Wong's LL Blog: February 2009

Friday, February 20, 2009

Assigning Thirty Activities to Four Conflicting Facilities with Less-Than-or-Equal-to Constraints

Jsun Yui Wong

The difference between the original Carlson and Nemhauser problem [2] and the problem of Davis, Devine, and Lutz [3] is "that their problem did not consider conflicting facilities," Davis, Devine, and Lutz [3, p. 225]. For the newer problem, "a cost is incurred if two activities are assigned to the same facility, or to two facilities whose operation is in conflict," Davis et al. [3, p. 224]. Dealing with an instance of the newer problem, the computer program below attempts to find the lowest cost of scheduling thirty courses in four time periods which are 8a.m. to 11 a.m., 10 a.m. to 1 p.m., noon to 3 p.m., and 2 p.m. to 5 p.m. The conflicts are specified in line 6 through line 9 of the following computer program.

In this paper, fourteen courses express through their professors their various preferences for their preferred time periods: courses 1 through 5 for period 1 or period 2, courses 6 through 9 for period 2 or period 3, and courses 10 through 14 for period 3 or period 4. These fourteen preferences are expressed in line 325 through line 643.

There are also the constraints that period one can handle only eleven courses or less and period four can handle only eleven courses or less. These two restrictions exemplify the less-than-or-equal-to constraints on pages 1096 of Arnold, Beckwith, and Jones [1] and are handled mainly by line 666 through line 804 below. Carlson and Nemhausser [2] "seek to find a conflict-minimizing schedule, but do not require that the schedule be balanced," [1, p. 1096].

The costs used in line 1001 through line 1435 of the computer program below come from Hillier [4] and Nugent, Vollmann, and Ruml [5, pp. 168-170].

In this paper, A(1)=2, A(2)=2, A(3)=2,..., and A(30)=2 stand for course 1 in period 2, course 2 in period 2, course 3 in period 2,..., and course 30 in period 2, respectively.

The computer program below is modelled after the computer program of the March 7 post "Assigning Activities to Conflicting Facilities To Minimize Conflict Cost" of the present blog.

