Description
Aluminum Company of Canada Limited (Alcan) was an integrated producer of aluminum products.
The Foil Mill produced aluminum foil of different widths for a variety of different end uses.
Space limitations required that a limited number of standard widths of aluminum foil be carried in stock from which customers’ orders were slit.
Low turnover on some standard widths and large scrap losses occurred when filling customers’ orders of certain widths.
Case Study on Operation Research
Click to edit Master subtitle style
Background
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Aluminum Company of Canada Limited (Alcan) was an integrated producer of aluminum products. The Foil Mill produced aluminum foil of different widths for a variety of different end uses. Space limitations required that a limited number of standard widths of aluminum foil be carried in stock from which customers’ orders were slit. Low turnover on some standard widths
Case Statement
Re-assessment of the current inventory policy in the Foil Mill of Aluminum Company of Canada Limited (Alcan)
Process
Separat or
Select coil Roll coil to from stock desired Customer Order Foil Mill in thickness & Slitter specifying finish width, gauge & surface was used to slit the coil to desired width § Slitter
§ §
Separator was used to slit and then separate coils which had been pack rolled in two layers. Rolling in two layers was done for thinner gauge orders to give sufficient strength to the foil for slitting.
Difficulties in Slitting Operation
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A minimum of 5 mm must be trimmed from each edge of the standard widths in order to guarantee clean edges. Two adjacent widths have tendency to interlock as they were being coiled. To break them apart required the use of a special tool & a sledge hammer which damages the outer edges of the foil. To overcome this, the core on which the foil was wound extended 2.5 mm on either side of the coil.
Selection of Standard Widths
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The customers could order any width, but some of possible widths had never been ordered. The number of different standard widths that could be held as inventory was constrained by space limitations. The Sheet Mill wanted the number of widths it produced kept to a minimum.
Scrap Loss
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Slitting multiple widths from wider standard widths resulted in less scrap than cutting a single width from a narrower standard width.
Scrap = (Standard Width – Customer Width) x Weight of Std. Width Roll Standard Width
Calculation of Scrap Loss
Standard Width Customer Width I 200 II III IV V 300 400 500 600 A 210 10 M M M M B 420 20 C 620 20 D 820 M M 20 M M F 1100 100 M M 100 M G 1300 100 100 100 M 100
210 –20 120
20 M M
200
M 120 20
Standard Width Customer I 200 Width II III IV V 300 400 500 600
A B C D E F 10/210 210 420 620 820 1100 1300 0.047610.047610.03225 0.090900.07692 M 9 9 8 9 3 0.285710.03225 0.07692 M M M 4 8 3 0.04761 0.07692 M M 0.02439 M 9 3 0.19354 0.09090 M M M M 8 9 0.03225 0.07692 M M M M 8 3
Calculation of Scrap Loss
Standard Width
Customer Width
A 210 95 M M M M 2000
B 420
C 620
D 820 M M 195 M M 8000
E 1100 1000 M M 1000 M 11000
F 1300 1000 1000 1000 M 1000 13000
I II III IV V
200 300 400 500 600
0.047619 x 190 194 Cij
1143 190 M M 4000 194 M 1161 194 6000
Cij
Assignment Problem
n n
n
Xij is defined as difference of ith standard width with jth customer width Cij is defined as the weight of width 210mm to the actual ith standard width being used for jth customer width Objective function is to minimize Z= Cij Xij subject to certain restrictions
Assignment Problem
Problem : Standard Width A = 210 B = 420 C = 620 D = 820 E = 1100 F = 1300
Customer Width I = 200 II = 300 III = 400 IV = 500 V = 600 VI = 0
Assignment Problem
Scrap loss Matrix
Standard Width Customer Width
A
95 M M M M 0
B
190 1143 190 M M 0
C
194 194 M 1161 194 0
D
M M 195 M M 0
E
F
I II III IV V VI
1000 1000 M M 1000 M 0 1000 1000 M 1000 0
Assignment Problem
Row Reduction
Standard Width Customer Width
A
0 M M M M 0
B
95 949 0 M M 0
C
99 0 M 161 0 0
