Karar Analizi Hedef Programlama - I 1 T.C 2011-2012 BAHAR YARIYILI PROJE-1 HEDEF PROGRAMLAMA HAZIRLAYANLAR 090203068 080203032 080203035 080203051 BURCU ONAY EREN ( 6 MART 2012) 2 .......................................................................................................................................... 3 1. ............................................................................................................................. 4 2. HEDEF PROGRAMLAMA ........................................................................................... 4 2.1. ................................................................. 5 2.2. ........................................................................................... 5 2.3. ................................................................................... 6 2.4. Hedef Progr .............................................................................. 6 2.5. ................................................................ 6 2.5.1. ........................................................................... 8 2.5.1.1. ........................................................................................ 8 2.5.1.2. ...................................................................................... 8 2.6. ....................................................................................... 12 2.6.1. ...................................................................... 12 2.6.2. ....................................................................... 14 2.6.3. ............................................................................. 16 2.6.4. - ........................................................ 17 2.6.5. ..................................................................... 23 2.6.6. ................................................................................... 24 2.6.7. ............................................................................... 29 3. UYGULAMA .............................................................................................................. 29 3.1. ....................................................................................................................... 29 3.2. ar modelinin ....................................................................................................................... 37 4. ................... 43 5. .............................................................................................. 46 6. KAYNAKLAR ............................................................................................................ 47 7. EKLER ........................................................................................................................ 50 3 da hemen hemen her alanda hayattaki bu karar verme problemlerin karar verme t Pr 4 1. birde . 2. HEDEF PROGRAMLAMA Hedef programlama ,1955 vd. Tamiz,vd.,1999). olmasa bile, he (Ignizio,1985). 5 2.1. Nakliye Problemleri, eleri (merger) Stratejisi, 2.2. Hed k olarak da ale getirecek bir yol bulunma (Kongar,2000)(Timor,2002). 6 2.3. d i - i + ih (Aslan, ve . 2.4. Hedef Programlamada; (Evren ve . 2.5. Hedef Programlama Matematik verirler. formda ifade edilir: Min Hedef denklemleri genel bir ifadedir. Hedef: . 7 si: Sapma: Hedef: sap k 1 >>>P 2 >>> P k i - ve d i + 1: di += 22000 20500 = 1500 ve d - di-= 20500 - olarak ifade edilir. W ki 1 . (dt-,dt+) r. dt- , ft ile Gt dt + ise ft ile Gt kildedir: ) ] ( . , ) , . . . . . . . . ( ) , ( [ 2 2 2 2 1 1 1 1 k k k k d d w p d d w p d d w p M i n8 j=1,2 Burada wi (d- wi (Evren ve 2.5.1. 1. . (Taha, 2000). 2.5.1.1. Min Z= w 1 G 1 + w 2 G 2 +...+ w n G n i, i ). 2.5.1.2. . i i b x g ) ( i i i i G d d x f ) ( i 0 j x , 0 , i i d d9 (Taha, 2000). Min G 1 =P 1 . . Min G n =P n P i >>>P i+1 1: - - - - hedeflemektedir. (Model- 2: - - - - 90 saattir. ef programlama modelini kurunuz. 2 1 d d M i n z 1 5 0 0 0 5 6 4 1 1 3 2 1 d d x x x 8 6 0 2 2 2 d d x 6 5 0 0 2 3 2 3 2 1 x x x 8 6 0 0 3 2 3 3 2 1 x x x 0 , , , , , , 2 2 1 1 3 2 1 d d d d x x x10 ; x1 x2 d1- d1 + : Hedeflenen su em d2 - d2+: Hedeflenen 3: - - - - saattir. mektir. Min z = 3 d1 + d2 - - 11 x1 + d1(-) d1(+) = 15 x2 + d2(-) d2(+) = 15 x1, x2, d1(-), d1(+), d2(-), d2(+) 4: - enin hedefleri ise; - - istememektedir. Problemin hedef programlama modelini kurunuz. ; x1 x2 d1- d1 + : Hedeflenen k d2 - 12 2.6. 