Karar Analizi Hedef Programlama - II i 2011-2012 BAHAR YARIYILI PROJE 1 HEDEF PROGRAMLAMA 080253009 080253033 080253038 MAHMUT YILMAZ 080253044 HAKAN KARACAN 05 MART 2012 i , . u konuda son 12 makaleler ve tezler incelendi. Uygulama olarakta, tip-2 diyabet ii ................................................................................................................................................. i .................................................................................................................................. ii .............................................................................................................................................1 2. HEDEF PROGRAMLAMA ............................................................................................................1 .............................................................................................2 .................................................................................2 ........................................................................................5 ....................................................................................................5 2.3. ............................................................................................... 10 ....................................................................... 14 ...................................................... 15 ............................................................................................................... 15 3. UYGULAMA ............................................................................................................................... 18 ....................................................................................................... 18 3.2. ....................................................................................................................... 18 ......................................................................................................................... 18 ............................................. 19 ............................................................................ 20 ..................................................................................... 25 ...................................................................................................... 25 ......... 31 ............................................................................................ 31 ................................................................................ 31 ................................................................................................... 31 ............................................ 33 ................................................................................................. 35 ................................................................................................................................... 42 1 1. Oysa n, amlamadan ve akademik bahsedil 1 2. HEDEF PROGRAMLAMA - Sapma: fark. : Hedef: k 2 1 >>>P 2 >>> P k i - ve d i + olarak ifade edilir. W ki . deki hedefler d i - i + belirlenir. Min [ m i 1 ( d i - +d i + ) a ] 1/a a=1 g k f i (x)+d i - -d i + =b i d i - ,d i + i d i - ,d i + =0, i 3 Burada b i i - ve di + - Hedef prog programlam Min [P 1 h 1 (d - ,d + ), P 2 h 2 (d - ,d + j h j (d - ,d + )] g k f i (x)+d i - -d i + =b i d i - ,d i + i d i - ,d i + =0, i Burada h j (d - ,d + j - j >>>P j+1 bunun j , P j+1 j+1 >P j . : dvd player i ma TL m TL net kar elde edilmektedir. To satmak 4 x 1 asinler x 2 Z max = 8x 1 + 12x 2 A.K.A. x 1 + 2x 2 40 x 1 30 x 2 15 keyfi olarak haftada 100 TL G 1 : 8x 1 + 12x 2 + d 1 - - d 1 + = 100 d 1 - *d 1 + = 0 1) d 1 - = d 1 + = 0 2) d 1 - > 0, d 1 + = 0 3) d 1 - = 0, d 1 + > 0 Min G 1 = d 1 - Burada d 1 - 1 + Fazla mesai hedefi: G 2 : x 1 + 2x 2 + d 2 - - d 2 + = 40 d 2 - * d 2 + = 0 Burada d 2 + 2 - Min G 2 = d 2 + 5 Pazarlama hedefi: G 3 : x 1 + d 3 - - d 3 + = 30 G 3 : x 2 +d 4 - - d 4 + = 15 d 3 - * d 3 + = 0 d 4 - * d 4 + = 0 istiyorsak d 3 - , d 4 - gerekir. Min G 3 = d 3 - Min G 3 = d 4 - . Min Z= w 1 G 1 + w 2 G 2 +...+ w n G n i, i 6 ve televizyon Tablo 1: verileri Radyo TV Maliyet (1000 TL) 4 8 1 8 24 2 in 100000 TL x 1 x 2 G 1 G 1 : 4x 1 +8x 2 +d 1 - -d 1 + = 45 Min G 1 = d 1 - 7 G 2 G 2 : 8x 1 +24x 2 +d 2 - -d 2 + = 100 Min G 2 = d 2 + x 1 +2x 2 10 x 1 6 x 1 , x 2 , d 1 - ,d 1 + , d 2 - , d 2 + 0 Min a= {2G 1 +G 2 }={2d 1 - + d 2 + } A.K.A 4x 1 + 8x 2 +d 1 - -d 1 + = 45 8x 1 +24x 2 +d 2 - -d 2 + = 100 x 1 +2x 2 10 x 1 6 x 1 , x 2 , d 1 - ,d 1 + , d 2 - , d 2 + 0 8 Resim 1: Resim 2: 9 4x 1 + 8x 2 =45 (1) (0, 5,625),(11,25, 0) 8x 1 +24x 2 =100 (2) (0, 4,167),(12,5, 0) x 1 +2x 2 =10 (3) (0, 5),(10, 0 ) x 1 =6 (4) (x 1 =6) G 10 1 2 + 1 - +d 2 + durumda d 1 - 4x 1+ 8x 2 +d 1 d 1 + =45 d 1 - =5 d 1 + = 0 8x 1 + 24x 2 +d 2 - -d 2 + =100 d 2 - =0 d 2 + =0 Min a = 2*5+0 = 10 x 1 +2x 2 =10 x 1 =6 4x 1 +8x 2 +d 1 - -d 1 + =45 d 1 - =5 d 1 + =0 8x 1 +24x 2 +d 2 - -d 2 + =100 d 2 - =4 d 2 + =0 Min a= 2d 1 - +d 2 + =10 1 - . 11 Min G 1 =P 1 . . . Min G n =P n P i >>>P i+1 SONY SONY Vaio1 ve SONY Vaio2 SONY SONY firmalardan temin edilmektedir. SONY edebilmektedir SONY SONY SONY P1: Haftada en az 200 adet SONY Vaio1 x 1 SONY Vaio1 adedi x 2 SONY Vaio2 adedi 12 Hedefler x 1 200 (SONY Vaio1) x 1 + x 2 200x 1 +500x 2 x 1 + 1,5x 2 Problemin hedef programlama modeli olarak ifadesi: G 1 : x 1 +d 1 - -d 1 + = 200 Min P 1 d 1 - G 2 : x 1 +x 2 +d 2 - -d 2 + = 500 Min P 1 d 1 - , P 2 d 2 - G 3 : 200x 1 +500x 2 +d 3 - -d 3 + = 250000 Min P 1 d 1 - , P 2 d 2 - , P 3 d 3 - G 4 : x 1 +1,5x 2 +d 4 - -d 4 + = 400 Min P 1 d 1 - , P 2 d 2 - , P 3 d 3 - , P 4 d 4 + Min a= { P 1 d 