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