2.6.1. Min z = d1 + d2 + d3 5: - - - - saattir. ; x1 x2 : Hava d1 d1 + d2 - + + - + 13 d2 + Min z = d1(-) + d2(-) x1 + d1(-) d1(+) -1) x2 + d2(-) d2(+) -2) x1, x2, d1(-), d1(+) , d2(-) , d2(+) 0 -1. Hedef K -1 Tablo- Tablo-1. (x1, x2) fonksiyonu d1- d1+ d2- d2+ Min z A (0, 30) 15 0 0 15 15 B (20, 0) 0 5 15 0 15 C (10, 20) 5 0 0 5 5 D (12.5, 15) 2.5 0 0 0 2.5 E (15, 10) 0 0 5 0 5 14 2.6.2. 6: daha Min z = 3 d1 + d2 x1 + d1(-) d1(+) = 15 x2 + d2(-) d2(+) = 15 x1, x2, d1- , d1+ , d2- , d2 + Fo -2, Tablo-3, Tablo- Tablo- A.K. Cj Temel 0 x1 0 x2 0 s1 0 s2 3 1 d 0 1 d 1 2 d 0 2 d 3 X1 1 0 0 0 1 -1 0 0 15 1 2 d 0 1 0 0 0 0 1 -1 15 0 s1 6 3 1 0 0 0 0 120 + - 15 Tablo-3.Birinci Simplek A.K. cj Temel 0 x1 0 x2 0 s1 0 s2 3 1 d 0 1 d 1 2 d 0 2 d 0 x1 1 0 0 0 1 -1 0 0 15 1 2 d 0 1 0 0 0 0 1 -1 15 0 s1 0 3 1 0 -6 6 0 0 30 0 s2 0 3 0 1 -3 3 0 0 45 zj cj - zj 0 0 1 -1 0 0 0 0 0 3 0 0 1 0 -1 1 15 Tablo-4 0 s2 3 3 0 1 0 0 0 0 90 zj cj - zj 1 -1 1 -1 0 0 0 0 3 0 -3 3 1 0 -1 1 60 A.K. cj Temel 0 x1 0 x2 0 s1 0 s2 3 1 d 0 1 d 1 2 d 0 2 d m 0 x1 1 0 0 0 1 -1 0 0 15 1 d2 0 0 -1/3 0 2 -2 1 -1 5 0 x2 0 1 1/3 0 -2 2 0 0 10 0 s2 0 0 -1 1 3 -3 0 0 15 16 T sapma yoktur. 2.6.3. Bir karar verici matematiksel optimizasyon modellerini Karar verici, terc Matematiksel olarak ifade edecek olursak; ( edefinde istenilen sonuca r her zaman daha belirlenebilir. Zj cj - zj 0 0 0 0 -1/3 1/3 0 0 2 1 -2 2 1 0 -1 1 5 17 fakat bu Karar vericiler hedef programlama yerine 2.6.4. - Hedef Programlama 2 kat olabilir. 7: 18 ablo-5, Tablo-6, Tablo-7, Tablo-8, Tablo- 19 Tablo-5 nci simpleks tablosu A.K. cj Temel 0 x1 0 x2 1 d1- 0 d1+ 1 d2- 0 d2+ 1 d3 - 0 d3+ 0 d4- 2 d4+ 1 d5- 0 d5+ 1 d1- 100 0 1 -1 -150 150 0 0 0 0 0 0 150 0 x2 0 1 0 0 1 -1 0 0 0 0 0 0 15 1 d3 - 1 0 0 0 0 0 1 -1 0 0 0 0 5 0 d4 - 4 0 0 0 -2 2 0 0 1 -1 0 0 15 1 d5 - 2 0 0 0 -2 2 0 0 0 0 1 -1 5 p4 cj - zj -1 0 1 0 1 0 0 1 0 2 1 0 p3 cj - zj 0 0 1 0 1 0 1 0 0 2 1 0 p2 cj - zj -100 0 0 1 151 -150 1 0 0 2 1 0 p1 cj - zj -2 0 1 0 3 -2 1 0 0 2 1 0 20 Tablo-6. A. K. cj Temel 0 x1 0 x2 1 d1 - 0 d1+ 1 d2 - 0 d2 + 1 d3 - 0 d3 + 0 d4 - 2 d4+ 1 d5 - 0 d5 + 0 d2 2/3 0 1/15 0 - 1/150 -1 1 0 0 0 0 0 0 1 0 x2 2/3 1 1/15 0 - 1/150 0 0 0 0 0 0 0 0 16 1 d3 1 0 0 0 0 0 1 -1 0 0 0 0 5 0 d4 8/3 0 - 1/75 1/75 0 0 0 0 1 -1 0 0 13 1 d5 2/3 0 - 1/75 1/75 0 0 0 0 0 0 1 -1 3 p4 cj - zj -1 0 1 0 1 0 0 1 0 2 1 0 p3 cj - zj 0 0 1 0 1 0 1 0 0 2 1 0 p2 cj - zj 0 0 1 0 1 0 1 0 0 2 1 0 p1 cj - zj -2/3 0 1 -1/75 1 0 1 0 0 2 0 1 21 Tablo-7. A.K. cj Tem el 0 x1 0 x 2 1 d1 - 0 d1+ 1 d2- 0 d2 + 1 d3 - 0 d3 + 0 d4 - 2 d4 + 1 d5 - 0 d5+ 0 x1 1 0 1/100 - 1/10 0 -3/2 3/2 0 0 0 0 0 0 3/2 0 x2 0 1 0 0 1 -1 0 0 0 0 0 0 15 1 d3 0 0 - 1/100 1/10 0 3/2 - 3/2 1 -1 0 0 0 0 7/2 0 d4 0 0 -1/25 1/25 4 -4 0 0 1 -1 0 0 9 1 d5 0 0 - 1/150 1/50 1 -1 0 0 0 0 1 -1 2 p4 cj - zj 0 0 101/1 00 - 1/10 0 -1/2 0 1 0 2 1 0 p3 cj - zj 0 0 1 0 1 0 1 0 0 2 1 0 p2 cj - zj 0 0 1 0 1 0 1 0 0 2 1 0 p1 cj - zj 0 0 151/1 50 - 1/50 0 1 1 0 0 2 0 1 22 Tablo-8. A.K. cj Temel 0 x1 0 x2 1 d1- 0 d1 + 1 d2- 0 d2+ 1 d3- 0 d3+ 0 d4- 2 d4+ 1 d5- 0 d5+ 0 x1 1 0 0 0 -1 1 0 0 0 0 1/2 -1/2 5/2 0 x2 0 1 0 0 0 -1 0 0 0 0 0 0 15 1 d3 0 0 0 0 1 -1 1 -1 0 0 -1/2 1/2 5/2 0 d4 0 0 0 0 2 -2 0 0 1 -1 -2 2 5 0 d1 0 0 -1 1 50 -50 0 0 0 0 50 -50 100 p4 cj - zj 0 0 1 0 0 1 0 1 0 2 1/2 -1/2 p3 cj - zj 0 0 1 0 1 0 1 0 0 2 1 0 p2 cj - zj 0 0 1 0 1 0 1 0 0 2 1 0 p1 cj - zj 0 0 1 0 1 0 1 0 0 2 1 0 23 Tablo-9. A.K. cj Temel 0 x1 0 x2 1 d1- 0 d1+ 1 d2 - 0 d2 + 1 d3- 0 d3 + 0 d4 - 2 d4 + 1 d5- 0 d5 + 0 x1 1 0 0 0 -1/2 1/2 0 0 1/4 -1/4 0 0 75/20 0 x2 0 1 0 0 1 -1 0 0 0 0 0 0 15 1 d3 - 0 0 0 0 1/2 -1/2 1 -1 -1/4 1/4 1/2 0 25/20 0 d5+ 0 0 0 0 1 -1 0 0 1/2 -1/2 -1 1 2.5 0 d1 + 0 0 1 1 100 -100 0 0 25 -25 0 0 225 p4 cj - zj 0 0 1 0 1/2 1/2 0 1 1/4 7/4 1 0 p3 cj - zj 0 0 1 0 1 0 1 0 0 2 1 0 p2 cj - zj 0 0 1 0 1 0 1 0 0 2 1 0 p1 cj - zj 0 0 1 0 1 0 1 0 0 2 1 0 2.6.5. wi(d-,d+) gi(x) bi ft(x)+dt--dt+=Gt ifadesi ise h Karabulut,2005). 