1 - , P 2 d 2 - , P 3 d 3 - , P 4 d 4 + } A.K.A. x 1 +d 1 - -d 1 + = 200 x 1 +x 2 +d 2 - -d 2 + = 500 200x 1 +500x 2 +d 3 - -d 3 + = 250000 x 1 + 1,5x 2 +d 4 - -d 4 + = 400 x 1 , x 2 , d 1 - , d 1 + , d 2 - , d 2 + , d 3 - , d 3 + , d 4 - ,d 4 + 13 d 1 - 1 - 2 - meyecek ve d 3 - 2 - 200x 1 +500x 2 +d 3 - - d 3 + = 250000 d 3 - = 60000 d 3 + = 0 14 x 1 +1,5x 2 +d 4 - -d 4 + = 400 d 4 + = 250 Nakliye Problemleri, Orman 15 16 Tablo 2: 17 Tablo 3: 18 3. UYGULAMA , Eylem -1 T Do Hedef Programlama ve Bir Diyet Probleminin U a y 3 3 1- Diyetteki protein 2- 3- 3 1- Maliyetimizi minimize etmektir. 2- 3- 1- gerekmektedir. 2- 3- - 4- 19 5- 1- 2- -ana yemek- (pilav-makarna)-meyveler) 3- 4- 5- 3 - Tablo 4: 19-30E 31-60E 60+E 19-30K 31-60K 60+K ortalama Enerji (kkal) 342.4 347 291.6 321.2 325.8 298.25 Protein (gr) 4.08 4.85 5.62 5.64 6.42 6.83 Kalsiyum (mg) 84 86 108 112 114 135 Demir (mg) 0.96 1.09 1.22 3.88 2.62 1.68 A Vitamini (IU) 1000 1000 1000 1000 1000 1000 Thiamin (mg) 0.04 0.02 0.02 0.08 0.06 0.08 Ribofilavin (mg) 0.3 0.24 0.2 0.22 0.18 0.17 Niasin (mg) 2.32 1.83 1.54 1.96 1.8 1.78 C Vitamini (mg) 12 12 12 15 15 12 20 19-30E 31-60E 60+E 19-30K 31-60K 60+K ortalama Enerji (kkal) 684.8 694 583.2 642.4 651.6 596.5 Protein (gr) 8.16 9.7 11.24 11.258 12.84 13.65 Kalsiyum (mg) 168 172 216 224 228 270 Demir (mg) 1.92 2.18 2.44 7.76 5.24 3.35 A Vitamini (IU) 2000 2000 2000 2000 2000 2000 Thiamin (mg) 0.08 0.04 0.04 0.16 0.12 0.15 Ribofilavin (mg) 0.6 0.48 0.4 0.44 0.36 0.33 Niasin (mg) 4.64 3.66 3.08 3.92 3.6 3.55 C Vitamini (mg) 24 24 24 30 30 24 3. 21 Tablo 5: Sabah K lanlanan M N YEMEKLER (kkal) (gr) (gr) (mg) (mg) A (IU) (mg) (mg) (mg) C (mg) (TL) 1 Yumurta (1 adet) 80 6.4 5.7 27 1.3 500 0.1 0.1 0 0 0.1 2 Beyaz peynir (30gr) 87 6.8 6.5 49 0.2 216 0 0.1 0.1 0 0.135 3 (30gr) 121 8.1 9.5 21 0.3 300 0 0.2 0 0 0.18 4 Zeytin (30gr) 62 0.5 6.3 23 0.5 18 0 0 0 0 0.15 5 250 0.5 27.6 6.3 0.07 1000 0 0.01 0.1 0 0.25 6 (domates- 20 2 5 3.2 0.9 354 0.2 0.3 0.1 0 0.3 7 (1 fincan) 0 0 0 0 0 0 0 0 0 0 0.1 8 (1 fincan) 96 5.25 4.5 180 0.15 225 0.06 0.32 0.15 1.5 0.15 9 Elma (1 adet) 101 0.5 0.5 9.6 0.6 48 0.0 0.1 0.3 9.6 0.25 10 Portakal (1 adet) 69 1.1 0.3 47.6 1.0 168 0.1 0.0 0.3 82.6 0.25 22 Tablo 6: YEMEKLER (kkal) (gr) (gr) (mg) (mg) A (IU) (mg) (mg) (mg) C (mg) (TL) 1 mercimek 183 7.9 6.7 24.9 2.3 182 0.2 0.1 0.7 2.2 0.141 2 115 3.3 5.8 42.9 0.5 208 0.1 0.1 0.3 0.3 0.151 3 Ezogelin 126.3 5.6 2.4 24 1.9 190 0.1 0.06 0.6 1.13 0.109 4 131.6 5.8 3.1 31 2.9 228 0.25 0.12 0.88 2.75 0.088 5 Tavuksuyu 177 9.5 12.5 6.5 0.65 309 0.05 0.09 0.5 2.13 0.75 6 186 9.6 9.4 28 2.5 298 0.04 0.2 0.5 10 0.449 7 114 1.2 6.2 5.3 0.2 303 0.01 0.08 0.3 3.6 0.75 8 115 1.8 6.3 6.2 0.2 303 0.05 0.04 0.2 0.3 0.483 9 Domates 161 3.4 9.6 59 0.5 410 0.1 0.1 0.5 1.3 0.398 10 184 2.8 11.5 6.5 0.5 200 0.1 0 0.5 0.0 0.613 11 348 16.9 23.1 20.3 2.8 