Nonlinear Integer/Continuous/Discrete Programming Solver

Monday, June 19, 2017

Solving a Double Row Layout Problem Having 16 Facilities

Jsun Yui Wong

Based on the computer program in Wong [17], the following computer program seeks to solve the problem named P16_a in Fischer, Fischer, and Hungerlander [10, p. 129, Table 1]. The data come from the PROP Instances-Amaral 2013 section of Anjos [8].

0 REM DEFDBL A-Z
1 DEFINT I, J, K, X, A
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), Y(33), C(33), CC(33)
3 DIM HS(49, 49)
4 DIM PE(49, 49)
5 DIM SD(49, 49)
27 HR(1) = 14: HR(2) = 11: HR(3) = 9: HR(4) = 5: HR(5) = 13

28 REM HR(6)=4:HR(7)=6:HR(8)=8:HR(9)=9
29 HR(6) = 5: HR(7) = 14: HR(8) = 7: HR(9) = 10: HR(10) = 11

30 HR(11) = 8: HR(12) = 14: HR(13) = 10: HR(14) = 11: HR(15) = 8: HR(16) = 5

31 FOR IL = 1 TO 16
32 FOR JL = 1 TO 16
33 READ HS(IL, JL)
34 NEXT JL
35 NEXT IL
61 DATA 999,0,5,0,5,2,10,3,1,5,5,5,0,0,5,4

62 DATA 0,999,3,10,5,1,5,1,2,4,2,5,0,10,10,3
63 DATA 5,3,999,2,0,5,2,4,4,5,0,0,0,5,1,0
64 DATA 0,10,2,999,1,0,5,2,1,0,10,2,2,0,2,1

66 DATA 5,5,0,1,999,5,6,5,2,5,2,0,5,1,1,1
67 DATA 2,1,5,0,5,999,5,2,1,6,0,0,10,0,2,0

68 DATA 10,5,2,5,6,5,999,0,0,0,5,10,2,2,5,1

69 DATA 3,1,4,2,5,2,0,999,1,1,10,10,2,0,10,2

70 DATA 1,2,4,1,2,1,0,1,999,2,0,3,5,5,0,5

71 DATA 5,4,5,0,5,6,0,1,2,999,5,5,0,5,1,0

72 DATA 5,2,0,10,2,0,5,10,0,5,999,5,2,5,1,10
73 DATA 5,5,0,2,0,0,10,10,3,5,5,999,2,10,5,0

74 DATA 0,0,0,2,5,10,2,2,5,0,2,2,999,2,2,1

75 DATA 0,10,5,0,1,0,2,0,5,5,5,10,2,999,5,5
76 DATA 5,10,1,2,1,2,5,10,0,1,1,5,2,5,999,3
77 DATA 4,3,0,1,1,0,1,2,5,0,10,0,1,5,3,999
78 FOR JJJJ = -32000 TO 32000
79 RANDOMIZE JJJJ
80 M = -1D+37

81 IMAX = 2 + FIX(RND * 13)

82 FOR J44 = 1 TO 16

83 A(J44) = J44
84 NEXT J44
111 REM IF RND < 1 / 4 THEN IMAX = 8 ELSE IF RND < 1 / 3 THEN IMAX = 9 ELSE IF RND < 1 / 2 THEN IMAX = 10 ELSE IMAX = 11

126 REM IMAR=10+FIX(RND*1000)
128 FOR I = 1 TO 1000

129 FOR KKQQ = 1 TO 16
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 III = 1 + FIX(RND * 16)
134 JJJ = 1 + FIX(RND * 16)
221 X(III) = A(JJJ)
223 X(JJJ) = A(III)
231 FOR J44 = 1 TO 16
233 FOR J45 = 1 TO 16
234 IF X(J44) = J45 THEN HHR(J44) = HR(J44) ELSE GOTO 238
237 Y(J45) = J44
238 NEXT J45
253 FOR ISE20 = 1 TO IMAX
254 C(ISE20) = .5 * HHR(Y(ISE20))
258 FOR ISE2000 = ISE20 + 1 TO IMAX
259 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))
263 NEXT ISE2000
269 NEXT ISE20
386 FOR ISE20N = IMAX + 1 TO 16
387 C(ISE20N) = .5 * HHR(Y(ISE20N))
388 FOR ISE2000N = ISE20N + 1 TO 16
389 C(ISE20N) = C(ISE20N) + HHR(Y(ISE2000N))
390 NEXT ISE2000N
391 NEXT ISE20N
395 NEXT J44
411 PROD = 0
412 FOR J44 = 1 TO 16
413 FOR J45 = J44 + 1 TO 16
414 PROD = PROD - HS(Y(J44), Y(J45)) * ABS(C(J44) - C(J45))
415 NEXT J45
416 NEXT J44
422 P = PROD
1111 IF P <= M THEN 1670
1452 M = P
1453 FOR KLX = 1 TO 16
1454 CC(KLX) = C(KLX)
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1559 Iimax = IMAX
1657 GOTO 128
1670 NEXT I
1889 IF M < -7371 THEN 1999

1901 PRINT A(1), A(2), A(3), A(4), A(5)
1902 PRINT A(6), A(7), A(8), A(9), A(10)
1903 PRINT A(11), A(12), A(13), A(14), A(15), A(16)

1905 REM PRINT CC(1), CC(2), CC(3), CC(4), CC(5)
1906 REM PRINT CC(6), CC(7), CC(8), CC(9), CC(10)
1907 REM PRINT CC(11), CC(12), CC(13), CC(14), CC(15)
1919 PRINT M, JJJJ, Iimax
1999 NEXT JJJJ

This computer program was run with qb64v1000-win [16]. The complete output through JJJJ=-29826 is shown below:

16 4 3 13 2
9 7 14 1 10
5 6 8 11 15
12
-7370 -31479 7

16 4 3 13 2
9 7 14 1 10
5 6 8 11 15
12
-7370 -31269 7

16 4 3 13 2
9 7 14 1 10
5 6 8 11 15
12
-7370 -30457 7

9 13 12 6 11
2 16 7 10 3
14 15 1 4 8
5
-7370 -29826 9

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 [16], the wall-clock time for obtaining the output through JJJJ=-29826 was five minutes.

Acknowledgment

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

References

[1] Andre R. S. Amaral (2006), On the Exact Solution of a Facility Layout Problem. European Journal of Operational Research 173 (2006), pp. 508-518.

[2] Andre R. S. Amaral (2008), An Exact Approach to the One-Dimensional Facility Layout Problem. Operations Research, Vol. 56, No. 4 (July-August, 2008), pp. 1026-1033.

[3] Andre R. S. Amaral (2011), Optimal Solutions for the Double Row Layout Problem. Optimization Letters, DOI 10.1007/s11590-011-0426-8, published on line 30 November 2011, Springer-Verlag 2011.

[4] Andre R. S. Amaral (2012), The Corridor Allocation Problem. Computers and Operations Research 39 (2012), pp. 3325-3330.

[5] Andre R. S. Amaral (2013), A Parallel Ordering Problem in Facilities Layout. Computers and Operations Research, Vol. 40, Issue 12, December 2013, pp. 2930-2939.

[6] Miguel F. Anjos, Anthony Vannelli, Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes. INFORMS Journal on Computing, Vol. 20, No. 4, Fall 2008, pp. 611-617.

[7] Miguel F. Anjos (2012), FLPLIB–Facility Layout Database. Retrieved on September 25 2012 from http://www.gerad.ca/files/Sites/Anjos/indexFR.html

[8] Miguel F. Anjos, FLPLIB–Facility Layout Database. http://www.miguelanjos.com.

[9] Miguel Anjos. QAP - A Quadratic Assignment Problem Library. www.anjos.mgi.polymtl.ca/qaplib/data.d/sko49.dat

[10] Anja Fischer, Frank Fischer. Philipp Hungerlaender, A New Exact Approach to the Space-Free Double Row Layout Problem.
K. Doerner et al. (eds) Operations Research Proceedings 2015. Springer 2017.

[11] S. S. Heragu, A. Kusiak. Efficient Models for the Facility Layout Problem. European Journal of Operational Research 53 (1), 1991, pp. 1-13.

[12] Philipp Hungerlaender, Miguel F. Anjos (January 2012), A Semidefinite Optimization Approach to Free-Space Multi-Row Facility Layout. Les Cahiers du GERAD. Retrieved from http://www.gerad.ca/fichiers/cahiers/G-2012-03.pdf

[13] Robert F. Love, Jsun Yui Wong (1976), On Solving a One-Dimensional Space Allocation Problem with Integer Programming, INFOR 14(2), pp. 139-143.

[14] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[15] C. E. Nugent, T. E Vollmann, J. Ruml (1968), An Experimental Comparison of Techniques for the Assignment of Facilities to Locations. Operations Research, Vol. 16, pp. 150-173.

[16] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64

[17] Jsun Yui Wong (2012, September 20). A General Nonlinear Integer/Discrete/Continuous Programming Solver Applied to the Corridor Allocation Problem with Fifteen Facilities, Fifth Edition. https://myblogsubstance.typepad.com/substance/2012/09/index.html/

[18] Ginger Yen (2008). Cutting-Plane Separation Strategies for Semidefinite Programming Models to Solve Single-Row Facility Layout Problems. A Master Thesis Presented to the University of Waterloo

Friday, May 19, 2017

Solving a k-Parallel Row Ordering Problem in Layout of 36 Facilities in 18 Rows

Jsun Yui Wong

Adapting to the computer program in Wong [14], the following computer program seeks to solve a k-parallel row ordering problem (k-PROP) of 36 facilities. Each row of the 18 rows has 2 facilities. See Amaral [5]. The data for flows and lengths used here can be found in Yen [15, pages 101-105 for flows and page 106 for lengths]. One notes that these lengths are the lengths of C.4.6 STE36-8 in Yen [15, p. 106].