2 DEFINT A-Z
4 DEFDBL M,T,P
5 DIM N(9),B(9),A(199),H(99),X(199),P(450),L(99),U(99),Q(977),R(444),T(999),Q1(222)
6 TBM(1,1)=1:TBM(1,2)=1
7 TBM(2,1)=1:TBM(2,2)=1:TBM(2,3)=1
8 TBM(3,2)=1:TBM(3,3)=1:TBM(3,4)=1
9 TBM(4,3)=1:TBM(4,4)=1
12 FOR JJJJ=-32000 TO 32000
14 RANDOMIZE JJJJ
16 M=-1D+17
20 A(1)=2:A(2)=2:A(3)=2:A(4)=2:A(5)=2:A(6)=2:A(7)=2
21 A(8)=3:A(9)=3:A(10)=3:A(11)=3:A(12)=3:A(13)=3:A(14)=3
25 A(15)=2:A(16)=2:A(17)=2:A(18)=2:A(19)=2:A(20)=2:A(21)=2:A(22)=2
27 A(23)=3:A(24)=3:A(25)=3:A(26)=3:A(27)=3:A(28)=3:A(29)=3:A(30)=3
126 IMAR=10+FIX(RND*1000)
128 FOR I=1 TO IMAR
129 FOR K=1 TO 30
131 X(K)=A(K)
132 NEXT K
251 IF RND<.17 THEN 325 ELSE IF RND<.16 THEN 431 ELSE IF RND<.24 THEN 533 ELSE 641
325 IAP2=1+FIX(RND*5)
328 X(IAP2)=1+FIX(RND*2)
339 GOTO 666
431 IAP3=6+FIX(RND*4)
435 X(IAP3)=2+FIX(RND*2)
444 GOTO 666
533 IAP4=10+FIX(RND*5)
536 X(IAP4)=3+FIX(RND*2)
547 GOTO 666
641 IAP1=15+FIX(RND*16)
643 X(IAP1)=1+FIX(RND*4)
666 SUM1=0:SUM2=0
701 FOR I11=1 TO 30
711 IF X(I11)=1 THEN 721 ELSE IF X(I11)=4 THEN 777 ELSE 791
721 SUM1=SUM1+1
773 GOTO 791
777 SUM2=SUM2+4
791 NEXT I11
801 IF SUM1>11 THEN 2670
804 IF SUM2>44 THEN 2670
1001 T(1)=5*100000!*(1/(100000!*(1-TBM(X(1),X(2)))+1))
1002 T(2)=2*100000!*(1/(100000!*(1-TBM(X(1),X(3)))+1))
1003 T(3)=4*100000!*(1/(100000!*(1-TBM(X(1),X(4)))+1))
1004 T(4)=1*100000!*(1/(100000!*(1-TBM(X(1),X(5)))+1))
1005 T(5)=0*100000!*(1/(100000!*(1-TBM(X(1),X(6)))+1))
1006 T(6)=0*100000!*(1/(100000!*(1-TBM(X(1),X(7)))+1))
1007 T(7)=6*100000!*(1/(100000!*(1-TBM(X(1),X(8)))+1))
1008 T(8)=2*100000!*(1/(100000!*(1-TBM(X(1),X(9)))+1))
1009 T(9)=1*100000!*(1/(100000!*(1-TBM(X(1),X(10)))+1))
1010 T(10)=1*100000!*(1/(100000!*(1-TBM(X(1),X(11)))+1))
1011 T(11)=1*100000!*(1/(100000!*(1-TBM(X(1),X(12)))+1))
1012 T(12)=3*100000!*(1/(100000!*(1-TBM(X(2),X(3)))+1))
1013 T(13)=0*100000!*(1/(100000!*(1-TBM(X(2),X(4)))+1))
1014 T(14)=2*100000!*(1/(100000!*(1-TBM(X(2),X(5)))+1))
1015 T(15)=2*100000!*(1/(100000!*(1-TBM(X(2),X(6)))+1))
1016 T(16)=2*100000!*(1/(100000!*(1-TBM(X(2),X(7)))+1))
1017 T(17)=0*100000!*(1/(100000!*(1-TBM(X(2),X(8)))+1))
1018 T(18)=4*100000!*(1/(100000!*(1-TBM(X(2),X(9)))+1))
1019 T(19)=5*100000!*(1/(100000!*(1-TBM(X(2),X(10)))+1))
1020 T(20)=0*100000!*(1/(100000!*(1-TBM(X(2),X(11)))+1))
1021 T(21)=0*100000!*(1/(100000!*(1-TBM(X(2),X(12)))+1))
1022 T(22)=0*100000!*(1/(100000!*(1-TBM(X(3),X(4)))+1))
1023 T(23)=0*100000!*(1/(100000!*(1-TBM(X(3),X(5)))+1))
1024 T(24)=0*100000!*(1/(100000!*(1-TBM(X(3),X(6)))+1))
1025 T(25)=0*100000!*(1/(100000!*(1-TBM(X(3),X(7)))+1))
1026 T(26)=5*100000!*(1/(100000!*(1-TBM(X(3),X(8)))+1))
1027 T(27)=5*100000!*(1/(100000!*(1-TBM(X(3),X(9)))+1))
1028 T(28)=2*100000!*(1/(100000!*(1-TBM(X(3),X(10)))+1))
1029 T(29)=2*100000!*(1/(100000!*(1-TBM(X(3),X(11)))+1))
1030 T(30)=2*100000!*(1/(100000!*(1-TBM(X(3),X(12)))+1))
1031 T(31)=5*100000!*(1/(100000!*(1-TBM(X(4),X(5)))+1))
1032 T(32)=2*100000!*(1/(100000!*(1-TBM(X(4),X(6)))+1))
1033 T(33)=2*100000!*(1/(100000!*(1-TBM(X(4),X(7)))+1))
1034 T(34)=10*100000!*(1/(100000!*(1-TBM(X(4),X(8)))+1))
1035 T(35)=0*100000!*(1/(100000!*(1-TBM(X(4),X(9)))+1))
1036 T(36)=0*100000!*(1/(100000!*(1-TBM(X(4),X(10)))+1))
1037 T(37)=5*100000!*(1/(100000!*(1-TBM(X(4),X(11)))+1))
1038 T(38)=5*100000!*(1/(100000!*(1-TBM(X(4),X(12)))+1))
1039 T(39)=10*100000!*(1/(100000!*(1-TBM(X(5),X(6)))+1))
1040 T(40)=0*100000!*(1/(100000!*(1-TBM(X(5),X(7)))+1))
1041 T(41)=0*100000!*(1/(100000!*(1-TBM(X(5),X(8)))+1))
1042 T(42)=0*100000!*(1/(100000!*(1-TBM(X(5),X(9)))+1))
1043 T(43)=5*100000!*(1/(100000!*(1-TBM(X(5),X(10)))+1))
1044 T(44)=1*100000!*(1/(100000!*(1-TBM(X(5),X(11)))+1))
1045 T(45)=1*100000!*(1/(100000!*(1-TBM(X(5),X(12)))+1))
1046 T(46)=5*100000!*(1/(100000!*(1-TBM(X(6),X(7)))+1))
1047 T(47)=1*100000!*(1/(100000!*(1-TBM(X(6),X(8)))+1))
1048 T(48)=1*100000!*(1/(100000!*(1-TBM(X(6),X(9)))+1))
1049 T(49)=5*100000!*(1/(100000!*(1-TBM(X(6),X(10)))+1))
1050 T(50)=4*100000!*(1/(100000!*(1-TBM(X(6),X(11)))+1))
1051 T(51)=0*100000!*(1/(100000!*(1-TBM(X(6),X(12)))+1))
1052 T(52)=10*100000!*(1/(100000!*(1-TBM(X(7),X(8)))+1))
1053 T(53)=5*100000!*(1/(100000!*(1-TBM(X(7),X(9)))+1))
1054 T(54)=2*100000!*(1/(100000!*(1-TBM(X(7),X(10)))+1))
1055 T(55)=3*100000!*(1/(100000!*(1-TBM(X(7),X(11)))+1))
1056 T(56)=3*100000!*(1/(100000!*(1-TBM(X(7),X(12)))+1))
1057 T(57)=0*100000!*(1/(100000!*(1-TBM(X(8),X(9)))+1))
1058 T(58)=0*100000!*(1/(100000!*(1-TBM(X(8),X(10)))+1))
1059 T(59)=5*100000!*(1/(100000!*(1-TBM(X(8),X(11)))+1))
1060 T(60)=0*100000!*(1/(100000!*(1-TBM(X(8),X(12)))+1))
1061 T(61)=0*100000!*(1/(100000!*(1-TBM(X(9),X(10)))+1))
1062 T(62)=10*100000!*(1/(100000!*(1-TBM(X(9),X(11)))+1))
1063 T(63)=10*100000!*(1/(100000!*(1-TBM(X(9),X(12)))+1))
1064 T(64)=5*100000!*(1/(100000!*(1-TBM(X(10),X(11)))+1))
1065 T(65)=0*100000!*(1/(100000!*(1-TBM(X(10),X(12)))+1))
1066 T(66)=2*100000!*(1/(100000!*(1-TBM(X(11),X(12)))+1))
1067 T(67)=4*100000!*(1/(100000!*(1-TBM(X(13),X(1)))+1))
1068 T(68)=10*100000!*(1/(100000!*(1-TBM(X(13),X(2)))+1))
1069 T(69)=5*100000!*(1/(100000!*(1-TBM(X(13),X(3)))+1))
1070 T(70)=2*100000!*(1/(100000!*(1-TBM(X(13),X(4)))+1))
1071 T(71)=0*100000!*(1/(100000!*(1-TBM(X(13),X(5)))+1))
1072 T(72)=2*100000!*(1/(100000!*(1-TBM(X(13),X(6)))+1))
1073 T(73)=5*100000!*(1/(100000!*(1-TBM(X(13),X(7)))+1))
1074 T(74)=5*100000!*(1/(100000!*(1-TBM(X(13),X(8)))+1))
1075 T(75)=10*100000!*(1/(100000!*(1-TBM(X(13),X(9)))+1))
1076 T(76)=0*100000!*(1/(100000!*(1-TBM(X(13),X(10)))+1))
1077 T(77)=0*100000!*(1/(100000!*(1-TBM(X(13),X(11)))+1))
1078 T(78)=3*100000!*(1/(100000!*(1-TBM(X(13),X(12)))+1))
1079 T(79)=0*100000!*(1/(100000!*(1-TBM(X(14),X(1)))+1))
1080 T(80)=5*100000!*(1/(100000!*(1-TBM(X(14),X(2)))+1))
1081 T(81)=5*100000!*(1/(100000!*(1-TBM(X(14),X(3)))+1))
1082 T(82)=5*100000!*(1/(100000!*(1-TBM(X(14),X(4)))+1))
1083 T(83)=5*100000!*(1/(100000!*(1-TBM(X(14),X(5)))+1))
1084 T(84)=5*100000!*(1/(100000!*(1-TBM(X(14),X(6)))+1))
1085 T(85)=1*100000!*(1/(100000!*(1-TBM(X(14),X(7)))+1))
1086 T(86)=0*100000!*(1/(100000!*(1-TBM(X(14),X(8)))+1))
1087 T(87)=0*100000!*(1/(100000!*(1-TBM(X(14),X(9)))+1))
1088 T(88)=0*100000!*(1/(100000!*(1-TBM(X(14),X(10)))+1))
1089 T(89)=5*100000!*(1/(100000!*(1-TBM(X(14),X(11)))+1))
1090 T(90)=3*100000!*(1/(100000!*(1-TBM(X(14),X(12)))+1))
1091 T(91)=10*100000!*(1/(100000!*(1-TBM(X(14),X(13)))+1))
1092 T(92)=0*100000!*(1/(100000!*(1-TBM(X(15),X(1)))+1))
1093 T(93)=0*100000!*(1/(100000!*(1-TBM(X(15),X(2)))+1))
1094 T(94)=5*100000!*(1/(100000!*(1-TBM(X(15),X(3)))+1))
1095 T(95)=0*100000!*(1/(100000!*(1-TBM(X(15),X(4)))+1))
1096 T(96)=5*100000!*(1/(100000!*(1-TBM(X(15),X(5)))+1))
1097 T(97)=10*100000!*(1/(100000!*(1-TBM(X(15),X(6)))+1))
1098 T(98)=0*100000!*(1/(100000!*(1-TBM(X(15),X(7)))+1))
1099 T(99)=0*100000!*(1/(100000!*(1-TBM(X(15),X(8)))+1))
1100 T(100)=2*100000!*(1/(100000!*(1-TBM(X(15),X(9)))+1))
1101 T(101)=5*100000!*(1/(100000!*(1-TBM(X(15),X(10)))+1))
1102 T(102)=0*100000!*(1/(100000!*(1-TBM(X(15),X(11)))+1))
1103 T(103)=0*100000!*(1/(100000!*(1-TBM(X(15),X(12)))+1))
1104 T(104)=2*100000!*(1/(100000!*(1-TBM(X(15),X(13)))+1))
1105 T(105)=4*100000!*(1/(100000!*(1-TBM(X(15),X(14)))+1))
1106 T(106)=0*100000!*(1/(100000!*(1-TBM(X(16),X(1)))+1))
1107 T(107)=0*100000!*(1/(100000!*(1-TBM(X(16),X(2)))+1))
1108 T(108)=4*100000!*(1/(100000!*(1-TBM(X(16),X(3)))+1))
1109 T(109)=5*100000!*(1/(100000!*(1-TBM(X(16),X(4)))+1))
1110 T(110)=0*100000!*(1/(100000!*(1-TBM(X(16),X(5)))+1))
1111 T(111)=5*100000!*(1/(100000!*(1-TBM(X(16),X(6)))+1))
1112 T(112)=10*100000!*(1/(100000!*(1-TBM(X(16),X(7)))+1))
1113 T(113)=4*100000!*(1/(100000!*(1-TBM(X(16),X(8)))+1))
1114 T(114)=3*100000!*(1/(100000!*(1-TBM(X(16),X(9)))+1))
1115 T(115)=5*100000!*(1/(100000!*(1-TBM(X(16),X(10)))+1))
1116 T(116)=1*100000!*(1/(100000!*(1-TBM(X(16),X(11)))+1))
1117 T(117)=0*100000!*(1/(100000!*(1-TBM(X(16),X(12)))+1))
1118 T(118)=4*100000!*(1/(100000!*(1-TBM(X(16),X(13)))+1))
1119 T(119)=1*100000!*(1/(100000!*(1-TBM(X(16),X(14)))+1))
1120 T(120)=4*100000!*(1/(100000!*(1-TBM(X(16),X(15)))+1))
1121 T(121)=5*100000!*(1/(100000!*(1-TBM(X(17),X(1)))+1))
1122 T(122)=0*100000!*(1/(100000!*(1-TBM(X(17),X(2)))+1))
1123 T(123)=0*100000!*(1/(100000!*(1-TBM(X(17),X(3)))+1))
1124 T(124)=1*100000!*(1/(100000!*(1-TBM(X(17),X(4)))+1))
1125 T(125)=2*100000!*(1/(100000!*(1-TBM(X(17),X(5)))+1))
1126 T(126)=0*100000!*(1/(100000!*(1-TBM(X(17),X(6)))+1))
1127 T(127)=2*100000!*(1/(100000!*(1-TBM(X(17),X(7)))+1))
1128 T(128)=5*100000!*(1/(100000!*(1-TBM(X(17),X(8)))+1))
1129 T(129)=0*100000!*(1/(100000!*(1-TBM(X(17),X(9)))+1))
1130 T(130)=5*100000!*(1/(100000!*(1-TBM(X(17),X(10)))+1))
1131 T(131)=0*100000!*(1/(100000!*(1-TBM(X(17),X(11)))+1))
1132 T(132)=0*100000!*(1/(100000!*(1-TBM(X(17),X(12)))+1))
1133 T(133)=2*100000!*(1/(100000!*(1-TBM(X(17),X(13)))+1))
1134 T(134)=0*100000!*(1/(100000!*(1-TBM(X(17),X(14)))+1))
1135 T(135)=5*100000!*(1/(100000!*(1-TBM(X(17),X(15)))+1))
1136 T(136)=0*100000!*(1/(100000!*(1-TBM(X(17),X(16)))+1))
1137 T(137)=6*100000!*(1/(100000!*(1-TBM(X(18),X(1)))+1))
1138 T(138)=2*100000!*(1/(100000!*(1-TBM(X(18),X(2)))+1))
1139 T(139)=6*100000!*(1/(100000!*(1-TBM(X(18),X(3)))+1))
1140 T(140)=1*100000!*(1/(100000!*(1-TBM(X(18),X(4)))+1))
1141 T(141)=1*100000!*(1/(100000!*(1-TBM(X(18),X(5)))+1))
1142 T(142)=5*100000!*(1/(100000!*(1-TBM(X(18),X(6)))+1))
1143 T(143)=1*100000!*(1/(100000!*(1-TBM(X(18),X(7)))+1))
1144 T(144)=2*100000!*(1/(100000!*(1-TBM(X(18),X(8)))+1))
1145 T(145)=2*100000!*(1/(100000!*(1-TBM(X(18),X(9)))+1))
1146 T(146)=0*100000!*(1/(100000!*(1-TBM(X(18),X(10)))+1))
1147 T(147)=2*100000!*(1/(100000!*(1-TBM(X(18),X(11)))+1))
1148 T(148)=0*100000!*(1/(100000!*(1-TBM(X(18),X(12)))+1))
1149 T(149)=2*100000!*(1/(100000!*(1-TBM(X(18),X(13)))+1))
1150 T(150)=5*100000!*(1/(100000!*(1-TBM(X(18),X(14)))+1))
1151 T(151)=1*100000!*(1/(100000!*(1-TBM(X(18),X(15)))+1))
1152 T(152)=3*100000!*(1/(100000!*(1-TBM(X(18),X(16)))+1))
1153 T(153)=2*100000!*(1/(100000!*(1-TBM(X(18),X(17)))+1))
1154 T(154)=3*100000!*(1/(100000!*(1-TBM(X(19),X(1)))+1))
1155 T(155)=0*100000!*(1/(100000!*(1-TBM(X(19),X(2)))+1))
1156 T(156)=3*100000!*(1/(100000!*(1-TBM(X(19),X(3)))+1))
1157 T(157)=1*100000!*(1/(100000!*(1-TBM(X(19),X(4)))+1))
1158 T(158)=0*100000!*(1/(100000!*(1-TBM(X(19),X(5)))+1))
1159 T(159)=0*100000!*(1/(100000!*(1-TBM(X(19),X(6)))+1))
1160 T(160)=10*100000!*(1/(100000!*(1-TBM(X(19),X(7)))+1))
1161 T(161)=10*100000!*(1/(100000!*(1-TBM(X(19),X(8)))+1))
1162 T(162)=0*100000!*(1/(100000!*(1-TBM(X(19),X(9)))+1))
1163 T(163)=5*100000!*(1/(100000!*(1-TBM(X(19),X(10)))+1))
1164 T(164)=0*100000!*(1/(100000!*(1-TBM(X(19),X(11)))+1))
1165 T(165)=0*100000!*(1/(100000!*(1-TBM(X(19),X(12)))+1))
1166 T(166)=1*100000!*(1/(100000!*(1-TBM(X(19),X(13)))+1))
1167 T(167)=3*100000!*(1/(100000!*(1-TBM(X(19),X(14)))+1))
1168 T(168)=0*100000!*(1/(100000!*(1-TBM(X(19),X(15)))+1))
1169 T(169)=0*100000!*(1/(100000!*(1-TBM(X(19),X(16)))+1))
1170 T(170)=2*100000!*(1/(100000!*(1-TBM(X(19),X(17)))+1))
1171 T(171)=5*100000!*(1/(100000!*(1-TBM(X(19),X(18)))+1))
1172 T(172)=0*100000!*(1/(100000!*(1-TBM(X(20),X(1)))+1))
1173 T(173)=1*100000!*(1/(100000!*(1-TBM(X(20),X(2)))+1))
1174 T(174)=2*100000!*(1/(100000!*(1-TBM(X(20),X(3)))+1))
1175 T(175)=1*100000!*(1/(100000!*(1-TBM(X(20),X(4)))+1))
1176 T(176)=0*100000!*(1/(100000!*(1-TBM(X(20),X(5)))+1))
1177 T(177)=0*100000!*(1/(100000!*(1-TBM(X(20),X(6)))+1))
1178 T(178)=1*100000!*(1/(100000!*(1-TBM(X(20),X(7)))+1))
1179 T(179)=6*100000!*(1/(100000!*(1-TBM(X(20),X(8)))+1))
1180 T(180)=0*100000!*(1/(100000!*(1-TBM(X(20),X(9)))+1))
1181 T(181)=2*100000!*(1/(100000!*(1-TBM(X(20),X(10)))+1))
1182 T(182)=0*100000!*(1/(100000!*(1-TBM(X(20),X(11)))+1))
1183 T(183)=2*100000!*(1/(100000!*(1-TBM(X(20),X(12)))+1))
1184 T(184)=0*100000!*(1/(100000!*(1-TBM(X(20),X(13)))+1))
1185 T(185)=10*100000!*(1/(100000!*(1-TBM(X(20),X(14)))+1))
1186 T(186)=1*100000!*(1/(100000!*(1-TBM(X(20),X(15)))+1))
1187 T(187)=2*100000!*(1/(100000!*(1-TBM(X(20),X(16)))+1))
1188 T(188)=0*100000!*(1/(100000!*(1-TBM(X(20),X(17)))+1))
1189 T(189)=1*100000!*(1/(100000!*(1-TBM(X(20),X(18)))+1))
1190 T(190)=0*100000!*(1/(100000!*(1-TBM(X(20),X(19)))+1))
1191 T(191)=1*100000!*(1/(100000!*(1-TBM(X(21),X(1)))+1))
1192 T(192)=6*100000!*(1/(100000!*(1-TBM(X(21),X(2)))+1))
1193 T(193)=5*100000!*(1/(100000!*(1-TBM(X(21),X(3)))+1))
1194 T(194)=2*100000!*(1/(100000!*(1-TBM(X(21),X(4)))+1))
1195 T(195)=2*100000!*(1/(100000!*(1-TBM(X(21),X(5)))+1))
1196 T(196)=0*100000!*(1/(100000!*(1-TBM(X(21),X(6)))+1))
1197 T(197)=5*100000!*(1/(100000!*(1-TBM(X(21),X(7)))+1))
1198 T(198)=0*100000!*(1/(100000!*(1-TBM(X(21),X(8)))+1))
1199 T(199)=4*100000!*(1/(100000!*(1-TBM(X(21),X(9)))+1))
1200 T(200)=3*100000!*(1/(100000!*(1-TBM(X(21),X(10)))+1))
1201 T(201)=0*100000!*(1/(100000!*(1-TBM(X(21),X(11)))+1))
1202 T(202)=0*100000!*(1/(100000!*(1-TBM(X(21),X(12)))+1))
1203 T(203)=6*100000!*(1/(100000!*(1-TBM(X(21),X(13)))+1))
1204 T(204)=0*100000!*(1/(100000!*(1-TBM(X(21),X(14)))+1))
1205 T(205)=0*100000!*(1/(100000!*(1-TBM(X(21),X(15)))+1))
1206 T(206)=2*100000!*(1/(100000!*(1-TBM(X(21),X(16)))+1))
1207 T(207)=0*100000!*(1/(100000!*(1-TBM(X(21),X(17)))+1))
1208 T(208)=2*100000!*(1/(100000!*(1-TBM(X(21),X(18)))+1))
1209 T(209)=5*100000!*(1/(100000!*(1-TBM(X(21),X(19)))+1))
1210 T(210)=5*100000!*(1/(100000!*(1-TBM(X(21),X(20)))+1))
1211 T(211)=10*100000!*(1/(100000!*(1-TBM(X(22),X(1)))+1))
1212 T(212)=1*100000!*(1/(100000!*(1-TBM(X(22),X(2)))+1))
1213 T(213)=5*100000!*(1/(100000!*(1-TBM(X(22),X(3)))+1))
1214 T(214)=2*100000!*(1/(100000!*(1-TBM(X(22),X(4)))+1))
1215 T(215)=0*100000!*(1/(100000!*(1-TBM(X(22),X(5)))+1))
1216 T(216)=10*100000!*(1/(100000!*(1-TBM(X(22),X(6)))+1))
1217 T(217)=5*100000!*(1/(100000!*(1-TBM(X(22),X(7)))+1))
1218 T(218)=5*100000!*(1/(100000!*(1-TBM(X(22),X(8)))+1))
1219 T(219)=0*100000!*(1/(100000!*(1-TBM(X(22),X(9)))+1))
1220 T(220)=5*100000!*(1/(100000!*(1-TBM(X(22),X(10)))+1))
1221 T(221)=6*100000!*(1/(100000!*(1-TBM(X(22),X(11)))+1))
1222 T(222)=4*100000!*(1/(100000!*(1-TBM(X(22),X(12)))+1))
1223 T(223)=2*100000!*(1/(100000!*(1-TBM(X(22),X(13)))+1))
1224 T(224)=0*100000!*(1/(100000!*(1-TBM(X(22),X(14)))+1))
1225 T(225)=5*100000!*(1/(100000!*(1-TBM(X(22),X(15)))+1))
1226 T(226)=0*100000!*(1/(100000!*(1-TBM(X(22),X(16)))+1))
1227 T(227)=0*100000!*(1/(100000!*(1-TBM(X(22),X(17)))+1))
1228 T(228)=10*100000!*(1/(100000!*(1-TBM(X(22),X(18)))+1))
1229 T(229)=5*100000!*(1/(100000!*(1-TBM(X(22),X(19)))+1))
1230 T(230)=2*100000!*(1/(100000!*(1-TBM(X(22),X(20)))+1))
1231 T(231)=4*100000!*(1/(100000!*(1-TBM(X(22),X(21)))+1))
1232 T(232)=0*100000!*(1/(100000!*(1-TBM(X(23),X(1)))+1))
1233 T(233)=0*100000!*(1/(100000!*(1-TBM(X(23),X(2)))+1))
1234 T(234)=2*100000!*(1/(100000!*(1-TBM(X(23),X(3)))+1))
1235 T(235)=4*100000!*(1/(100000!*(1-TBM(X(23),X(4)))+1))
1236 T(236)=5*100000!*(1/(100000!*(1-TBM(X(23),X(5)))+1))
1237 T(237)=0*100000!*(1/(100000!*(1-TBM(X(23),X(6)))+1))
1238 T(238)=2*100000!*(1/(100000!*(1-TBM(X(23),X(7)))+1))
1239 T(239)=5*100000!*(1/(100000!*(1-TBM(X(23),X(8)))+1))
1240 T(240)=5*100000!*(1/(100000!*(1-TBM(X(23),X(9)))+1))
1241 T(241)=0*100000!*(1/(100000!*(1-TBM(X(23),X(10)))+1))
1242 T(242)=6*100000!*(1/(100000!*(1-TBM(X(23),X(11)))+1))
1243 T(243)=5*100000!*(1/(100000!*(1-TBM(X(23),X(12)))+1))
1244 T(244)=1*100000!*(1/(100000!*(1-TBM(X(23),X(13)))+1))
1245 T(245)=4*100000!*(1/(100000!*(1-TBM(X(23),X(14)))+1))
1246 T(246)=0*100000!*(1/(100000!*(1-TBM(X(23),X(15)))+1))
1247 T(247)=2*100000!*(1/(100000!*(1-TBM(X(23),X(16)))+1))
1248 T(248)=6*100000!*(1/(100000!*(1-TBM(X(23),X(17)))+1))
1249 T(249)=10*100000!*(1/(100000!*(1-TBM(X(23),X(18)))+1))
1250 T(250)=1*100000!*(1/(100000!*(1-TBM(X(23),X(19)))+1))
1251 T(251)=1*100000!*(1/(100000!*(1-TBM(X(23),X(20)))+1))
1252 T(252)=0*100000!*(1/(100000!*(1-TBM(X(23),X(21)))+1))
1253 T(253)=5*100000!*(1/(100000!*(1-TBM(X(23),X(22)))+1))
1254 T(254)=10*100000!*(1/(100000!*(1-TBM(X(24),X(1)))+1))
1255 T(255)=1*100000!*(1/(100000!*(1-TBM(X(24),X(2)))+1))
1256 T(256)=1*100000!*(1/(100000!*(1-TBM(X(24),X(3)))+1))
1257 T(257)=0*100000!*(1/(100000!*(1-TBM(X(24),X(4)))+1))
1258 T(258)=1*100000!*(1/(100000!*(1-TBM(X(24),X(5)))+1))
1259 T(259)=0*100000!*(1/(100000!*(1-TBM(X(24),X(6)))+1))
1260 T(260)=3*100000!*(1/(100000!*(1-TBM(X(24),X(7)))+1))
1261 T(261)=2*100000!*(1/(100000!*(1-TBM(X(24),X(8)))+1))
1262 T(262)=2*100000!*(1/(100000!*(1-TBM(X(24),X(9)))+1))
1263 T(263)=5*100000!*(1/(100000!*(1-TBM(X(24),X(10)))+1))
1264 T(264)=0*100000!*(1/(100000!*(1-TBM(X(24),X(11)))+1))
1265 T(265)=10*100000!*(1/(100000!*(1-TBM(X(24),X(12)))+1))
1266 T(266)=5*100000!*(1/(100000!*(1-TBM(X(24),X(13)))+1))
1267 T(267)=2*100000!*(1/(100000!*(1-TBM(X(24),X(14)))+1))
1268 T(268)=2*100000!*(1/(100000!*(1-TBM(X(24),X(15)))+1))
1269 T(269)=0*100000!*(1/(100000!*(1-TBM(X(24),X(16)))+1))
1270 T(270)=5*100000!*(1/(100000!*(1-TBM(X(24),X(17)))+1))
1271 T(271)=4*100000!*(1/(100000!*(1-TBM(X(24),X(18)))+1))
1272 T(272)=0*100000!*(1/(100000!*(1-TBM(X(24),X(19)))+1))
1273 T(273)=3*100000!*(1/(100000!*(1-TBM(X(24),X(20)))+1))
1274 T(274)=1*100000!*(1/(100000!*(1-TBM(X(24),X(21)))+1))
1275 T(275)=0*100000!*(1/(100000!*(1-TBM(X(24),X(22)))+1))
1276 T(276)=0*100000!*(1/(100000!*(1-TBM(X(24),X(23)))+1))
1277 T(277)=2*100000!*(1/(100000!*(1-TBM(X(25),X(1)))+1))
1278 T(278)=2*100000!*(1/(100000!*(1-TBM(X(25),X(2)))+1))
1279 T(279)=0*100000!*(1/(100000!*(1-TBM(X(25),X(3)))+1))
1280 T(280)=2*100000!*(1/(100000!*(1-TBM(X(25),X(4)))+1))
1281 T(281)=0*100000!*(1/(100000!*(1-TBM(X(25),X(5)))+1))
1282 T(282)=0*100000!*(1/(100000!*(1-TBM(X(25),X(6)))+1))
1283 T(283)=5*100000!*(1/(100000!*(1-TBM(X(25),X(7)))+1))
1284 T(284)=5*100000!*(1/(100000!*(1-TBM(X(25),X(8)))+1))
1285 T(285)=0*100000!*(1/(100000!*(1-TBM(X(25),X(9)))+1))
1286 T(286)=2*100000!*(1/(100000!*(1-TBM(X(25),X(10)))+1))
1287 T(287)=4*100000!*(1/(100000!*(1-TBM(X(25),X(11)))+1))
1288 T(288)=1*100000!*(1/(100000!*(1-TBM(X(25),X(12)))+1))
1289 T(289)=5*100000!*(1/(100000!*(1-TBM(X(25),X(13)))+1))
1290 T(290)=0*100000!*(1/(100000!*(1-TBM(X(25),X(14)))+1))
1291 T(291)=0*100000!*(1/(100000!*(1-TBM(X(25),X(15)))+1))
1292 T(292)=5*100000!*(1/(100000!*(1-TBM(X(25),X(16)))+1))
1293 T(293)=3*100000!*(1/(100000!*(1-TBM(X(25),X(17)))+1))
1294 T(294)=0*100000!*(1/(100000!*(1-TBM(X(25),X(18)))+1))
1295 T(295)=5*100000!*(1/(100000!*(1-TBM(X(25),X(19)))+1))
1296 T(296)=1*100000!*(1/(100000!*(1-TBM(X(25),X(20)))+1))
1297 T(297)=0*100000!*(1/(100000!*(1-TBM(X(25),X(21)))+1))
1298 T(298)=4*100000!*(1/(100000!*(1-TBM(X(25),X(22)))+1))
1299 T(299)=4*100000!*(1/(100000!*(1-TBM(X(25),X(23)))+1))
1300 T(300)=5*100000!*(1/(100000!*(1-TBM(X(25),X(24)))+1))
1301 T(301)=1*100000!*(1/(100000!*(1-TBM(X(26),X(1)))+1))
1302 T(302)=2*100000!*(1/(100000!*(1-TBM(X(26),X(2)))+1))
1303 T(303)=0*100000!*(1/(100000!*(1-TBM(X(26),X(3)))+1))
1304 T(304)=0*100000!*(1/(100000!*(1-TBM(X(26),X(4)))+1))
1305 T(305)=2*100000!*(1/(100000!*(1-TBM(X(26),X(5)))+1))
1306 T(306)=4*100000!*(1/(100000!*(1-TBM(X(26),X(6)))+1))
1307 T(307)=0*100000!*(1/(100000!*(1-TBM(X(26),X(7)))+1))
1308 T(308)=0*100000!*(1/(100000!*(1-TBM(X(26),X(8)))+1))
1309 T(309)=5*100000!*(1/(100000!*(1-TBM(X(26),X(9)))+1))
1310 T(310)=10*100000!*(1/(100000!*(1-TBM(X(26),X(10)))+1))
1311 T(311)=5*100000!*(1/(100000!*(1-TBM(X(26),X(11)))+1))
1312 T(312)=0*100000!*(1/(100000!*(1-TBM(X(26),X(12)))+1))
1313 T(313)=0*100000!*(1/(100000!*(1-TBM(X(26),X(13)))+1))
1314 T(314)=0*100000!*(1/(100000!*(1-TBM(X(26),X(14)))+1))
1315 T(315)=0*100000!*(1/(100000!*(1-TBM(X(26),X(15)))+1))
1316 T(316)=0*100000!*(1/(100000!*(1-TBM(X(26),X(16)))+1))
1317 T(317)=5*100000!*(1/(100000!*(1-TBM(X(26),X(17)))+1))
1318 T(318)=0*100000!*(1/(100000!*(1-TBM(X(26),X(18)))+1))
1319 T(319)=2*100000!*(1/(100000!*(1-TBM(X(26),X(19)))+1))
1320 T(320)=5*100000!*(1/(100000!*(1-TBM(X(26),X(20)))+1))
1321 T(321)=0*100000!*(1/(100000!*(1-TBM(X(26),X(21)))+1))
1322 T(322)=4*100000!*(1/(100000!*(1-TBM(X(26),X(22)))+1))
1323 T(323)=4*100000!*(1/(100000!*(1-TBM(X(26),X(23)))+1))
1324 T(324)=5*100000!*(1/(100000!*(1-TBM(X(26),X(24)))+1))
1325 T(325)=1*100000!*(1/(100000!*(1-TBM(X(26),X(25)))+1))
1326 T(326)=1*100000!*(1/(100000!*(1-TBM(X(27),X(1)))+1))
1327 T(327)=5*100000!*(1/(100000!*(1-TBM(X(27),X(2)))+1))
1328 T(328)=3*100000!*(1/(100000!*(1-TBM(X(27),X(3)))+1))
1329 T(329)=2*100000!*(1/(100000!*(1-TBM(X(27),X(4)))+1))
1330 T(330)=1*100000!*(1/(100000!*(1-TBM(X(27),X(5)))+1))
1331 T(331)=0*100000!*(1/(100000!*(1-TBM(X(27),X(6)))+1))
1332 T(332)=2*100000!*(1/(100000!*(1-TBM(X(27),X(7)))+1))
1333 T(333)=5*100000!*(1/(100000!*(1-TBM(X(27),X(8)))+1))
1334 T(334)=2*100000!*(1/(100000!*(1-TBM(X(27),X(9)))+1))
1335 T(335)=10*100000!*(1/(100000!*(1-TBM(X(27),X(10)))+1))
1336 T(336)=3*100000!*(1/(100000!*(1-TBM(X(27),X(11)))+1))
1337 T(337)=0*100000!*(1/(100000!*(1-TBM(X(27),X(12)))+1))
1338 T(338)=0*100000!*(1/(100000!*(1-TBM(X(27),X(13)))+1))
1339 T(339)=4*100000!*(1/(100000!*(1-TBM(X(27),X(14)))+1))
1340 T(340)=5*100000!*(1/(100000!*(1-TBM(X(27),X(15)))+1))
1341 T(341)=5*100000!*(1/(100000!*(1-TBM(X(27),X(16)))+1))
1342 T(342)=0*100000!*(1/(100000!*(1-TBM(X(27),X(17)))+1))
1343 T(343)=5*100000!*(1/(100000!*(1-TBM(X(27),X(18)))+1))
1344 T(344)=1*100000!*(1/(100000!*(1-TBM(X(27),X(19)))+1))
1345 T(345)=6*100000!*(1/(100000!*(1-TBM(X(27),X(20)))+1))
1346 T(346)=0*100000!*(1/(100000!*(1-TBM(X(27),X(21)))+1))
1347 T(347)=5*100000!*(1/(100000!*(1-TBM(X(27),X(22)))+1))
1348 T(348)=1*100000!*(1/(100000!*(1-TBM(X(27),X(23)))+1))
1349 T(349)=0*100000!*(1/(100000!*(1-TBM(X(27),X(24)))+1))
1350 T(350)=0*100000!*(1/(100000!*(1-TBM(X(27),X(25)))+1))
1351 T(351)=0*100000!*(1/(100000!*(1-TBM(X(27),X(26)))+1))
1352 T(352)=1*100000!*(1/(100000!*(1-TBM(X(28),X(1)))+1))
1353 T(353)=1*100000!*(1/(100000!*(1-TBM(X(28),X(2)))+1))
1354 T(354)=1*100000!*(1/(100000!*(1-TBM(X(28),X(3)))+1))
1355 T(355)=2*100000!*(1/(100000!*(1-TBM(X(28),X(4)))+1))
1356 T(356)=0*100000!*(1/(100000!*(1-TBM(X(28),X(5)))+1))
1357 T(357)=10*100000!*(1/(100000!*(1-TBM(X(28),X(6)))+1))
1358 T(358)=0*100000!*(1/(100000!*(1-TBM(X(28),X(7)))+1))
1359 T(359)=5*100000!*(1/(100000!*(1-TBM(X(28),X(8)))+1))
1360 T(360)=2*100000!*(1/(100000!*(1-TBM(X(28),X(9)))+1))
1361 T(361)=1*100000!*(1/(100000!*(1-TBM(X(28),X(10)))+1))
1362 T(362)=2*100000!*(1/(100000!*(1-TBM(X(28),X(11)))+1))
1363 T(363)=0*100000!*(1/(100000!*(1-TBM(X(28),X(12)))+1))
1364 T(364)=1*100000!*(1/(100000!*(1-TBM(X(28),X(13)))+1))
1365 T(365)=2*100000!*(1/(100000!*(1-TBM(X(28),X(14)))+1))
1366 T(366)=1*100000!*(1/(100000!*(1-TBM(X(28),X(15)))+1))
1367 T(367)=2*100000!*(1/(100000!*(1-TBM(X(28),X(16)))+1))
1368 T(368)=0*100000!*(1/(100000!*(1-TBM(X(28),X(17)))+1))
1369 T(369)=0*100000!*(1/(100000!*(1-TBM(X(28),X(18)))+1))
1370 T(370)=2*100000!*(1/(100000!*(1-TBM(X(28),X(19)))+1))
1371 T(371)=5*100000!*(1/(100000!*(1-TBM(X(28),X(20)))+1))
1372 T(372)=5*100000!*(1/(100000!*(1-TBM(X(28),X(21)))+1))
1373 T(373)=0*100000!*(1/(100000!*(1-TBM(X(28),X(22)))+1))
1374 T(374)=0*100000!*(1/(100000!*(1-TBM(X(28),X(23)))+1))
1375 T(375)=1*100000!*(1/(100000!*(1-TBM(X(28),X(24)))+1))
1376 T(376)=10*100000!*(1/(100000!*(1-TBM(X(28),X(25)))+1))
1377 T(377)=0*100000!*(1/(100000!*(1-TBM(X(28),X(26)))+1))
1378 T(378)=0*100000!*(1/(100000!*(1-TBM(X(28),X(27)))+1))
1379 T(379)=0*100000!*(1/(100000!*(1-TBM(X(29),X(1)))+1))
1380 T(380)=10*100000!*(1/(100000!*(1-TBM(X(29),X(2)))+1))
1381 T(381)=0*100000!*(1/(100000!*(1-TBM(X(29),X(3)))+1))
1382 T(382)=5*100000!*(1/(100000!*(1-TBM(X(29),X(4)))+1))
1383 T(383)=2*100000!*(1/(100000!*(1-TBM(X(29),X(5)))+1))
1384 T(384)=1*100000!*(1/(100000!*(1-TBM(X(29),X(6)))+1))
1385 T(385)=1*100000!*(1/(100000!*(1-TBM(X(29),X(7)))+1))
1386 T(386)=0*100000!*(1/(100000!*(1-TBM(X(29),X(8)))+1))
1387 T(387)=5*100000!*(1/(100000!*(1-TBM(X(29),X(9)))+1))
1388 T(388)=5*100000!*(1/(100000!*(1-TBM(X(29),X(10)))+1))
1389 T(389)=2*100000!*(1/(100000!*(1-TBM(X(29),X(11)))+1))
1390 T(390)=0*100000!*(1/(100000!*(1-TBM(X(29),X(12)))+1))
1391 T(391)=5*100000!*(1/(100000!*(1-TBM(X(29),X(13)))+1))
1392 T(392)=5*100000!*(1/(100000!*(1-TBM(X(29),X(14)))+1))
1393 T(393)=1*100000!*(1/(100000!*(1-TBM(X(29),X(15)))+1))
1394 T(394)=5*100000!*(1/(100000!*(1-TBM(X(29),X(16)))+1))
1395 T(395)=5*100000!*(1/(100000!*(1-TBM(X(29),X(17)))+1))
1396 T(396)=0*100000!*(1/(100000!*(1-TBM(X(29),X(18)))+1))
1397 T(397)=10*100000!*(1/(100000!*(1-TBM(X(29),X(19)))+1))
1398 T(398)=5*100000!*(1/(100000!*(1-TBM(X(29),X(20)))+1))
1399 T(399)=0*100000!*(1/(100000!*(1-TBM(X(29),X(21)))+1))
1400 T(400)=2*100000!*(1/(100000!*(1-TBM(X(29),X(22)))+1))
1401 T(401)=2*100000!*(1/(100000!*(1-TBM(X(29),X(23)))+1))
1402 T(402)=0*100000!*(1/(100000!*(1-TBM(X(29),X(24)))+1))
1403 T(403)=1*100000!*(1/(100000!*(1-TBM(X(29),X(25)))+1))
1404 T(404)=0*100000!*(1/(100000!*(1-TBM(X(29),X(26)))+1))
1405 T(405)=0*100000!*(1/(100000!*(1-TBM(X(29),X(27)))+1))
1406 T(406)=2*100000!*(1/(100000!*(1-TBM(X(29),X(28)))+1))
1407 T(407)=1*100000!*(1/(100000!*(1-TBM(X(30),X(1)))+1))
1408 T(408)=5*100000!*(1/(100000!*(1-TBM(X(30),X(2)))+1))
1409 T(409)=2*100000!*(1/(100000!*(1-TBM(X(30),X(3)))+1))
1410 T(410)=5*100000!*(1/(100000!*(1-TBM(X(30),X(4)))+1))
1411 T(411)=1*100000!*(1/(100000!*(1-TBM(X(30),X(5)))+1))
1412 T(412)=1*100000!*(1/(100000!*(1-TBM(X(30),X(6)))+1))
1413 T(413)=3*100000!*(1/(100000!*(1-TBM(X(30),X(7)))+1))
1414 T(414)=2*100000!*(1/(100000!*(1-TBM(X(30),X(8)))+1))
1415 T(415)=2*100000!*(1/(100000!*(1-TBM(X(30),X(9)))+1))
1416 T(416)=2*100000!*(1/(100000!*(1-TBM(X(30),X(10)))+1))
1417 T(417)=10*100000!*(1/(100000!*(1-TBM(X(30),X(11)))+1))
1418 T(418)=1*100000!*(1/(100000!*(1-TBM(X(30),X(12)))+1))
1419 T(419)=5*100000!*(1/(100000!*(1-TBM(X(30),X(13)))+1))
1420 T(420)=5*100000!*(1/(100000!*(1-TBM(X(30),X(14)))+1))
1421 T(421)=0*100000!*(1/(100000!*(1-TBM(X(30),X(15)))+1))
1422 T(422)=10*100000!*(1/(100000!*(1-TBM(X(30),X(16)))+1))
1423 T(423)=1*100000!*(1/(100000!*(1-TBM(X(30),X(17)))+1))
1424 T(424)=0*100000!*(1/(100000!*(1-TBM(X(30),X(18)))+1))
1425 T(425)=10*100000!*(1/(100000!*(1-TBM(X(30),X(19)))+1))
1426 T(426)=3*100000!*(1/(100000!*(1-TBM(X(30),X(20)))+1))
1427 T(427)=0*100000!*(1/(100000!*(1-TBM(X(30),X(21)))+1))
1428 T(428)=5*100000!*(1/(100000!*(1-TBM(X(30),X(22)))+1))
1429 T(429)=2*100000!*(1/(100000!*(1-TBM(X(30),X(23)))+1))
1430 T(430)=0*100000!*(1/(100000!*(1-TBM(X(30),X(24)))+1))
1431 T(431)=0*100000!*(1/(100000!*(1-TBM(X(30),X(25)))+1))
1432 T(432)=0*100000!*(1/(100000!*(1-TBM(X(30),X(26)))+1))
1433 T(433)=10*100000!*(1/(100000!*(1-TBM(X(30),X(27)))+1))
1434 T(434)=2*100000!*(1/(100000!*(1-TBM(X(30),X(28)))+1))
1435 T(435)=2*100000!*(1/(100000!*(1-TBM(X(30),X(29)))+1))
2151 P1NEW=0
2152 FOR KAU7=1 TO 435
2153 P1NEW=P1NEW+T(KAU7)
2154 NEXT KAU7
2450 P=-P1NEW
2451 IF P<=M THEN 2670
2657 FOR KEW=1 TO 30
2658 A(KEW)=X(KEW)
2659 NEXT KEW
2661 M=P
2666 GOTO 128
2670 NEXT I
2890 IF M>-46011111# THEN 2911 ELSE 2999
2911 PRINT A(1),A(2),A(3)
2912 PRINT A(4),A(5),A(6)
2913 PRINT A(7),A(8),A(9)
2914 PRINT A(10),A(11),A(12)
2915 PRINT A(13),A(14),A(15)
2916 PRINT A(16),A(17),A(18)
2917 PRINT A(19),A(20),A(21)
2918 PRINT A(22),A(23),A(24)
2919 PRINT A(25),A(26),A(27)
2920 PRINT A(28),A(29),A(30)
2925 PRINT JJJJ,M
2999 NEXT JJJJ