164 0.2 0.2 3 13.8 3.629 12 309 15.4 16.4 70 2.5 282 0.2 0.2 4.1 15.2 2.276 13 311 18.6 18.5 18.2 3.1 114 0.1 0.2 5.2 13.9 3.907 14 417 16.2 14.6 15.1 2 360 0.1 0.1 2.8 5.4 2.411 15 225 4.6 5 15 4 120 0.1 0.2 4.7 14.8 0.687 16 Barbunya 328 13.3 8.2 14 3.3 496.6 0.21 0.2 4.8 3.8 0.864 17 489 52.3 20 50.5 5.6 233 0.2 0.3 1.2 5 2.344 18 346 36.1 19 45 84.2 0.1 0.1 0.3 0.3 1.854 19 461 19.8 27.4 13.1 2.4 200 0.1 0.2 2.2 0.0 2.722 20 391 22.8 26.8 40 2.44 3007 0.26 0.26 7.14 11 3.370 21 303 14.7 15.7 35.3 2.9 4228 0.2 0.2 4.2 13.7 2.185 23 22 231 12.8 15.6 16.1 2 360 0.1 0.1 2.8 5.4 2.200 23 182.5 22.3 8.1 11 1 73 0.2 0.2 12.9 2.0 1.357 24 musakka 201 9.6 11.9 47.5 2.7 539 0.1 0.2 2.7 20.3 1.596 25 Etli taze fasulye 222 11.1 11.8 94.8 3.6 1412 0.2 0.3 3 41.3 2.555 26 Etli bezelye 298 18.3 12 47.1 4.2 950 0.6 0.3 5.3 41.4 2.210 27 Etli bamya 286 12.2 9.6 156 2.38 958 0.3 0.39 2.93 3.0 3.650 28 118.6 9.1 4.6 149.3 1.8 693 0.1 0.3 2.4 21.7 1.346 29 166 9.1 11.5 51.7 2.7 521 0.1 0.1 2.2 6.9 1.452 30 Etli nohut 350 17.4 16.5 75.4 4.9 231 0.3 0.2 2.7 2.3 2.600 31 696 34 46 41 5.4 328 0.4 0.4 6.0 27.6 3.635 32 patates 76 2.1 0.1 7 0.6 0.0 0.2 0.2 3.8 20 1.056 33 (etsiz) 108.8 2.8 4.4 12 0.7 10.0 0.1 0.2 2.7 5.0 0.799 34 Kabak kalye (etsiz) 248 11.9 14.3 158.1 2.1 748 0.2 0.3 2.7 25.9 0.992 35 Bezelye (etsiz) 145.3 4.7 5.1 26 1 640 0.5 0.2 5.0 27 1.145 36 Taze fasulye (etsiz) 166 9.1 11.5 51.7 2.7 521 0.1 0.2 2.2 6.9 1.090 37 Bamya (etsiz) 63.6 2.1 2.8 92 0.6 520 0.1 0.2 1.2 31 2.055 38 Konserve bezelye (etsiz) 145.3 4.7 5.1 26 1.9 690 0.5 0.2 5.0 8 1.185 39 Konserve taze fasulye (etsiz) 177 3.5 10.4 90.7 2.5 1252 0.1 0.2 1.2 38 2.005 40 Ispanak (etsiz) 99 5.2 3 50 1.1 320 0.2 0.25 1.0 5 1.004 41 but 259 26.2 10.5 31.5 2.6 120 0.2 0.2 12.9 14.6 1.202 42 114 23.2 1.7 11 0.7 28 0.2 0.2 12.9 1.0 1.305 43 336 4.7 12.6 7.5 0.6 303 0.1 0.1 1.0 0.0 0.609 44 Sebzeli bulgur 291 6.5 12.9 25 1.9 305 0.2 0.0 2.2 10.5 0.59 45 makarna 505 19.4 21.3 278.6 1.6 704 0.2 0.3 0.9 0.4 0.53 46 337 7.1 12.1 11.2 1.7 336 0.1 0.0 0.8 0.3 0.55 24 47 Patatesli tepsi 421 15 17.7 108.6 5.5 527 0.3 0.2 4.9 3.3 1.018 48 (peynirli) 146.8 4.5 6.8 26.4 2.2 956 0.2 0.1 1.5 4.0 0.754 49 469 11.5 30.2 22.9 2.1 755 0.2 0.1 2.0 3.0 0.752 50 58 1.4 3.6 33 0.98 1456 0.07 0.06 2.64 40.0 0.35 51 10 0.6 0.2 17 2.1 100.0 0.0 0.02 0.0 7.0 0.25 52 Portakal 69 1.1 0.3 47.6 1 168 0.1 0.0 0.3 82.6 0.25 53 Elma 101 0.5 0.5 9.6 1.6 48.0 0.0 0.1 0.3 9.6 0.25 54 57 1.1 0.4 41.3 1.4 43 0.0 0.1 0.6 99.8 0.25 55 Erik 59 0.7 0.2 11.3 0.6 135 0.0 0.0 0.6 6.8 0.25 56 38 0.2 0.5 14 0.6 312 0.0 0.0 0.2 7.8 0.25 57 131 4.5 8.4 166.1 0.5 234 0.1 0.3 0.2 0.2 0.45 58 Ayran 90 7 2.7 248 0.2 190 0.06 0.3 0.16 1.0 0.25 59 148 7.1 6.5 300 0.3 300 0.2 0.5 0.3 3.0 0.35 60 118.4 5.7 5.2 240 0.24 240 0.16 0.4 0.24 2.4 0.4 25 3. s y 3. aliyet, enerji ve besin - Bu a 26 Tablo 7: Normalize E Gereken Kalori M 19-30E 31-60E 60+E 19-30K 31-60K 60+K ortalama Enerji (kkal) 0.3865 0.3916 0.3291 0.3625 0.3677 0.3366 Protein (gr) 0.1310 0.1557 0.1804 0.1811 0.2061 0.2193 (gr) 0.2598 0.2513 0.2126 0.2058 0.1971 0.1780 Kalsiyum (mg) 0.2291 0.2345 0.2945 0.3054 0.3109 0.3681 Demir (mg) 0.1912 0.2171 0.2430 0.7729 0.5219 0.3347 A Vitamini (IU) 0.3535 0.3535 0.3535 0.3535 0.3535 0.3535 Thiamin (mg) 0.0870 0.0435 0.0435 0.1739 0.1304 0.1739 Ribofilavin (mg) 0.2655 0.2124 0.1770 0.1947 0.1593 0.1504 Niasin (mg) 2.2095 1.7429 1.4667 1.8667 1.7143 1.6952 C Vitamini (mg) 0.1281 0.1281 0.1281 0.1601 0.1601 0.1281 19-30E 31-60E 60+E 19-30K 31-60K 60+K ortalama Enerji (kkal) 0.0520 0.0527 0.0443 0.0488 0.0495 0.0453 Protein (gr) 0.0129 0.0154 0.0178 0.0178 0.0203 0.0216 0.0546 0.0529 0.0447 0.0433 0.0415 0.0374 Kalsiyum (mg) 0.0491 0.0502 0.0631 0.0654 0.0666 0.0788 Demir (mg) 0.0166 0.0189 0.0211 0.0672 0.0454 0.0290 A Vitamini (IU) 0.0668 0.0668 0.0668 0.0668 0.0668 0.0668 Thiamin (mg) 0.0084 0.0042 0.0042 0.0167 0.0126 0.0157 Ribofilavin (mg) 0.0573 0.0458 0.0382 0.0420 0.0344 0.0315 Niasin (mg) 0.0296 0.0233 0.0196 0.0250 0.0229 0.0226 C Vitamini (mg) 0.0317 0.0317 0.0317 0.0397 0.0397 0.0317 27 Tablo 8: Normalize Edi KAHVALTI YEMEKLER (kkal) (gr) (gr) (mg) (mg) A (IU) (mg) (mg) (mg) C (mg) (TL) 1 Yumurta (1 adet) 0.0903 0.2055 0.0865 0.0736 0.2590 0.1767 0.2174 0.0885 0.0000 0.0000 0.0536 2 Beyaz peynir (30gr) 0.0982 0.2183 0.0986 0.1336 0.0398 0.0764 0.0000 0.0885 0.0952 0.0000 0.0724 3 (30gr) 0.1366 0.2600 0.1442 0.0573 0.0598 0.1060 0.0000 0.1770 0.0000 0.0000 0.0965 4 Zeytin (30gr) 0.0700 0.0161 0.0956 0.0627 0.0996 0.0064 0.0000 0.0000 0.0000 0.0000 0.0804 5 0.2822 0.0161 0.4188 0.0172 0.0139 0.3535 0.0000 0.0088 0.0952 0.0000 0.1340 6 - 0.0226 0.0642 0.0759 0.0087 0.1793 0.1251 0.4348 0.2655 0.0952 0.0000 0.1609 7 fincan) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0536 8 fincan) 0.1084 0.1685 0.0683 0.4909 0.0299 0.0795 0.1304 0.2832 0.1429 0.0160 0.0804 9 Elma (1 adet) 0.1140 0.0161 0.0076 0.0262 0.1195 0.0170 0.0000 0.0885 0.2857 0.1025 0.1340 10 Portakal (1 adet) 0.0779 0.0353 0.0046 0.1298 0.1992 0.0594 0.2174 0.0000 0.2857 0.8815 0.1340 28 Tablo 9: YEMEKLER (kkal) (gr) (gr) (mg) (mg) A (IU) (mg) (mg) (mg) C (mg) (TL) 1 mercimek 0.0139 0.0125 0.0107 0.0073 0.0199 0.0061 0.0209 0.0096 0.0045 0.0029 0.0000023 2 0.0087 0.0052 0.0093 0.0125 0.0043 0.0069 0.0105 0.0096 0.0019 0.0004 0.0000025 3 Ezogelin 0.0096 0.0089 0.0038 0.0070 0.0165 0.0063 0.0105 0.0057 0.0038 0.0015 0.0000018 4 0.0100 0.0092 0.0049 0.0091 0.0251 0.0076 0.0262 0.0115 0.0056 0.0036 0.0000015 5 Tavuksuyu 0.0135 0.0150 0.0199 0.0019 0.0056 0.0103 0.0052 0.0086 0.0032 0.0028 0.0000124 6 0.0141 0.0152 0.0150 0.0082 0.0216 0.0100 0.0042 0.0191 0.0032 0.0132 0.0000074 7 0.0087 0.0019 0.0099 0.0015 0.0017 