0 REM DEFDBL A-Z

1 DEFINT I, J, K, X

2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(39), J44(2002), J(99), AA(99), HR(39), HHR(39), Y(39), C(39), CC(39), RA(99)

3 DIM HS(49, 49)

4 DIM PE(49, 49)

5 DIM SD(49, 49)

17 HR(1) = 4: HR(2) = 2: HR(3) = 3: HR(4) = 2: HR(5) = 3: HR(6) = 1: HR(7) = 3: HR(8) = 1: HR(9) = 3

18 HR(10) = 4: HR(11) = 5: HR(12) = 2: HR(13) = 2: HR(14) = 3: HR(15) = 3: HR(16) = 3: HR(17) = 5: HR(18) = 3: HR(19) = 3: HR(20) = 5

19 HR(21) = 2: HR(22) = 5: HR(23) = 3

20 HR(24) = 3: HR(25) = 5: HR(26) = 4: HR(27) = 4: HR(28) = 3: HR(29) = 4: HR(30) = 3

29 HR(31) = 2: HR(32) = 2: HR(33) = 3: HR(34) = 2: HR(35) = 5: HR(36) = 3

31 FOR IL = 1 TO 36

32 FOR JL = 1 TO 36

33 READ HS(IL, JL)

34 NEXT JL

35 NEXT IL

41 DATA 9999,0,0,2,1,7,9,0,4,75,7,12,22,7,1,0,0,0,0,23,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

42 DATA 0,9999,0,0,0,0,4,16,0,8,0,0,16,0,0,0,0,6,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

43 DATA 0,0,9999,0,0,4,16,20,0,0,0,0,20,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
44 DATA 2,0,0,9999,29,5,18,47,23,2,4,0,48,0,4,0,0,0,0,25,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
45 DATA 1,0,0,29,9999,18,12,25,0,0,4,0,25,0,3,0,0,0,0,18,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0
46 DATA 7,0,4,5,18,9999,4,2,0,1,23,2,19,0,0,0,0,0,2,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
47 DATA 9,4,16,18,12,4,9999,0,14,72,7,8,39,8,40,8,0,8,4,7,0,0,0,0,0,0,0,28,8,0,0,0,0,0,0,0
48 DATA 0,16,20,47,25,2,0,9999,10,71,2,0,0,0,0,0,0,41,0,0,0,0,0,0,0,0,7,8,0,0,0,0,0,0,0,0
49 DATA 4,0,0,23,0,0,14,10,9999,14,0,0,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
50 DATA 75,8,0,2,0,1,72,71,14,9999,11,1,17,0,1,0,0,17,0,15,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
51 DATA 7,0,0,4,4,23,7,2,0,11,9999,316,33,8,2,0,0,0,8,34,0,0,6,0,0,0,10,0,0,6,0,0,0,0,0,0
52 DATA 12,0,0,0,0,2,8,0,0,1,316,9999,157,25,4,0,0,1,0,0,0,0,0,0,22,0,1,0,0,0,0,0,0,0,0,0
53 DATA 22,16,20,48,25,19,39,0,18,17,33,157,9999,11,6,0,0,6,0,5,8,3,10,0,0,0,9,11,2,0,0,1,0,0,0,0
54 DATA 7,0,0,0,0,0,8,0,0,0,8,25,11,9999,3,0,0,1,1,21,0,1,0,2,0,0,5,0,0,3,2,5,5,4,0,0
55 DATA 1,0,0,4,3,0,40,0,0,1,2,4,6,3,9999,19,0,2,2,12,0,0,0,0,0,0,0,7,3,0,0,0,0,0,0,0
56 DATA 0,0,0,0,0,0,8,0,0,0,0,0,0,0,19,9999,0,6,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
57 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9999,40,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
58 DATA 0,6,0,0,0,0,8,41,0,17,0,1,6,1,2,6,40,9999,0,26,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
59 DATA 0,0,0,0,0,2,4,0,0,0,8,0,0,1,2,0,0,0,9999,13,9,0,7,0,0,0,0,27,16,3,0,20,0,4,0,0
60 DATA 23,4,4,25,18,19,7,0,0,15,34,0,5,21,12,1,0,26,13,9999,11,4,36,0,0,0,16,18,9,10,1,28,6,2,0,0
61 DATA 0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,9,11,9999,36,6,0,8,0,2,0,0,0,0,0,0,0,0,0
62 DATA 0,0,0,0,3,0,0,0,0,0,0,0,3,1,0,0,0,0,0,4,36,9999,0,0,0,0,4,0,0,0,0,0,0,0,0,0
63 DATA 0,0,0,0,0,0,0,0,0,0,6,0,10,0,0,0,0,0,7,36,6,0,9999,0,0,12,9,0,0,0,0,0,0,0,0,0
64 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,9999,26,0,5,0,0,0,0,0,0,0,0,0
65 DATA 0,0,0,0,0,0,0,0,0,0,0,22,0,0,0,0,0,0,0,0,8,0,0,26,9999,35,2,0,0,0,0,0,0,0,0,0
66 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,35,9999,4,0,0,0,0,0,0,0,0,0
67 DATA 0,0,0,0,0,0,0,7,0,0,10,1,9,5,0,0,0,0,0,16,2,4,9,5,2,4,9999,0,0,0,0,0,0,0,0,0
68 DATA 0,0,0,0,0,0,28,8,0,0,0,0,11,0,7,0,0,0,27,18,0,0,0,0,0,0,0,9999,10,22,4,6,4,12,0,0
69 DATA 0,0,0,0,0,0,8,0,0,0,0,0,2,0,3,0,0,0,16,9,0,0,0,0,0,0,0,10,9999,19,12,0,0,0,0,0
70 DATA 0,0,0,0,0,0,0,0,0,0,6,0,0,3,0,0,0,0,3,10,0,0,0,0,0,0,0,22,19,9999,19,4,5,8,0,0
71 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,1,0,0,0,0,0,0,0,4,12,19,9999,0,3,13,0,0
72 DATA 0,0,0,0,0,0,0,0,0,0,0,0,1,5,0,0,0,0,20,28,0,0,0,0,0,0,0,6,0,4,0,9999,18,24,0,0
73 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,5,0,0,0,0,0,6,0,0,0,0,0,0,0,4,0,5,3,18,9999,20,0,0
74 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,4,2,0,0,0,0,0,0,0,12,0,8,13,24,20,9999,0,0

75 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9999,0

76 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9999

88 FOR JJJJ = -32000 TO 32000

89 RANDOMIZE JJJJ

90 M = -1D+37

91 FOR J44 = 1 TO 36

93 A(J44) = J44

94 NEXT J44

128 FOR I = 1 TO 1000

129 FOR KKQQ = 1 TO 36

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

133 III = 1 + FIX(RND * 36)

134 JJJ = 1 + FIX(RND * 36)

137 X(III) = A(JJJ)
139 X(JJJ) = A(III)

231 FOR J44 = 1 TO 36

233 FOR J45 = 1 TO 36

234 IF X(J44) = J45 THEN HHR(J44) = HR(J44) ELSE GOTO 238

237 Y(J45) = J44

238 NEXT J45

244 FOR RN = 1 TO 18

251 FOR ISE20 = (RN - 1) * 2 + 1 TO RN * 2

254 C(ISE20) = .5 * HHR(Y(ISE20))

258 FOR ISE2000 = ISE20 + 1 TO RN * 2

259 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

263 NEXT ISE2000

269 NEXT ISE20

299 NEXT RN

499 NEXT J44

551 FOR RN = 1 TO 18

601 FOR J77 = (RN - 1) * 2 + 1 TO RN * 2

605 IF X(J77) > RN * 2 THEN 1670

609 NEXT J77
610 NEXT RN

811 PROD = 0

812 FOR J44 = 1 TO 36

813 FOR J45 = J44 + 1 TO 36

814 PROD = PROD - HS(Y(J44), Y(J45)) * ABS(C(J44) - C(J45))

815 NEXT J45

816 NEXT J44

822 P = PROD

1111 IF P <= M THEN 1670

1452 M = P

1453 FOR KLX = 1 TO 36

1454 CC(KLX) = C(KLX)

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1657 GOTO 128

1670 NEXT I

1889 REM IF M < -999999 THEN 1999

1891 PRINT A(1), A(2), A(3), A(4), A(5)

1892 PRINT A(6), A(7), A(8), A(9), A(10)

1893 PRINT A(11), A(12), A(13), A(14), A(15)

1894 PRINT A(16), A(17), A(18), A(19), A(20)

1896 PRINT A(21), A(22), A(23), A(24), A(25)

1897 PRINT A(26), A(27), A(28), A(29), A(30)

1898 PRINT A(31), A(32), A(33), A(34), A(35), A(36), M, JJJJ

1999 NEXT JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [13]. The complete output through JJJJ=-31996 is shown below:

2 1 4 3 6
5 8 7 9 10
12 11 13 14 16
15 17 18 19 20
21 22 24 23 25
26 27 28 29 30
32 31 33 34 35
36 -5032 -32000

2 1 3 4 6
5 8 7 9 10
11 12 14 13 16
15 17 18 19 20
22 21 23 24 26
25 27 28 29 30
32 31 33 34 36
35 -4844 -31999

2 1 3 4 6
5 8 7 9 10
11 12 14 13 16
15 17 18 19 20
22 21 23 24 26
25 27 28 29 30
32 31 33 34 35
36 -4844 -31998

2 1 3 4 6
5 7 8 9 10
11 12 14 13 16
15 17 18 19 20
22 21 23 24 26
25 27 28 29 30
32 31 33 34 35
36 -4920 -31997

2 1 3 4 6
5 7 8 9 10
12 11 13 14 15
16 17 18 19 20
21 22 24 23 25
26 27 28 29 30
32 31 33 34 35
36 -5230 -31996

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 [13], the wall-clock time for obtaining the output through JJJJ=-31996 was 10 seconds.