24 2.6.6. programlama ir . : Ax =b x 0 b A Bu b . A ~ (Ax)i = bi x 0 ~ bi : i bi maksimum miktarda di -2 25 -2 i (x bi bi di bi + di B max Ax)i (bi di )] di [(bi + di ) (Ax)i ] di [0,1] x 0 8: Belediyel erine getiren 26 resi Belediye Vergileri ve bunlara ait tahmin edi den meydana gelmektedir. rgisi, Emlak (Arazi Vergisi, Bina Vergisi, Arsa Vergisi ) Vergisi, ul edilebilir maksimum sapmalar Tablo . Kabul edilebilir maksimum sapmalar hedeften simetrik Tablo 10 27 gibi ifade edilir. X1 + X 2 + X3 + X 4 + X5 + X 6 + X 7 + X8 + X9 + X10 = 6.494.480.000.000 X1 = 12.000.000.000 ~ X 2 = 40.000.000.000 ~ X3 = 3.450.000.000.000 ~ X 4 = 120.000.000.000 ~ X5 = 580.000.000.000 ~ X 6 = 420.000.000.000 ~ X 7 = 1.050.000.000.000 ~ X8 = 1.480.000.000 ~ X9 = 820.000.000.000 ~ X10 = 1.000.000.000 X i 0 , i=1,2,...,10 - -3: Toplam Vergi hedefi i 28 def iki tane X1 + X 2 + X 3 + X 4 + X 5 + X 6 + X 7 + X8 + X 9 + X10 X1 + X 2 + X 3 + X 4 + X 5 + X 6 + X 7 + X8 + X 9 + X10 + Tablo 11 de Tablo-11 larak 1.0 Umarusman, 2003). 29 2.6.7. ok a karar verme rekli 3. UYGULAMA 3.1. 1- 2- olarak verilebilir.) 30 3- - ir.) 4- olur. 5- 6- kar Tablo 31 Tablo-12: Sabah kah timizasy , yemeklerin . Bu sorun . ba da Bu sorunu - enerji ve bes ulan Tablo-13 teki gibidir. 32 Tablo-13 x i 1, x 2, x 3 karar 4 5, x 6 7, 10 odele 33 topl Burada, c i , - 1 ve d + 1 burada d - 1 + 1 def programlama modelinin ama 1- def, Burada a i j ir. d - 2 ve d + 2 modelinin ama 34 2- Burada b i ), B j - 2 ve d + 2 3- Burada e i ), E j stermektedir. d - 2 ve d + 2 4- Burada k i ), k j - 2 ve d + 2 5- Burada m i ), M j - 2 ve d + 2 35 6- Burada n i ), N j - 2 ve d + 2 nde 7- Burada p i ), P j - 2 ve d + 2 8- Burada r i ), R j - 2 ve d + 2 9- 36 Burada s i ), S j d - 2 ve d + 2 10- Burada v i ), V j - 2 ve d + 2 hedef pro Burada y i i - 12 ve d + 12 olan eksi ve art mikt i i - 12 + 12 37 H - -2 -1de -2 de - 3.2. nde 38 39 Tablo- 40 Tablo- 41 x i 2. grupta 27 adet 1, x 2, 9 10, x 11, 36 karar 37, x 38, 43 44, x 45, x 54 Modelde x i - i i 1- 2- 3- Yemekler ard ar 1.grupta 9 adet, 2. grupta 27 adet 3. grupta 7 adet ve 4. grupta 11 adet yemek x i + x j + x k + x l = 0 42 Bu - x i + x j + x k + x l + x m + x n + x p + x r = 0 - . hedefler ol n) 43 -30 - - - - -5de - -7 de , - -9 de ver 4. vd (2001) vd - vd 44 Terzi vd Alp ellerinin matematiksel Sungur vd llerinden birisi olan ve (2009) - - Altan ve Ediz(2009) Ayan (2010) Akdeniz vd (2007) (2005) (2009) Karaman vd.,(2007) 45 Tablo 15 Yazarlar Problem tipi vd (1998) Rasyonel ve Ekonomik Hayvan Besleme Hedef programlama ve Eren (2001) (2001) hedef programlama ve Umarusman (2003) Vergi optimizasyonu Hedef programlama (2005) Performans Hedef programlama ve Karabulut (2005) lanlama (2005) atama Dinamik hedef programlama Terzi vd (2006) Hedef programlama (2007) D hedef programlama Karaman vd.(2007) -maliyet-kalite eniyilemesi Alp (2008) (2009) Modellenen Stokastik Ve hedef programlama Altan ve Ediz(2009) Hedef programlama (2009) (2009) Programlama (2009) Dengeleme problemi Hedef programlama Ayan(2009) Akdeniz ve Aras (2010) Plast Vericinin Optimal lama 46 5. da hedef . Hedef ildi. Uygulama olarak kullan hedef - o 6.1 kabul edilebilir sapmala 47 6. KAYNAKLAR Akdeniz .A ,Ara , , Cilt: 12, Sa -19,2010 Alp S., , , -91, 2008 Ediz A., , 11 / 3 .79 92, 2009 , www.ozyazilim.com.tr,2003 ,,Say : 34, ss.69-90, Temmuz-Aral k, 2009 l Application of Lineer sma saati sistemi i in bi programlama modeli isi ktisadi ve Dergisi,2 s.1-18, Temmuz- , 2009 Journal of Naval Science and Engineering, Vol. 5, No.2, pp. 55-74, 2009 , 19, 1, 89-95, 2004 -1 hedef Gazi Dergisi, 16(1-2), 41-52, 2001. Rasyonel ve Ekonomik Hayvan Beslemede Hedef Programlamadan Yararlanma ,1998 48 Evren R. F. , Tezi s.54,1992 Dergisi (9),2005 Review of Social, Economic & Business Studies, Vol.2, 242-255,2003 t Review of Social Economic & Business Studies,2,244,1994 Ignizio, J Introduction to Goal Programming , Sage Publications Inc., USA,1985 -Maliyet-Kalite 2007 ogramlama , ,2007 Sempozyumu, 2005 Alp on Research An , 2000 - Tezi,2001 - Proceedings Of The Third ,2000 ri makinelere atama Review of Social, Economic & Business Studies, Vol.7/8, 359- 383,2006 D , -96 ISSN: 1302-3284,2009 , Bursa,2009 49 B.,Erol S., Demirel niversitesi ktisadi ve dari Birimler F , c.6 s.2 s.185-191, 2001 ,TMMOB Harita ve , Ankara,2009 s.348,s.349,s.352,2000 Tamiz M., Mirrazavi S.K., Jones D.F., Extensions of Pareto efficiency analysis to Integer Goal Programming , Omega, The International Journal of Management Science 27, 179-188, 1999 Terz , Hacaloglu S.E., Alada , i i i in bir karar destek - 2006/2 ,2002 ., i i iye i sigorta rketlerini erlendirilmes Dergisi , -39,2005 www.google.com/hedef-programlama www.habibkocak.net/dosyalar/1.DPKararverme.ppt