Jsun Yui Wong
The computer program listed below seeks to solve the following goal programming formulation from Varshney, Najmussehar, and Ahsan [85, p. 1002]:
Minimize X(1) + X(2)
subject to
(676.53805 / X(3) + 374.83501 / X(4) + 272.05508 / X(5) + 288.54504 / X(6)) - X(1) <= 11.13003
(1077.13728 / X(3) + 447.33203 / X(4) + 131.54568 / X(5) + 330.56571 / X(6)) - X(2) <= 12.12468
(2.4 * X(3) + 3.4 * X(4) + 4 * X(5) + 4.6 * X(6)) <= 1900
2<= X(3) <= 320
2<=X(4) <= 210
2<=X(5) <= 270
2<=X(6) <= 200
X(1), X(2)>=0; X(3) through X(6) are general integer variables.
The following computer program is used to solve the problem above.
0 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 = -4E+250
103 A(1) = RND
108 A(2) = RND
109 IF RND < .5 THEN A(3) = 160 - RND * 50 ELSE A(3) = 160 + RND * 50
113 IF RND < .5 THEN A(4) = 105 - RND * 50 ELSE A(4) = 105 + RND * 50
115 IF RND < .5 THEN A(5) = 135 - RND * 50 ELSE A(5) = 135 + RND * 50
116 IF RND < .5 THEN A(6) = 100 - RND * 50 ELSE A(6) = 100 + RND * 50
128 FOR I = 0 TO FIX(RND * 300000)
129 FOR KKQQ = 1 TO 6
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO FIX(1 + RND * 3.3)
143 J = 1 + FIX(RND * 6)
152 REM IF J < 3 THEN GOTO 156 ELSE GOTO 162
154 IF RND < .5 THEN GOTO 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 * 6.3) ELSE X(J) = A(J) + FIX(1 + RND * 6.3)
164 REM IF A(J) = 0 THEN X(J) = 1 ELSE X(J) = 0
169 NEXT IPP
171 X(3) = INT(X(3))
173 X(4) = INT(X(4))
175 X(5) = INT(X(5))
176 X(6) = INT(X(6))
182 IF X(1) < 0## THEN 1670
184 IF X(2) < 0## THEN 1670
188 IF X(3) < 2## THEN 1670
189 IF X(4) < 2## THEN 1670
190 IF X(5) < 2## THEN 1670
191 IF X(6) < 2## THEN 1670
193 IF X(3) > 320## THEN 1670
194 IF X(4) > 210## THEN 1670
195 IF X(5) > 270## THEN 1670
196 IF X(6) > 200## THEN 1670
228 IF (676.53805 / X(3) + 374.83501 / X(4) + 272.05508 / X(5) + 288.54504 / X(6)) - X(1) > 11.13003 THEN 1670
229 IF (1077.13728 / X(3) + 447.33203 / X(4) + 131.54568 / X(5) + 330.56571 / X(6)) - X(2) > 12.12468 THEN 1670
233 IF (2.4 * X(3) + 3.4 * X(4) + 4 * X(5) + 4.6 * X(6)) > 1900 THEN 1670
489 P = -X(1) - X(2)
1111 IF P <= M THEN 1670
1420 M = P
1444 FOR KLX = 1 TO 6
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -.246 THEN 1999
1926 PRINT A(1), A(2), A(3), A(4), A(5), A(6), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [90]. The complete output of a single run through JJJJ= -30275 is shown below:
9.674157287082608D-02 .1485398705384711 239
141 91 105 -.2452814434092971
-30860
9.674157287082608D-02 .1485398705384711 239
141 91 105 -.2452814434092971
-30800
.1173664774474452 .1251813065901958 244
140 90 104 -.242547784037641
-30275
.
.
.
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 [90], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -30275 was 10 minutes, total, including the time for “Creating .EXE file." One can compare the computational results above with those in Varshney, Najmussehar, and Ahsan [85, p. 1002].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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