Jsun Yui Wong

The computer program listed below seeks to solve the following integer programming formulation (that uses the weight criterion approach) from page 122 of Ali and Hasan [1]:

Maximize .47*long1+.53*log2

where long1 = (1 - .35 ^ (4 + X(1))) * (1 - .45 ^ (2 + X(2))) * (1 - .3 ^ (3 + X(3)))

long2 = (1 - .3 ^ (3 + X(4))) * (1 - .45 ^ (2 + X(5))) * (1 - .4 ^ (2 + X(6))) * (1 - .35 ^ (3 + X(7)))

subject to

140 * (X(1) + EXP(.25 * X(1))) + 110 * (X(2) + EXP(.25 * X(2))) + 150 * (X(3) + EXP(.25 * X(3))) + 70 * (X(4) + EXP(.25 * X(4))) + 30 * (X(5) + EXP(.25 * X(5))) + 45 * (X(6) + EXP(.25 * X(6))) + 65 * (X(7) + EXP(.25 * X(7))) <= 3000

1<= X(1) <=4

1<= X(2) <= 4

1<= X(3) <= 7

1<= X(4) <= 5

1<= X(5) <= 8

1<= X(6) <= 10

1<= X(7) <= 7

X(1) through X(7) are integer variables.

Whereas in an earlier edition line 128 is 128 FOR I = 1 TO FIX(6000 + RND * 6000),

here line 128 is 128 FOR I = 1 TO FIX(1000 + RND * 1000).

0 REM DEFDBL A-Z

1 DEFINT K

2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J44(2002), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(22), CC(20), RR(20), WW(20), AL(50), SW(50), SV(50), C2(22), C3(22), C4(22), C5(22)

81 FOR JJJJ = -32000 TO 32000

85 RANDOMIZE JJJJ

87 M = -3E+50

111 REM EPSILON = RND * .5

113 FOR J44 = 1 TO 7

120 A(J44) = 1 + FIX((RND * 9))

125 NEXT J44

128 FOR I = 1 TO FIX(1000 + RND * 1000)

129 FOR KKQQ = 1 TO 7

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

151 FOR IPP = 1 TO FIX(1 + RND * 3)

153 J = 1 + FIX(RND * 7)

154 IF RND < .5 THEN 156 ELSE GOTO 162

156 R = (1 - RND * 2) * A(J)

158 X(J) = A(J) + (RND ^ (RND * 15)) * R

161 GOTO 169

162 IF RND < .5 THEN X(J) = A(J) - FIX(1 + RND * 2) ELSE X(J) = A(J) + FIX(1 + RND * 2)

169 NEXT IPP

170 FOR J44 = 1 TO 7

171 X(J44) = INT(X(J44))

172 IF X(J44) < 1 THEN 1670

173 NEXT J44

174 IF X(1) > 4 THEN 1670

175 IF X(2) > 4 THEN 1670

176 IF X(3) > 7 THEN 1670

177 IF X(4) > 5 THEN 1670

178 IF X(5) > 8 THEN 1670

179 IF X(6) > 10 THEN 1670

180 IF X(7) > 7 THEN 1670

411 IF 140 * (X(1) + EXP(.25 * X(1))) + 110 * (X(2) + EXP(.25 * X(2))) + 150 * (X(3) + EXP(.25 * X(3))) + 70 * (X(4) + EXP(.25 * X(4))) + 30 * (X(5) + EXP(.25 * X(5))) + 45 * (X(6) + EXP(.25 * X(6))) + 65 * (X(7) + EXP(.25 * X(7))) > 3000 THEN 1670

423 long1 = (1 - .35 ^ (4 + X(1))) * (1 - .45 ^ (2 + X(2))) * (1 - .3 ^ (3 + X(3)))

425 long2 = (1 - .3 ^ (3 + X(4))) * (1 - .45 ^ (2 + X(5))) * (1 - .4 ^ (2 + X(6))) * (1 - .35 ^ (3 + X(7)))

459 PDU = (.47 * long1 + .53 * long2)

466 P = PDU

1111 IF P <= M THEN 1670

1450 M = P

1454 FOR KLX = 1 TO 7

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1557 GOTO 128

1670 NEXT I

1889 IF M < -99999999 THEN 1999

1923 PRINT A(1), A(2), A(3), A(4), A(5)

1924 PRINT A(6), A(7), M, JJJJ

1999 NEXT JJJJ

This BASIC computer program was run with QB64v1000-win [79]. The complete output of a single run through JJJJ= -31983 is showm below:

1 4 2 2 6

5 4 .9891418 -31999

1 4 2 3 6

5 3 .989409 -31988

1 4 2 3 6

5 3 .989409 -31983

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and QB64v1000-win [79], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31983 was 1 second, not including the time for “Creating .EXE file" (15 seconds, total, including the time for “Creating .EXE file"). One can compare the computational results above with those on page 122 of Ali and Hasan [1] and with those in Table 2 of Ali and Hasan [1, p. 123].

**Acknowledgment**

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

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