Acknowledgment

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

References

[1] Andre R. S. Amaral (2006), On the Exact Solution of a Facility Layout Problem. European Journal of Operational Research 173 (2006), pp. 508-518.

[2] Andre R. S. Amaral (2008), An Exact Approach to the One-Dimensional Facility Layout Problem. Operations Research, Vol. 56, No. 4 (July-August, 2008), pp. 1026-1033.

[3] Andre R. S. Amaral (2011), Optimal Solutions for the Double Row Layout Problem. Optimization Letters, DOI 10.1007/s11590-011-0426-8, published on line 30 November 2011, Springer-Verlag 2011.

[4] Andre R. S. Amaral (2012), The Corridor Allocation Problem. Computers and Operations Research 39 (2012), pp. 3325-3330.

[5] Andre R. S. Amaral (2013), A Parallel Ordering Problem in Facilities Layout. Computers and Operations Research, Vol. 40, Issue 12, December 2013, pp. 2930-2939.

[6] Miguel F. Anjos, Anthony Vannelli, Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes. INFORMS Journal on Computing, Vol. 20, No. 4, Fall 2008, pp. 611-617.

[7] Miguel F. Anjos (2012), FLPLIB–Facility Layout Database. Retrieved on September 25 2012 from http://www.gerad.ca/files/Sites/Anjos/indexFR.html

[8] Miguel F. Anjos, FLPLIB–Facility Layout Database. http://www.miguelanjos.com.

[9] S. S. Heragu, A. Kusiak. Efficient Models for the Facility Layout Problem. European Journal of Operational Research 53 (1), 1991, pp. 1-13.

[10] Philipp Hungerlaender, Miguel F. Anjos (January 2012), A Semidefinite Optimization Approach to Free-Space Multi-Row Facility Layout. Les Cahiers du GERAD. Retrieved from http://www.gerad.ca/fichiers/cahiers/G-2012-03.pdf

[11] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[12] C. E. Nugent, T. E Vollmann, J. Ruml (1968), An Experimental Comparison of Techniques for the Assignment of Facilities to Locations. Operations Research, Vol. 16, pp. 150-173.

[13] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64

[14] Jsun Yui Wong (2012, September 17). A General Nonlinear Integer/Discrete/Continuous Programming Solver Applied to the Corridor Allocation Problem with Eleven Facilities, Third Edition. https://myblogsubstance.typepad.com/substance/2012/09/index.html/

[15] Ginger Yen (2008). Cutting-Plane Separation Strategies for Semidefinite Programming Models to Solve Single-Row Facility Layout Problems. A Master Thesis Presented to the University of Waterloo. UWSpace. http://hdl.handle.net/10012/4104.

Wednesday, May 10, 2017

Solving a k-Parallel Row Ordering Problem of 5 Rows and 36 Facilities

Jsun Yui Wong

Adapting to the computer program in Wong [14], the following computer program seeks to solve a k-parallel row ordering problem (k-PROP) of 36 facilities with the first four rows each having 7 facilities and the fifth row having 8 facilities. See Amaral [5]. The data for flows and lengths used here can be found in Yen [15, pages 101-105 for flows and page 106 for lengths].

0 REM DEFDBL A-Z

1 DEFINT I, J, K, X

2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(39), J44(2002), J(99), AA(99), HR(39), HHR(39), Y(39), C(39), CC(39), RA(99)

3 DIM HS(49, 49)

4 DIM PE(49, 49)

5 DIM SD(49, 49)

9 HR(31) = 2: HR(32) = 2: HR(33) = 2: HR(34) = 1: HR(35) = 2: HR(36) = 2

17 HR(1) = 2: HR(2) = 1: HR(3) = 2: HR(4) = 1: HR(5) = 2: HR(6) = 3: HR(7) = 2: HR(8) = 2: HR(9) = 2

18 HR(10) = 2: HR(11) = 2: HR(12) = 2: HR(13) = 3: HR(14) = 2: HR(15) = 3: HR(16) = 3: HR(17) = 2: HR(18) = 2: HR(19) = 2: HR(20) = 2

29 HR(21) = 2: HR(22) = 2: HR(23) = 1

30 HR(24) = 3: HR(25) = 2: HR(26) = 2: HR(27) = 2: HR(28) = 1: HR(29) = 2: HR(30) = 2

31 FOR IL = 1 TO 36

32 FOR JL = 1 TO 36

33 READ HS(IL, JL)

34 NEXT JL

35 NEXT IL

41 DATA 9999,0,0,2,1,7,9,0,4,75,7,12,22,7,1,0,0,0,0,23,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

42 DATA 0,9999,0,0,0,0,4,16,0,8,0,0,16,0,0,0,0,6,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

43 DATA 0,0,9999,0,0,4,16,20,0,0,0,0,20,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
44 DATA 2,0,0,9999,29,5,18,47,23,2,4,0,48,0,4,0,0,0,0,25,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
45 DATA 1,0,0,29,9999,18,12,25,0,0,4,0,25,0,3,0,0,0,0,18,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0
46 DATA 7,0,4,5,18,9999,4,2,0,1,23,2,19,0,0,0,0,0,2,19,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
47 DATA 9,4,16,18,12,4,9999,0,14,72,7,8,39,8,40,8,0,8,4,7,0,0,0,0,0,0,0,28,8,0,0,0,0,0,0,0
48 DATA 0,16,20,47,25,2,0,9999,10,71,2,0,0,0,0,0,0,41,0,0,0,0,0,0,0,0,7,8,0,0,0,0,0,0,0,0
49 DATA 4,0,0,23,0,0,14,10,9999,14,0,0,18,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
50 DATA 75,8,0,2,0,1,72,71,14,9999,11,1,17,0,1,0,0,17,0,15,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
51 DATA 7,0,0,4,4,23,7,2,0,11,9999,316,33,8,2,0,0,0,8,34,0,0,6,0,0,0,10,0,0,6,0,0,0,0,0,0
52 DATA 12,0,0,0,0,2,8,0,0,1,316,9999,157,25,4,0,0,1,0,0,0,0,0,0,22,0,1,0,0,0,0,0,0,0,0,0
53 DATA 22,16,20,48,25,19,39,0,18,17,33,157,9999,11,6,0,0,6,0,5,8,3,10,0,0,0,9,11,2,0,0,1,0,0,0,0
54 DATA 7,0,0,0,0,0,8,0,0,0,8,25,11,9999,3,0,0,1,1,21,0,1,0,2,0,0,5,0,0,3,2,5,5,4,0,0
55 DATA 1,0,0,4,3,0,40,0,0,1,2,4,6,3,9999,19,0,2,2,12,0,0,0,0,0,0,0,7,3,0,0,0,0,0,0,0
56 DATA 0,0,0,0,0,0,8,0,0,0,0,0,0,0,19,9999,0,6,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
57 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9999,40,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
58 DATA 0,6,0,0,0,0,8,41,0,17,0,1,6,1,2,6,40,9999,0,26,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
59 DATA 0,0,0,0,0,2,4,0,0,0,8,0,0,1,2,0,0,0,9999,13,9,0,7,0,0,0,0,27,16,3,0,20,0,4,0,0
60 DATA 23,4,4,25,18,19,7,0,0,15,34,0,5,21,12,1,0,26,13,9999,11,4,36,0,0,0,16,18,9,10,1,28,6,2,0,0
61 DATA 0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,9,11,9999,36,6,0,8,0,2,0,0,0,0,0,0,0,0,0
62 DATA 0,0,0,0,3,0,0,0,0,0,0,0,3,1,0,0,0,0,0,4,36,9999,0,0,0,0,4,0,0,0,0,0,0,0,0,0
63 DATA 0,0,0,0,0,0,0,0,0,0,6,0,10,0,0,0,0,0,7,36,6,0,9999,0,0,12,9,0,0,0,0,0,0,0,0,0
64 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,9999,26,0,5,0,0,0,0,0,0,0,0,0
65 DATA 0,0,0,0,0,0,0,0,0,0,0,22,0,0,0,0,0,0,0,0,8,0,0,26,9999,35,2,0,0,0,0,0,0,0,0,0
66 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,12,0,35,9999,4,0,0,0,0,0,0,0,0,0
67 DATA 0,0,0,0,0,0,0,7,0,0,10,1,9,5,0,0,0,0,0,16,2,4,9,5,2,4,9999,0,0,0,0,0,0,0,0,0
68 DATA 0,0,0,0,0,0,28,8,0,0,0,0,11,0,7,0,0,0,27,18,0,0,0,0,0,0,0,9999,10,22,4,6,4,12,0,0
69 DATA 0,0,0,0,0,0,8,0,0,0,0,0,2,0,3,0,0,0,16,9,0,0,0,0,0,0,0,10,9999,19,12,0,0,0,0,0
70 DATA 0,0,0,0,0,0,0,0,0,0,6,0,0,3,0,0,0,0,3,10,0,0,0,0,0,0,0,22,19,9999,19,4,5,8,0,0
71 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,1,0,0,0,0,0,0,0,4,12,19,9999,0,3,13,0,0
72 DATA 0,0,0,0,0,0,0,0,0,0,0,0,1,5,0,0,0,0,20,28,0,0,0,0,0,0,0,6,0,4,0,9999,18,24,0,0
73 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,5,0,0,0,0,0,6,0,0,0,0,0,0,0,4,0,5,3,18,9999,20,0,0
74 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,4,2,0,0,0,0,0,0,0,12,0,8,13,24,20,9999,0,0