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 806 810 M 806 0
I II III IV V VI
Assignment Problem
Row Reduction
Standard Width Customer Width
A
0 M M M M 0
B
95 949 0 M M 0
C
99 0 M 161 0 0
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 806 810 M 806 0
I II III IV V VI
Assignment Problem
Row Reduction
Standard Width Customer Width
A
0 M M M M 0
B
95 949 0 M M 0
C
99 0 M 161 0 0
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 806 810 M 806 0
I II III IV V VI
Assignment Problem
Row Reduction
Standard Width Customer Width
A
0 M M M M 0
B
95 949 0 M M 0
C
99 0 M 161 0 0
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 806 810 M 806 0
I II III IV V VI
Assignment Problem
Second Iteration
Standard Width Customer Width
A
0 M M M M 0
B
95 143 0 M M 0
C
905 0 M 967 0 806
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 0 810 M 806 0
I II III IV V VI
Assignment Problem
Standard Width Customer Width
A
0 M M M M 0
B
95 143 0 M M 0
C
905 0 M 967 0 806
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 0 810 M 0 0
I II III IV V VI
Assignment Problem
Final Assignment:
Standard Width Customer Width
A
0 M M M M 0
B
95 143 0 M M 0
C
905 0 M 967 0 806
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 0 810 M 0 0
I II III IV V VI
Assignment Problem
The assignments are:
Customer Width Standard Width Scrap (in Kg) 95 194 190 1000 1000 0 2479
I II III IV V VI
Total Scrap
A C B E F D
Verification using Tora Software
Input Data:
Output pdf
Conclusion
ü ü ü ü
ü
Lowest scrap value is achieved using Assignment Method Manual calculations are verified using Tora software Scrap Loss matrix can be modified based on forecast The above procedure sets a base for determining an appropriate inventory policy Further Tora or other OR software can be used to handle large amount of data
doc_913107734.pptx
Aluminum Company of Canada Limited (Alcan) was an integrated producer of aluminum products.
The Foil Mill produced aluminum foil of different widths for a variety of different end uses.
Space limitations required that a limited number of standard widths of aluminum foil be carried in stock from which customers’ orders were slit.
Low turnover on some standard widths and large scrap losses occurred when filling customers’ orders of certain widths.
Case Study on Operation Research
Click to edit Master subtitle style
Background
n
n
n
n
Aluminum Company of Canada Limited (Alcan) was an integrated producer of aluminum products. The Foil Mill produced aluminum foil of different widths for a variety of different end uses. Space limitations required that a limited number of standard widths of aluminum foil be carried in stock from which customers’ orders were slit. Low turnover on some standard widths
Case Statement
Re-assessment of the current inventory policy in the Foil Mill of Aluminum Company of Canada Limited (Alcan)
Process
Separat or
Select coil Roll coil to from stock desired Customer Order Foil Mill in thickness & Slitter specifying finish width, gauge & surface was used to slit the coil to desired width § Slitter
§ §
Separator was used to slit and then separate coils which had been pack rolled in two layers. Rolling in two layers was done for thinner gauge orders to give sufficient strength to the foil for slitting.
Difficulties in Slitting Operation
n
n
n
A minimum of 5 mm must be trimmed from each edge of the standard widths in order to guarantee clean edges. Two adjacent widths have tendency to interlock as they were being coiled. To break them apart required the use of a special tool & a sledge hammer which damages the outer edges of the foil. To overcome this, the core on which the foil was wound extended 2.5 mm on either side of the coil.
Selection of Standard Widths
n
n
n
The customers could order any width, but some of possible widths had never been ordered. The number of different standard widths that could be held as inventory was constrained by space limitations. The Sheet Mill wanted the number of widths it produced kept to a minimum.
Scrap Loss
n
Slitting multiple widths from wider standard widths resulted in less scrap than cutting a single width from a narrower standard width.