0.0101 0.0010 0.0076 0.0019 0.0048 0.0000124 8 0.0087 0.0028 0.0101 0.0018 0.0017 0.0101 0.0052 0.0038 0.0013 0.0004 0.0000080 9 Domates 0.0122 0.0054 0.0153 0.0172 0.0043 0.0137 0.0105 0.0096 0.0032 0.0017 0.0000066 10 0.0140 0.0044 0.0183 0.0019 0.0043 0.0067 0.0105 0.0000 0.0032 0.0000 0.0000102 11 0.0264 0.0268 0.0369 0.0059 0.0242 0.0055 0.0209 0.0191 0.0191 0.0182 0.0601043 12 0.0235 0.0244 0.0262 0.0204 0.0216 0.0094 0.0209 0.0191 0.0261 0.0201 0.0376956 13 0.0236 0.0294 0.0295 0.0053 0.0268 0.0038 0.0105 0.0191 0.0331 0.0184 0.0647086 14 0.0317 0.0256 0.0233 0.0044 0.0173 0.0120 0.0105 0.0096 0.0178 0.0071 0.0399315 15 0.0171 0.0073 0.0080 0.0044 0.0346 0.0040 0.0105 0.0191 0.0299 0.0196 0.0000114 16 Barbunya 0.0249 0.0211 0.0131 0.0041 0.0286 0.0166 0.0220 0.0191 0.0306 0.0050 0.0000143 17 0.0372 0.0828 0.0319 0.0147 0.0485 0.0078 0.0209 0.0287 0.0076 0.0066 0.0388219 29 18 sote 0.0263 0.0572 0.0303 0.0131 0.0000 0.0028 0.0105 0.0096 0.0019 0.0004 0.0307064 19 0.0350 0.0313 0.0437 0.0038 0.0208 0.0067 0.0105 0.0191 0.0140 0.0000 0.0450824 20 0.0297 0.0361 0.0428 0.0117 0.0211 0.1004 0.0272 0.0248 0.0455 0.0145 0.0558147 21 0.0230 0.0233 0.0250 0.0103 0.0251 0.1412 0.0209 0.0191 0.0268 0.0181 0.0361885 22 0.0176 0.0203 0.0249 0.0047 0.0173 0.0120 0.0105 0.0096 0.0178 0.0071 0.0364369 23 0.0139 0.0353 0.0129 0.0032 0.0087 0.0024 0.0209 0.0191 0.0822 0.0026 0.0224749 24 musakka 0.0153 0.0152 0.0190 0.0139 0.0234 0.0180 0.0105 0.0191 0.0172 0.0268 0.0264333 25 Etli taze fasulye 0.0169 0.0176 0.0188 0.0277 0.0312 0.0472 0.0209 0.0287 0.0191 0.0546 0.0423165 26 Etli bezelye 0.0226 0.0290 0.0191 0.0138 0.0364 0.0317 0.0628 0.0287 0.0338 0.0547 0.0366025 27 Etli bamya 0.0217 0.0193 0.0153 0.0456 0.0206 0.0320 0.0314 0.0372 0.0187 0.0040 0.0604521 28 0.0090 0.0144 0.0073 0.0436 0.0156 0.0231 0.0105 0.0287 0.0153 0.0287 0.0222928 29 0.0126 0.0144 0.0183 0.0151 0.0234 0.0174 0.0105 0.0096 0.0140 0.0091 0.0240484 30 Etli nohut 0.0266 0.0275 0.0263 0.0220 0.0424 0.0077 0.0314 0.0191 0.0172 0.0030 0.0430618 31 0.0529 0.0538 0.0734 0.0120 0.0468 0.0110 0.0418 0.0382 0.0382 0.0365 0.0602037 32 patates 0.0058 0.0033 0.0002 0.0020 0.0052 0.0000 0.0209 0.0191 0.0242 0.0264 0.0174897 33 0.0083 0.0044 0.0070 0.0035 0.0061 0.0003 0.0105 0.0191 0.0172 0.0066 0.0000132 34 Kabak kalye (etsiz) 0.0188 0.0188 0.0228 0.0462 0.0182 0.0250 0.0209 0.0287 0.0172 0.0342 0.0000164 35 Bezelye (etsiz) 0.0110 0.0074 0.0081 0.0076 0.0087 0.0214 0.0523 0.0191 0.0318 0.0357 0.0189637 36 Taze fasulye (etsiz) 0.0126 0.0144 0.0183 0.0151 0.0234 0.0174 0.0105 0.0191 0.0140 0.0091 0.0180528 37 Bamya (etsiz) 0.0048 0.0033 0.0045 0.0269 0.0052 0.0174 0.0105 0.0191 0.0076 0.0410 0.0340354 38 Konserve bezelye (etsiz) 0.0110 0.0074 0.0081 0.0076 0.0165 0.0230 0.0523 0.0191 0.0318 0.0106 0.0196262 39 Konserve taze fasulye (etsiz) 0.0135 