This BASIC computer program was run with the IBM basica/D interpreter, and its best candidate solutions, which are interpreted in accordance with line 2911 through line 2925, through JJJJ=-29401 are presented below.

2 1 1
1 2 2
3 3 2
4 4 4
4 4 4
1 1 4
1 1 3
1 1 1
3 4 1
4 4 4
-31742 -45600670.99329007

1 1 2
1 2 2
3 3 2
4 4 4
4 4 4
1 1 4
1 1 4
1 1 1
3 4 2
1 4 4
-29401 -44900677.99322007

2 1 1
1 2 2
3 3 2
4 4 4
4 4 4
1 1 4
1 1 4
1 1 1
3 4 1
4 4 3
-29038 -45400672.99327007

The output above was produced in 110 minutes on a personal computer with an Intel 2.66 GHz. chip and the IBM interpreter, which is slower than the corresponding compiler.

References

[1] L. R. Arnold, R. E. Beckwith, C. M. Jones, Scheduling the 41st-ORSA-meeting sessions: the visiting-fireman problem, II, Operations Research 21 (1973) 1095-1103.

[2] R. C. Carlson, G. L. Nemhauser, Scheduling to minimize interaction cost, Operations Research 14 (1966) 52-58.

[3] F. E. Davis, M. D. Devine, R. P. Lutz, Scheduling activities among conflicting facilities to minimize conflict, Mathematical Programming 6 (1974) 224-228.

[4] F. S. Hillier, Quantitative tools for plant layout analysis, J. Indust. Eng. 14 (1963) 33-40.

[5] C. E. Nugent, T. E. Vollmann, J. Ruml, An experimental comparison of techniques for the assignment of facilities to locations, Operations Research 16 (1968) 150-173.

Thursday, February 19, 2009

Assigning Thirty Activities to Four Conflicting Facilities

Assigning Thirty Activities to Four Conflicting Facilities

Jsun Yui Wong

The difference between the original Carlson and Nemhauser problem [1] and the problem of Davis, Devine, and Lutz [2] is "that their problem did not consider conflicting facilities," Davis, Devine, and Lutz [2, p. 225]. For the newer problem, "a cost is incurred if two activities are assigned to the same facility, or to two facilities whose operation is in conflict," Davis et al. [2, p. 224]. Dealing with an instance of the newer problem, the computer program below attempts to find the lowest cost of scheduling thirty courses in four time periods which are 8a.m. to 11 a.m., 10 a.m. to 1 p.m., noon to 3 p.m., and 2 p.m. to 5 p.m. The conflicts are specified in line 6 through line 9 of the following computer program.