www.slideshare.net/cakirengin/hedef-programlama-presentation 50 7. EKLER Ek-1:1.G MIN D1A+D2E+D2A+D3E+D3A+D4A+D5E+D5A+D6E+D6A+D7A+D7E+D8A+D8E+D9A+D9E+ D10E+D10A+D11A+D11E+2D12A SUBJECT TO X1+X2+X3=1 X4=1 X5+X6=1 X7+X8+X9+X10=1 0.0873X1+0.0267X2+0.1880X3+0.0922X4+0.1319X5+0.0430X6+0.0159X7+0.0972X8+0.1589 X9+0.1589X10-D1A=0 0.723X1+0.0786X2+0.1093X3+0.056X4+0.2258X5+0.2177X6+0.0867X8+0.912X9+0.0623X10 +D2E-D2A=0.2902 0.2196X1+0.2333X2+0.279X3+0.0172X4+0.0172X5+0.1801X8+0.0172X9+0.0377X10+D3E- D3A=0.1935 0.0741X1+0.0845X2+0.1235X3+0.0819X4+0.3589X5+0.2081X6+0.0585X8+0.0065X9+0.0039 X10+D4E-D4A=0.1763 0.0743X1+0.1348X2+0.0578X3+0.0264X4+0.0173X5+0.4952X8+0.0264X9+0.1309X10+D5E- D5A=0.3081 0.3155X1+0.0485X2+0.0728X3+0.1214X4+0.017X5+0.0364X8+0.1456X9+0.2427X10+D6E- D6A=0.9417 0.1739X1+0.0751X2+0.1043X3+0.0063X4+0.3478X5+0.1391X6+0.0783X8+0.0167X9+0.0584 X10+D7E-D7A=0.3478 0.3846X1+0.2308X8+0.3846X10+D8E-D8A=0.3077 0.1205X1+0.1205X2+0.2410X3+0.012X5+0.3855X8+0.1205X9+D9E-D9A=0.2651 0.1053X1+0.1053X5+0.1579X8+0.3158X9+0.3158X10+D10E-D10A=2.0632 0.016X8+0.1025X9+0.8815X10+D11E-D11A=0.1601 D12E-D12A=0 END INTE X1 INTE X2 INTE X3 INTE X4 INTE X5 INTE X6 INTE X7 INTE X8 INTE X9 INTE X1 51 n ; 0.3333x2+0.3333x4+0.3333x6+0.3333x9- . Ek 2: OBJECTIVE FUNCTION VALUE 1) 4.046300 VARIABLE VALUE REDUCED COST X1 0.000000 0.699100 X2 1.000000 0.044200 X3 0.000000 0.223900 X4 1.000000 -0.906800 X5 0.000000 0.234400 X6 1.000000 0.329700 X7 0.000000 0.015900 X8 0.000000 -0.484000 X9 0.000000 0.572100 X10 1.000000 0.781100 D1A 0.320800 0.000000 D2E 0.000000 2.000000 D2A 0.124400 0.000000 D3E 0.000000 2.000000 D3A 0.094700 0.000000 D4A 0.202100 0.000000 D5E 0.016000 0.000000 D5A 0.000000 2.000000 D6E 0.529100 0.000000 D6A 0.000000 2.000000 D7A 0.000000 2.000000 D7E 0.068900 0.000000 D8A 0.076900 0.000000 D8E 0.000000 2.000000 D9A 0.000000 2.000000 D9E 0.144600 0.000000 D10E 1.747400 0.000000 D10A 0.000000 2.000000 D11A 0.721400 0.000000 D11E 0.000000 2.000000 D12A 0.000000 2.000000 D4E 0.000000 1.000000 D12E 0.000000 0.000000 52 Ek 3: OBJECTIVE FUNCTION VALUE 1) 5.135300 VARIABLE VALUE REDUCED COST X1 0.000000 2.046900 X2 0.000000 1.861000 X3 1.000000 1.432500 X4 1.000000 0.772400 X5 1.000000 0.930000 X6 0.000000 1.274500 X7 0.000000 0.015900 X8 0.000000 -0.327400 X9 0.000000 1.272100 X10 1.000000 0.897900 D1A 0.571000 0.000000 D2E 0.000000 2.000000 D2A 0.163200 0.000000 D3E 0.000000 2.000000 D3A 0.157600 0.000000 D4A 0.391900 0.000000 D5E 0.075700 0.000000 D5A 0.000000 2.000000 D6E 0.487800 0.000000 D6A 0.000000 2.000000 D7A 0.169000 0.000000 D7E 0.000000 2.000000 D8A 0.076900 0.000000 D8E 0.000000 2.000000 D9A 0.000000 2.000000 D9E 0.012100 0.000000 D10E 1.642100 0.000000 D10A 0.000000 2.000000 D11A 0.721400 0.000000 D11E 0.000000 2.000000 D12A 0.333300 0.000000 D4E 0.000000 1.000000 53 Ek-4: MIN D1A + D2E + D2A + D3E + D3A + D4A + D5E + D5A + D6E + D6A + D7E + D7A + D8E + D8A + D9E + D9A + D10E + D10A + D11E + D11A + 2D12A SUBJECT TO 2) X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 = 1 3) X10 + X11 + X12 + X13 + X14 + X15 + X16 + X17 + X18 + X19 + X20 + X21 + X22 + X23 + X24 + X25 + X26 + X27 +X28 + X29 + X30 + X31 + X32 + X33 + X34 + X35 + X36 = 1 4) X37 + X38 + X39 + X40 + X41 + X42 + X43 = 1 5) X44 + X45 + X46 + X47 + X48 + X49 + X50 + X51 + X52 + X53 + X54 = 1 6) 0.0050 X1 + 0.0045 X2 + 0.0047 X3 + 0.0047 X4 + 0.0035 X5 + 0.0014 X6 + 0.0034 X7 + 0.0017 X8 + 0.0021 X9 + 0.0641 X10 + 0.0480 X11 + 0.0638 X12 + 0.0229 X13 + 0.0501 X14 + 0.0467 X15 + 0.0361 X16 + 0.0334 X17 + 0.0287 X18 + 0.279 X19 + 0.0293 X20 + 0.0379 X21 + 0.0258 X22 + 0.0236 X23 + 0.0247 X24 + 0.0832 X25 + 0.0023 X26 + 0.0057 X27 + 0.0060 X28 + 0.0092 X29 + 0.0084 X30 + 0.0150 X31 + 0.0112 X32 + 0.0111 X33 + 0.0141 X34 + 0.0340 X35 + 0.0340 X36 + 0.0050 X37 + 0.0032 X38 + 0.0091 X39 + 0.0035 X40 +0.0107 X41 + 0.0145 X42 + 0.0137 X43 + 0.0072 X44 + 0.0099 X45 + 0.0082 X46 + 0.0082 X47 + 0.0187 X48 + 0.0070 X49 + 0.0117 X50 + 0.0088 X51 + 0.0062 X52 + 0.0124 X53 + 0.0140 X54 D1A = 0 7)0.0165 X1 + 0.0104 X2 + 0.0114 X3 + 0.0119 X4 + 0.0160 X5 + 0.0103 X6 + 0.0104 X7 + 0.0145 X8 + 0.0166 X9 + 0.0314 X10 + 0.0279 X11 + 0.0281 X12 + 0.0417 X13 + 0.0353 X14 + 0.0274 X15 + 0.0209 X16 + 0.0165 X17 + 0.0182 X18 + 0.0201 X19 + 0.0269 X20 + 0.0168 X21 + 0.0107 X22 + 0.0150 X23 + 0.0316 X24 + 0.0629 X25 + 0.0069 