0.0055 0.0166 0.0265 0.0216 0.0418 0.0105 0.0191 0.0076 0.0502 0.0332073 40 Ispanak (etsiz) 0.0075 0.0082 0.0048 0.0146 0.0095 0.0107 0.0209 0.0239 0.0064 0.0066 0.0166285 30 41 but 0.0197 0.0415 0.0168 0.0092 0.0225 0.0040 0.0209 0.0191 0.0822 0.0193 0.0199078 42 0.0087 0.0367 0.0027 0.0032 0.0061 0.0009 0.0209 0.0191 0.0822 0.0013 0.0216137 43 0.0255 0.0074 0.0201 0.0022 0.0052 0.0101 0.0105 0.0096 0.0064 0.0000 0.0000101 44 Sebzeli bulgur 0.0221 0.0103 0.0206 0.0073 0.0165 0.0102 0.0209 0.0000 0.0140 0.0139 0.0000098 45 makarna 0.0384 0.0307 0.0340 0.0813 0.0139 0.0235 0.0209 0.0287 0.0057 0.0005 0.0000088 46 makarna 0.0256 0.0112 0.0193 0.0033 0.0147 0.0112 0.0105 0.0000 0.0051 0.0004 0.0000091 47 Patatesli tepsi 0.0320 0.0237 0.0282 0.0317 0.0476 0.0176 0.0314 0.0191 0.0312 0.0044 0.0168603 48 (peynirli) 0.0112 0.0071 0.0108 0.0077 0.0190 0.0319 0.0209 0.0096 0.0096 0.0053 0.0000125 49 0.0356 0.0182 0.0482 0.0067 0.0182 0.0252 0.0209 0.0096 0.0127 0.0040 0.0000125 50 0.0044 0.0022 0.0057 0.0096 0.0085 0.0486 0.0073 0.0057 0.0168 0.0529 0.0000058 51 0.0008 0.0009 0.0003 0.0050 0.0182 0.0033 0.0000 0.0019 0.0000 0.0093 0.0000041 52 Portakal 0.0052 0.0017 0.0005 0.0139 0.0087 0.0056 0.0105 0.0000 0.0019 0.1092 0.0000041 53 Elma 0.0077 0.0008 0.0008 0.0028 0.0139 0.0016 0.0000 0.0096 0.0019 0.0127 0.0000041 54 0.0043 0.0017 0.0006 0.0121 0.0121 0.0014 0.0000 0.0096 0.0038 0.1319 0.0000041 55 Erik 0.0045 0.0011 0.0003 0.0033 0.0052 0.0045 0.0000 0.0000 0.0038 0.0090 0.0000041 56 0.0029 0.0003 0.0008 0.0041 0.0052 0.0104 0.0000 0.0000 0.0013 0.0103 0.0000041 57 0.0100 0.0071 0.0134 0.0485 0.0043 0.0078 0.0105 0.0287 0.0013 0.0003 0.0000075 58 Ayran 0.0068 0.0111 0.0043 0.0724 0.0017 0.0063 0.0063 0.0287 0.0010 0.0013 0.0000041 59 0.0112 0.0112 0.0104 0.0876 0.0026 0.0100 0.0209 0.0478 0.0019 0.0040 0.0000058 60 0.0090 0.0090 0.0083 0.0701 0.0021 0.0080 0.0167 0.0382 0.0015 0.0032 0.0000066 31 3. 3.7.1. X 1 = Yumurta, X 2 = beyaz peynir . X X 30= etli nohut. D1A D1E 3.7.2 minimize etmektir. MIN D1A + D2E + D2A + D3E + D3A + D4A + D5E + D5A + D6E + D6A + D7E + D7A + D8E + D8A + D9E + D9A + D10E + D10A + D11E + D11A + 2D12A 3.7.3. X 1 + X 2 + X 3 = 1 X 4 = 1 32 - X 5 + X 6 = 1 X 7 + X 8 + X 9 + X 10 = 1 0,0397X1 + 0,0318X2 +0,0464X3 +0,0272X4 +0,1517X5 +0,0768X6 +0,0662X7+ 0,1391X8 + 0,1987X9 +0,2225X10 D1A=0 D1A 0,0723X1+0,0786X2+0,1093X3+0,0560X4+0,2258X5+0,2177X6+0,0000X7+0,0867X8+0,0 912X9+0,0623X10+D2E-D2A= 0,2196X1+0,2333X2+0,2779X3+0,0172X4+0,0172X5+0,0000X6+0,0000X7+0,1801X8+0,0 172X9+ 0,0377X10+D3E-D3A= 0,0741X1+0,0845X2+0,1235X3+0,0819X4+0,3589X5+0,2081X6+0,0000X7+0,0585X8+0,0 065X9+ 0,003910+D4E+D4A= 0 X1 + 0 X2 +0 X3 +0 X4 +0 X5 +0 X6 +0 X7+ 0 X8 + 0 X9 +0 X10 +D12E D12A =0 2, X 4, X 5, X 9, 0 X1 + 1 X2 +0 X3 +1 X4 +1 X5 +0 X6 +0 X7+ 0 X8 + 1 X9 +0 X10 +D12E D12A =0 33 : minimize