75 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9999,0

76 DATA 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,9999

88 FOR JJJJ = -32000 TO 32000

89 RANDOMIZE JJJJ

90 M = -1D+37

91 FOR J44 = 1 TO 36

93 A(J44) = J44

94 NEXT J44

121 REM IF RND < 1 / 4 THEN IMAX = 17 ELSE IF RND < 1 / 3 THEN IMAX = 17 ELSE IF RND < 1 / 2 THEN IMAX = 17 ELSE IMAX = 17

128 FOR I = 1 TO 10000

129 FOR KKQQ = 1 TO 36

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

133 III = 1 + FIX(RND * 36)

134 JJJ = 1 + FIX(RND * 36)

137 X(III) = A(JJJ)
139 X(JJJ) = A(III)

231 FOR J44 = 1 TO 36

233 FOR J45 = 1 TO 36

234 IF X(J44) = J45 THEN HHR(J44) = HR(J44) ELSE GOTO 238

237 Y(J45) = J44

238 NEXT J45
253 FOR ISE20 = 1 TO 7

254 C(ISE20) = .5 * HHR(Y(ISE20))

258 FOR ISE2000 = ISE20 + 1 TO 7

259 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

263 NEXT ISE2000

269 NEXT ISE20

386 FOR ISE20 = 8 TO 14

387 C(ISE20) = .5 * HHR(Y(ISE20))

308 FOR ISE2000 = ISE20 + 1 TO 14

389 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

390 NEXT ISE2000

391 NEXT ISE20

396 FOR ISE20 = 15 TO 21

397 C(ISE20) = .5 * HHR(Y(ISE20))

398 FOR ISE2000 = ISE20 + 1 TO 21

399 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

400 NEXT ISE2000

401 NEXT ISE20

403 FOR ISE20 = 22 TO 28

404 C(ISE20) = .5 * HHR(Y(ISE20))

405 FOR ISE2000 = ISE20 + 1 TO 28

406 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

407 NEXT ISE2000

408 NEXT ISE20
413 FOR ISE20 = 29 TO 36

414 C(ISE20) = .5 * HHR(Y(ISE20))

415 FOR ISE2000 = ISE20 + 1 TO 36

416 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

417 NEXT ISE2000

418 NEXT ISE20

499 NEXT J44

601 FOR J77 = 1 TO 7

605 IF X(J77) > 7 THEN 1670

609 NEXT J77

611 FOR J77 = 8 TO 14

615 IF X(J77) > 14 THEN 1670

619 NEXT J77

621 FOR J77 = 15 TO 21

622 IF X(J77) > 21 THEN 1670

629 NEXT J77

631 FOR J77 = 22 TO 28

635 IF X(J77) > 28 THEN 1670

639 NEXT J77

641 FOR J77 = 29 TO 36

645 IF X(J77) > 36 THEN 1670

649 NEXT J77

811 PROD = 0

812 FOR J44 = 1 TO 36

813 FOR J45 = J44 + 1 TO 36

814 PROD = PROD - HS(Y(J44), Y(J45)) * ABS(C(J44) - C(J45))

815 NEXT J45

816 NEXT J44

822 P = PROD

1111 IF P <= M THEN 1670

1452 M = P

1453 FOR KLX = 1 TO 36

1454 CC(KLX) = C(KLX)

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1559 IIMAX = IMAX

1657 GOTO 128

1670 NEXT I

1889 IF M < -7270 THEN 1999

1891 PRINT A(1), A(2), A(3), A(4), A(5)

1892 PRINT A(6), A(7), A(8), A(9), A(10)

1893 PRINT A(11), A(12), A(13), A(14), A(15)

1894 PRINT A(16), A(17), A(18), A(19), A(20)

1896 PRINT A(21), A(22), A(23), A(24), A(25)

1897 PRINT A(26), A(27), A(28), A(29), A(30)

1898 PRINT A(31), A(32), A(33), A(34), A(35), A(36), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [13]. The complete output through JJJJ=-31962 is shown below:

5 2 1 4 6
7 3 9 8 10
13 12 11 14 18
15 16 17 20 19
21 28 26 22 23
24 27 25 32 33
31 35 36 34 30
29 -7259.5 -31980

5 2 1 4 6
7 3 9 8 10
13 12 11 14 18
15 16 17 20 19
21 28 26 22 23
24 27 25 32 33
31 35 36 34 29
30 -7259.5 -31976

5 2 1 4 6
7 3 9 8 10
13 12 11 14 18
15 16 17 20 19
21 28 26 22 23
24 27 25 32 33
31 35 36 34 29
30 -7259.5 -31962

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 [13], the wall-clock time for obtaining the output through JJJJ=-31962 was two minutes and a half.

Acknowledgment

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

References

[1] Andre R. S. Amaral (2006), On the Exact Solution of a Facility Layout Problem. European Journal of Operational Research 173 (2006), pp. 508-518.

[2] Andre R. S. Amaral (2008), An Exact Approach to the One-Dimensional Facility Layout Problem. Operations Research, Vol. 56, No. 4 (July-August, 2008), pp. 1026-1033.

[3] Andre R. S. Amaral (2011), Optimal Solutions for the Double Row Layout Problem. Optimization Letters, DOI 10.1007/s11590-011-0426-8, published on line 30 November 2011, Springer-Verlag 2011.

[4] Andre R. S. Amaral (2012), The Corridor Allocation Problem. Computers and Operations Research 39 (2012), pp. 3325-3330.

[5] Andre R. S. Amaral (2013), A Parallel Ordering Problem in Facilities Layout. Computers and Operations Research, Vol. 40, Issue 12, December 2013, pp. 2930-2939.

[6] Miguel F. Anjos, Anthony Vannelli, Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes. INFORMS Journal on Computing, Vol. 20, No. 4, Fall 2008, pp. 611-617.

[7] Miguel F. Anjos (2012), FLPLIB–Facility Layout Database. Retrieved on September 25 2012 from http://www.gerad.ca/files/Sites/Anjos/indexFR.html

[8] Miguel F. Anjos, FLPLIB–Facility Layout Database. http://www.miguelanjos.com.

[9] S. S. Heragu, A. Kusiak. Efficient Models for the Facility Layout Problem. European Journal of Operational Research 53 (1), 1991, pp. 1-13.

[10] Philipp Hungerlaender, Miguel F. Anjos (January 2012), A Semidefinite Optimization Approach to Free-Space Multi-Row Facility Layout. Les Cahiers du GERAD. Retrieved from http://www.gerad.ca/fichiers/cahiers/G-2012-03.pdf

[11] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[12] C. E. Nugent, T. E Vollmann, J. Ruml (1968), An Experimental Comparison of Techniques for the Assignment of Facilities to Locations. Operations Research, Vol. 16, pp. 150-173.

[13] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64

[14] Jsun Yui Wong (2012, September 17). A General Nonlinear Integer/Discrete/Continuous Programming Solver Applied to the Corridor Allocation Problem with Eleven Facilities, Third Edition. https://myblogsubstance.typepad.com/substance/2012/09/index.html/

[15] Ginger Yen (2008). Cutting-Plane Separation Strategies for Semidefinite Programming Models to Solve Single-Row Facility Layout Problems. A Master Thesis Presented to the University of Waterloo.

Monday, May 8, 2017

Solving An Instance of a K=4 Parallel Ordering Problem of Layout of 23 Facilities

Jsun Yui Wong

Adapting to the computer program in Wong [12], the following computer program seeks to solve the parallel row ordering problem (PROP) of 23 facilities with the first three rows each with 6 facilities and the fourth row with 5 facilities; see Amaral [5]. The data can be found in Amaral [5] and Anjos [8].

