In a tandem cold-rolling mill, a strip is successively reduced in gauge at each stand as it passes through the mill. The optimal scheduling of a tandem mill is an important but difficult task. In this work, a scheduling problem is considered as an optimization problem which minimizes the total specific power and satisfies certain constraints. Since the material properties and friction coefficient are not known precisely, they are treated as fuzzy numbers. The fuzzy set theory is applied to find out an optimum drafting pattern. The methodology is illustrated by means of a few examples. It is observed that the schedule in which the maximum reduction is achieved in the first pass results in minimum specific power; however, its reliability is poor. Optimization using fuzzy set theory provides a solution which meets the twin requirements of high reliability and minimum power. [S1087-1357(00)00902-3]

1.
Dixit
,
U. S.
, and
Dixit
,
P. M.
,
1996
, “
A finite-element analysis of flat rolling and application of fuzzy set theory
,”
Int. J. Mach. Tools Manufact.
,
36
, pp.
947
969
.
2.
Avitzur, B., 1962, “Pass reduction schedule for optimum production of a hot strip mill,” Iron Steel Eng., Dec., pp. 104–114.
3.
Bryant, G. F., and Spooner, P. D., 1973, “On-line adoption of tandem mill schedules,” Automation of Tandem Mills, Bryant, G. F., ed., The Iron and Steel Institute, London.
4.
Bryant, G. F., Halliday, J. M., and Spooner, P. D., 1973, “Optimal scheduling of a tandem cold-rolling mill,” Automation of Tandem Mills, Bryant, G. F., ed., The Iron and Steel Institute, London.
5.
,
L. A.
,
1965
, “
Fuzzy Sets
,”
Inf. Control.
,
8
, pp.
338
353
.
6.
Kaufmann, A., and Gupta, M. M., 1985, Introduction of Fuzzy Arithmetic: Theory and Applications, Van Nostrand Reinhold Company Inc., New York.
7.
Klier, G. J., and Folger, T. A., 1993, Fuzzy Sets, Uncertainty and Information, Prentice-Hall of India Private Limited, New Delhi.
8.
Dixit
,
U. S.
, and
Dixit
,
P. M.
,
1997
, “
A study on residual stresses in rolling
,”
Int. J. Mach. Tools Manuf.
,
37
, pp.
837
853
.
9.
Zhu
,
Y. D.
, and
Avitzur
,
B.
,
1988
, “
Criteria for the prevention of split ends
,”
ASME J. Eng. Ind.
,
110
, pp.
162
172
.
10.
Avitzur
,
B.
,
Van Tyne
,
C. J.
, and
Turczyn
,
S.
,
1988
, “
The prevention of central bursts during rolling
,”
ASME J. Eng. Ind.
,
110
, pp.
173
178
.
11.
Wanheim
,
T.
, and
Bay
,
N.
,
1978
, “
A model for friction in metal forming processes
,”
Ann. CIRP
,
27
, pp.
189
194
.
12.
Fletcher, R., 1981, Practical Methods of Optimization, Vol. 2, Constrained Optimization, Wiley, New York and Toronto.
13.
Valliappan
,
S.
, and
Pham
,
T. D.
,
1993
, “
Fuzzy finite element analysis of a foundation on an elastic soil medium
,”
Int. J. Numer. Anal. Methods Geomech.
,
17
, pp.
771
789
.
14.
Valliappan
,
S.
, and
Pham
,
T. D.
,
1995
, “
Elasto-plastic finite element analysis with fuzzy parameters
,”
Int. J. Numer. Methods Eng.
,
38
, pp.
531
548
.
15.
,
L. A.
,
1976
, “
A fuzzy-algorithmic approach to the definition of complex or imprecise concepts
,”
Int. J. Man-Mach. Stud.
,
8
, pp.
249
291
.
16.
De Luca
,
A.
, and
Termini
,
A.
,
1972
, “
A Definition of Nonprobabilistic Entropy in the Setting of Fuzzy Set Theory
,”
Inf. Control.
,
20
, pp.
301
312
.