The two computer programs listed below seek to solve the two formulations in Khan, Maiti, and Ahsan [49, p. 705].
1. Example 1 in Khan, Maiti, and Ahsan [49]
Minimize
.5 * X(5) + .5 * X(6)
subject to
-(-14566711.59 / X(1) - 221179342.00 / X(2) - 607364036.51 / X(3) - 88587552.79 / X(4)) -X(5) <= 96754589.11
-(-1580.89 / X(1) - 123578.82 / X(2) - 190094.68 / X(3) - 4727.52 / X(4)) - x(6)<=27061.62
15 * X(1) + 7 * X(2) + 5 * X(3) + 9 * X(4) <= 200
2<=X(1)<=8
2<=X(2)<=34
2<=X(3)<=45
2<=X(4)<=12
X(5)>=0
X(6)>=0
where X(1) through X(4) are integer variables, and X(5) and X(6) are continuous variables.
One notes and line 243 line 244, which are 243 X(5) = -(-14566711.59 / X(1) - 221179342.00 / X(2) - 607364036.51 / X(3) - 88587552.79 / X(4)) - 96754589.11 and 244 X(6) = -(-1580.89 / X(1) - 123578.82 / X(2) - 190094.68 / X(3) - 4727.52 / X(4)) - 27061.62 from the long inequality constraints above. That is a search for active constraint/s aiming towards optimality; please see Bernau [11].
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
86 M = -3E+50
118 FOR J44 = 1 TO 4
119 A(J44) = 2 + (RND * 5)
120 NEXT J44
123 A(5) = RND * 1000
125 A(6) = RND * 10
128 FOR I = 1 TO 9000
129 FOR KKQQ = 1 TO 6
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
151 FOR IPP = 1 TO FIX(1 + RND * 5)
153 J = 1 + FIX(RND * 6)
154 IF J < 4.5 THEN GOTO 163 ELSE GOTO 156
155 REM GOTO 162
156 r = (1 - RND * 2) * A(J)
158 X(J) = A(J) + (RND ^ (RND * 15)) * r
161 GOTO 169
162 REM IF RND < .5 THEN X(J) = A(J) - INT(RND * 15) ELSE X(J) = A(J) + INT(RND * 15)
163 IF RND < .5 THEN X(J) = A(J) - INT(RND * 5) ELSE X(J) = A(J) + INT(RND * 5)
164 REM IF A(J) = 0 THEN X(J) = 1 ELSE X(J) = 0
169 NEXT IPP
215 FOR J44 = 1 TO 4
216 X(J44) = INT(X(J44))
217 REM X(4) = INT(X(4))
218 IF X(J44) < 2 THEN 1670
219 NEXT J44
222 REM IF X(9) < 0## THEN 1670
225 IF X(1) > 8 THEN 1670
226 IF X(2) > 34 THEN 1670
227 IF X(3) > 45 THEN 1670
228 IF X(4) > 12 THEN 1670
229 IF X(5) < 0## THEN 1670
230 IF X(6) < 0## THEN 1670
243 X(5) = -(-14566711.59 / X(1) - 221179342.00 / X(2) - 607364036.51 / X(3) - 88587552.79 / X(4)) - 96754589.11
244 X(6) = -(-1580.89 / X(1) - 123578.82 / X(2) - 190094.68 / X(3) - 4727.52 / X(4)) - 27061.62
245 IF X(5) < 0## THEN 1670
246 IF X(6) < 0## THEN 1670
297 IF 15 * X(1) + 7 * X(2) + 5 * X(3) + 9 * X(4) > 200 THEN 1670
1108 P = -.5 * X(5) - .5 * X(6)
1111 IF P <= M THEN 1670
1450 M = P
1454 FOR KLX = 1 TO 6
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1533 dol = 15 * X(1) + 7 * X(2) + 5 * X(3) + 9 * X(4)
1557 GOTO 128
1670 NEXT I
1889 IF M < -999999999 THEN 1999
1933 PRINT A(1), A(2), A(3), A(4)
1936 PRINT A(5), A(6), M, JJJJ, dol
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [95]. The complete output of a single run through JJJJ= -31996 is shown below:
2 7 17 4
4.936974495649338D-03 3746.862142857145 -1873.43353991582
-32000 200
2 7 17 4
4.936974495649338D-03 3746.862142857145 -1873.43353991582
-31999 200
2 7 17 4
4.936974495649338D-03 3746.862142857145 -1873.43353991582
-31998 200
2 7 17 4
4.936974495649338D-03 3746.862142857145 -1873.43353991582
-31997 200
2 7 17 4
4.936974495649338D-03 3746.862142857145 -1873.43353991582
-31996 200
.