In this paper, fourteen courses express through their professors their various preferences for their preferred time periods: courses 1 through 5 for period 1 or period 2, courses 6 through 9 for period 2 or period 3, and courses 10 through 14 for period 3 or period 4. These fourteen preferences are expressed in line 325 through line 643.

The costs used in line 1001 through line 1435 of the computer program below come from Hillier [3] and Nugent, Vollmann, and Ruml [4, pp. 168-170].

In this paper, A(1)=1, A(2)=1, A(3)=1,..., and A(30)=1 stand for course 1 in period 1, course 2 in period 1, course 3 in period 1,..., and course 30 in period 1, respectively.

The computer program below is modelled after the computer program of the March 7 post "Assigning Activities to Conflicting Facilities To Minimize Conflict Cost" of the present blog.

2 DEFINT A-Z
4 DEFDBL M,T,P
5 DIM N(9),B(9),A(199),H(99),X(199),P(450),L(99),U(99),Q(977),R(444),T(999),Q1(222)
6 TBM(1,1)=1:TBM(1,2)=1
7 TBM(2,1)=1:TBM(2,2)=1:TBM(2,3)=1
8 TBM(3,2)=1:TBM(3,3)=1:TBM(3,4)=1
9 TBM(4,3)=1:TBM(4,4)=1
12 FOR JJJJ=-32000 TO 32000
14 RANDOMIZE JJJJ
16 M=-1D+17
20 A(1)=1:A(2)=1:A(3)=1:A(4)=1:A(5)=1:A(6)=2:A(7)=2:A(8)=2:A(9)=2
21 A(10)=3:A(11)=3:A(12)=3:A(13)=3:A(14)=3
31 FOR IAP7=15 TO 30
35 A(IAP7)=1+FIX(RND*4)
39 NEXT IAP7
126 IMAR=10+FIX(RND*1000)
128 FOR I=1 TO IMAR
129 FOR K=1 TO 30
131 X(K)=A(K)
132 NEXT K
251 IF RND<.17 THEN 325 ELSE IF RND<.16 THEN 431 ELSE IF RND<.24 THEN 533 ELSE 641
325 IAP2=1+FIX(RND*5)
328 X(IAP2)=1+FIX(RND*2)
339 GOTO 1001
431 IAP3=6+FIX(RND*4)
435 X(IAP3)=2+FIX(RND*2)
444 GOTO 1001
533 IAP4=10+FIX(RND*5)
536 X(IAP4)=3+FIX(RND*2)
547 GOTO 1001
641 IAP1=15+FIX(RND*16)
643 X(IAP1)=1+FIX(RND*4)
1001 T(1)=5*100000!*(1/(100000!*(1-TBM(X(1),X(2)))+1))
1002 T(2)=2*100000!*(1/(100000!*(1-TBM(X(1),X(3)))+1))
1003 T(3)=4*100000!*(1/(100000!*(1-TBM(X(1),X(4)))+1))
1004 T(4)=1*100000!*(1/(100000!*(1-TBM(X(1),X(5)))+1))
1005 T(5)=0*100000!*(1/(100000!*(1-TBM(X(1),X(6)))+1))
1006 T(6)=0*100000!*(1/(100000!*(1-TBM(X(1),X(7)))+1))
1007 T(7)=6*100000!*(1/(100000!*(1-TBM(X(1),X(8)))+1))
1008 T(8)=2*100000!*(1/(100000!*(1-TBM(X(1),X(9)))+1))
1009 T(9)=1*100000!*(1/(100000!*(1-TBM(X(1),X(10)))+1))
1010 T(10)=1*100000!*(1/(100000!*(1-TBM(X(1),X(11)))+1))
1011 T(11)=1*100000!*(1/(100000!*(1-TBM(X(1),X(12)))+1))
1012 T(12)=3*100000!*(1/(100000!*(1-TBM(X(2),X(3)))+1))
1013 T(13)=0*100000!*(1/(100000!*(1-TBM(X(2),X(4)))+1))
1014 T(14)=2*100000!*(1/(100000!*(1-TBM(X(2),X(5)))+1))
1015 T(15)=2*100000!*(1/(100000!*(1-TBM(X(2),X(6)))+1))
1016 T(16)=2*100000!*(1/(100000!*(1-TBM(X(2),X(7)))+1))
1017 T(17)=0*100000!*(1/(100000!*(1-TBM(X(2),X(8)))+1))
1018 T(18)=4*100000!*(1/(100000!*(1-TBM(X(2),X(9)))+1))
1019 T(19)=5*100000!*(1/(100000!*(1-TBM(X(2),X(10)))+1))
1020 T(20)=0*100000!*(1/(100000!*(1-TBM(X(2),X(11)))+1))
1021 T(21)=0*100000!*(1/(100000!*(1-TBM(X(2),X(12)))+1))
1022 T(22)=0*100000!*(1/(100000!*(1-TBM(X(3),X(4)))+1))
1023 T(23)=0*100000!*(1/(100000!*(1-TBM(X(3),X(5)))+1))
1024 T(24)=0*100000!*(1/(100000!*(1-TBM(X(3),X(6)))+1))
1025 T(25)=0*100000!*(1/(100000!*(1-TBM(X(3),X(7)))+1))
1026 T(26)=5*100000!*(1/(100000!*(1-TBM(X(3),X(8)))+1))
1027 T(27)=5*100000!*(1/(100000!*(1-TBM(X(3),X(9)))+1))
1028 T(28)=2*100000!*(1/(100000!*(1-TBM(X(3),X(10)))+1))
1029 T(29)=2*100000!*(1/(100000!*(1-TBM(X(3),X(11)))+1))
1030 T(30)=2*100000!*(1/(100000!*(1-TBM(X(3),X(12)))+1))
1031 T(31)=5*100000!*(1/(100000!*(1-TBM(X(4),X(5)))+1))
1032 T(32)=2*100000!*(1/(100000!*(1-TBM(X(4),X(6)))+1))
1033 T(33)=2*100000!*(1/(100000!*(1-TBM(X(4),X(7)))+1))
1034 T(34)=10*100000!*(1/(100000!*(1-TBM(X(4),X(8)))+1))
1035 T(35)=0*100000!*(1/(100000!*(1-TBM(X(4),X(9)))+1))
1036 T(36)=0*100000!*(1/(100000!*(1-TBM(X(4),X(10)))+1))
1037 T(37)=5*100000!*(1/(100000!*(1-TBM(X(4),X(11)))+1))
1038 T(38)=5*100000!*(1/(100000!*(1-TBM(X(4),X(12)))+1))
1039 T(39)=10*100000!*(1/(100000!*(1-TBM(X(5),X(6)))+1))
1040 T(40)=0*100000!*(1/(100000!*(1-TBM(X(5),X(7)))+1))
1041 T(41)=0*100000!*(1/(100000!*(1-TBM(X(5),X(8)))+1))
1042 T(42)=0*100000!*(1/(100000!*(1-TBM(X(5),X(9)))+1))
1043 T(43)=5*100000!*(1/(100000!*(1-TBM(X(5),X(10)))+1))
1044 T(44)=1*100000!*(1/(100000!*(1-TBM(X(5),X(11)))+1))
1045 T(45)=1*100000!*(1/(100000!*(1-TBM(X(5),X(12)))+1))
1046 T(46)=5*100000!*(1/(100000!*(1-TBM(X(6),X(7)))+1))
1047 T(47)=1*100000!*(1/(100000!*(1-TBM(X(6),X(8)))+1))
1048 T(48)=1*100000!*(1/(100000!*(1-TBM(X(6),X(9)))+1))
1049 T(49)=5*100000!*(1/(100000!*(1-TBM(X(6),X(10)))+1))
1050 T(50)=4*100000!*(1/(100000!*(1-TBM(X(6),X(11)))+1))
1051 T(51)=0*100000!*(1/(100000!*(1-TBM(X(6),X(12)))+1))
1052 T(52)=10*100000!*(1/(100000!*(1-TBM(X(7),X(8)))+1))
1053 T(53)=5*100000!*(1/(100000!*(1-TBM(X(7),X(9)))+1))
1054 T(54)=2*100000!*(1/(100000!*(1-TBM(X(7),X(10)))+1))
1055 T(55)=3*100000!*(1/(100000!*(1-TBM(X(7),X(11)))+1))
1056 T(56)=3*100000!*(1/(100000!*(1-TBM(X(7),X(12)))+1))
1057 T(57)=0*100000!*(1/(100000!*(1-TBM(X(8),X(9)))+1))
1058 T(58)=0*100000!*(1/(100000!*(1-TBM(X(8),X(10)))+1))
1059 T(59)=5*100000!*(1/(100000!*(1-TBM(X(8),X(11)))+1))
1060 T(60)=0*100000!*(1/(100000!*(1-TBM(X(8),X(12)))+1))
1061 T(61)=0*100000!*(1/(100000!*(1-TBM(X(9),X(10)))+1))
1062 T(62)=10*100000!*(1/(100000!*(1-TBM(X(9),X(11)))+1))
1063 T(63)=10*100000!*(1/(100000!*(1-TBM(X(9),X(12)))+1))
1064 T(64)=5*100000!*(1/(100000!*(1-TBM(X(10),X(11)))+1))
1065 T(65)=0*100000!*(1/(100000!*(1-TBM(X(10),X(12)))+1))
1066 T(66)=2*100000!*(1/(100000!*(1-TBM(X(11),X(12)))+1))
1067 T(67)=4*100000!*(1/(100000!*(1-TBM(X(13),X(1)))+1))
1068 T(68)=10*100000!*(1/(100000!*(1-TBM(X(13),X(2)))+1))
1069 T(69)=5*100000!*(1/(100000!*(1-TBM(X(13),X(3)))+1))
1070 T(70)=2*100000!*(1/(100000!*(1-TBM(X(13),X(4)))+1))
1071 T(71)=0*100000!*(1/(100000!*(1-TBM(X(13),X(5)))+1))
1072 T(72)=2*100000!*(1/(100000!*(1-TBM(X(13),X(6)))+1))
1073 T(73)=5*100000!*(1/(100000!*(1-TBM(X(13),X(7)))+1))
1074 T(74)=5*100000!*(1/(100000!*(1-TBM(X(13),X(8)))+1))
1075 T(75)=10*100000!*(1/(100000!*(1-TBM(X(13),X(9)))+1))
1076 T(76)=0*100000!*(1/(100000!*(1-TBM(X(13),X(10)))+1))
1077 T(77)=0*100000!*(1/(100000!*(1-TBM(X(13),X(11)))+1))
1078 T(78)=3*100000!*(1/(100000!*(1-TBM(X(13),X(12)))+1))
1079 T(79)=0*100000!*(1/(100000!*(1-TBM(X(14),X(1)))+1))
1080 T(80)=5*100000!*(1/(100000!*(1-TBM(X(14),X(2)))+1))
1081 T(81)=5*100000!*(1/(100000!*(1-TBM(X(14),X(3)))+1))
1082 T(82)=5*100000!*(1/(100000!*(1-TBM(X(14),X(4)))+1))
1083 T(83)=5*100000!*(1/(100000!*(1-TBM(X(14),X(5)))+1))
1084 T(84)=5*100000!*(1/(100000!*(1-TBM(X(14),X(6)))+1))
1085 T(85)=1*100000!*(1/(100000!*(1-TBM(X(14),X(7)))+1))
1086 T(86)=0*100000!*(1/(100000!*(1-TBM(X(14),X(8)))+1))
1087 T(87)=0*100000!*(1/(100000!*(1-TBM(X(14),X(9)))+1))
1088 T(88)=0*100000!*(1/(100000!*(1-TBM(X(14),X(10)))+1))
1089 T(89)=5*100000!*(1/(100000!*(1-TBM(X(14),X(11)))+1))
1090 T(90)=3*100000!*(1/(100000!*(1-TBM(X(14),X(12)))+1))
1091 T(91)=10*100000!*(1/(100000!*(1-TBM(X(14),X(13)))+1))
1092 T(92)=0*100000!*(1/(100000!*(1-TBM(X(15),X(1)))+1))
1093 T(93)=0*100000!*(1/(100000!*(1-TBM(X(15),X(2)))+1))
1094 T(94)=5*100000!*(1/(100000!*(1-TBM(X(15),X(3)))+1))
1095 T(95)=0*100000!*(1/(100000!*(1-TBM(X(15),X(4)))+1))
1096 T(96)=5*100000!*(1/(100000!*(1-TBM(X(15),X(5)))+1))
1097 T(97)=10*100000!*(1/(100000!*(1-TBM(X(15),X(6)))+1))
1098 T(98)=0*100000!*(1/(100000!*(1-TBM(X(15),X(7)))+1))
1099 T(99)=0*100000!*(1/(100000!*(1-TBM(X(15),X(8)))+1))
1100 T(100)=2*100000!*(1/(100000!*(1-TBM(X(15),X(9)))+1))
1101 T(101)=5*100000!*(1/(100000!*(1-TBM(X(15),X(10)))+1))
1102 T(102)=0*100000!*(1/(100000!*(1-TBM(X(15),X(11)))+1))
1103 T(103)=0*100000!*(1/(100000!*(1-TBM(X(15),X(12)))+1))
1104 T(104)=2*100000!*(1/(100000!*(1-TBM(X(15),X(13)))+1))
1105 T(105)=4*100000!*(1/(100000!*(1-TBM(X(15),X(14)))+1))
1106 T(106)=0*100000!*(1/(100000!*(1-TBM(X(16),X(1)))+1))
1107 T(107)=0*100000!*(1/(100000!*(1-TBM(X(16),X(2)))+1))
1108 T(108)=4*100000!*(1/(100000!*(1-TBM(X(16),X(3)))+1))
1109 T(109)=5*100000!*(1/(100000!*(1-TBM(X(16),X(4)))+1))
1110 T(110)=0*100000!*(1/(100000!*(1-TBM(X(16),X(5)))+1))
1111 T(111)=5*100000!*(1/(100000!*(1-TBM(X(16),X(6)))+1))
1112 T(112)=10*100000!*(1/(100000!*(1-TBM(X(16),X(7)))+1))
1113 T(113)=4*100000!*(1/(100000!*(1-TBM(X(16),X(8)))+1))
1114 T(114)=3*100000!*(1/(100000!*(1-TBM(X(16),X(9)))+1))
1115 T(115)=5*100000!*(1/(100000!*(1-TBM(X(16),X(10)))+1))
1116 T(116)=1*100000!*(1/(100000!*(1-TBM(X(16),X(11)))+1))
1117 T(117)=0*100000!*(1/(100000!*(1-TBM(X(16),X(12)))+1))
1118 T(118)=4*100000!*(1/(100000!*(1-TBM(X(16),X(13)))+1))
1119 T(119)=1*100000!*(1/(100000!*(1-TBM(X(16),X(14)))+1))
1120 T(120)=4*100000!*(1/(100000!*(1-TBM(X(16),X(15)))+1))
1121 T(121)=5*100000!*(1/(100000!*(1-TBM(X(17),X(1)))+1))
1122 T(122)=0*100000!*(1/(100000!*(1-TBM(X(17),X(2)))+1))
1123 T(123)=0*100000!*(1/(100000!*(1-TBM(X(17),X(3)))+1))
1124 T(124)=1*100000!*(1/(100000!*(1-TBM(X(17),X(4)))+1))
1125 T(125)=2*100000!*(1/(100000!*(1-TBM(X(17),X(5)))+1))
1126 T(126)=0*100000!*(1/(100000!*(1-TBM(X(17),X(6)))+1))
1127 T(127)=2*100000!*(1/(100000!*(1-TBM(X(17),X(7)))+1))
1128 T(128)=5*100000!*(1/(100000!*(1-TBM(X(17),X(8)))+1))
1129 T(129)=0*100000!*(1/(100000!*(1-TBM(X(17),X(9)))+1))
1130 T(130)=5*100000!*(1/(100000!*(1-TBM(X(17),X(10)))+1))
1131 T(131)=0*100000!*(1/(100000!*(1-TBM(X(17),X(11)))+1))
1132 T(132)=0*100000!*(1/(100000!*(1-TBM(X(17),X(12)))+1))
1133 T(133)=2*100000!*(1/(100000!*(1-TBM(X(17),X(13)))+1))
1134 T(134)=0*100000!*(1/(100000!*(1-TBM(X(17),X(14)))+1))
1135 T(135)=5*100000!*(1/(100000!*(1-TBM(X(17),X(15)))+1))
1136 T(136)=0*100000!*(1/(100000!*(1-TBM(X(17),X(16)))+1))
1137 T(137)=6*100000!*(1/(100000!*(1-TBM(X(18),X(1)))+1))
1138 T(138)=2*100000!*(1/(100000!*(1-TBM(X(18),X(2)))+1))
1139 T(139)=6*100000!*(1/(100000!*(1-TBM(X(18),X(3)))+1))
1140 T(140)=1*100000!*(1/(100000!*(1-TBM(X(18),X(4)))+1))
1141 T(141)=1*100000!*(1/(100000!*(1-TBM(X(18),X(5)))+1))
1142 T(142)=5*100000!*(1/(100000!*(1-TBM(X(18),X(6)))+1))
1143 T(143)=1*100000!*(1/(100000!*(1-TBM(X(18),X(7)))+1))
1144 T(144)=2*100000!*(1/(100000!*(1-TBM(X(18),X(8)))+1))
1145 T(145)=2*100000!*(1/(100000!*(1-TBM(X(18),X(9)))+1))
1146 T(146)=0*100000!*(1/(100000!*(1-TBM(X(18),X(10)))+1))
1147 T(147)=2*100000!*(1/(100000!*(1-TBM(X(18),X(11)))+1))
1148 T(148)=0*100000!*(1/(100000!*(1-TBM(X(18),X(12)))+1))
1149 T(149)=2*100000!*(1/(100000!*(1-TBM(X(18),X(13)))+1))
1150 T(150)=5*100000!*(1/(100000!*(1-TBM(X(18),X(14)))+1))
1151 T(151)=1*100000!*(1/(100000!*(1-TBM(X(18),X(15)))+1))
1152 T(152)=3*100000!*(1/(100000!*(1-TBM(X(18),X(16)))+1))
1153 T(153)=2*100000!*(1/(100000!*(1-TBM(X(18),X(17)))+1))
1154 T(154)=3*100000!*(1/(100000!*(1-TBM(X(19),X(1)))+1))
1155 T(155)=0*100000!*(1/(100000!*(1-TBM(X(19),X(2)))+1))
1156 T(156)=3*100000!*(1/(100000!*(1-TBM(X(19),X(3)))+1))
1157 T(157)=1*100000!*(1/(100000!*(1-TBM(X(19),X(4)))+1))
1158 T(158)=0*100000!*(1/(100000!*(1-TBM(X(19),X(5)))+1))
1159 T(159)=0*100000!*(1/(100000!*(1-TBM(X(19),X(6)))+1))
1160 T(160)=10*100000!*(1/(100000!*(1-TBM(X(19),X(7)))+1))
1161 T(161)=10*100000!*(1/(100000!*(1-TBM(X(19),X(8)))+1))
1162 T(162)=0*100000!*(1/(100000!*(1-TBM(X(19),X(9)))+1))
1163 T(163)=5*100000!*(1/(100000!*(1-TBM(X(19),X(10)))+1))
1164 T(164)=0*100000!*(1/(100000!*(1-TBM(X(19),X(11)))+1))
1165 T(165)=0*100000!*(1/(100000!*(1-TBM(X(19),X(12)))+1))
1166 T(166)=1*100000!*(1/(100000!*(1-TBM(X(19),X(13)))+1))
1167 T(167)=3*100000!*(1/(100000!*(1-TBM(X(19),X(14)))+1))
1168 T(168)=0*100000!*(1/(100000!*(1-TBM(X(19),X(15)))+1))
1169 T(169)=0*100000!*(1/(100000!*(1-TBM(X(19),X(16)))+1))
1170 T(170)=2*100000!*(1/(100000!*(1-TBM(X(19),X(17)))+1))
1171 T(171)=5*100000!*(1/(100000!*(1-TBM(X(19),X(18)))+1))
1172 T(172)=0*100000!*(1/(100000!*(1-TBM(X(20),X(1)))+1))
1173 T(173)=1*100000!*(1/(100000!*(1-TBM(X(20),X(2)))+1))
1174 T(174)=2*100000!*(1/(100000!*(1-TBM(X(20),X(3)))+1))
1175 T(175)=1*100000!*(1/(100000!*(1-TBM(X(20),X(4)))+1))
1176 T(176)=0*100000!*(1/(100000!*(1-TBM(X(20),X(5)))+1))
1177 T(177)=0*100000!*(1/(100000!*(1-TBM(X(20),X(6)))+1))
1178 T(178)=1*100000!*(1/(100000!*(1-TBM(X(20),X(7)))+1))
1179 T(179)=6*100000!*(1/(100000!*(1-TBM(X(20),X(8)))+1))
1180 T(180)=0*100000!*(1/(100000!*(1-TBM(X(20),X(9)))+1))
1181 T(181)=2*100000!*(1/(100000!*(1-TBM(X(20),X(10)))+1))
1182 T(182)=0*100000!*(1/(100000!*(1-TBM(X(20),X(11)))+1))
1183 T(183)=2*100000!*(1/(100000!*(1-TBM(X(20),X(12)))+1))
1184 T(184)=0*100000!*(1/(100000!*(1-TBM(X(20),X(13)))+1))
1185 T(185)=10*100000!*(1/(100000!*(1-TBM(X(20),X(14)))+1))
1186 T(186)=1*100000!*(1/(100000!*(1-TBM(X(20),X(15)))+1))
1187 T(187)=2*100000!*(1/(100000!*(1-TBM(X(20),X(16)))+1))
1188 T(188)=0*100000!*(1/(100000!*(1-TBM(X(20),X(17)))+1))
1189 T(189)=1*100000!*(1/(100000!*(1-TBM(X(20),X(18)))+1))
1190 T(190)=0*100000!*(1/(100000!*(1-TBM(X(20),X(19)))+1))
1191 T(191)=1*100000!*(1/(100000!*(1-TBM(X(21),X(1)))+1))
1192 T(192)=6*100000!*(1/(100000!*(1-TBM(X(21),X(2)))+1))
1193 T(193)=5*100000!*(1/(100000!*(1-TBM(X(21),X(3)))+1))
1194 T(194)=2*100000!*(1/(100000!*(1-TBM(X(21),X(4)))+1))
1195 T(195)=2*100000!*(1/(100000!*(1-TBM(X(21),X(5)))+1))
1196 T(196)=0*100000!*(1/(100000!*(1-TBM(X(21),X(6)))+1))
1197 T(197)=5*100000!*(1/(100000!*(1-TBM(X(21),X(7)))+1))
1198 T(198)=0*100000!*(1/(100000!*(1-TBM(X(21),X(8)))+1))
1199 T(199)=4*100000!*(1/(100000!*(1-TBM(X(21),X(9)))+1))
1200 T(200)=3*100000!*(1/(100000!*(1-TBM(X(21),X(10)))+1))
1201 T(201)=0*100000!*(1/(100000!*(1-TBM(X(21),X(11)))+1))
1202 T(202)=0*100000!*(1/(100000!*(1-TBM(X(21),X(12)))+1))
1203 T(203)=6*100000!*(1/(100000!*(1-TBM(X(21),X(13)))+1))
1204 T(204)=0*100000!*(1/(100000!*(1-TBM(X(21),X(14)))+1))
1205 T(205)=0*100000!*(1/(100000!*(1-TBM(X(21),X(15)))+1))
1206 T(206)=2*100000!*(1/(100000!*(1-TBM(X(21),X(16)))+1))
1207 T(207)=0*100000!*(1/(100000!*(1-TBM(X(21),X(17)))+1))
1208 T(208)=2*100000!*(1/(100000!*(1-TBM(X(21),X(18)))+1))
1209 T(209)=5*100000!*(1/(100000!*(1-TBM(X(21),X(19)))+1))
1210 T(210)=5*100000!*(1/(100000!*(1-TBM(X(21),X(20)))+1))
