procmean.gms

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procmean.gms : Optimal Process Mean

Find the optimal process mean when the quality characteristic
follows a Beta distribution and using a linear quality loss.

References:

Chen, C H, and Chou, C Y, Determining the Optimum Process Mean under a Beta Distribution. Journal of the Chinese Institute of Industrial Engineers 18 (3) (2003), 27--32.
Phillips, M D, and Cho, B R, Determining the Optimum Process Mean under a Beta Distribution. A Nonlinear model for determining the most economic process mean under a beta distribution 7 (2000), 61--74.

Small Model of Type: NLP

$Title Optimal Process Mean (PROCMEAN,SEQ=301) $ontext Find the optimal process mean when the quality characteristic follows a Beta distribution and using a linear quality loss. Erwin Kalvelagen, April 2004 Chen, C H, and Chou, C Y, Determining the Optimum Process Mean under a Beta Distribution. Journal of the Chinese Institute of Industrial Engineers 18 (3) (2003), 27--32. Phillips, M D, and Cho, B R, Determining the Optimum Process Mean under a Beta Distribution. A Nonlinear model for determining the most economic process mean under a beta distribution 7 (2000), 61--74. $offtext scalars a 'minimum value of quality characteristic' /113/ b 'maximum value of quality characteristic' /119/ alpha 'shape parameter' /2/ beta 'shape parameter' /4/ T 'target value' /115/ k1 'quality loss coefficient when x<T' /2/ k2 'quality loss coefficient when x>T' /3/ ; scalars g1,g2,g3; g1 = gamma(alpha+beta)/(gamma(alpha)*gamma(beta)); g2 = gamma(alpha+1)*gamma(beta)/gamma(alpha+beta+1); g3 = g1*g2; variables TC 'Total expected cost per unit' delta 'location parameter' y 'transformation' ; equations tcdef 'cost model' ydef ; tcdef.. tc =e= k1*T*betareg(y,alpha,beta) - k1*{(delta+a)*betareg(y,alpha,beta) +(b-a)*betareg(y,alpha+1,beta)*g3} + k2*{(delta+a)*[1-betareg(y,alpha,beta)] +(b-a)*[1-betareg(y,alpha+1,beta)*g3]} - k2*T*[1-betareg(y,alpha,beta)]; ydef.. y =e= (T-delta-a)/(b-a); y.lo = 0.0001; y.up = 0.9999; y.l = 0.5; model m /all/; solve m using nlp minimizing tc;