.
.
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 [95], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31996 was 3 seconds, not including the time for “Creating .EXE file.” One can compare the computational results above with those in Khan, Maiti, and Ahsan [49, p. 704, Table 3], where one can see the following numbers: 2, 7, 17, 4, 200.
2. Example 2 in Khan, Maiti, and Ahsan [49]
Only the four different measurement costs in Example 1 are changed to 7.5; please see the following line 297 and line 1533.
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
86 M = -3E+50
118 FOR J44 = 1 TO 4
119 A(J44) = 2 + (RND * 5)
120 NEXT J44
123 A(5) = RND * 1000
125 A(6) = RND * 10
128 FOR I = 1 TO 9000
129 FOR KKQQ = 1 TO 6
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
151 FOR IPP = 1 TO FIX(1 + RND * 5)
153 J = 1 + FIX(RND * 6)
154 IF J < 4.5 THEN GOTO 163 ELSE GOTO 156
155 REM GOTO 162
156 r = (1 - RND * 2) * A(J)
158 X(J) = A(J) + (RND ^ (RND * 15)) * r
161 GOTO 169
162 REM IF RND < .5 THEN X(J) = A(J) - INT(RND * 15) ELSE X(J) = A(J) + INT(RND * 15)
163 IF RND < .5 THEN X(J) = A(J) - INT(RND * 5) ELSE X(J) = A(J) + INT(RND * 5)
164 REM IF A(J) = 0 THEN X(J) = 1 ELSE X(J) = 0
169 NEXT IPP
215 FOR J44 = 1 TO 4
216 X(J44) = INT(X(J44))
217 REM X(4) = INT(X(4))
218 IF X(J44) < 2 THEN 1670
219 NEXT J44
222 REM IF X(9) < 0## THEN 1670
225 IF X(1) > 8 THEN 1670
226 IF X(2) > 34 THEN 1670
227 IF X(3) > 45 THEN 1670
228 IF X(4) > 12 THEN 1670
229 IF X(5) < 0## THEN 1670
230 IF X(6) < 0## THEN 1670
243 X(5) = -(-14566711.59 / X(1) - 221179342.00 / X(2) - 607364036.51 / X(3) - 88587552.79 / X(4)) - 96754589.11
244 X(6) = -(-1580.89 / X(1) - 123578.82 / X(2) - 190094.68 / X(3) - 4727.52 / X(4)) - 27061.62
245 IF X(5) < 0## THEN 1670
246 IF X(6) < 0## THEN 1670
297 IF 7.5 *( X(1) + X(2) + X(3) + X(4) ) > 200 THEN 1670
1108 P = -.5 * X(5) - .5 * X(6)
1111 IF P <= M THEN 1670
1450 M = P
1454 FOR KLX = 1 TO 6
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1533 dol = 7.5 *( X(1) + X(2) + X(3) + X(4) )
1557 GOTO 128
1670 NEXT I
1889 IF M < -999999999 THEN 1999
1933 PRINT A(1), A(2), A(3), A(4)
1936 PRINT A(5), A(6), M, JJJJ, dol
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [95]. The complete output of a single run through JJJJ= -31996 is shown below:
2 7 12 5
10456995.80930953 8169.669476190476 -5232582.739392861
-32000 195
2 7 12 5
10456995.80930953 8169.669476190476 -5232582.739392861
-31999 195
2 7 12 5
10456995.80930953 8169.669476190476 -5232582.739392861
-31998 195
2 7 12 5
10456995.80930953 8169.669476190476 -5232582.739392861
-31997 195
2 7 12 5
10456995.80930953 8169.669476190476 -5232582.739392861
-31996 195
.
.
.
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 [95], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31996 was 3 seconds, not including the time for “Creating .EXE file.” One can compare the computational results above with those in Khan, Maiti, and Ahsan [49, p. 706, Table 4], where one can see the following numbers: 2, 7, 12, 5, 195.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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