1211 T(211)=10*100000!*(1/(100000!*(1-TBM(X(22),X(1)))+1))
1212 T(212)=1*100000!*(1/(100000!*(1-TBM(X(22),X(2)))+1))
1213 T(213)=5*100000!*(1/(100000!*(1-TBM(X(22),X(3)))+1))
1214 T(214)=2*100000!*(1/(100000!*(1-TBM(X(22),X(4)))+1))
1215 T(215)=0*100000!*(1/(100000!*(1-TBM(X(22),X(5)))+1))
1216 T(216)=10*100000!*(1/(100000!*(1-TBM(X(22),X(6)))+1))
1217 T(217)=5*100000!*(1/(100000!*(1-TBM(X(22),X(7)))+1))
1218 T(218)=5*100000!*(1/(100000!*(1-TBM(X(22),X(8)))+1))
1219 T(219)=0*100000!*(1/(100000!*(1-TBM(X(22),X(9)))+1))
1220 T(220)=5*100000!*(1/(100000!*(1-TBM(X(22),X(10)))+1))
1221 T(221)=6*100000!*(1/(100000!*(1-TBM(X(22),X(11)))+1))
1222 T(222)=4*100000!*(1/(100000!*(1-TBM(X(22),X(12)))+1))
1223 T(223)=2*100000!*(1/(100000!*(1-TBM(X(22),X(13)))+1))
1224 T(224)=0*100000!*(1/(100000!*(1-TBM(X(22),X(14)))+1))
1225 T(225)=5*100000!*(1/(100000!*(1-TBM(X(22),X(15)))+1))
1226 T(226)=0*100000!*(1/(100000!*(1-TBM(X(22),X(16)))+1))
1227 T(227)=0*100000!*(1/(100000!*(1-TBM(X(22),X(17)))+1))
1228 T(228)=10*100000!*(1/(100000!*(1-TBM(X(22),X(18)))+1))
1229 T(229)=5*100000!*(1/(100000!*(1-TBM(X(22),X(19)))+1))
1230 T(230)=2*100000!*(1/(100000!*(1-TBM(X(22),X(20)))+1))
1231 T(231)=4*100000!*(1/(100000!*(1-TBM(X(22),X(21)))+1))
1232 T(232)=0*100000!*(1/(100000!*(1-TBM(X(23),X(1)))+1))
1233 T(233)=0*100000!*(1/(100000!*(1-TBM(X(23),X(2)))+1))
1234 T(234)=2*100000!*(1/(100000!*(1-TBM(X(23),X(3)))+1))
1235 T(235)=4*100000!*(1/(100000!*(1-TBM(X(23),X(4)))+1))
1236 T(236)=5*100000!*(1/(100000!*(1-TBM(X(23),X(5)))+1))
1237 T(237)=0*100000!*(1/(100000!*(1-TBM(X(23),X(6)))+1))
1238 T(238)=2*100000!*(1/(100000!*(1-TBM(X(23),X(7)))+1))
1239 T(239)=5*100000!*(1/(100000!*(1-TBM(X(23),X(8)))+1))
1240 T(240)=5*100000!*(1/(100000!*(1-TBM(X(23),X(9)))+1))
1241 T(241)=0*100000!*(1/(100000!*(1-TBM(X(23),X(10)))+1))
1242 T(242)=6*100000!*(1/(100000!*(1-TBM(X(23),X(11)))+1))
1243 T(243)=5*100000!*(1/(100000!*(1-TBM(X(23),X(12)))+1))
1244 T(244)=1*100000!*(1/(100000!*(1-TBM(X(23),X(13)))+1))
1245 T(245)=4*100000!*(1/(100000!*(1-TBM(X(23),X(14)))+1))
1246 T(246)=0*100000!*(1/(100000!*(1-TBM(X(23),X(15)))+1))
1247 T(247)=2*100000!*(1/(100000!*(1-TBM(X(23),X(16)))+1))
1248 T(248)=6*100000!*(1/(100000!*(1-TBM(X(23),X(17)))+1))
1249 T(249)=10*100000!*(1/(100000!*(1-TBM(X(23),X(18)))+1))
1250 T(250)=1*100000!*(1/(100000!*(1-TBM(X(23),X(19)))+1))
1251 T(251)=1*100000!*(1/(100000!*(1-TBM(X(23),X(20)))+1))
1252 T(252)=0*100000!*(1/(100000!*(1-TBM(X(23),X(21)))+1))
1253 T(253)=5*100000!*(1/(100000!*(1-TBM(X(23),X(22)))+1))
1254 T(254)=10*100000!*(1/(100000!*(1-TBM(X(24),X(1)))+1))
1255 T(255)=1*100000!*(1/(100000!*(1-TBM(X(24),X(2)))+1))
1256 T(256)=1*100000!*(1/(100000!*(1-TBM(X(24),X(3)))+1))
1257 T(257)=0*100000!*(1/(100000!*(1-TBM(X(24),X(4)))+1))
1258 T(258)=1*100000!*(1/(100000!*(1-TBM(X(24),X(5)))+1))
1259 T(259)=0*100000!*(1/(100000!*(1-TBM(X(24),X(6)))+1))
1260 T(260)=3*100000!*(1/(100000!*(1-TBM(X(24),X(7)))+1))
1261 T(261)=2*100000!*(1/(100000!*(1-TBM(X(24),X(8)))+1))
1262 T(262)=2*100000!*(1/(100000!*(1-TBM(X(24),X(9)))+1))
1263 T(263)=5*100000!*(1/(100000!*(1-TBM(X(24),X(10)))+1))
1264 T(264)=0*100000!*(1/(100000!*(1-TBM(X(24),X(11)))+1))
1265 T(265)=10*100000!*(1/(100000!*(1-TBM(X(24),X(12)))+1))
1266 T(266)=5*100000!*(1/(100000!*(1-TBM(X(24),X(13)))+1))
1267 T(267)=2*100000!*(1/(100000!*(1-TBM(X(24),X(14)))+1))
1268 T(268)=2*100000!*(1/(100000!*(1-TBM(X(24),X(15)))+1))
1269 T(269)=0*100000!*(1/(100000!*(1-TBM(X(24),X(16)))+1))
1270 T(270)=5*100000!*(1/(100000!*(1-TBM(X(24),X(17)))+1))
1271 T(271)=4*100000!*(1/(100000!*(1-TBM(X(24),X(18)))+1))
1272 T(272)=0*100000!*(1/(100000!*(1-TBM(X(24),X(19)))+1))
1273 T(273)=3*100000!*(1/(100000!*(1-TBM(X(24),X(20)))+1))
1274 T(274)=1*100000!*(1/(100000!*(1-TBM(X(24),X(21)))+1))
1275 T(275)=0*100000!*(1/(100000!*(1-TBM(X(24),X(22)))+1))
1276 T(276)=0*100000!*(1/(100000!*(1-TBM(X(24),X(23)))+1))
1277 T(277)=2*100000!*(1/(100000!*(1-TBM(X(25),X(1)))+1))
1278 T(278)=2*100000!*(1/(100000!*(1-TBM(X(25),X(2)))+1))
1279 T(279)=0*100000!*(1/(100000!*(1-TBM(X(25),X(3)))+1))
1280 T(280)=2*100000!*(1/(100000!*(1-TBM(X(25),X(4)))+1))
1281 T(281)=0*100000!*(1/(100000!*(1-TBM(X(25),X(5)))+1))
1282 T(282)=0*100000!*(1/(100000!*(1-TBM(X(25),X(6)))+1))
1283 T(283)=5*100000!*(1/(100000!*(1-TBM(X(25),X(7)))+1))
1284 T(284)=5*100000!*(1/(100000!*(1-TBM(X(25),X(8)))+1))
1285 T(285)=0*100000!*(1/(100000!*(1-TBM(X(25),X(9)))+1))
1286 T(286)=2*100000!*(1/(100000!*(1-TBM(X(25),X(10)))+1))
1287 T(287)=4*100000!*(1/(100000!*(1-TBM(X(25),X(11)))+1))
1288 T(288)=1*100000!*(1/(100000!*(1-TBM(X(25),X(12)))+1))
1289 T(289)=5*100000!*(1/(100000!*(1-TBM(X(25),X(13)))+1))
1290 T(290)=0*100000!*(1/(100000!*(1-TBM(X(25),X(14)))+1))
1291 T(291)=0*100000!*(1/(100000!*(1-TBM(X(25),X(15)))+1))
1292 T(292)=5*100000!*(1/(100000!*(1-TBM(X(25),X(16)))+1))
1293 T(293)=3*100000!*(1/(100000!*(1-TBM(X(25),X(17)))+1))
1294 T(294)=0*100000!*(1/(100000!*(1-TBM(X(25),X(18)))+1))
1295 T(295)=5*100000!*(1/(100000!*(1-TBM(X(25),X(19)))+1))
1296 T(296)=1*100000!*(1/(100000!*(1-TBM(X(25),X(20)))+1))
1297 T(297)=0*100000!*(1/(100000!*(1-TBM(X(25),X(21)))+1))
1298 T(298)=4*100000!*(1/(100000!*(1-TBM(X(25),X(22)))+1))
1299 T(299)=4*100000!*(1/(100000!*(1-TBM(X(25),X(23)))+1))
1300 T(300)=5*100000!*(1/(100000!*(1-TBM(X(25),X(24)))+1))
1301 T(301)=1*100000!*(1/(100000!*(1-TBM(X(26),X(1)))+1))
1302 T(302)=2*100000!*(1/(100000!*(1-TBM(X(26),X(2)))+1))
1303 T(303)=0*100000!*(1/(100000!*(1-TBM(X(26),X(3)))+1))
1304 T(304)=0*100000!*(1/(100000!*(1-TBM(X(26),X(4)))+1))
1305 T(305)=2*100000!*(1/(100000!*(1-TBM(X(26),X(5)))+1))
1306 T(306)=4*100000!*(1/(100000!*(1-TBM(X(26),X(6)))+1))
1307 T(307)=0*100000!*(1/(100000!*(1-TBM(X(26),X(7)))+1))
1308 T(308)=0*100000!*(1/(100000!*(1-TBM(X(26),X(8)))+1))
1309 T(309)=5*100000!*(1/(100000!*(1-TBM(X(26),X(9)))+1))
1310 T(310)=10*100000!*(1/(100000!*(1-TBM(X(26),X(10)))+1))
1311 T(311)=5*100000!*(1/(100000!*(1-TBM(X(26),X(11)))+1))
1312 T(312)=0*100000!*(1/(100000!*(1-TBM(X(26),X(12)))+1))
1313 T(313)=0*100000!*(1/(100000!*(1-TBM(X(26),X(13)))+1))
1314 T(314)=0*100000!*(1/(100000!*(1-TBM(X(26),X(14)))+1))
1315 T(315)=0*100000!*(1/(100000!*(1-TBM(X(26),X(15)))+1))
1316 T(316)=0*100000!*(1/(100000!*(1-TBM(X(26),X(16)))+1))
1317 T(317)=5*100000!*(1/(100000!*(1-TBM(X(26),X(17)))+1))
1318 T(318)=0*100000!*(1/(100000!*(1-TBM(X(26),X(18)))+1))
1319 T(319)=2*100000!*(1/(100000!*(1-TBM(X(26),X(19)))+1))
1320 T(320)=5*100000!*(1/(100000!*(1-TBM(X(26),X(20)))+1))
1321 T(321)=0*100000!*(1/(100000!*(1-TBM(X(26),X(21)))+1))
1322 T(322)=4*100000!*(1/(100000!*(1-TBM(X(26),X(22)))+1))
1323 T(323)=4*100000!*(1/(100000!*(1-TBM(X(26),X(23)))+1))
1324 T(324)=5*100000!*(1/(100000!*(1-TBM(X(26),X(24)))+1))
1325 T(325)=1*100000!*(1/(100000!*(1-TBM(X(26),X(25)))+1))
1326 T(326)=1*100000!*(1/(100000!*(1-TBM(X(27),X(1)))+1))
1327 T(327)=5*100000!*(1/(100000!*(1-TBM(X(27),X(2)))+1))
1328 T(328)=3*100000!*(1/(100000!*(1-TBM(X(27),X(3)))+1))
1329 T(329)=2*100000!*(1/(100000!*(1-TBM(X(27),X(4)))+1))
1330 T(330)=1*100000!*(1/(100000!*(1-TBM(X(27),X(5)))+1))
1331 T(331)=0*100000!*(1/(100000!*(1-TBM(X(27),X(6)))+1))
1332 T(332)=2*100000!*(1/(100000!*(1-TBM(X(27),X(7)))+1))
1333 T(333)=5*100000!*(1/(100000!*(1-TBM(X(27),X(8)))+1))
1334 T(334)=2*100000!*(1/(100000!*(1-TBM(X(27),X(9)))+1))
1335 T(335)=10*100000!*(1/(100000!*(1-TBM(X(27),X(10)))+1))
1336 T(336)=3*100000!*(1/(100000!*(1-TBM(X(27),X(11)))+1))
1337 T(337)=0*100000!*(1/(100000!*(1-TBM(X(27),X(12)))+1))
1338 T(338)=0*100000!*(1/(100000!*(1-TBM(X(27),X(13)))+1))
1339 T(339)=4*100000!*(1/(100000!*(1-TBM(X(27),X(14)))+1))
1340 T(340)=5*100000!*(1/(100000!*(1-TBM(X(27),X(15)))+1))
1341 T(341)=5*100000!*(1/(100000!*(1-TBM(X(27),X(16)))+1))
1342 T(342)=0*100000!*(1/(100000!*(1-TBM(X(27),X(17)))+1))
1343 T(343)=5*100000!*(1/(100000!*(1-TBM(X(27),X(18)))+1))
1344 T(344)=1*100000!*(1/(100000!*(1-TBM(X(27),X(19)))+1))
1345 T(345)=6*100000!*(1/(100000!*(1-TBM(X(27),X(20)))+1))
1346 T(346)=0*100000!*(1/(100000!*(1-TBM(X(27),X(21)))+1))
1347 T(347)=5*100000!*(1/(100000!*(1-TBM(X(27),X(22)))+1))
1348 T(348)=1*100000!*(1/(100000!*(1-TBM(X(27),X(23)))+1))
1349 T(349)=0*100000!*(1/(100000!*(1-TBM(X(27),X(24)))+1))
1350 T(350)=0*100000!*(1/(100000!*(1-TBM(X(27),X(25)))+1))
1351 T(351)=0*100000!*(1/(100000!*(1-TBM(X(27),X(26)))+1))
1352 T(352)=1*100000!*(1/(100000!*(1-TBM(X(28),X(1)))+1))
1353 T(353)=1*100000!*(1/(100000!*(1-TBM(X(28),X(2)))+1))
1354 T(354)=1*100000!*(1/(100000!*(1-TBM(X(28),X(3)))+1))
1355 T(355)=2*100000!*(1/(100000!*(1-TBM(X(28),X(4)))+1))
1356 T(356)=0*100000!*(1/(100000!*(1-TBM(X(28),X(5)))+1))
1357 T(357)=10*100000!*(1/(100000!*(1-TBM(X(28),X(6)))+1))
1358 T(358)=0*100000!*(1/(100000!*(1-TBM(X(28),X(7)))+1))
1359 T(359)=5*100000!*(1/(100000!*(1-TBM(X(28),X(8)))+1))
1360 T(360)=2*100000!*(1/(100000!*(1-TBM(X(28),X(9)))+1))
1361 T(361)=1*100000!*(1/(100000!*(1-TBM(X(28),X(10)))+1))
1362 T(362)=2*100000!*(1/(100000!*(1-TBM(X(28),X(11)))+1))
1363 T(363)=0*100000!*(1/(100000!*(1-TBM(X(28),X(12)))+1))
1364 T(364)=1*100000!*(1/(100000!*(1-TBM(X(28),X(13)))+1))
1365 T(365)=2*100000!*(1/(100000!*(1-TBM(X(28),X(14)))+1))
1366 T(366)=1*100000!*(1/(100000!*(1-TBM(X(28),X(15)))+1))
1367 T(367)=2*100000!*(1/(100000!*(1-TBM(X(28),X(16)))+1))
1368 T(368)=0*100000!*(1/(100000!*(1-TBM(X(28),X(17)))+1))
1369 T(369)=0*100000!*(1/(100000!*(1-TBM(X(28),X(18)))+1))
1370 T(370)=2*100000!*(1/(100000!*(1-TBM(X(28),X(19)))+1))
1371 T(371)=5*100000!*(1/(100000!*(1-TBM(X(28),X(20)))+1))
1372 T(372)=5*100000!*(1/(100000!*(1-TBM(X(28),X(21)))+1))
1373 T(373)=0*100000!*(1/(100000!*(1-TBM(X(28),X(22)))+1))
1374 T(374)=0*100000!*(1/(100000!*(1-TBM(X(28),X(23)))+1))
1375 T(375)=1*100000!*(1/(100000!*(1-TBM(X(28),X(24)))+1))
1376 T(376)=10*100000!*(1/(100000!*(1-TBM(X(28),X(25)))+1))
1377 T(377)=0*100000!*(1/(100000!*(1-TBM(X(28),X(26)))+1))
1378 T(378)=0*100000!*(1/(100000!*(1-TBM(X(28),X(27)))+1))
1379 T(379)=0*100000!*(1/(100000!*(1-TBM(X(29),X(1)))+1))
1380 T(380)=10*100000!*(1/(100000!*(1-TBM(X(29),X(2)))+1))
1381 T(381)=0*100000!*(1/(100000!*(1-TBM(X(29),X(3)))+1))
1382 T(382)=5*100000!*(1/(100000!*(1-TBM(X(29),X(4)))+1))
1383 T(383)=2*100000!*(1/(100000!*(1-TBM(X(29),X(5)))+1))
1384 T(384)=1*100000!*(1/(100000!*(1-TBM(X(29),X(6)))+1))
1385 T(385)=1*100000!*(1/(100000!*(1-TBM(X(29),X(7)))+1))
1386 T(386)=0*100000!*(1/(100000!*(1-TBM(X(29),X(8)))+1))
1387 T(387)=5*100000!*(1/(100000!*(1-TBM(X(29),X(9)))+1))
1388 T(388)=5*100000!*(1/(100000!*(1-TBM(X(29),X(10)))+1))
1389 T(389)=2*100000!*(1/(100000!*(1-TBM(X(29),X(11)))+1))
1390 T(390)=0*100000!*(1/(100000!*(1-TBM(X(29),X(12)))+1))
1391 T(391)=5*100000!*(1/(100000!*(1-TBM(X(29),X(13)))+1))
1392 T(392)=5*100000!*(1/(100000!*(1-TBM(X(29),X(14)))+1))
1393 T(393)=1*100000!*(1/(100000!*(1-TBM(X(29),X(15)))+1))
1394 T(394)=5*100000!*(1/(100000!*(1-TBM(X(29),X(16)))+1))
1395 T(395)=5*100000!*(1/(100000!*(1-TBM(X(29),X(17)))+1))
1396 T(396)=0*100000!*(1/(100000!*(1-TBM(X(29),X(18)))+1))
1397 T(397)=10*100000!*(1/(100000!*(1-TBM(X(29),X(19)))+1))
1398 T(398)=5*100000!*(1/(100000!*(1-TBM(X(29),X(20)))+1))
1399 T(399)=0*100000!*(1/(100000!*(1-TBM(X(29),X(21)))+1))
1400 T(400)=2*100000!*(1/(100000!*(1-TBM(X(29),X(22)))+1))
1401 T(401)=2*100000!*(1/(100000!*(1-TBM(X(29),X(23)))+1))
1402 T(402)=0*100000!*(1/(100000!*(1-TBM(X(29),X(24)))+1))
1403 T(403)=1*100000!*(1/(100000!*(1-TBM(X(29),X(25)))+1))
1404 T(404)=0*100000!*(1/(100000!*(1-TBM(X(29),X(26)))+1))
1405 T(405)=0*100000!*(1/(100000!*(1-TBM(X(29),X(27)))+1))
1406 T(406)=2*100000!*(1/(100000!*(1-TBM(X(29),X(28)))+1))
1407 T(407)=1*100000!*(1/(100000!*(1-TBM(X(30),X(1)))+1))
1408 T(408)=5*100000!*(1/(100000!*(1-TBM(X(30),X(2)))+1))
1409 T(409)=2*100000!*(1/(100000!*(1-TBM(X(30),X(3)))+1))
1410 T(410)=5*100000!*(1/(100000!*(1-TBM(X(30),X(4)))+1))
1411 T(411)=1*100000!*(1/(100000!*(1-TBM(X(30),X(5)))+1))
1412 T(412)=1*100000!*(1/(100000!*(1-TBM(X(30),X(6)))+1))
1413 T(413)=3*100000!*(1/(100000!*(1-TBM(X(30),X(7)))+1))
1414 T(414)=2*100000!*(1/(100000!*(1-TBM(X(30),X(8)))+1))
1415 T(415)=2*100000!*(1/(100000!*(1-TBM(X(30),X(9)))+1))
1416 T(416)=2*100000!*(1/(100000!*(1-TBM(X(30),X(10)))+1))
1417 T(417)=10*100000!*(1/(100000!*(1-TBM(X(30),X(11)))+1))
1418 T(418)=1*100000!*(1/(100000!*(1-TBM(X(30),X(12)))+1))
1419 T(419)=5*100000!*(1/(100000!*(1-TBM(X(30),X(13)))+1))
1420 T(420)=5*100000!*(1/(100000!*(1-TBM(X(30),X(14)))+1))
1421 T(421)=0*100000!*(1/(100000!*(1-TBM(X(30),X(15)))+1))
1422 T(422)=10*100000!*(1/(100000!*(1-TBM(X(30),X(16)))+1))
1423 T(423)=1*100000!*(1/(100000!*(1-TBM(X(30),X(17)))+1))
1424 T(424)=0*100000!*(1/(100000!*(1-TBM(X(30),X(18)))+1))
1425 T(425)=10*100000!*(1/(100000!*(1-TBM(X(30),X(19)))+1))
1426 T(426)=3*100000!*(1/(100000!*(1-TBM(X(30),X(20)))+1))
1427 T(427)=0*100000!*(1/(100000!*(1-TBM(X(30),X(21)))+1))
1428 T(428)=5*100000!*(1/(100000!*(1-TBM(X(30),X(22)))+1))
1429 T(429)=2*100000!*(1/(100000!*(1-TBM(X(30),X(23)))+1))
1430 T(430)=0*100000!*(1/(100000!*(1-TBM(X(30),X(24)))+1))
1431 T(431)=0*100000!*(1/(100000!*(1-TBM(X(30),X(25)))+1))
1432 T(432)=0*100000!*(1/(100000!*(1-TBM(X(30),X(26)))+1))
1433 T(433)=10*100000!*(1/(100000!*(1-TBM(X(30),X(27)))+1))
1434 T(434)=2*100000!*(1/(100000!*(1-TBM(X(30),X(28)))+1))
1435 T(435)=2*100000!*(1/(100000!*(1-TBM(X(30),X(29)))+1))
2151 P1NEW=0
2152 FOR KAU7=1 TO 435
2153 P1NEW=P1NEW+T(KAU7)
2154 NEXT KAU7
2450 P=-P1NEW
2451 IF P<=M THEN 2670
2657 FOR KEW=1 TO 30
2658 A(KEW)=X(KEW)
2659 NEXT KEW
2661 M=P
2666 GOTO 128
2670 NEXT I
2890 IF M>-43588888# THEN 2911 ELSE 2999
2911 PRINT A(1),A(2),A(3)
2912 PRINT A(4),A(5),A(6)
2913 PRINT A(7),A(8),A(9)
2914 PRINT A(10),A(11),A(12)
2915 PRINT A(13),A(14),A(15)
2916 PRINT A(16),A(17),A(18)
2917 PRINT A(19),A(20),A(21)
2918 PRINT A(22),A(23),A(24)
2919 PRINT A(25),A(26),A(27)
2920 PRINT A(28),A(29),A(30)
2925 PRINT JJJJ,M
2999 NEXT JJJJ

