Using the general-purpose nonlinear programming solver used in this blog many times for over a decade instead of a dynamic programming approach used in Hillier and Lieberman [37]
Jsun Yui Wong
Modeled on the general-purpose nonlinear programming solver used in this blog many times for over a decade, the computer program listed below attempts to solve Example 4—Scheduling Employment Levels in Hillier and Lieberman [37, pp. 444-450].
One notes the following line 473, which is 473 P = -200 * (X(1) – 255) ^ 2 – 2000 * (X(1) – 220) – 200 * (X(2) – X(1)) ^ 2 – 2000 * (X(2) – 240) – 200 * (X(3) – X(2)) ^ 2 – 2000 * (X(3) – 200) – 200 * (255 – X(3)) ^ 2, which is from the last column of Table 10.3 Data for the Local Job Shop Problem [37, p. 445].
This paper uses the general-purpose nonlinear programming solver used in this blog many times for over a decade instead of the dynamic programming approach used in Hillier and Lieberman [37, pp. 444-450].
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
86 M = -3E+50
114 A(1) = 200 + FIX(RND * 20)
115 A(2) = 200 + FIX(RND * 20)
116 A(3) = 200 + FIX(RND * 20)
117 A(4) = 255
128 FOR I = 1 TO 3000
129 FOR KKQQ = 1 TO 4
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
151 FOR IPP = 1 TO FIX(1 + RND * 5)
153 J = 1 + FIX(RND * 4)
154 IF J < 5 THEN GOTO 156 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
163 IF RND < .5 THEN X(J) = A(J) – INT(RND * 15) ELSE X(J) = A(J) + INT(RND * 15)
164 REM IF A(J) = 0 THEN X(J) = 1 ELSE X(J) = 0
169 NEXT IPP
172 REM X(1) = (X(1))
174 REM X(2) = INT(X(2))
176 REM X(3) = INT(X(3))
178 REM X(4) = INT(X(4))
334 IF X(1) < 220 THEN 1670
335 IF X(1) > 255 THEN 1670
337 IF X(2) < 240 THEN 1670
339 IF X(2) > 255 THEN 1670
342 IF X(3) < 200 THEN 1670
344 IF X(3) > 255 THEN 1670
347 X(4) = 255
473 P = -200 * (X(1) – 255) ^ 2 – 2000 * (X(1) – 220) – 200 * (X(2) – X(1)) ^ 2 – 2000 * (X(2) – 240) – 200 * (X(3) – X(2)) ^ 2 – 2000 * (X(3) – 200) – 200 * (255 – X(3)) ^ 2
1111 IF P <= M THEN 1670
1450 M = P
1454 FOR KLX = 1 TO 4
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -9999999 THEN 1999
1933 PRINT A(1), A(2), A(3), A(4), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [102]. Its complete output of one run through JJJJ= -31996 is shown below:
247.4944 244.9882 247.4897 255 -185000
-32000
247.4928 244.99 247.494 255 -185000
-31999
247.4993 244.9948 247.4978 255 -185000
-31998
247.51 245.0105 247.5092 255 -185000
-31997
247.5039 245.0023 247.5041 255 -185000
-31996
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. By using the following computer system and QB64v1000-win [102], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31996 was one second, counting from “Starting program…”. One can compare the computational procedure above with that in Hillier and Lieberman [37, pp. 444-450].
The computational results presented above were obtained from the following computer system:
Processor: Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz 2.26 GHz
Installed memory (RAM): 4.00GB (3.87 GB usable)
System type: 64-bit Operating System.
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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