0 REM DEFDBL A-Z

1 DEFINT I, J, K, X

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), Y(33), C(33), CC(33)

3 DIM HS(49, 49)

4 DIM PE(49, 49)

5 DIM SD(49, 49)

17 HR(1) = 5: HR(2) = 13: HR(3) = 9: HR(4) = 6: HR(5) = 5: HR(6) = 10: HR(7) = 5: HR(8) = 9: HR(9) = 9

18 HR(10) = 5: HR(11) = 8: HR(12) = 12: HR(13) = 8: HR(14) = 11: HR(15) = 11: HR(16) = 8: HR(17) = 10: HR(18) = 6: HR(19) = 8: HR(20) = 14

29 HR(21) = 12: HR(22) = 8: HR(23) = 11

31 FOR IL = 1 TO 23

32 FOR JL = 1 TO 23

33 READ HS(IL, JL)

34 NEXT JL

35 NEXT IL

42 DATA 9999,3,2,0,0,2,10,5,0,5,2,5,0,0,2,0,5,6,3,0,1,10,0

43 DATA 3,9999,4,0,10,4,0,0,2,2,1,0,5,0,0,0,0,2,0,1,6,1,0

44 DATA 2,4,9999,3,4,0,5,5,5,1,4,1,0,4,0,4,0,6,3,2,5,5,2

45 DATA 0,0,3,9999,0,0,0,2,2,0,6,0,2,5,2,5,1,1,1,1,2,2,4

46 DATA 0,10,4,0,9999,5,2,0,0,0,0,2,0,0,0,0,2,1,0,0,2,0,5

47 DATA 2,4,0,0,5,9999,1,2,2,1,4,10,10,2,5,5,0,5,0,0,0,10,0

48 DATA 10,0,5,0,2,1,9999,10,10,5,10,10,6,0,0,10,2,1,10,1,5,5,2

49 DATA 5,0,5,2,0,2,10,9999,1,3,5,0,0,0,2,4,5,2,10,6,0,5,5

50 DATA 0,2,5,2,0,2,10,1,9999,10,2,1,5,2,0,3,0,2,0,0,4,0,5

51 DATA 5,2,1,0,0,1,5,3,10,9999,5,5,6,0,1,5,5,0,5,2,3,5,0

52 DATA 2,1,4,6,0,4,10,5,2,5,9999,0,0,1,2,1,0,2,0,0,0,6,6

53 DATA 5,0,1,0,2,10,10,0,1,5,0,9999,5,5,2,0,0,0,0,2,0,4,5

54 DATA 0,5,0,2,0,10,6,0,5,6,0,5,9999,2,0,4,2,2,1,0,6,2,1

55 DATA 0,0,4,5,0,2,0,0,2,0,1,5,2,9999,2,1,0,5,3,10,0,0,4

56 DATA 2,0,0,2,0,5,0,2,0,1,2,2,0,2,9999,4,5,1,0,1,0,5,0

57 DATA 0,0,4,5,0,5,10,4,3,5,1,0,4,1,4,9999,0,3,0,2,2,0,2

58 DATA 5,0,0,1,2,0,2,5,0,5,0,0,2,0,5,0,9999,2,2,0,0,0,6

59 DATA 6,2,6,1,1,5,1,2,2,0,2,0,2,5,1,3,2,9999,5,1,2,10,10

60 DATA 3,0,3,1,0,0,10,10,0,5,0,0,1,3,0,0,2,5,9999,0,5,5,1

61 DATA 0,1,2,1,0,0,1,6,0,2,0,2,0,10,1,2,0,1,0,9999,5,2,1

62 DATA 1,6,5,2,2,0,5,0,4,3,0,0,6,0,0,2,0,2,5,5,9999,4,0

63 DATA 10,1,5,2,0,10,5,5,0,5,6,4,2,0,5,0,0,10,5,2,4,9999,5

64 DATA 0,0,2,4,5,0,2,5,5,0,6,5,1,4,0,2,6,10,1,1,0,5,9999

88 FOR JJJJ = -32000 TO 32000

89 RANDOMIZE JJJJ

90 M = -1D+37

91 FOR J44 = 1 TO 23

93 A(J44) = J44

94 NEXT J44

111 REM IF RND < 1 / 4 THEN IMAX = 4 ELSE IF RND < 1 / 3 THEN IMAX = 4 ELSE IF RND < 1 / 2 THEN IMAX = 4 ELSE IMAX = 4

128 FOR I = 1 TO 5000

129 FOR KKQQ = 1 TO 23

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

133 III = 1 + FIX(RND * 23)

134 JJJ = 1 + FIX(RND * 23)

137 X(III) = A(JJJ)

139 X(JJJ) = A(III)

231 FOR J44 = 1 TO 23

233 FOR J45 = 1 TO 23

234 IF X(J44) = J45 THEN HHR(J44) = HR(J44) ELSE GOTO 238

237 Y(J45) = J44

238 NEXT J45

253 FOR ISE20 = 1 TO 6

254 C(ISE20) = .5 * HHR(Y(ISE20))

258 FOR ISE2000 = ISE20 + 1 TO 6

259 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

263 NEXT ISE2000

269 NEXT ISE20

386 FOR ISE20 = 7 TO 12

387 C(ISE20) = .5 * HHR(Y(ISE20))

308 FOR ISE2000 = ISE20 + 1 TO 12

389 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

390 NEXT ISE2000

391 NEXT ISE20

396 FOR ISE20 = 13 TO 18

397 C(ISE20) = .5 * HHR(Y(ISE20))

398 FOR ISE2000 = ISE20 + 1 TO 18

399 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

400 NEXT ISE2000

401 NEXT ISE20

403 FOR ISE20 = 19 TO 23

404 C(ISE20) = .5 * HHR(Y(ISE20))

405 FOR ISE2000 = ISE20 + 1 TO 23

406 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

407 NEXT ISE2000

408 NEXT ISE20

409 NEXT J44

601 FOR J77 = 1 TO 6

605 IF X(J77) > 6 THEN 1670

609 NEXT J77

611 FOR J77 = 7 TO 12

615 IF X(J77) > 12 THEN 1670

619 NEXT J77

621 FOR J77 = 13 TO 18

622 IF X(J77) > 18 THEN 1670

629 NEXT J77

631 FOR J77 = 19 TO 23

635 IF X(J77) > 23 THEN 1670

639 NEXT J77

811 PROD = 0

812 FOR J44 = 1 TO 23

813 FOR J45 = J44 + 1 TO 23

814 PROD = PROD - HS(Y(J44), Y(J45)) * ABS(C(J44) - C(J45))

815 NEXT J45

816 NEXT J44

1082 P = PROD

1111 IF P <= M THEN 1670

1452 M = P

1453 FOR KLX = 1 TO 23

1454 CC(KLX) = C(KLX)

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1559 IIMAX = IMAX

1657 GOTO 128

1670 NEXT I

1891 PRINT A(1), A(2), A(3), A(4), A(5)

1892 PRINT A(6), A(7), A(8), A(9), A(10)

1893 PRINT A(11), A(12), A(13), A(14), A(15)

1894 PRINT A(16), A(17), A(18), A(19), A(20), A(21), A(22), A(23)

1991 PRINT CC(1), CC(2), CC(3), CC(4), CC(5)

1992 PRINT CC(6), CC(7), CC(8), CC(9), CC(10)

1993 PRINT CC(11), CC(12), CC(13), CC(14), CC(15)

1994 PRINT CC(16), CC(17), CC(18), CC(19), CC(20), CC(21), CC(22), CC(23)

1995 PRINT M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [11]. The output through JJJJ=-31993 is summarized below:

.
.
.
-8537 -32000

.
.
.
-8537 -31999

.
.
.
-8591 -31998

.
.
.
-8431 -31997

.
.
.
-8591 -31996

.
.
.
-8537 -31995

.
.
.
-8673 -31994

3 6 2 1 5
4 9 8 11 10
7 12 17 18 14
16 13 15 20 23
22 21 19
45 37.5 30.5 23 15.5
6.5 44 35.5 28.5 23.5
16.5 6 49 38.5 30
23 15 5.5 47.5 38
30 20 7
-8203 -31993

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 [11], the wall-clock time for obtaining the output through JJJJ=-31993 was 15 seconds.

Acknowledgment

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

References

[1] Andre R. S. Amaral (2006), On the Exact Solution of a Facility Layout Problem. European Journal of Operational Research 173 (2006), pp. 508-518.

[2] Andre R. S. Amaral (2008), An Exact Approach to the One-Dimensional Facility Layout Problem. Operations Research, Vol. 56, No. 4 (July-August, 2008), pp. 1026-1033.

[3] Andre R. S. Amaral (2011), Optimal Solutions for the Double Row Layout Problem. Optimization Letters, DOI 10.1007/s11590-011-0426-8, published on line 30 November 2011, Springer-Verlag 2011.

[4] Andre R. S. Amaral (2012), The Corridor Allocation Problem. Computers and Operations Research 39 (2012), pp. 3325-3330.

[5] Andre R. S. Amaral (2013), A Parallel Ordering Problem in Facilities Layout. Computers and Operations Research, Vol. 40, Issue 12, December 2013, pp. 2930-2939.

[6] Miguel F. Anjos, Anthony Vannelli, Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes. INFORMS Journal on Computing, Vol. 20, No. 4, Fall 2008, pp. 611-617.

[7] Miguel F. Anjos (2012), FLPLIB--Facility Layout Database. Retrieved on September 25 2012 from www.gerad.ca/files/Sites/Anjos/indexFR.html

[8] Miguel F. Anjos, FLPLIB--Facility Layout Database. www.miguelanjos.com.

[9] Philipp Hungerlaender, Miguel F. Anjos (January 2012), A Semidefinite Optimization Approach to Free-Space Multi-Row Facility Layout. Les Cahiers du GERAD. Retrieved from www.gerad.ca/fichiers/cahiers/G-2012-03.pdf

[10] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[11] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64

[12] Jsun Yui Wong (2012, September 17). A General Nonlinear Integer/Discrete/Continuous Programming Solver Applied to the Corridor Allocation Problem with Eleven Facilities, Third Edition. https://myblogsubstance.typepad.com/substance/2012/09/index.html/

Monday, April 24, 2017

Solving a Single-Row Facility Layout Problem of 30 Facilities of Heragu and Kusiak

Jsun Yui Wong

Adapting to the computer program in Wong [14], the following computer program seeks to solve the single-row facility layout problem of 30 facilities in Heragu and Kusiak [9, Page 9, Problem 8, Table 1]. The lengths are specified below in line 17 through line 30. The 30x30 matrix of line 42 through line 71 below is based on a matrix in Nugent, Vollmann, and Ruml [12].