This BASIC computer program was run with the IBM basica/D interpreter, and its computational results, interpreted in accordance with line 2911 through line 2925, through JJJJ=-31977 are presented below.

1 1 1
1 1 3
3 3 2
4 4 4
4 4 4
1 1 4
1 1 4
1 1 1
3 4 1
1 4 4
-31999 -43500691.99308007

1 1 1
1 1 3
3 3 2
3 4 4
4 4 4
1 1 4
1 1 4
1 1 1
4 4 1
1 4 4
-31992 -43500691.99308007

1 1 1
1 1 3
3 3 2
4 4 4
4 4 4
1 1 4
1 1 4
1 1 1
4 4 1
1 4 4
-31991 -43500691.99308007

1 1 1
1 1 3
3 3 2
4 4 4
4 4 4
1 1 4
1 1 4
1 1 1
3 4 1
1 4 4
-31989 -43500691.99308007

1 1 1
1 1 3
3 3 2
4 4 4
4 4 4
1 1 4
1 1 4
1 1 1
4 4 1
1 4 4
-31987 -43500691.99308007

1 1 1
1 1 3
3 3 2
4 4 4
4 4 4
1 1 4
1 1 4
1 1 1
4 4 1
1 4 4
-31985 -43500691.99308007

1 1 1
1 1 3
3 3 2
4 4 4
4 4 4
1 1 4
1 1 4
1 1 1
4 4 1
1 4 4
-31979 -43500691.99308007

1 1 1
1 1 3
3 3 2
4 4 4
4 4 4
1 1 4
1 1 4
1 1 1
4 4 1
1 4 4
-31977 -43500691.99308007

The output above was produced in 80 seconds on a personal computer with an Intel 2.66 GHz. chip and the IBM interpreter, which is slower than the corresponding compiler.

The candidate solution above at JJJJ=-31998 reveals the assignment of courses 1, 2, 3, 4, 5, 16, 17, 19, 20, 22, 23, 24, 27, and 28 to period 1, course 9 to period 2, courses 6, 7, 8, and 25 to period 3, and courses 10, 11, 12, 13, 14, 15, 18, 21, 26, 29, and 30 to period 4 for the total cost of 435.

References

[1] R. C. Carlson, G. L. Nemhauser, Scheduling to minimize interaction cost, Operations Research 14 (1966) 52-58.

[2] F. E. Davis, M. D. Devine, R. P. Lutz, Scheduling activities among conflicting facilities to minimize conflict, Mathematical Programming 6 (1974) 224-228.

[3] F. S. Hillier, Quantitative tools for plant layout analysis, J. Indust. Eng. 14 (1963) 33-40.

[4] C. E. Nugent, T. E. Vollmann, J. Ruml, An experimental comparison of techniques for the assignment of facilities to locations, Operations Research 16 (1968) 150-173.

Wednesday, February 18, 2009

Assigning Activities to Conflicting Facilities

Jsun Yui Wong

The difference between the original Carlson and Nemhauser problem [1] and the problem of Davis, Devine, and Lutz [2] is "that their problem did not consider conflicting facilities," Davis, Devine, and Lutz [2, p. 225]. For the newer problem, "a cost is incurred if two activities are assigned to the same facility, or to two facilities whose operation is in conflict," Davis et al. [2, p. 224]. Dealing with an instance of the newer problem, the computer program below attempts to find the lowest cost of scheduling twenty-five courses in four time periods which are 8 a.m. to 11 a.m., 10 a.m. to 1 p.m., noon to 3 p.m., and 2 p.m. to 5 p.m. The conflicts are specified in line 6 through line 9 of the following computer program.

The costs used in line 1001 through line 1300 of the computer program below come from Hillier [3] and Nugent, Vollmann, and Ruml [4, pp. 168-170].

In this paper, A(1)=1, A(2)=1, A(3)=1,..., and A(25)=1 stand for course 1 in period 1, course 2 in period 1, course 3 in period 1,..., and course 25 in period 1, respectively.

The computer program below is modelled after the computer program of the March 7 post "Assigning Activities to Conflicting Facilities To Minimize Conflict Cost" of the present blog.