etmektir. MIN D1A + D2E + D2A + D3E + D3A + D4A + D5E + D5A + D6E + D6A + D7E + D7A + X 1 + X 2 + X 3 + X 4+ X 5 + X 6 + X 7 + X 8 + X 9 + X 10 = 1 X 11 + X 12 41 + X 42 = 1 P LAV-MAKARNA- X 43 + X 44 48 + X 49 = 1 SALATA-MEYVE- X 50 + X 51 59 + X 60 = 1 34 D1A=0 -D2A= KISITI -D3A= KISITI KISITI 0 X1 + 0 X2 +0 X3 +0 X4 +0 X5 +0 X6 +0 X7+ 0 X8 + 0 X9 +0 X10 +D12E D12A =0 35 4. - 19- 36 1. Resim 3: 37 1. Resim 4: 38 1. Resim 5 39 Tablo 10: 19-30 19 - 30 Erkek KAHVALTI Pazartesi Cuma Cumartesi Pazar Beyaz peynir (30gr) (30gr) Yumurta (1 adet) Beyaz peynir (30gr) peyniri (30gr) Yumurta (1 adet) Beyaz peynir (30gr) Zeytin (30gr) Zeytin (30gr) Zeytin (30gr) Zeytin (30gr) Zeytin (30gr) Zeytin (30gr) Zeytin (30gr) (20gr) (domates- (20gr) (domates- (20gr) (domates- (20gr) Elma (1 adet) (1 fincan) (1 fincan) Elma (1 adet) Portakal (1 adet) (1 fincan) (1 fincan) 19 - KAHVALTI Pazartesi Cuma Cumartesi Pazar Beyaz peynir (30gr) Yumurta (1 adet) peyniri (30gr) Yumurta (1 adet) Beyaz peynir (30gr) (30gr) Yumurta (1 adet) Zeytin (30gr) Zeytin (30gr) Zeytin (30gr) Zeytin (30gr) Zeytin (30gr) Zeytin (30gr) Zeytin (30gr) (domates- (20gr) (domates- (20gr) (domates- (20gr) (domates- Elma (1 adet) (1 fincan) Portakal (1 adet) Elma (1 adet) (1 fincan) (1 fincan) Portakal (1 adet) 40 19 - 30 Erkek Pazartesi Cuma Cumartesi Pazar Domates Tavuksuyu Ezogelin mercimek Domates Kabak kalye (etsiz) Taze fasulye (etsiz) kabak patates musakka Bezelye (etsiz) Arpa Serpme (peynirli) Sebzeli bulgur Patatesli tepsi Arpa Sebzeli bulgur Yeni (malta Elma Ayran 19 - Pazartesi Cuma Cumartesi Pazar Yayla Tavuksuyu Brokoli Kabak kalye (etsiz) Bamya (etsiz) musakka Barbunya Bezelye (etsiz) Serpme (peynirli) Sebzeli bulgur Serpme makarna makarna Arpa Patatesli tepsi Erik Portakal 41 19 - 30 Erkek Pazartesi Cuma Cumartesi Pazar Yayla Sebze Brokoli (etsiz) Bamya (etsiz) Ispanak (etsiz) Konserve taze fasulye (etsiz) Barbunya Konserve bezelye (etsiz) makarna Serpme makarna Serpme (peynirli) makarna makarna Patatesli tepsi Erik salata Portakal Yeni (malta Elma 19 - Pazartesi Cuma Cumartesi Pazar Domates Ezogelin Sebze mercimek kabak Konserve taze fasulye (etsiz) (etsiz) Taze fasulye (etsiz) Ispanak (etsiz) patates Konserve bezelye (etsiz) makarna Arpa Patatesli tepsi Serpme (peynirli) Sebzeli bulgur makarna Yeni (malta Elma salata Ayran 42 2007 Doktora Tezi, 2010 -91 , 2003. Temmuz- -90 Baynal - ktisadi ve dari - -18 Prosesive 0-1 Hedef , 2001 43 Gazi Fak. Der. Cilt 19, No 1, 2004 Tezi, 2007 A.B.D., 2004 A.B.D., 2008 -191 , 1992 A.B.D., 2001 Review of Social, Economic & Business Studies, Vol.2, 242-255 , 2000. 44 Lisans Tezi, 2010 -187 -13, 2000 -1 T Do Hedef Programlama ve Bir Diyet Probleminin U 2001 2003 2001, s.199 2003 Lisans Tezi, 2000 anter -96 ISSN: 1302- 3284 45 -27 i Dergisi 37, 1, (2008) 49-64, 2008 TMMOB Harita ve Ankara , 2003 - 2004