0 REM DEFDBL A-Z

1 DEFINT I, J, K, X

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), Y(33), C(33), CC(33)

3 DIM HS(49, 49)

4 DIM PE(49, 49)

5 DIM SD(49, 49)

17 HR(1) = 3: HR(2) = 9: HR(3) = 3: HR(4) = 7: HR(5) = 3: HR(6) = 7: HR(7) = 5: HR(8) = 9: HR(9) = 6

18 HR(10) = 5: HR(11) = 3: HR(12) = 9: HR(13) = 3: HR(14) = 7: HR(15) = 3: HR(16) = 7: HR(17) = 5: HR(18) = 9: HR(19) = 6: HR(20) = 5

29 HR(21) = 3: HR(22) = 9: HR(23) = 3

30 HR(24) = 7: HR(25) = 3: HR(26) = 7: HR(27) = 5: HR(28) = 9: HR(29) = 6: HR(30) = 5

31 FOR IL = 1 TO 30

32 FOR JL = 1 TO 30

33 READ HS(IL, JL)

34 NEXT JL

35 NEXT IL
36 REM

42 DATA 9999,3,2,0,0,2,10,5,0,5,2,5,0,0,2,0,5,6,3,0,1,10,0,10,2,1,1,1,0,1

43 DATA 3,9999,4,0,10,4,0,0,2,2,1,0,5,0,0,0,0,2,0,1,6,1,0,1,2,2,5,1,10,5

44 DATA 2,4,9999,3,4,0,5,5,5,1,4,1,0,4,0,4,0,6,3,2,5,5,2,1,0,0,3,1,0,2

45 DATA 0,0,3,9999,0,0,0,2,2,0,6,0,2,5,2,5,1,1,1,1,2,2,4,0,2,0,2,2,5,5

46 DATA 0,10,4,0,9999,5,2,0,0,0,0,2,0,0,0,0,2,1,0,0,2,0,5,1,0,2,1,0,2,1

47 DATA 2,4,0,0,5,9999,1,2,2,1,4,10,10,2,5,5,0,5,0,0,0,10,0,0,0,4,0,10,1,1

48 DATA 10,0,5,0,2,1,9999,10,10,5,10,10,6,0,0,10,2,1,10,1,5,5,2,3,5,0,2,0,1,3

49 DATA 5,0,5,2,0,2,10,9999,1,3,5,0,0,0,2,4,5,2,10,6,0,5,5,2,5,0,5,5,0,2

50 DATA 0,2,5,2,0,2,10,1,9999,10,2,1,5,2,0,3,0,2,0,0,4,0,5,2,0,5,2,2,5,2

51 DATA 5,2,1,0,0,1,5,3,10,9999,5,5,6,0,1,5,5,0,5,2,3,5,0,5,2,10,10,1,5,2

52 DATA 2,1,4,6,0,4,10,5,2,5,9999,0,0,1,2,1,0,2,0,0,0,6,6,0,4,5,3,2,2,10

53 DATA 5,0,1,0,2,10,10,0,1,5,0,9999,5,5,2,0,0,0,0,2,0,4,5,10,1,0,0,0,0,1

54 DATA 0,5,0,2,0,10,6,0,5,6,0,5,9999,2,0,4,2,2,1,0,6,2,1,5,5,0,0,1,5,5

55 DATA 0,0,4,5,0,2,0,0,2,0,1,5,2,9999,2,1,0,5,3,10,0,0,4,2,0,0,4,2,5,5

56 DATA 2,0,0,2,0,5,0,2,0,1,2,2,0,2,9999,4,5,1,0,1,0,5,0,2,0,0,5,1,1,0

57 DATA 0,0,4,5,0,5,10,4,3,5,1,0,4,1,4,9999,0,3,0,2,2,0,2,0,5,0,5,2,5,10

58 DATA 5,0,0,1,2,0,2,5,0,5,0,0,2,0,5,0,9999,2,2,0,0,0,6,5,3,5,0,0,5,1

59 DATA 6,2,6,1,1,5,1,2,2,0,2,0,2,5,1,3,2,9999,5,1,2,10,10,4,0,0,5,0,0,0

60 DATA 3,0,3,1,0,0,10,10,0,5,0,0,1,3,0,0,2,5,9999,0,5,5,1,0,5,2,1,2,10,10

61 DATA 0,1,2,1,0,0,1,6,0,2,0,2,0,10,1,2,0,1,0,9999,5,2,1,3,1,5,6,5,5,3

62 DATA 1,6,5,2,2,0,5,0,4,3,0,0,6,0,0,2,0,2,5,5,9999,4,0,1,0,0,0,5,0,0

63 DATA 10,1,5,2,0,10,5,5,0,5,6,4,2,0,5,0,0,10,5,2,4,9999,5,0,4,4,5,0,2,5

64 DATA 0,0,2,4,5,0,2,5,5,0,6,5,1,4,0,2,6,10,1,1,0,5,9999,0,4,4,1,0,2,2

65 DATA 10,1,1,0,1,0,3,2,2,5,0,10,5,2,2,0,5,4,0,3,1,0,0,9999,5,5,0,1,0,0

66 DATA 2,2,0,2,0,0,5,5,0,2,4,1,5,0,0,5,3,0,5,1,0,4,4,5,9999,1,0,10,1,0

67 DATA 1,2,0,0,2,4,0,0,5,10,5,0,0,0,0,0,5,0,2,5,0,4,4,5,1,9999,0,0,0,0

68 DATA 1,5,3,2,1,0,2,5,2,10,3,0,0,4,5,5,0,5,1,6,0,5,1,0,0,0,9999,0,0,10

69 DATA 1,1,1,2,0,10,0,5,2,1,2,0,1,2,1,2,0,0,2,5,5,0,0,1,10,0,0,9999,2,2

70 DATA 0,10,0,5,2,1,1,0,5,5,2,0,5,5,1,5,5,0,10,5,0,2,2,0,1,0,0,2,9999,2

71 DATA 1,5,2,5,1,1,3,2,2,2,10,1,5,5,0,10,1,0,10,3,0,5,2,0,0,0,10,2,2,9999

87 REM

88 FOR JJJJ = -32000 TO 32000

89 RANDOMIZE JJJJ

90 M = -1D+37

91 FOR J44 = 1 TO 30

93 A(J44) = J44

94 NEXT J44

111 IF RND < 1 / 4 THEN IMAX = 30 ELSE IF RND < 1 / 3 THEN IMAX = 30 ELSE IF RND < 1 / 2 THEN IMAX = 30 ELSE IMAX = 30

128 FOR I = 1 TO 10000

129 FOR KKQQ = 1 TO 30

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

133 III = 1 + FIX(RND * 30)

134 JJJ = 1 + FIX(RND * 30)

137 X(III) = A(JJJ)

139 X(JJJ) = A(III)

231 FOR J44 = 1 TO 30

233 FOR J45 = 1 TO 30

234 IF X(J44) = J45 THEN HHR(J44) = HR(J44) ELSE GOTO 238

237 Y(J45) = J44

238 NEXT J45

253 FOR ISE20 = 1 TO IMAX

254 C(ISE20) = .5 * HHR(Y(ISE20))

258 FOR ISE2000 = ISE20 + 1 TO IMAX

259 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

263 NEXT ISE2000

269 NEXT ISE20

386 FOR ISE20N = IMAX + 1 TO 30

387 C(ISE20N) = .5 * HHR(Y(ISE20N))

388 FOR ISE2000N = ISE20N + 1 TO 30

389 C(ISE20N) = C(ISE20N) + HHR(Y(ISE2000N))

390 NEXT ISE2000N

391 NEXT ISE20N

395 NEXT J44

401 FOR J77 = 1 TO 30

405 IF X(J77) > 30 THEN 1670

409 NEXT J77

411 PROD = 0

412 FOR J44 = 1 TO 30

413 FOR J45 = J44 + 1 TO 30

414 PROD = PROD - HS(Y(J44), Y(J45)) * ABS(C(J44) - C(J45))

415 NEXT J45

416 NEXT J44

422 P = PROD

1111 IF P <= M THEN 1670

1452 M = P

1453 FOR KLX = 1 TO 30

1454 CC(KLX) = C(KLX)

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1559 IIMAX = IMAX

1657 GOTO 128

1670 NEXT I

1889 IF M < -44970 THEN 1999

1891 PRINT A(1), A(2), A(3), A(4), A(5)

1892 PRINT A(6), A(7), A(8), A(9), A(10)

1893 PRINT A(11), A(12), A(13), A(14), A(15)

1894 PRINT A(16), A(17), A(18), A(19), A(20)

1896 PRINT A(21), A(22), A(23), A(24), A(25)

1897 PRINT A(26), A(27), A(28), A(29), A(30)

1929 PRINT M, JJJJ, A(1), A(2), A(3)

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [13]. The complete output through JJJJ=-31705 is shown below:

10 1 18 29 2
6 17 25 15 14
19 4 13 28 8
22 7 9 24 27
16 11 12 5 20
3 21 30 26 23
-44965 -31886 10 1 18

10 1 18 29 2
6 17 25 15 14
19 4 13 28 8
22 7 9 24 27
16 11 12 5 20
3 21 30 26 23
-44965 -31710 10 1 18

10 1 18 29 2
6 17 25 15 14
19 4 13 28 8
22 7 9 24 27
16 11 12 5 20
3 21 30 26 23
-44965 -31705 10 1 18

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 [13], the wall-clock time for obtaining the output through JJJJ=-31705 was 38 minutes.

Acknowledgment

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

References

[1] Andre R. S. Amaral (2006), On the Exact Solution of a Facility Layout Problem. European Journal of Operational Research 173 (2006), pp. 508-518.