2 DEFINT A-Z
4 DEFDBL M,T,P
5 DIM N(9),B(9),A(199),H(99),X(199),P(450),L(99),U(99),Q(977),R(444),T(999),Q1(222)
6 TBM(1,1)=1:TBM(1,2)=1
7 TBM(2,1)=1:TBM(2,2)=1:TBM(2,3)=1
8 TBM(3,2)=1:TBM(3,3)=1:TBM(3,4)=1
9 TBM(4,3)=1:TBM(4,4)=1
12 FOR JJJJ=-32000 TO 32000
14 RANDOMIZE JJJJ
16 M=-1D+17
91 FOR IAP0=1 TO 25
92 A(IAP0)=1+FIX(RND*4)
93 NEXT IAP0
126 IMAR=10+FIX(RND*1000)
128 FOR I=1 TO IMAR
129 FOR K=1 TO 25
131 X(K)=A(K)
132 NEXT K
241 IAP1=1+FIX(RND*25)
243 X(IAP1)=1+FIX(RND*4)
1001 T(1)=5*100000!*(1/(100000!*(1-TBM(X(1),X(2)))+1))
1002 T(2)=2*100000!*(1/(100000!*(1-TBM(X(1),X(3)))+1))
1003 T(3)=4*100000!*(1/(100000!*(1-TBM(X(1),X(4)))+1))
1004 T(4)=1*100000!*(1/(100000!*(1-TBM(X(1),X(5)))+1))
1005 T(5)=0*100000!*(1/(100000!*(1-TBM(X(1),X(6)))+1))
1006 T(6)=0*100000!*(1/(100000!*(1-TBM(X(1),X(7)))+1))
1007 T(7)=6*100000!*(1/(100000!*(1-TBM(X(1),X(8)))+1))
1008 T(8)=2*100000!*(1/(100000!*(1-TBM(X(1),X(9)))+1))
1009 T(9)=1*100000!*(1/(100000!*(1-TBM(X(1),X(10)))+1))
1010 T(10)=1*100000!*(1/(100000!*(1-TBM(X(1),X(11)))+1))
1011 T(11)=1*100000!*(1/(100000!*(1-TBM(X(1),X(12)))+1))
1012 T(12)=3*100000!*(1/(100000!*(1-TBM(X(2),X(3)))+1))
1013 T(13)=0*100000!*(1/(100000!*(1-TBM(X(2),X(4)))+1))
1014 T(14)=2*100000!*(1/(100000!*(1-TBM(X(2),X(5)))+1))
1015 T(15)=2*100000!*(1/(100000!*(1-TBM(X(2),X(6)))+1))
1016 T(16)=2*100000!*(1/(100000!*(1-TBM(X(2),X(7)))+1))
1017 T(17)=0*100000!*(1/(100000!*(1-TBM(X(2),X(8)))+1))
1018 T(18)=4*100000!*(1/(100000!*(1-TBM(X(2),X(9)))+1))
1019 T(19)=5*100000!*(1/(100000!*(1-TBM(X(2),X(10)))+1))
1020 T(20)=0*100000!*(1/(100000!*(1-TBM(X(2),X(11)))+1))
1021 T(21)=0*100000!*(1/(100000!*(1-TBM(X(2),X(12)))+1))
1022 T(22)=0*100000!*(1/(100000!*(1-TBM(X(3),X(4)))+1))
1023 T(23)=0*100000!*(1/(100000!*(1-TBM(X(3),X(5)))+1))
1024 T(24)=0*100000!*(1/(100000!*(1-TBM(X(3),X(6)))+1))
1025 T(25)=0*100000!*(1/(100000!*(1-TBM(X(3),X(7)))+1))
1026 T(26)=5*100000!*(1/(100000!*(1-TBM(X(3),X(8)))+1))
1027 T(27)=5*100000!*(1/(100000!*(1-TBM(X(3),X(9)))+1))
1028 T(28)=2*100000!*(1/(100000!*(1-TBM(X(3),X(10)))+1))
1029 T(29)=2*100000!*(1/(100000!*(1-TBM(X(3),X(11)))+1))
1030 T(30)=2*100000!*(1/(100000!*(1-TBM(X(3),X(12)))+1))
1031 T(31)=5*100000!*(1/(100000!*(1-TBM(X(4),X(5)))+1))
1032 T(32)=2*100000!*(1/(100000!*(1-TBM(X(4),X(6)))+1))
1033 T(33)=2*100000!*(1/(100000!*(1-TBM(X(4),X(7)))+1))
1034 T(34)=10*100000!*(1/(100000!*(1-TBM(X(4),X(8)))+1))
1035 T(35)=0*100000!*(1/(100000!*(1-TBM(X(4),X(9)))+1))
1036 T(36)=0*100000!*(1/(100000!*(1-TBM(X(4),X(10)))+1))
1037 T(37)=5*100000!*(1/(100000!*(1-TBM(X(4),X(11)))+1))
1038 T(38)=5*100000!*(1/(100000!*(1-TBM(X(4),X(12)))+1))
1039 T(39)=10*100000!*(1/(100000!*(1-TBM(X(5),X(6)))+1))
1040 T(40)=0*100000!*(1/(100000!*(1-TBM(X(5),X(7)))+1))
1041 T(41)=0*100000!*(1/(100000!*(1-TBM(X(5),X(8)))+1))
1042 T(42)=0*100000!*(1/(100000!*(1-TBM(X(5),X(9)))+1))
1043 T(43)=5*100000!*(1/(100000!*(1-TBM(X(5),X(10)))+1))
1044 T(44)=1*100000!*(1/(100000!*(1-TBM(X(5),X(11)))+1))
1045 T(45)=1*100000!*(1/(100000!*(1-TBM(X(5),X(12)))+1))
1046 T(46)=5*100000!*(1/(100000!*(1-TBM(X(6),X(7)))+1))
1047 T(47)=1*100000!*(1/(100000!*(1-TBM(X(6),X(8)))+1))
1048 T(48)=1*100000!*(1/(100000!*(1-TBM(X(6),X(9)))+1))
1049 T(49)=5*100000!*(1/(100000!*(1-TBM(X(6),X(10)))+1))
1050 T(50)=4*100000!*(1/(100000!*(1-TBM(X(6),X(11)))+1))
1051 T(51)=0*100000!*(1/(100000!*(1-TBM(X(6),X(12)))+1))
1052 T(52)=10*100000!*(1/(100000!*(1-TBM(X(7),X(8)))+1))
1053 T(53)=5*100000!*(1/(100000!*(1-TBM(X(7),X(9)))+1))
1054 T(54)=2*100000!*(1/(100000!*(1-TBM(X(7),X(10)))+1))
1055 T(55)=3*100000!*(1/(100000!*(1-TBM(X(7),X(11)))+1))
1056 T(56)=3*100000!*(1/(100000!*(1-TBM(X(7),X(12)))+1))
1057 T(57)=0*100000!*(1/(100000!*(1-TBM(X(8),X(9)))+1))
1058 T(58)=0*100000!*(1/(100000!*(1-TBM(X(8),X(10)))+1))
1059 T(59)=5*100000!*(1/(100000!*(1-TBM(X(8),X(11)))+1))
1060 T(60)=0*100000!*(1/(100000!*(1-TBM(X(8),X(12)))+1))
1061 T(61)=0*100000!*(1/(100000!*(1-TBM(X(9),X(10)))+1))
1062 T(62)=10*100000!*(1/(100000!*(1-TBM(X(9),X(11)))+1))
1063 T(63)=10*100000!*(1/(100000!*(1-TBM(X(9),X(12)))+1))
1064 T(64)=5*100000!*(1/(100000!*(1-TBM(X(10),X(11)))+1))
1065 T(65)=0*100000!*(1/(100000!*(1-TBM(X(10),X(12)))+1))
1066 T(66)=2*100000!*(1/(100000!*(1-TBM(X(11),X(12)))+1))
1067 T(67)=4*100000!*(1/(100000!*(1-TBM(X(13),X(1)))+1))
1068 T(68)=10*100000!*(1/(100000!*(1-TBM(X(13),X(2)))+1))
1069 T(69)=5*100000!*(1/(100000!*(1-TBM(X(13),X(3)))+1))
1070 T(70)=2*100000!*(1/(100000!*(1-TBM(X(13),X(4)))+1))
1071 T(71)=0*100000!*(1/(100000!*(1-TBM(X(13),X(5)))+1))
1072 T(72)=2*100000!*(1/(100000!*(1-TBM(X(13),X(6)))+1))
1073 T(73)=5*100000!*(1/(100000!*(1-TBM(X(13),X(7)))+1))
1074 T(74)=5*100000!*(1/(100000!*(1-TBM(X(13),X(8)))+1))
1075 T(75)=10*100000!*(1/(100000!*(1-TBM(X(13),X(9)))+1))
1076 T(76)=0*100000!*(1/(100000!*(1-TBM(X(13),X(10)))+1))
1077 T(77)=0*100000!*(1/(100000!*(1-TBM(X(13),X(11)))+1))
1078 T(78)=3*100000!*(1/(100000!*(1-TBM(X(13),X(12)))+1))
1079 T(79)=0*100000!*(1/(100000!*(1-TBM(X(14),X(1)))+1))
1080 T(80)=5*100000!*(1/(100000!*(1-TBM(X(14),X(2)))+1))
1081 T(81)=5*100000!*(1/(100000!*(1-TBM(X(14),X(3)))+1))
1082 T(82)=5*100000!*(1/(100000!*(1-TBM(X(14),X(4)))+1))
1083 T(83)=5*100000!*(1/(100000!*(1-TBM(X(14),X(5)))+1))
1084 T(84)=5*100000!*(1/(100000!*(1-TBM(X(14),X(6)))+1))
1085 T(85)=1*100000!*(1/(100000!*(1-TBM(X(14),X(7)))+1))
1086 T(86)=0*100000!*(1/(100000!*(1-TBM(X(14),X(8)))+1))
1087 T(87)=0*100000!*(1/(100000!*(1-TBM(X(14),X(9)))+1))
1088 T(88)=0*100000!*(1/(100000!*(1-TBM(X(14),X(10)))+1))
1089 T(89)=5*100000!*(1/(100000!*(1-TBM(X(14),X(11)))+1))
1090 T(90)=3*100000!*(1/(100000!*(1-TBM(X(14),X(12)))+1))
1091 T(91)=10*100000!*(1/(100000!*(1-TBM(X(14),X(13)))+1))
1092 T(92)=0*100000!*(1/(100000!*(1-TBM(X(15),X(1)))+1))
1093 T(93)=0*100000!*(1/(100000!*(1-TBM(X(15),X(2)))+1))
1094 T(94)=5*100000!*(1/(100000!*(1-TBM(X(15),X(3)))+1))
1095 T(95)=0*100000!*(1/(100000!*(1-TBM(X(15),X(4)))+1))
1096 T(96)=5*100000!*(1/(100000!*(1-TBM(X(15),X(5)))+1))
1097 T(97)=10*100000!*(1/(100000!*(1-TBM(X(15),X(6)))+1))
1098 T(98)=0*100000!*(1/(100000!*(1-TBM(X(15),X(7)))+1))
1099 T(99)=0*100000!*(1/(100000!*(1-TBM(X(15),X(8)))+1))
1100 T(100)=2*100000!*(1/(100000!*(1-TBM(X(15),X(9)))+1))
1101 T(101)=5*100000!*(1/(100000!*(1-TBM(X(15),X(10)))+1))
1102 T(102)=0*100000!*(1/(100000!*(1-TBM(X(15),X(11)))+1))
1103 T(103)=0*100000!*(1/(100000!*(1-TBM(X(15),X(12)))+1))
1104 T(104)=2*100000!*(1/(100000!*(1-TBM(X(15),X(13)))+1))
1105 T(105)=4*100000!*(1/(100000!*(1-TBM(X(15),X(14)))+1))
1106 T(106)=0*100000!*(1/(100000!*(1-TBM(X(16),X(1)))+1))
1107 T(107)=0*100000!*(1/(100000!*(1-TBM(X(16),X(2)))+1))
1108 T(108)=4*100000!*(1/(100000!*(1-TBM(X(16),X(3)))+1))
1109 T(109)=5*100000!*(1/(100000!*(1-TBM(X(16),X(4)))+1))
1110 T(110)=0*100000!*(1/(100000!*(1-TBM(X(16),X(5)))+1))
1111 T(111)=5*100000!*(1/(100000!*(1-TBM(X(16),X(6)))+1))
1112 T(112)=10*100000!*(1/(100000!*(1-TBM(X(16),X(7)))+1))
1113 T(113)=4*100000!*(1/(100000!*(1-TBM(X(16),X(8)))+1))
1114 T(114)=3*100000!*(1/(100000!*(1-TBM(X(16),X(9)))+1))
1115 T(115)=5*100000!*(1/(100000!*(1-TBM(X(16),X(10)))+1))
1116 T(116)=1*100000!*(1/(100000!*(1-TBM(X(16),X(11)))+1))
1117 T(117)=0*100000!*(1/(100000!*(1-TBM(X(16),X(12)))+1))
1118 T(118)=4*100000!*(1/(100000!*(1-TBM(X(16),X(13)))+1))
1119 T(119)=1*100000!*(1/(100000!*(1-TBM(X(16),X(14)))+1))
1120 T(120)=4*100000!*(1/(100000!*(1-TBM(X(16),X(15)))+1))
1121 T(121)=5*100000!*(1/(100000!*(1-TBM(X(17),X(1)))+1))
1122 T(122)=0*100000!*(1/(100000!*(1-TBM(X(17),X(2)))+1))
1123 T(123)=0*100000!*(1/(100000!*(1-TBM(X(17),X(3)))+1))
1124 T(124)=1*100000!*(1/(100000!*(1-TBM(X(17),X(4)))+1))
1125 T(125)=2*100000!*(1/(100000!*(1-TBM(X(17),X(5)))+1))
1126 T(126)=0*100000!*(1/(100000!*(1-TBM(X(17),X(6)))+1))
1127 T(127)=2*100000!*(1/(100000!*(1-TBM(X(17),X(7)))+1))
1128 T(128)=5*100000!*(1/(100000!*(1-TBM(X(17),X(8)))+1))
1129 T(129)=0*100000!*(1/(100000!*(1-TBM(X(17),X(9)))+1))
1130 T(130)=5*100000!*(1/(100000!*(1-TBM(X(17),X(10)))+1))
1131 T(131)=0*100000!*(1/(100000!*(1-TBM(X(17),X(11)))+1))
1132 T(132)=0*100000!*(1/(100000!*(1-TBM(X(17),X(12)))+1))
1133 T(133)=2*100000!*(1/(100000!*(1-TBM(X(17),X(13)))+1))
1134 T(134)=0*100000!*(1/(100000!*(1-TBM(X(17),X(14)))+1))
1135 T(135)=5*100000!*(1/(100000!*(1-TBM(X(17),X(15)))+1))
1136 T(136)=0*100000!*(1/(100000!*(1-TBM(X(17),X(16)))+1))
1137 T(137)=6*100000!*(1/(100000!*(1-TBM(X(18),X(1)))+1))
1138 T(138)=2*100000!*(1/(100000!*(1-TBM(X(18),X(2)))+1))
1139 T(139)=6*100000!*(1/(100000!*(1-TBM(X(18),X(3)))+1))
1140 T(140)=1*100000!*(1/(100000!*(1-TBM(X(18),X(4)))+1))
1141 T(141)=1*100000!*(1/(100000!*(1-TBM(X(18),X(5)))+1))
1142 T(142)=5*100000!*(1/(100000!*(1-TBM(X(18),X(6)))+1))
1143 T(143)=1*100000!*(1/(100000!*(1-TBM(X(18),X(7)))+1))
1144 T(144)=2*100000!*(1/(100000!*(1-TBM(X(18),X(8)))+1))
1145 T(145)=2*100000!*(1/(100000!*(1-TBM(X(18),X(9)))+1))
1146 T(146)=0*100000!*(1/(100000!*(1-TBM(X(18),X(10)))+1))
1147 T(147)=2*100000!*(1/(100000!*(1-TBM(X(18),X(11)))+1))
1148 T(148)=0*100000!*(1/(100000!*(1-TBM(X(18),X(12)))+1))
1149 T(149)=2*100000!*(1/(100000!*(1-TBM(X(18),X(13)))+1))
1150 T(150)=5*100000!*(1/(100000!*(1-TBM(X(18),X(14)))+1))
1151 T(151)=1*100000!*(1/(100000!*(1-TBM(X(18),X(15)))+1))
1152 T(152)=3*100000!*(1/(100000!*(1-TBM(X(18),X(16)))+1))
1153 T(153)=2*100000!*(1/(100000!*(1-TBM(X(18),X(17)))+1))
1154 T(154)=3*100000!*(1/(100000!*(1-TBM(X(19),X(1)))+1))
1155 T(155)=0*100000!*(1/(100000!*(1-TBM(X(19),X(2)))+1))
1156 T(156)=3*100000!*(1/(100000!*(1-TBM(X(19),X(3)))+1))
1157 T(157)=1*100000!*(1/(100000!*(1-TBM(X(19),X(4)))+1))
1158 T(158)=0*100000!*(1/(100000!*(1-TBM(X(19),X(5)))+1))
1159 T(159)=0*100000!*(1/(100000!*(1-TBM(X(19),X(6)))+1))
1160 T(160)=10*100000!*(1/(100000!*(1-TBM(X(19),X(7)))+1))
1161 T(161)=10*100000!*(1/(100000!*(1-TBM(X(19),X(8)))+1))
1162 T(162)=0*100000!*(1/(100000!*(1-TBM(X(19),X(9)))+1))
1163 T(163)=5*100000!*(1/(100000!*(1-TBM(X(19),X(10)))+1))
1164 T(164)=0*100000!*(1/(100000!*(1-TBM(X(19),X(11)))+1))
1165 T(165)=0*100000!*(1/(100000!*(1-TBM(X(19),X(12)))+1))
1166 T(166)=1*100000!*(1/(100000!*(1-TBM(X(19),X(13)))+1))
1167 T(167)=3*100000!*(1/(100000!*(1-TBM(X(19),X(14)))+1))
1168 T(168)=0*100000!*(1/(100000!*(1-TBM(X(19),X(15)))+1))
1169 T(169)=0*100000!*(1/(100000!*(1-TBM(X(19),X(16)))+1))
1170 T(170)=2*100000!*(1/(100000!*(1-TBM(X(19),X(17)))+1))
1171 T(171)=5*100000!*(1/(100000!*(1-TBM(X(19),X(18)))+1))
1172 T(172)=0*100000!*(1/(100000!*(1-TBM(X(20),X(1)))+1))
1173 T(173)=1*100000!*(1/(100000!*(1-TBM(X(20),X(2)))+1))
1174 T(174)=2*100000!*(1/(100000!*(1-TBM(X(20),X(3)))+1))
1175 T(175)=1*100000!*(1/(100000!*(1-TBM(X(20),X(4)))+1))
1176 T(176)=0*100000!*(1/(100000!*(1-TBM(X(20),X(5)))+1))
1177 T(177)=0*100000!*(1/(100000!*(1-TBM(X(20),X(6)))+1))
1178 T(178)=1*100000!*(1/(100000!*(1-TBM(X(20),X(7)))+1))
1179 T(179)=6*100000!*(1/(100000!*(1-TBM(X(20),X(8)))+1))
1180 T(180)=0*100000!*(1/(100000!*(1-TBM(X(20),X(9)))+1))
1181 T(181)=2*100000!*(1/(100000!*(1-TBM(X(20),X(10)))+1))
1182 T(182)=0*100000!*(1/(100000!*(1-TBM(X(20),X(11)))+1))
1183 T(183)=2*100000!*(1/(100000!*(1-TBM(X(20),X(12)))+1))
1184 T(184)=0*100000!*(1/(100000!*(1-TBM(X(20),X(13)))+1))
1185 T(185)=10*100000!*(1/(100000!*(1-TBM(X(20),X(14)))+1))
1186 T(186)=1*100000!*(1/(100000!*(1-TBM(X(20),X(15)))+1))
1187 T(187)=2*100000!*(1/(100000!*(1-TBM(X(20),X(16)))+1))
1188 T(188)=0*100000!*(1/(100000!*(1-TBM(X(20),X(17)))+1))
1189 T(189)=1*100000!*(1/(100000!*(1-TBM(X(20),X(18)))+1))
1190 T(190)=0*100000!*(1/(100000!*(1-TBM(X(20),X(19)))+1))
1191 T(191)=1*100000!*(1/(100000!*(1-TBM(X(21),X(1)))+1))
1192 T(192)=6*100000!*(1/(100000!*(1-TBM(X(21),X(2)))+1))
1193 T(193)=5*100000!*(1/(100000!*(1-TBM(X(21),X(3)))+1))
1194 T(194)=2*100000!*(1/(100000!*(1-TBM(X(21),X(4)))+1))
1195 T(195)=2*100000!*(1/(100000!*(1-TBM(X(21),X(5)))+1))
1196 T(196)=0*100000!*(1/(100000!*(1-TBM(X(21),X(6)))+1))
1197 T(197)=5*100000!*(1/(100000!*(1-TBM(X(21),X(7)))+1))
1198 T(198)=0*100000!*(1/(100000!*(1-TBM(X(21),X(8)))+1))
1199 T(199)=4*100000!*(1/(100000!*(1-TBM(X(21),X(9)))+1))
1200 T(200)=3*100000!*(1/(100000!*(1-TBM(X(21),X(10)))+1))
1201 T(201)=0*100000!*(1/(100000!*(1-TBM(X(21),X(11)))+1))
1202 T(202)=0*100000!*(1/(100000!*(1-TBM(X(21),X(12)))+1))
1203 T(203)=6*100000!*(1/(100000!*(1-TBM(X(21),X(13)))+1))
1204 T(204)=0*100000!*(1/(100000!*(1-TBM(X(21),X(14)))+1))
1205 T(205)=0*100000!*(1/(100000!*(1-TBM(X(21),X(15)))+1))
1206 T(206)=2*100000!*(1/(100000!*(1-TBM(X(21),X(16)))+1))
1207 T(207)=0*100000!*(1/(100000!*(1-TBM(X(21),X(17)))+1))
1208 T(208)=2*100000!*(1/(100000!*(1-TBM(X(21),X(18)))+1))
1209 T(209)=5*100000!*(1/(100000!*(1-TBM(X(21),X(19)))+1))
1210 T(210)=5*100000!*(1/(100000!*(1-TBM(X(21),X(20)))+1))
1211 T(211)=10*100000!*(1/(100000!*(1-TBM(X(22),X(1)))+1))
1212 T(212)=1*100000!*(1/(100000!*(1-TBM(X(22),X(2)))+1))
1213 T(213)=5*100000!*(1/(100000!*(1-TBM(X(22),X(3)))+1))
1214 T(214)=2*100000!*(1/(100000!*(1-TBM(X(22),X(4)))+1))
1215 T(215)=0*100000!*(1/(100000!*(1-TBM(X(22),X(5)))+1))
1216 T(216)=10*100000!*(1/(100000!*(1-TBM(X(22),X(6)))+1))
1217 T(217)=5*100000!*(1/(100000!*(1-TBM(X(22),X(7)))+1))
1218 T(218)=5*100000!*(1/(100000!*(1-TBM(X(22),X(8)))+1))
1219 T(219)=0*100000!*(1/(100000!*(1-TBM(X(22),X(9)))+1))
1220 T(220)=5*100000!*(1/(100000!*(1-TBM(X(22),X(10)))+1))
1221 T(221)=6*100000!*(1/(100000!*(1-TBM(X(22),X(11)))+1))
1222 T(222)=4*100000!*(1/(100000!*(1-TBM(X(22),X(12)))+1))
1223 T(223)=2*100000!*(1/(100000!*(1-TBM(X(22),X(13)))+1))
1224 T(224)=0*100000!*(1/(100000!*(1-TBM(X(22),X(14)))+1))
1225 T(225)=5*100000!*(1/(100000!*(1-TBM(X(22),X(15)))+1))
1226 T(226)=0*100000!*(1/(100000!*(1-TBM(X(22),X(16)))+1))
1227 T(227)=0*100000!*(1/(100000!*(1-TBM(X(22),X(17)))+1))
1228 T(228)=10*100000!*(1/(100000!*(1-TBM(X(22),X(18)))+1))
1229 T(229)=5*100000!*(1/(100000!*(1-TBM(X(22),X(19)))+1))
1230 T(230)=2*100000!*(1/(100000!*(1-TBM(X(22),X(20)))+1))
1231 T(231)=4*100000!*(1/(100000!*(1-TBM(X(22),X(21)))+1))
1232 T(232)=0*100000!*(1/(100000!*(1-TBM(X(23),X(1)))+1))
1233 T(233)=0*100000!*(1/(100000!*(1-TBM(X(23),X(2)))+1))
1234 T(234)=2*100000!*(1/(100000!*(1-TBM(X(23),X(3)))+1))
1235 T(235)=4*100000!*(1/(100000!*(1-TBM(X(23),X(4)))+1))
1236 T(236)=5*100000!*(1/(100000!*(1-TBM(X(23),X(5)))+1))
1237 T(237)=0*100000!*(1/(100000!*(1-TBM(X(23),X(6)))+1))
1238 T(238)=2*100000!*(1/(100000!*(1-TBM(X(23),X(7)))+1))
1239 T(239)=5*100000!*(1/(100000!*(1-TBM(X(23),X(8)))+1))
1240 T(240)=5*100000!*(1/(100000!*(1-TBM(X(23),X(9)))+1))
1241 T(241)=0*100000!*(1/(100000!*(1-TBM(X(23),X(10)))+1))
1242 T(242)=6*100000!*(1/(100000!*(1-TBM(X(23),X(11)))+1))
1243 T(243)=5*100000!*(1/(100000!*(1-TBM(X(23),X(12)))+1))
1244 T(244)=1*100000!*(1/(100000!*(1-TBM(X(23),X(13)))+1))
1245 T(245)=4*100000!*(1/(100000!*(1-TBM(X(23),X(14)))+1))
1246 T(246)=0*100000!*(1/(100000!*(1-TBM(X(23),X(15)))+1))
1247 T(247)=2*100000!*(1/(100000!*(1-TBM(X(23),X(16)))+1))
1248 T(248)=6*100000!*(1/(100000!*(1-TBM(X(23),X(17)))+1))
1249 T(249)=10*100000!*(1/(100000!*(1-TBM(X(23),X(18)))+1))
1250 T(250)=1*100000!*(1/(100000!*(1-TBM(X(23),X(19)))+1))
1251 T(251)=1*100000!*(1/(100000!*(1-TBM(X(23),X(20)))+1))
1252 T(252)=0*100000!*(1/(100000!*(1-TBM(X(23),X(21)))+1))
1253 T(253)=5*100000!*(1/(100000!*(1-TBM(X(23),X(22)))+1))
1254 T(254)=10*100000!*(1/(100000!*(1-TBM(X(24),X(1)))+1))
1255 T(255)=1*100000!*(1/(100000!*(1-TBM(X(24),X(2)))+1))
1256 T(256)=1*100000!*(1/(100000!*(1-TBM(X(24),X(3)))+1))
1257 T(257)=0*100000!*(1/(100000!*(1-TBM(X(24),X(4)))+1))
1258 T(258)=1*100000!*(1/(100000!*(1-TBM(X(24),X(5)))+1))
1259 T(259)=0*100000!*(1/(100000!*(1-TBM(X(24),X(6)))+1))
1260 T(260)=3*100000!*(1/(100000!*(1-TBM(X(24),X(7)))+1))
1261 T(261)=2*100000!*(1/(100000!*(1-TBM(X(24),X(8)))+1))
1262 T(262)=2*100000!*(1/(100000!*(1-TBM(X(24),X(9)))+1))
1263 T(263)=5*100000!*(1/(100000!*(1-TBM(X(24),X(10)))+1))
1264 T(264)=0*100000!*(1/(100000!*(1-TBM(X(24),X(11)))+1))
1265 T(265)=10*100000!*(1/(100000!*(1-TBM(X(24),X(12)))+1))
1266 T(266)=5*100000!*(1/(100000!*(1-TBM(X(24),X(13)))+1))
1267 T(267)=2*100000!*(1/(100000!*(1-TBM(X(24),X(14)))+1))
1268 T(268)=2*100000!*(1/(100000!*(1-TBM(X(24),X(15)))+1))
1269 T(269)=0*100000!*(1/(100000!*(1-TBM(X(24),X(16)))+1))
1270 T(270)=5*100000!*(1/(100000!*(1-TBM(X(24),X(17)))+1))
1271 T(271)=4*100000!*(1/(100000!*(1-TBM(X(24),X(18)))+1))
1272 T(272)=0*100000!*(1/(100000!*(1-TBM(X(24),X(19)))+1))
1273 T(273)=3*100000!*(1/(100000!*(1-TBM(X(24),X(20)))+1))
1274 T(274)=1*100000!*(1/(100000!*(1-TBM(X(24),X(21)))+1))
1275 T(275)=0*100000!*(1/(100000!*(1-TBM(X(24),X(22)))+1))
1276 T(276)=0*100000!*(1/(100000!*(1-TBM(X(24),X(23)))+1))
1277 T(277)=2*100000!*(1/(100000!*(1-TBM(X(25),X(1)))+1))
1278 T(278)=2*100000!*(1/(100000!*(1-TBM(X(25),X(2)))+1))
1279 T(279)=0*100000!*(1/(100000!*(1-TBM(X(25),X(3)))+1))
1280 T(280)=2*100000!*(1/(100000!*(1-TBM(X(25),X(4)))+1))
1281 T(281)=0*100000!*(1/(100000!*(1-TBM(X(25),X(5)))+1))
1282 T(282)=0*100000!*(1/(100000!*(1-TBM(X(25),X(6)))+1))
1283 T(283)=5*100000!*(1/(100000!*(1-TBM(X(25),X(7)))+1))
1284 T(284)=5*100000!*(1/(100000!*(1-TBM(X(25),X(8)))+1))
1285 T(285)=0*100000!*(1/(100000!*(1-TBM(X(25),X(9)))+1))
1286 T(286)=2*100000!*(1/(100000!*(1-TBM(X(25),X(10)))+1))
1287 T(287)=4*100000!*(1/(100000!*(1-TBM(X(25),X(11)))+1))
1288 T(288)=1*100000!*(1/(100000!*(1-TBM(X(25),X(12)))+1))
1289 T(289)=5*100000!*(1/(100000!*(1-TBM(X(25),X(13)))+1))
1290 T(290)=0*100000!*(1/(100000!*(1-TBM(X(25),X(14)))+1))
1291 T(291)=0*100000!*(1/(100000!*(1-TBM(X(25),X(15)))+1))
1292 T(292)=5*100000!*(1/(100000!*(1-TBM(X(25),X(16)))+1))
1293 T(293)=3*100000!*(1/(100000!*(1-TBM(X(25),X(17)))+1))
1294 T(294)=0*100000!*(1/(100000!*(1-TBM(X(25),X(18)))+1))
1295 T(295)=5*100000!*(1/(100000!*(1-TBM(X(25),X(19)))+1))
1296 T(296)=1*100000!*(1/(100000!*(1-TBM(X(25),X(20)))+1))
1297 T(297)=0*100000!*(1/(100000!*(1-TBM(X(25),X(21)))+1))
1298 T(298)=4*100000!*(1/(100000!*(1-TBM(X(25),X(22)))+1))
1299 T(299)=4*100000!*(1/(100000!*(1-TBM(X(25),X(23)))+1))
1300 T(300)=5*100000!*(1/(100000!*(1-TBM(X(25),X(24)))+1))
2151 P1NEW=0
2152 FOR KAU7=1 TO 300
2153 P1NEW=P1NEW+T(KAU7)
2154 NEXT KAU7
2450 P=-P1NEW
2451 IF P<=M THEN 2670
2657 FOR KEW=1 TO 25
2658 A(KEW)=X(KEW)
2659 NEXT KEW
2661 M=P
2666 GOTO 128
2670 NEXT I
2890 IF M>-27111111# THEN 2911 ELSE 2999
2911 PRINT A(1),A(2),A(3)
2912 PRINT A(4),A(5),A(6)
2913 PRINT A(7),A(8),A(9)
2914 PRINT A(10),A(11),A(12)
2915 PRINT A(13),A(14),A(15)
2916 PRINT A(16),A(17),A(18)
2917 PRINT A(19),A(20),A(21)
2918 PRINT A(22),A(23),A(24)
2925 PRINT A(25),JJJJ,M
2999 NEXT JJJJ