X26 + 0.0098 X27 + 0.0224 X28 + 0.0131 X29 + 0.0150 X30 + 0.0057 X31 + 0.0131 X32 + 0.0131 X32 + 0.0160 X33 + 0.0089 X34 +0.0234 X35 + 0.0103 X36 + 0.0304 X37 + 0.0263 X38 + 0.0456 X39 + 0.0304 X40 + 0.0380 X41 + 0.0133 X42 + 0.0424 X43 + 0.0052 X44 + 0.0009 X45 + 0.0062 X46 + 0.0091 X47 + 0.0051 X48 + 0.0053 X49 + 0.0034 X50 + 0.0118 X51 + 0.0081 X52 + 0.0134 X53 + 0.0107 X54 + D2E D2A = 0.0619 8)0.0158 X1 + 0.0066 X2 + 0.0112 X3 + 0.0116 X4 + 0.0190 X5 + 0.0024 X6 + 0.0036 X7 + 0.0068 X8 + 0.0056 X9 + 0.0338 X10 + 0.0308 X11 + 0.0372 X12 + 0.0396 X13 + 0.0456 X14 + 0.0294 X15 + 0.0256 X16 + 0.0446 X17 + 0.0192 X18 + 0.0222 X19 + 0.0366 X20 + 0.0244 X21 +0.0182 X22 + 0.0182 X23 + 0.0348 X24 + 0.0681 X25 + 0.0042 X26 + 0.0056 X27 + 0.0238 X28 + 0.0094 X29 + 0.0182 X30 + 0.0042 X31 + 0.0094 X32 + 0.0070 X33 + 0.0104 X34 + 0.0525 X35 + 0.0464 X36 + 0.0094 X37 + 0.0130 X38 + 0.0388 X39 + 0.0142 X40 + 0.0300 X41 + 0.0090 X42 + 0.0230 X43 + 0.0028 X44 + 0.0012 X45 + 0.0022 X46 + 0.0010 X47 + 0.0022 X48 + 0.0014 X49 + 0.0004 X50 + 0.0090 X51 + 0.0140 X52 + 0.0142 X53 + 0.0114 X54 + D3E D3A = 0.0163 54 Ek- 9)0.0122 X1 + 0.0105 X2 + 0.0044 X3 + 0.0056 X4 + 0.0227 X5 + 0.0113 X6 + 0.0114 X7 + 0.0174 X8 + 0.0209 X9 + 0.0420 X10 + 0.0298 X11 + 0.0336 X12 + 0.0498 X13 + 0.0487 X14 + 0.0285 X15 + 0.0283 X16 + 0.0147 X17 + 0.0216 X18 + 0.0214 X19 + 0.0218 X20 + 0.0174 X21 + 0.0084 X22 + 0.0209 X23 + 0.0300 X24 + 0.0835 X25 + 0.0002 X26 + 0.0080 X27 + 0.0260 X28 + 0.0093 X29 + 0.0209 X30 + 0.0051 X31 + 0.0093 X32 + 0.0189 X33 + 0.0054 X34 + 0.0191 X35 + 0.0031 X36 + 0.0229 X37 + 0.0234 X38 + 0.0387 X39 + 0.0220 X40 + 0.0321 X41 + 0.0124 X42 + 0.0548 X43 + 0.0065 X44 + 0.0004 X45 + 0.0005 X46 + 0.0009 X47 + 0.0007 X48 + 0.0004 X49 + 0.0009 X50 +0.0153 X51 + 0.0049 X52 + 0.0118 X53 + 0.0094 X54 + D4E D4A = 0.0622 10)0.0076 X1 + 0.0132 X2 + 0.0074 X3 + 0.0095 X4 + 0.0020 X5 + 0.0016 X6 + 0.0019 X7 + 0.0181 X8 +0.0020 X9 + 0.0062 X10 + 0.0215 X11 + 0.0056 X12 + 0.0040 X13 + 0.0123 X14 + 0.0108 X15 + 0.0049 X16 + 0.0034 X17 + 0.0146 X18 + 0.0291 X19 + 0.0145 X20 + 0.0479 X21 + 0.0458 X22 + 0.0159 X23 + 0.0231 X24 + 0.0126 X25 + 0.0021 X26 + 0.0037 X27 + 0.0485 X28 + 0.0080 X29 + 0.0159 X30 + 0.0282 X31 + 0.0080 X32 + 0.0278 X33 + 0.0154 X34 + 0.0097 X35 + 0.0034 X36 + 0.0023 X37 + 0.0077 X38 + 0.0855 X39 + 0.0034 X40 + 0.0333 X41 + 0.0081 X42 + 0.0070 X43 + 0.0101 X44 + 0.0052 X45 + 0.0146 X46 + 0.0029 X47 + 0.0127 X48 + 0.0035 X49 + 0.0043 X50 + 0.0510 X51 + 0.0761 X52 + 0.0921 X53 + 0.0737 X54 + D5E D5A = 0.0516 11) 0.0237 X1 + 0.0052 X2 + 0.0196 X3 + 0.0299 X4 + 0.0067 X5 + 0.0021 X6 + 0.0021 X7 + 0.0052 X8 + 0.0052 X9 + 0.0289 X10 + 0.0258 X11 + 0.0320 X12 + 0.0247 X13 + 0.0252 X14 + 0.0299 X15 + 0.0206 X16 + 0.0103 X17 + 0.0278 X18 + 0.0371 X19 + 0.0433 X20 + 0.0245 X21 + 0.0186 X22 + 0.0278 X23 + 0.0505 X24 + 0.0557 X25 + 0.0062 X26 + 0.0072 X27 + 0.0217 X28 + 0.0196 X29 + 0.0278 X30 + 0.0062 X31 + 0.0196 X32 + 0.0258 X33 + 0.0113 X34 + 0.0268 X35 + 0.0072 X36 + 0.0062 X37 + 0.0196 X38 4 0.0165 X39 + 0.0072 X40 + 0.0567 X41 + 0.0227 X42 + 0.0217 X43 + 0.0101 X44 + 0.0217 X45 + 0.0103 X46 + 0.0062 X47 + 0.0144 X48 + 0.0062 X49 + 0.0062 X50 + 0.0052 X51 + 0.0021 X52 + 0.0031 X53 + 0.0025 X54 + D6E D6A = 0.0198 12) 0.0064 X1 + 0.0073 X2 + 0.0067 X3 + 0.0080 X4 + 0.0109 X5 + 0.0107 X6 + 0.0107 X7 + 0.0145 X8 + 0.0071 X9 + 0.0058 X10 + 0.0099 X11 + 0.0040 X12 + 0.0071 X13 + 0.1061 X14 + 0.1491 X15 + 0.0127 X16 + 0.0026 X17 + 0.0190 X18 + 0.0498 X19 + 0.0335 X20 + 0.0338 X21 + 0.0244 X22 + 0.0184 X23 + 0.0081 X24 + 0.0116 X25 + 0.0000 X26 + 0.0004 X27 + 0.0264 X28 + 0.0226 X29 + 0.0184 X30 + 0.0183 X31 + 0.0243 X32 + 0.0442 X33 + 0.0113 X34 + 0.0042 X35 + 0.0010 X36 + 0.0106 X37 + 0.0108 X38 + 0.0248 X39 + 0.0119 X40 + 0.0186 X41 + 0.0337 X42 + 0.0266 X43 + 0.0514 X44 + 0.0035 X45 + 0.0059 X46 + 0.0017 X47 + 0.0015 X48 + 0.0048 X49 + 0.0110 X50 + 0.0083 X51 + 0.0067 X52 + 0.0106 X53 + 0.0085 X54 + D7E D7A = 0.0705 55 Ek- 13) 0.0229 X1+ 0.0114 X2 + 0.0114 X3 + 0.0286 X4 + 0.0057 X5 + 0.0000 X6 + 0.0000 X7 + 0.0114 X8 + 0.0114 X9 + 0.0229 X10 + 0.0229 X11 + 0.0114 X12 + 0.0114 X13 + 0.0297 X14 + 0.0229 X15 + 0.0114 X16 + 0.0229 X17 + 0.0114 X18 + 0.0229 X19 + 0.0686 X20 + 0.0343 X21 + 0.0114 X22 + 0.0114 X23 + 0.0343 X24 + 0.0457 X25 + 0.0229 X26 + 0.0114 X27 + 0.0229 X28 + 