[2] Andre R. S. Amaral (2008), An Exact Approach to the One-Dimensional Facility Layout Problem. Operations Research, Vol. 56, No. 4 (July-August, 2008), pp. 1026-1033.

[3] Andre R. S. Amaral (2011), Optimal Solutions for the Double Row Layout Problem. Optimization Letters, DOI 10.1007/s11590-011-0426-8, published on line 30 November 2011, Springer-Verlag 2011.

[4] Andre R. S. Amaral (2012), The Corridor Allocation Problem. Computers and Operations Research 39 (2012), pp. 3325-3330.

[5] Andre R. S. Amaral (2013), A Parallel Ordering Problem in Facilities Layout. Computers and Operations Research, Vol. 40, Issue 12, December 2013, pp. 2930-2939.

[6] Miguel F. Anjos, Anthony Vannelli, Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes. INFORMS Journal on Computing, Vol. 20, No. 4, Fall 2008, pp. 611-617.

[7] Miguel F. Anjos (2012), FLPLIB--Facility Layout Database. Retrieved on September 25 2012 from www.gerad.ca/files/Sites/Anjos/indexFR.html

[8] Miguel F. Anjos, FLPLIB--Facility Layout Database. www.miguelanjos.com.

[9] S. S.Heragu, A. Kusiak. Efficient Models for the Facility Layout Problem. European Journal of Operational Research, 53 (1), 1991, pp. 1-13.

[10] Philipp Hungerlaender, Miguel F. Anjos (January 2012), A Semidefinite Optimization Approach to Free-Space Multi-Row Facility Layout. Les Cahiers du GERAD. Retrieved from www.gerad.ca/fichiers/cahiers/G-2012-03.pdf

[11] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[12] C. E. Nugent, T. E Vollmann, J. Ruml (1968), An Experimental Comparison of Techniques for the Assignment of Facilities to Locations. Operations Research, Vol. 16, pp. 150-173.

[13] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64

[14] Jsun Yui Wong (2012, September 17). A General Nonlinear Integer/Discrete/Continuous Programming Solver Applied to the Corridor Allocation Problem with Eleven Facilities, Third Edition. https://myblogsubstance.typepad.com/substance/2012/09/index.html/

Tuesday, April 18, 2017

Solving Another Instance of a Parallel Ordering Problem of 23-Facility Layout

Jsun Yui Wong

Adapting to the computer program in Wong [12], the following computer program seeks to solve the parallel row ordering problem (PROP) of 23 facilities with the first row of 4 facilities and the second row of 19 facilities in Amaral [5, p. 2938, Table A4]. The data can be found in Amaral [5] and Anjos [8]. This is the instance {P23_c, L n/5 ]}, Amaral [5, p. 2938].

0 REM DEFDBL A-Z

1 DEFINT I, J, K, X

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), Y(33), C(33), CC(33)

3 DIM HS(49, 49)

4 DIM PE(49, 49)

5 DIM SD(49, 49)

17 HR(1) = 5: HR(2) = 13: HR(3) = 9: HR(4) = 6: HR(5) = 5: HR(6) = 10: HR(7) = 5: HR(8) = 9: HR(9) = 9

18 HR(10) = 5: HR(11) = 8: HR(12) = 12: HR(13) = 8: HR(14) = 11: HR(15) = 11: HR(16) = 8: HR(17) = 10: HR(18) = 6: HR(19) = 8: HR(20) = 14

29 HR(21) = 12: HR(22) = 8: HR(23) = 11

31 FOR IL = 1 TO 23

32 FOR JL = 1 TO 23

33 READ HS(IL, JL)

34 NEXT JL

35 NEXT IL

42 DATA 9999,3,2,0,0,2,10,5,0,5,2,5,0,0,2,0,5,6,3,0,1,10,0

43 DATA 3,9999,4,0,10,4,0,0,2,2,1,0,5,0,0,0,0,2,0,1,6,1,0

44 DATA 2,4,9999,3,4,0,5,5,5,1,4,1,0,4,0,4,0,6,3,2,5,5,2

45 DATA 0,0,3,9999,0,0,0,2,2,0,6,0,2,5,2,5,1,1,1,1,2,2,4

46 DATA 0,10,4,0,9999,5,2,0,0,0,0,2,0,0,0,0,2,1,0,0,2,0,5

47 DATA 2,4,0,0,5,9999,1,2,2,1,4,10,10,2,5,5,0,5,0,0,0,10,0

48 DATA 10,0,5,0,2,1,9999,10,10,5,10,10,6,0,0,10,2,1,10,1,5,5,2

49 DATA 5,0,5,2,0,2,10,9999,1,3,5,0,0,0,2,4,5,2,10,6,0,5,5

50 DATA 0,2,5,2,0,2,10,1,9999,10,2,1,5,2,0,3,0,2,0,0,4,0,5

51 DATA 5,2,1,0,0,1,5,3,10,9999,5,5,6,0,1,5,5,0,5,2,3,5,0

52 DATA 2,1,4,6,0,4,10,5,2,5,9999,0,0,1,2,1,0,2,0,0,0,6,6

53 DATA 5,0,1,0,2,10,10,0,1,5,0,9999,5,5,2,0,0,0,0,2,0,4,5

54 DATA 0,5,0,2,0,10,6,0,5,6,0,5,9999,2,0,4,2,2,1,0,6,2,1

55 DATA 0,0,4,5,0,2,0,0,2,0,1,5,2,9999,2,1,0,5,3,10,0,0,4

56 DATA 2,0,0,2,0,5,0,2,0,1,2,2,0,2,9999,4,5,1,0,1,0,5,0

57 DATA 0,0,4,5,0,5,10,4,3,5,1,0,4,1,4,9999,0,3,0,2,2,0,2

58 DATA 5,0,0,1,2,0,2,5,0,5,0,0,2,0,5,0,9999,2,2,0,0,0,6

59 DATA 6,2,6,1,1,5,1,2,2,0,2,0,2,5,1,3,2,9999,5,1,2,10,10

60 DATA 3,0,3,1,0,0,10,10,0,5,0,0,1,3,0,0,2,5,9999,0,5,5,1

61 DATA 0,1,2,1,0,0,1,6,0,2,0,2,0,10,1,2,0,1,0,9999,5,2,1

62 DATA 1,6,5,2,2,0,5,0,4,3,0,0,6,0,0,2,0,2,5,5,9999,4,0

63 DATA 10,1,5,2,0,10,5,5,0,5,6,4,2,0,5,0,0,10,5,2,4,9999,5

64 DATA 0,0,2,4,5,0,2,5,5,0,6,5,1,4,0,2,6,10,1,1,0,5,9999

88 FOR JJJJ = -32000 TO 32033

89 RANDOMIZE JJJJ

90 M = -1D+37

91 FOR J44 = 1 TO 23

93 A(J44) = J44

94 NEXT J44

111 IF RND < 1 / 4 THEN IMAX = 4 ELSE IF RND < 1 / 3 THEN IMAX = 4 ELSE IF RND < 1 / 2 THEN IMAX = 4 ELSE IMAX = 4

128 FOR I = 1 TO 5000

129 FOR KKQQ = 1 TO 23

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

133 III = 1 + FIX(RND * 23)

134 JJJ = 1 + FIX(RND * 23)

137 X(III) = A(JJJ)

139 X(JJJ) = A(III)

231 FOR J44 = 1 TO 23

233 FOR J45 = 1 TO 23

234 IF X(J44) = J45 THEN HHR(J44) = HR(J44) ELSE GOTO 238

237 Y(J45) = J44

238 NEXT J45

253 FOR ISE20 = 1 TO IMAX

254 C(ISE20) = .5 * HHR(Y(ISE20))

258 FOR ISE2000 = ISE20 + 1 TO IMAX

259 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

263 NEXT ISE2000

269 NEXT ISE20

386 FOR ISE20N = IMAX + 1 TO 23

387 C(ISE20N) = .5 * HHR(Y(ISE20N))

388 FOR ISE2000N = ISE20N + 1 TO 23

389 C(ISE20N) = C(ISE20N) + HHR(Y(ISE2000N))

390 NEXT ISE2000N

391 NEXT ISE20N

395 NEXT J44

401 FOR J77 = 1 TO 4

405 IF X(J77) > 4 THEN 1670

409 NEXT J77

411 PROD = 0

412 FOR J44 = 1 TO 23

413 FOR J45 = J44 + 1 TO 23

414 PROD = PROD - HS(Y(J44), Y(J45)) * ABS(C(J44) - C(J45))

415 NEXT J45

416 NEXT J44

422 P = PROD

1111 IF P <= M THEN 1670

1452 M = P

1453 FOR KLX = 1 TO 23

1454 CC(KLX) = C(KLX)

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1559 IIMAX = IMAX

1657 GOTO 128

1670 NEXT I

1889 IF M < -27563 THEN 1999

1891 PRINT A(1), A(2), A(3), A(4), A(5)

1892 PRINT A(6), A(7), A(8), A(9), A(10)

1893 PRINT A(11), A(12), A(13), A(14), A(15)

1894 PRINT A(16), A(17), A(18), A(19), A(20), A(21), A(22), A(23)

1895 GOTO 1919

1896 PRINT A(26), A(27), A(28), A(29), A(30)

1905 PRINT CC(1), CC(2), CC(3), CC(4), CC(5)

1906 PRINT CC(6), CC(7), CC(8), CC(9)

1919 PRINT M, JJJJ, IIMAX, A(1), A(2)

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [11]. The complete output through
JJJJ=-31959 is shown below:

1 4 3 2 22
11 17 14 21 18
16 9 20 6 7
19 8 12 15 5
23 13 10
-27553 -31990 4 1 4

1 4 3 2 22
11 17 14 21 18
16 9 20 6 7
19 8 12 15 5
23 13 10
-27553 -31979 4 1 4

1 4 3 2 22
11 17 15 21 18
14 9 20 6 7
19 8 12 16 5
23 13 10
-27563 -31959 4 1 4

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 [11], the wall-clock time for obtaining the output through JJJJ=-31959 was 65 seconds.