This BASIC computer program was run with the IBM basica/D interpreter, and its computational results, interpreted in accordance with line 2911 through line 2925, through JJJJ=-31764 are presented below.

4 1 1
1 4 1
4 4 3
4 1 4
1 4 3
1 1 4
2 1 4
1 1 1
4 -31951 -27000517.99482006

1 4 4
4 1 4
2 1 1
1 4 1
4 1 1
4 4 1
4 4 1
4 4 4
1 -31849 -27000517.99482006

4 2 1
1 4 2
4 4 4
4 1 4
1 4 4
1 1 4
1 2 4
2 1 1
4 -31848 -27000517.99482006

1 4 4
4 1 4
1 1 1
1 4 1
4 1 1
3 4 1
4 3 1
3 4 4
1 -31827 -27000517.99482006

1 3 3
4 1 4
1 1 1
1 4 1
4 1 1
3 4 1
4 4 1
4 3 4
1 -31824 -27000517.99482006

4 2 1
2 4 2
4 4 4
4 2 4
1 4 4
1 2 4
2 1 4
1 2 1
4 -31764 -27000517.99482006

The candidate solution above at JJJJ=-31951 reveals the assignment of courses 2, 3, 4, 6, 11, 13, 16, 17, 20, 22, 23, and 24 to period 1, course 19 to period 2, courses 9 and 15 to period 3, and courses 1, 5, 7, 8, 10, 12, 14, 18, 21, and 25 to period 4 for the total cost of 270.

These solutions were produced in 7 minutes on a personal computer with an Intel 2.66 GHz. chip and the IBM interpreter, which is slower than the corresponding compiler.

References

[1] R. C. Carlson, G. L. Nemhauser, Scheduling to minimize interaction cost, Operations Research 14 (1966) 52-58.

[2] F. E. Davis, M. D. Devine, R. P. Lutz, Scheduling activities among conflicting facilities to minimize conflict, Mathematical Programming 6 (1974) 224-228.

[3] F. S. Hillier, Quantitative tools for plant layout analysis, J. Indust. Eng. 14 (1963) 33-40.

[4] C. E. Nugent, T. E. Vollmann, J. Ruml, An experimental comparison of techniques for the assignment of facilities to locations, Operations Research 16 (1968) 150-173.

Saturday, February 14, 2009

ERRATA

Jsun Yui Wong
230 IF A(K)-(N(K)-B(K))/H(K)^J250 L(K)=B(K)
of my Google-Blogger posts should be replaced by
230 IF A(K)-(N(K)-B(K))/H(K)^J less than B(K) THEN 250 ELSE 260
250 L(K)=B(K).

(The "less than" above should be replaced by <.)

Wong's LL Blog