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Case Study on Operation Research
Background 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 Statement
Re-assessment of the current inventory policy in the Foil Mill of Aluminum Company of Canada Limited (Alcan)
Process
Slitter was used to slit the coil to desired width 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.
Select coil from stock in
Foil Mill
Roll coil to desired
thickness & finish
Separator
SlitterCustomer Order
specifying width, gauge &
surface
Difficulties in Slitting Operation 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 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
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
A B C D F G
210 420 620 820 1100 1300
I 200 10 20 20 M 100 100
II 300 M 120 20 M M 100
III 400 M 20 M 20 M 100
IV 500 M M 120 M 100 M
V 600 M M 20 M M 100
A B C D E F
210 420 620 820 1100 1300
I 200 0.047619 0.047619 0.032258 M 0.090909 0.076923
II 300 M 0.285714 0.032258 M M 0.076923
III 400 M 0.047619 M 0.02439 M 0.076923
IV 500 M M 0.193548 M 0.090909 M
V 600 M M 0.032258 M M 0.076923
Standard Width
Customer Width
Standard Width
Customer Width
210 – 200
10/210
Calculation of Scrap Loss
A B C D E F
210 420 620 820 1100 1300
I 200 95 190 194 M 1000 1000
II 300 M 1143 194 M M 1000
III 400 M 190 M 195 M 1000
IV 500 M M 1161 M 1000 M
V 600 M M 194 M M 1000
Cij 2000 4000 6000 8000 11000 13000
Standard Width
Customer Width0.047619 x
Cij
Assignment Problem
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 Customer WidthA = 210 I = 200B = 420 II = 300C = 620 III = 400D = 820 IV = 500E = 1100 V = 600F = 1300 VI = 0
Assignment Problem
I 95 190 194 M 1000 1000
II M 1143 194 M M 1000
III M 190 M 195 M 1000
IV M M 1161 M 1000 M
V M M 194 M M 1000
VI 0 0 0 0 0 0
Standard
WidthCustomer Width
A B C D E FScrap loss Matrix
Assignment Problem
I 0 95 99 M 905 905
II M 949 0 M M 806
III M 0 M 5 M 810
IV M M 161 M 0 M
V M M 0 M M 806
VI 0 0 0 0 0 0
Standard
WidthCustomer Width
A B C D E FRow Reduction
Assignment Problem
I 0 95 99 M 905 905
II M 949 0 M M 806
III M 0 M 5 M 810
IV M M 161 M 0 M
V M M 0 M M 806
VI 0 0 0 0 0 0
Standard
WidthCustomer Width
A B C D E FRow Reduction
Assignment Problem
I 0 95 99 M 905 905
II M 949 0 M M 806
III M 0 M 5 M 810
IV M M 161 M 0 M
V M M 0 M M 806
VI 0 0 0 0 0 0
Standard
WidthCustomer Width
A B C D E FRow Reduction
Assignment Problem
I 0 95 99 M 905 905
II M 949 0 M M 806
III M 0 M 5 M 810
IV M M 161 M 0 M
V M M 0 M M 806
VI 0 0 0 0 0 0
Standard
WidthCustomer Width
A B C D E FRow Reduction
Assignment Problem
I 0 95 905 M 905 905
II M 143 0 M M 0
III M 0 M 5 M 810
IV M M 967 M 0 M
V M M 0 M M 806
VI 0 0 806 0 0 0
Standard
WidthCustomer Width
A B C D E FSecond Iteration
Assignment Problem
I 0 95 905 M 905 905
II M 143 0 M M 0
III M 0 M 5 M 810
IV M M 967 M 0 M
V M M 0 M M 0
VI 0 0 806 0 0 0
Standard
WidthCustomer Width
A B C D E F
Assignment Problem
I 0 95 905 M 905 905
II M 143 0 M M 0
III M 0 M 5 M 810
IV M M 967 M 0 M
V M M 0 M M 0
VI 0 0 806 0 0 0
Standard
WidthCustomer Width
A B C D E FFinal Assignment:
Assignment Problem
The assignments are:Customer
WidthStandard
WidthScrap (in Kg)
I A 95
II C 194
III B 190
IV E 1000
V F 1000
VI D 0
Total Scrap 2479
Verification using Tora Software
Input Data:
Output pdf
Conclusion
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
Reference
Book: Cases in Operation Research by Cristoph Haehling von
Lanzenauer
Case : ALCANby Cristoph Haehling von
LanzenauerD D Wright