1S


The total cost becomes

C  CR1  CR 2  CO1  CO 2  CS 1

Constraints:

The first constraint is that the number of units of each tool in stage 1 and stage 2 should
be same.

R1T  O1T  S1T  R 2T  O 2T

Similarly, three more equations can be made for other tools, viz. Hoe, Rake and Shovel.

The second constraint is the sheet metal. The quantity of sheet metal used should be
less than or equal to the total available. Since, the metal is used in stage 1 only;
therefore, only stage 1 units are to be considered.

1.2  R1T  O1T   1.6( R1H  O1H )  2.2  R1R  O1R   1.5  R1S  O1S   10000

The third constraint is to meet the sales contracted sales. The production unit for each
unit should be more than or equal to the contracted sales. The total number of units
produced of each kind of tool can either be calculated from 1st stage or from 2nd stage.

R 2T  O 2T  1800
R 2 H  O 2 H  1400
R 2 R  O 2 R  1550
R 2S  O 2S  1700

The final constraint is to meet the hours available for each operation.

For Regular Stamping Hours


0.04 R1T  0.18 R1H  0.06 R1R  0.14 R1S  500
For Regular Drilling Hours
0.05R1T  0.14 R1H  0.12 R1S  400
For Regular Assembly Hours
0.06 R 2T  0.11R 2 H  0.05 R2 R  0.11R2 S  600
For Regular Finishing Hours
0.05R 2T  0.21R 2 H  0.02 R2 R  0.13R2 S  550
For Regular Packaging Hours
0.03R 2T  0.18R 2 H  0.05R 2 R  0.10 R 2S  500
Similar hour constrains exist for overtime production
0.04O1T  0.18O1H  0.06O1R  0.14O1S  100
0.05O1T  0.14O1H  0.12O1S  100
0.06O 2T  0.11O 2 H  0.05O 2 R  0.11O 2 S  100
0.05O 2T  0.21O 2 H  0.02O 2 R  0.13O 2 S  100
0.03O 2T  0.18O 2 H  0.05O 2 R  0.10O2 S  100

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