Scrap = (Standard Width – Customer Width) x Weight of Std. Width Roll Standard Width
Calculation of Scrap Loss
Standard Width Customer Width I 200 II III IV V 300 400 500 600 A 210 10 M M M M B 420 20 C 620 20 D 820 M M 20 M M F 1100 100 M M 100 M G 1300 100 100 100 M 100
210 –20 120
20 M M
200
M 120 20
Standard Width Customer I 200 Width II III IV V 300 400 500 600
A B C D E F 10/210 210 420 620 820 1100 1300 0.047610.047610.03225 0.090900.07692 M 9 9 8 9 3 0.285710.03225 0.07692 M M M 4 8 3 0.04761 0.07692 M M 0.02439 M 9 3 0.19354 0.09090 M M M M 8 9 0.03225 0.07692 M M M M 8 3
Calculation of Scrap Loss
Standard Width
Customer Width
A 210 95 M M M M 2000
B 420
C 620
D 820 M M 195 M M 8000
E 1100 1000 M M 1000 M 11000
F 1300 1000 1000 1000 M 1000 13000
I II III IV V
200 300 400 500 600
0.047619 x 190 194 Cij
1143 190 M M 4000 194 M 1161 194 6000
Cij
Assignment Problem
n n
n
Xij is defined as difference of ith standard width with jth customer width Cij is defined as the weight of width 210mm to the actual ith standard width being used for jth customer width Objective function is to minimize Z= Cij Xij subject to certain restrictions
Assignment Problem
Problem : Standard Width A = 210 B = 420 C = 620 D = 820 E = 1100 F = 1300
Customer Width I = 200 II = 300 III = 400 IV = 500 V = 600 VI = 0
Assignment Problem
Scrap loss Matrix
Standard Width Customer Width
A
95 M M M M 0
B
190 1143 190 M M 0
C
194 194 M 1161 194 0
D
M M 195 M M 0
E
F
I II III IV V VI
1000 1000 M M 1000 M 0 1000 1000 M 1000 0
Assignment Problem
Row Reduction
Standard Width Customer Width
A
0 M M M M 0
B
95 949 0 M M 0
C
99 0 M 161 0 0
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 806 810 M 806 0
I II III IV V VI
Assignment Problem
Row Reduction
Standard Width Customer Width
A
0 M M M M 0
B
95 949 0 M M 0
C
99 0 M 161 0 0
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 806 810 M 806 0
I II III IV V VI
Assignment Problem
Row Reduction
Standard Width Customer Width
A
0 M M M M 0
B
95 949 0 M M 0
C
99 0 M 161 0 0
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 806 810 M 806 0
I II III IV V VI
Assignment Problem
Row Reduction
Standard Width Customer Width
A
0 M M M M 0
B
95 949 0 M M 0
C
99 0 M 161 0 0
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 806 810 M 806 0
I II III IV V VI
Assignment Problem
Second Iteration
Standard Width Customer Width
A
0 M M M M 0
B
95 143 0 M M 0
C
905 0 M 967 0 806
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 0 810 M 806 0
I II III IV V VI
Assignment Problem
Standard Width Customer Width
A
0 M M M M 0
B
95 143 0 M M 0
C
905 0 M 967 0 806
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 0 810 M 0 0
I II III IV V VI
Assignment Problem
Final Assignment:
Standard Width Customer Width
A
0 M M M M 0
B
95 143 0 M M 0
C
905 0 M 967 0 806
D
M M 5 M M 0
E
905 M M 0 M 0
F
905 0 810 M 0 0
I II III IV V VI
Assignment Problem
The assignments are:
Customer Width Standard Width Scrap (in Kg) 95 194 190 1000 1000 0 2479
I II III IV V VI
Total Scrap
A C B E F D
Verification using Tora Software
Input Data:
Output pdf
Conclusion
ü ü ü ü
ü
Lowest scrap value is achieved using Assignment Method Manual calculations are verified using Tora software Scrap Loss matrix can be modified based on forecast The above procedure sets a base for determining an appropriate inventory policy Further Tora or other OR software can be used to handle large amount of data
doc_913107734.pptx