0.0571 X29 + 0.0114 X30 + 0.0114 X31 + 0.0571 X32 + 0.0114 X33 + 0.0229 X34 + 0.0229 X35 + 0.0229 X36 + 0.0114 X37 + 0.0229 X38 + 0.0229 X39 + 0.0114 X40 + 0.0343 X41 + 0.0229 X42 + 0.0229 X43 + 0.0080 X44 + 0.0000 X45 + 0.0114 X46 + 0.0000 X47 + 0.0000 X48 + 0.0000 X49 + 0.0000 X50 + 0.0114 X51 + 0.0069 X52 + 0.0229 X53 + 0.0183 X54 + D8E D8A = 0.0091 14) 0.0105 X1 + 0.0105 X2 + 0.0063 X3 + 0.0126 X4 + 0.0095 X5 + 0.0000 X6 + 0.0000 X7 + 0.0105 X8 + 0.0000 X9 + 0.0211 X10 + 0.0211 X11 + 0.0211 X12 + 0.0211 X13 + 0.0274 X14 + 0.0211 X15 + 0.0105 X16 + 0.0211 X17 + 0.0211 X18 + 0.0316 X19 + 0.0316 X20 + 0.0411 X21 + 0.0316 X22 + 0.0105 X23 + 0.0211 X24 + 0.0421 X25 + 0.0211 X26 + 0.0211 X27 + 0.0316 X28 + 0.0211 X29 + 0.0211 X30 + 0.0211 X31 + 0.0211 X32 + 0.0211 X33 + 0.0526 X34 + 0.0211 X35 + 0.0211 X36 + 0.0105 X37 + 0.0000 X38 + 0.0316 X39 + 0.0000 X40 + 0.0211 X41 + 0.0105 X42 + 0.0105 X43 + 0.0063 X44 + 0.0021 X45 + 0.0000 X46 + 0.0105 X47 + 0.0105 X48 + 0.0000 X49 + 0.0000 X50 + 0.0316 X51 + 0.0316 X52 + 0.0526 X53 + 0.0421 X54 + D9E D9A = 0.0632 15) 0.0049 X1 + 0.0021 X2 + 0.0042 X3 + 0.0061 X4 + 0.0244 X5 + 0.0021 X6 + 0.0041 X7 + 0.0035 X8 + 0.0035 X9 + 0.0209 X10 + 0.0285 X11 + 0.0362 X12 + 0.0153 X13 + 0.0497 X14 + 0.0292 X15 + 0.0195 X16 + 0.0898 X17 + 0.0188 X18 + 0.0209 X19 + 0.0369 X20 + 0.0204 X21 + 0.0167 X22 + 0.0153 X23 + 0.0188 X24 + 0.0418 X25 + 0.0264 X26 + 0.0188 X27 + 0.0188 X28 + 0.0348 X29 + 0.0153 X30 + 0.0084 X31 + 0.0348 X32 + 0.0084 X33 + 0.0070 X34 + 0.0898 X35 + 0.0898 X36 + 0.0070 X37 + 0.0153 X38 + 0.0063 X39 + 0.0056 X40 + 0.0341 X41 + 0.0104 X42 + 0.0139 X43 + 0.0045 X44 + 0.0000 X45 + 0.0021 X46 + 0.0021 X47 + 0.0042 X48 + 0.0048 X49 + 0.0014 X50 + 0.0014 X51 + 0.0011 X52 + 0.0021 X53 + 0.0017 X54 + D10E D10A = 0.0323 16) 0.0031 X1 + 0.0004 X2 + 0.0061 X3 + 0.0038 X4 + 0.0030 X5 + 0.0050 X6 + 0.0004 X7 + 0.0018 X8 + 0.0000 X9 + 0.0192 X10 + 0.0212 X11 + 0.0194 X12 + 0.0000 X13 + 0.0153 X14 + 0.0191 X15 + 0.0075 X16 + 0.0028 X17 + 0.0283 X18 + 0.0576 X19 + 0.0577 X20 + 0.0042 X21 + 0.0303 X22 + 0.0096 X23 + 0.0032 X24 + 0.0385 X25 + 0.0279 X26 + 0.0070 X27 + 0.0361 X28 + 0.0376 X29 + 0.0096 X30 + 0.0432 X31 + 0.0112 X32 + 0.0530 X33 + 0.0070 X34 + 0.0204 X35 + 0.0041 X36 + 0.0000 X37 + 0.0146 X38 + 0.0006 X39 + 0.0004 X40 + 0.0046 X41 + 0.0056 X42 + 0.0042 X43 +0.0558 X44 + 0.0098 X45 + 0.1152 X46 + 0.0134 X47 + 0.1391 X48 + 0.0095 X49 + 0.0109 X50 + 0.0003 X51 + 0.0014 X52 + 0.0042 X53 + 0.0033 X54 + D11E D11A = 0.0335 56 Ek- 17) 0.0000 X1 + 0.0000 X2 + 0.0000 X3 + 0.0000 X4 + 0.0000 X5 + 0.0000 X6 + 0.0000 X7 + 0.0000 X8 + 0.0000 X9 + 0.0000 X10 + 0.0000 X11 + 0.0000 X12 + 0.0000 X13 + 0.0000 X14 + 0.0000 X15 + 0.0000 X16 + 0.0000 X17 + 0.0000 X18 + 0.0000 X19 + 0.0000 X20 + 0.0000 X21 + 0.0000 X22 + 0.0000 X23 + 0.0000 X24 + 0.0000 X25 + 0.0000 X26 + 0.0000 X27 + 0.0000 X28 + 0.0000 X29 + 0.0000 X30 + 0.0000 X31 + 0.0000 X32 + 0.0000 X33 + 0.0000 X34 + 0.0000 X35 + 0.0000 X36 + 0.0000 X37 + 0.0000 X38 + 0.0000 X39 + 0.0000 X40 + 0.0000 X41 + 0.0000 X42 + 0.0000 X43 + 0.0000 X44 + 0.0000 X45 + 0.0000 X46 + 0.0000 X47 + 0.0000 X48 + 0.0000 X49 + 0.0000 X50 + 0.0000 X51 + 0.0000 X52 + 0.0000 X53 + 0.0000 X54 D12A = 0 END INTE X1 INTE X28 INTE X2 INTE X29 INTE X3 INTE X30 INTE X4 INTE X31 INTE X5 INTE X32 INTE X6 INTE X33 INTE X7 INTE X34 INTE X8 INTE X35 INTE X9 INTE X36 INTE X10 INTE X37 INTE X11 INTE X38 INTE X12 INTE X39 INTE X13 INTE X40 INTE X14 INTE X41 INTE X15 INTE X42 INTE X16 INTE X43 INTE X17 INTE X44 INTE X18 INTE X45 INTE X19 INTE X46 Ek-4 : INTE X20 INTE X47 INTE X21 INTE X48 INTE X22 INTE X49 INTE X23 INTE X50 INTE X24 INTE X51 INTE X25 INTE X52 INTE X26 INTE X53 INTE X27 INTE X54 57 17) 0.0000 X1 + 0.0000 X2 + 0.0000 X3 + 0.0000 X4 + 0.0000 X5 + 0.2500 X6 + 0.0000 X7 + 0.0000 X8+ 0.0000 X9 + 0.0000 X10 + 0.0000 X11 + 0.0000 X12 + 0.0000 X13 + 0.0000 X14 + 0.0000 X15+ 0.0000 X16 + 0.0000 X17 + 0.0000 X18 + 0.0000 X19 + 0.0000 X20 + 0.0000 X21 + 0.0000 X22+ 0.0000 X23 + 0.0000 X24 + 0.0000 X25 + 0.2500 X26 + 0.0000 X27 + 0.0000 X28 + 0.0000 X29+ 0.0000 X30 + 0.0000 X31 + 0.0000 X32 + 0.0000 X33 + 0.0000 X34 + 0.0000 X35 + 0.0000 X36+ 0.2500 X37 + 0.0000 X38 + 0.0000 X39 + 0.0000 X40 + 0.0000 X41 + 0.0000 X42 + 0.0000 X43 +0.0000 X44 + 0.0000 X45 + 0.0000 X46 + 0.0000 X47 + 0.0000 X48 + 0.0000 X49 + 0.0000 X50 + 0.2500 X51 + 0.0000 X52 + 0.0000 X53 + 0.0000 X54 D12A = 0 18) X6 + X26 + X37 + X51 = 0 58 Ek- 17) 0.0000 X1 + 0.0000 X2 + 0.0000 X3 + 0.0000 X4 + 0.0000 X5 + 0.1250 X6 + 0.1250 X7 + 0.0000 X8 + 0.0000 X9 + 0.0000 X10 + 0.0000 X11 + 0.0000 X12 + 0.0000 X13 + 0.0000 X14 + 0.0000 X15 + 0.0000 X16 + 0.0000 X17 + 0.0000 X18 + 0.0000 X19 + 0.0000 X20 + 0.0000 X21 + 0.1250 X22 + 0.0000 X23 + 0.0000 X24 + 0.0000 X25 + 0.1250 X26 + 0.0000 X27 + 0.0000 X28 + 0.0000 X29 + 0.0000 X30 + 0.0000 X31 + 0.0000 X32 + 0.0000 X33 + 0.0000 X34 + 0.0000 X35 + 0.0000 X36 + 0.1250 X37 + 0.0000 X38 + 0.0000 X39 + 0.1250 X40 + 0.0000 X41 + 0.0000 X42 + 0.0000 X43 + 0.0000 X44 + 0.0000 X45 + 0.0000 X46 + 0.1250 X47 + 0.0000 X48 + 0.0000 X49 + 0.0000 X50 + 0.1250 X51 + 0.0000 X52 + 0.0000 X53 + 0.0000 X54 D12A = 0 18) X6 + X26 + X37 + X51 + X7 + X22 + X40 + X47 = 0 17) 0.0000 X1 + 0.0000 X2 + 0.0000 X3 + 0.0000 X4 + 0.0000 X5 + 0.0833 X6 + 0.1250 X7 + 0.0833 X8 + 0.0000 X9 + 0.0000 X10 + 0.0000 X11 + 0.0000 X12 + 0.0000 X13 + 0.0000 X14 + 0.0000 X15 + 0.0000 X16 + 0.0000 X17 + 0.0000 X18 + 0.0000 X19 + 0.0000 X20 + 0.0000 X21 + 0.0833 X22 + 0.0000 X23 + 0.0000 X24 + 0.0000 X25 + 0.0833 X26 + 0.0000 X27 + 0.0000 X28 + 0.0000 X29 + 0.0000 X30 + 0.0000 X31 + 0.0000 X32 + 0.0000 X33 + 0.0833 X34 + 0.0000 X35 + 0.0000 X36 + 0.0833 X37 + 0.0833 X38 + 0.0000 X39 + 0.0833 X40 + 0.0000 X41 + 0.0000 X42 + 0.0000 X43 + 0.0000 X44 + 0.0000 X45 + 0.0000 X46 + 0.0833 X47 + 0.0000 X48 + 0.0833 X49 + 0.0000 X50 + 0.0833 X51 + 0.0000 X52 + 0.0000 X53 + 0.0000 X54 D12A = 0 18) X6 + X26 + X37 + X51 + X7 + X22 + X40 + X47 + X8 + X34 + X38 + X49 = 0 59 Ek-6: OBJECTIVE FUNCTION VALUE 1) 0.1691000 VARIABLE VALUE REDUCED COST X1 0.000000 0.011000 X28 0.000000 -0.002900 X2 0.000000 0.017500 X29 0.000000 0.029400 X3 0.000000 0.002900 X30 0.000000 -0.000200 X4 0.000000 0.008400 X31 0.000000 0.015000 X5 0.000000 0.019000 X32 0.000000 0.049000 X6 1.000000 -0.016400 X33 0.000000 -0.063800 X7 0.000000 -0.000400 X34 0.000000 0.018300 X8 0.000000 0.000100 X35 0.000000 0.212300 X9 0.000000 0.002000 X36 0.000000 0.252100 X10 0.000000 0.231100 X37 1.000000 -1.007600 X11 0.000000 0.187100 X38 0.000000 -0.999600 X12 0.000000 0.238300 X39 0.000000 -0.929200 X13 0.000000 0.064600 X40 0.000000 -1.001300 X14 0.000000 0.125700 X41 0.000000 -0.964500 X15 0.000000 0.029800 X42 0.000000 -0.977400 X16 0.000000 0.130900 X43 0.000000 -0.983800 X17 0.000000 0.238300 X44 0.000000 -0.074600 X18 0.000000 0.061700 X45 0.000000 0.008000 X19 0.000000 1.012200 X46 0.000000 -0.074500 X20 0.000000 0.078100 X47 0.000000 -0.002100 X21 0.000000 0.155500 X48 0.000000 -0.076700 X22 0.000000 0.077000 X49 0.000000 0.011900 X23 0.000000 0.071200 X50 0.000000 0.021400 X24 0.000000 0.092600 X51 1.000000 0.050800 X25 0.000000 0.287500 X52 0.000000 0.073000 D1A 0.017500 0.000000 D2E 0.002500 0.000000 D2A 0.000000 2.000000 D3E 0.000000 2.000000 D3A 0.008700 0.000000 D4A 0.000000 1.000000 D5E 0.000000 2.000000 D5A 0.005400 0.000000 D6E 0.000100 0.000000 D6A 0.000000 2.000000 D7E 0.040900 0.000000 D7A 0.000000 2.000000 D8E 0.000000 2.000000 D8A 0.036600 0.000000 D9E 0.000000 0.000000 D9A 0.000000 2.000000 D10E 0.000000 2.000000 D10A 0.004600 0.000000 D11E 0.000300 0.000000 D11A 0.000000 2.000000 D12A 0.000000 2.000000 X26 1.000000 0.000000 X27 0.000000 0.014100 X53 0.000000 0.097000 X54 0.000000 0.094000 D4E 0.012500 0.00000 60 Ek-7: OBJECTIVE FUNCTION VALUE 1) 0.1510000 VARIABLE VALUE REDUCED COST X1 0.000000 1.039800 X28 0.000000 0.069300 X2 0.000000 1.011000 X29 0.000000 0.058800 X3 0.000000 1.031800 X30 0.000000 0.031000 X4 0.000000 1.049500 X31 0.000000 0.064200 X5 0.000000 0.979100 X32 0.000000 0.019600 X6 0.000000 0.968700 X33 0.000000 0.055900 X7 1.000000 0.986200 X34 0.000000 0.010800 X8 0.000000 1.002000 X35 0.000000 0.037300 X9 0.000000 0.999100 X36 0.000000 0.005300 X10 0.000000 0.105400 X37 0.000000 -0.044900 X11 0.000000 0.092300 X38 0.000000 0.028600 X12 0.000000 0.089500 X39 0.000000 0.065100 X13 0.000000 0.026900 X40 1.000000 -0.007800 X14 0.000000 -0.030800 X41 0.000000 0.057800 X15 0.000000 -0.058500 X42 0.000000 0.014900 X16 0.000000 0.052000 X43 0.000000 -0.000900 X17 0.000000 -0.003100 X44 0.000000 -0.033600 X18 0.000000 0.062400 X45 0.000000 -0.018900 X19 0.000000 0.335000 X46 0.000000 0.087500 X20 0.000000 0.130600 X47 1.000000 -0.051900 X21 0.000000 0.070600 X48 0.000000 0.105600 X22 1.000000 0.076200 X49 0.000000 -0.047500 X23 0.000000 0.056800 X50 0.000000 -0.042500 X24 0.000000 0.100500 X51 0.000000 -0.048300 X25 0.000000 0.154900 X52 0.000000 -0.001000 D1A 0.040900 0.000000 D2E 0.001300 0.000000 D2A 0.000000 2.000000 D3E 0.000000 2.000000 D3A 0.020700 0.000000 D4A 0.000000 1.000000 D5E 0.000000 2.000000 D5A 0.002400 0.000000 D6E 0.000000 2.000000 D6A 0.014300 0.000000 D7E 0.021800 0.000000 D7A 0.000000 2.000000 D8E 0.000000 2.000000 D8A 0.013700 0.000000 D9E 0.021100 0.000000 D9A 0.000000 2.000000 D10E 0.003800 0.000000 D10A 0.000000 2.000000 D11E 0.000000 2.000000 D11A 0.011000 0.000000 D12A 0.000000 2.000000 X26 0.000000 0.000000 X27 0.000000 0.000000 X53 0.000000 0.010000 X54 0.000000 0.000000 D4E 0.019500 0.00000 61 Ek-8 OBJECTIVE FUNCTION VALUE 1) 0.1572000 VARIABLE VALUE REDUCED COST X1 0.000000 -0.104000 X28 0.000000 -0.078500 X2 0.000000 -0.138600 X29 0.000000 -0.011000 X3 0.000000 -0.117600 X30 0.000000 0.001400 X4 0.000000 -0.099500 X31 0.000000 -0.057200 X5 0.000000 -0.153300 X32 0.000000 0.002600 X6 0.000000 0.853800 X33 0.000000 -0.084300 X7 0.000000 0.859200 X34 1.000000 -0.012600 X8 1.000000 -0.160200 X35 0.000000 -0.001500 X9 0.000000 -0.127300 X36 0.000000 0.011700 X10 0.000000 0.076000 X37 0.000000 -0.028800 X11 0.000000 0.028300 X38 1.000000 -1.016000 X12 0.000000 0.060900 X39 0.000000 -1.107100 X13 0.000000 0.040300 X40 0.000000 -0.015400 X14 0.000000 -0.064600 X41 0.000000 -1.018000 X15 0.000000 -0.096900 X42 0.000000 -1.012500 X16 0.000000 0.048600 X43 0.000000 -1.023300 X17 0.000000 0.005900 X44 0.000000 0.017200 X18 0.000000 -0.002000 X45 0.000000 0.133700 X19 0.000000 0.183000 X46 0.000000 0.010500 X20 0.000000 0.007600 X47 0.000000 1.098100 X21 0.000000 -0.012200 X48 0.000000 -0.015400 X22 0.000000 0.945400 X49 1.000000 0.109100 X23 0.000000 0.027200 X50 0.000000 0.109700 X24 0.000000 0.069300 X51 0.000000 1.052400 X25 0.000000 0.074100 X52 0.000000 0.026600 D1A 0.026000 0.000000 D2E 0.006900 0.000000 D2A 0.000000 2.000000 D3E 0.000000 2.000000 D3A 0.015300 0.000000 D4A 0.000000 1.000000 D5E 0.006900 0.000000 D5A 0.000000 2.000000 D6E 0.000000 2.000000 D6A 0.022500 0.000000 D7E 0.029100 0.000000 D7A 0.000000 2.000000 D8E 0.000000 2.000000 D8A 0.048100 0.000000 D9E 0.000100 0.000000 D9A 0.000000 2.000000 D10E 0.001700 0.000000 D10A 0.000000 2.000000 D11E 0.000600 0.000000 D11A 0.000000 2.000000 D12A 0.000000 2.000000 X26 0.000000 0.982100 X27 0.000000 0.000000 X53 0.000000 0.000000 X54 0.000000 0.028600 D4E 0.015600 0.000000 62 Ek-9: OBJECTIVE FUNCTION VALUE 1) 0.1892000 VARIABLE VALUE REDUCED COST X1 0.000000 -0.915000 X28 0.000000 0.112500 X2 1.000000 -0.957700 X29 0.000000 0.066700 X3 0.000000 -0.941000 X30 0.000000 0.054300 X4 0.000000 -0.921100 X31 1.000000 0.053100 X5 0.000000 -0.966200 X32 0.000000 0.053700 X6 0.000000 -0.978700 X33 0.000000 0.079200 X7 0.000000 -0.981600 X34 0.000000 0.006400 X8 0.000000 -0.951600 X35 0.000000 0.075600 X9 0.000000 -0.946800 X36 0.000000 0.001400 X10 0.000000 0.182600 X37 0.000000 0.059500 X11 0.000000 0.150300 X38 0.000000 0.104600 X12 0.000000 0.151700 X39 0.000000 0.195000 X13 0.000000 0.132500 X40 0.000000 0.075000 X14 0.000000 0.060900 X41 0.000000 0.165900 X15 0.000000 -0.002800 X42 0.000000 0.053900 X16 0.000000 0.094500 X43 1.000000 0.138700 X17 0.000000 0.017000 X44 0.000000 -0.047500 X18 0.000000 0.092800 X45 0.000000 -0.047500 X19 0.000000 0.369000 X46 0.000000 0.069600 X20 0.000000 0.178600 X47 0.000000 -0.063600 X21 0.000000 0.094000 X48 0.000000 0.085700 X22 0.000000 0.078400 X49 0.000000 -0.067300 X23 0.000000 0.080100 X50 1.000000 -0.065600 X24 0.000000 0.166100 X51 0.000000 -0.019500 X25 0.000000 0.336600 X52 0.000000 -0.010700 D1A 0.044900 0.000000 D2E 0.000000 2.000000 D2A 0.000000 0.000000 D3E 0.000000 2.000000 D3A 0.017900 0.000000 D4A 0.009100 0.000000 D5E 0.000000 2.000000 D5A 0.001100 0.000000 D6E 0.000000 2.000000 D6A 0.019500 0.000000 D7E 0.007300 0.000000 D7A 0.000000 2.000000 D8E 0.000000 2.000000 D8A 0.036600 0.000000 D9E 0.021100 0.000000 D9A 0.000000 2.000000 D10E 0.006500 0.000000 D10A 0.000000 2.000000 D11E 0.000000 2.000000 D11A 0.025200 0.000000 D12A 0.000000 2.000000 X26 0.000000 0.007100 X27 0.000000 0.000000 X53 0.000000 0.017800 X54 0.000000 0.000000 D4E 0.000000 1.00000