Acknowledgment

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

References

[1] Andre R. S. Amaral (2006), On the Exact Solution of a Facility Layout Problem. European Journal of Operational Research 173 (2006), pp. 508-518.

[2] Andre R. S. Amaral (2008), An Exact Approach to the One-Dimensional Facility Layout Problem. Operations Research, Vol. 56, No. 4 (July-August, 2008), pp. 1026-1033.

[3] Andre R. S. Amaral (2011), Optimal Solutions for the Double Row Layout Problem. Optimization Letters, DOI 10.1007/s11590-011-0426-8, published on line 30 November 2011, Springer-Verlag 2011.

[4] Andre R. S. Amaral (2012), The Corridor Allocation Problem. Computers and Operations Research 39 (2012), pp. 3325-3330.

[5] Andre R. S. Amaral (2013), A Parallel Ordering Problem in Facilities Layout. Computers and Operations Research, Vol. 40, Issue 12, December 2013, pp. 2930-2939.

[6] Miguel F. Anjos, Anthony Vannelli, Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes. INFORMS Journal on Computing, Vol. 20, No. 4, Fall 2008, pp. 611-617.

[7] Miguel F. Anjos (2012), FLPLIB--Facility Layout Database. Retrieved on September 25 2012 from www.gerad.ca/files/Sites/Anjos/indexFR.html

[8] Miguel F. Anjos, FLPLIB--Facility Layout Database. www.miguelanjos.com.

[9] Philipp Hungerlaender, Miguel F. Anjos (January 2012), A Semidefinite Optimization Approach to Free-Space Multi-Row Facility Layout. Les Cahiers du GERAD. Retrieved from www.gerad.ca/fichiers/cahiers/G-2012-03.pdf

[10] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[11] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64

[12] Jsun Yui Wong (2012, September 17). A General Nonlinear Integer/Discrete/Continuous Programming Solver Applied to the Corridor Allocation Problem with Eleven Facilities, Third Edition. https://myblogsubstance.typepad.com/substance/2012/09/index.html/

Monday, April 17, 2017

Solving a Parallel Ordering Problem of 23-Facility Layout

Jsun Yui Wong

Adapting to the computer program in Wong [12], the following computer program seeks to solve the parallel row ordering problem (PROP) of 23 facilities with the first row of 4 facilities and the second row of 19 facilities from Amaral [5, p. 2938, Table A4]. The data can be found from Amaral [5] and Anjos [8]. This is the instance {P23_a, L n/5 ]}, Amaral [5, p. 2938].

0 REM DEFDBL A-Z

1 DEFINT I, J, K, X, A

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), Y(33), C(33), CC(33)

3 DIM HS(49, 49)

4 DIM PE(49, 49)

5 DIM SD(49, 49)

17 HR(1) = 3: HR(2) = 9: HR(3) = 3: HR(4) = 7: HR(5) = 3: HR(6) = 7: HR(7) = 5: HR(8) = 9: HR(9) = 6

18 HR(10) = 5: HR(11) = 3: HR(12) = 9: HR(13) = 3: HR(14) = 7: HR(15) = 3: HR(16) = 7: HR(17) = 5: HR(18) = 9: HR(19) = 6: HR(20) = 5

29 HR(21) = 3: HR(22) = 9: HR(23) = 3

31 FOR IL = 1 TO 23

32 FOR JL = 1 TO 23

33 READ HS(IL, JL)

34 NEXT JL

35 NEXT IL

42 DATA 9999,3,2,0,0,2,10,5,0,5,2,5,0,0,2,0,5,6,3,0,1,10,0

43 DATA 3,9999,4,0,10,4,0,0,2,2,1,0,5,0,0,0,0,2,0,1,6,1,0

44 DATA 2,4,9999,3,4,0,5,5,5,1,4,1,0,4,0,4,0,6,3,2,5,5,2

45 DATA 0,0,3,9999,0,0,0,2,2,0,6,0,2,5,2,5,1,1,1,1,2,2,4

46 DATA 0,10,4,0,9999,5,2,0,0,0,0,2,0,0,0,0,2,1,0,0,2,0,5

47 DATA 2,4,0,0,5,9999,1,2,2,1,4,10,10,2,5,5,0,5,0,0,0,10,0

48 DATA 10,0,5,0,2,1,9999,10,10,5,10,10,6,0,0,10,2,1,10,1,5,5,2

49 DATA 5,0,5,2,0,2,10,9999,1,3,5,0,0,0,2,4,5,2,10,6,0,5,5

50 DATA 0,2,5,2,0,2,10,1,9999,10,2,1,5,2,0,3,0,2,0,0,4,0,5

51 DATA 5,2,1,0,0,1,5,3,10,9999,5,5,6,0,1,5,5,0,5,2,3,5,0

52 DATA 2,1,4,6,0,4,10,5,2,5,9999,0,0,1,2,1,0,2,0,0,0,6,6

53 DATA 5,0,1,0,2,10,10,0,1,5,0,9999,5,5,2,0,0,0,0,2,0,4,5

54 DATA 0,5,0,2,0,10,6,0,5,6,0,5,9999,2,0,4,2,2,1,0,6,2,1

55 DATA 0,0,4,5,0,2,0,0,2,0,1,5,2,9999,2,1,0,5,3,10,0,0,4

56 DATA 2,0,0,2,0,5,0,2,0,1,2,2,0,2,9999,4,5,1,0,1,0,5,0

57 DATA 0,0,4,5,0,5,10,4,3,5,1,0,4,1,4,9999,0,3,0,2,2,0,2

58 DATA 5,0,0,1,2,0,2,5,0,5,0,0,2,0,5,0,9999,2,2,0,0,0,6

59 DATA 6,2,6,1,1,5,1,2,2,0,2,0,2,5,1,3,2,9999,5,1,2,10,10

60 DATA 3,0,3,1,0,0,10,10,0,5,0,0,1,3,0,0,2,5,9999,0,5,5,1

61 DATA 0,1,2,1,0,0,1,6,0,2,0,2,0,10,1,2,0,1,0,9999,5,2,1

62 DATA 1,6,5,2,2,0,5,0,4,3,0,0,6,0,0,2,0,2,5,5,9999,4,0

63 DATA 10,1,5,2,0,10,5,5,0,5,6,4,2,0,5,0,0,10,5,2,4,9999,5

64 DATA 0,0,2,4,5,0,2,5,5,0,6,5,1,4,0,2,6,10,1,1,0,5,9999

88 FOR JJJJ = -32000 TO 32000

89 RANDOMIZE JJJJ

90 M = -1D+37

91 FOR J44 = 1 TO 23

93 A(J44) = J44

94 NEXT J44

111 IF RND < 1 / 4 THEN IMAX = 4 ELSE IF RND < 1 / 3 THEN IMAX = 4 ELSE IF RND < 1 / 2 THEN IMAX = 4 ELSE IMAX = 4

128 FOR I = 1 TO 5000

129 FOR KKQQ = 1 TO 23

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

133 III = 1 + FIX(RND * 23)

134 JJJ = 1 + FIX(RND * 23)

137 X(III) = A(JJJ)

139 X(JJJ) = A(III)

231 FOR J44 = 1 TO 23

233 FOR J45 = 1 TO 23

234 IF X(J44) = J45 THEN HHR(J44) = HR(J44) ELSE GOTO 238

237 Y(J45) = J44

238 NEXT J45

253 FOR ISE20 = 1 TO IMAX

254 C(ISE20) = .5 * HHR(Y(ISE20))

258 FOR ISE2000 = ISE20 + 1 TO IMAX

259 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))

263 NEXT ISE2000

269 NEXT ISE20

386 FOR ISE20N = IMAX + 1 TO 23

387 C(ISE20N) = .5 * HHR(Y(ISE20N))

388 FOR ISE2000N = ISE20N + 1 TO 23

389 C(ISE20N) = C(ISE20N) + HHR(Y(ISE2000N))

390 NEXT ISE2000N

391 NEXT ISE20N

395 NEXT J44

401 FOR J77 = 1 TO 4

405 IF X(J77) > 4 THEN 1670

409 NEXT J77

411 PROD = 0

412 FOR J44 = 1 TO 23

413 FOR J45 = J44 + 1 TO 23

414 PROD = PROD - HS(Y(J44), Y(J45)) * ABS(C(J44) - C(J45))

415 NEXT J45

416 NEXT J44

422 P = PROD

1111 IF P <= M THEN 1670

1452 M = P

1453 FOR KLX = 1 TO 23

1454 CC(KLX) = C(KLX)

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1559 IIMAX = IMAX

1657 GOTO 128

1670 NEXT I

1889 IF M < -18730 THEN 1999

1891 PRINT A(1), A(2), A(3), A(4), A(5)

1892 PRINT A(6), A(7), A(8), A(9), A(10)

1893 PRINT A(11), A(12), A(13), A(14), A(15)

1894 PRINT A(16), A(17), A(18), A(19), A(20), A(21), A(22), A(23)

1895 GOTO 1919

1896 PRINT A(26), A(27), A(28), A(29), A(30)

1905 PRINT CC(1), CC(2), CC(3), CC(4), CC(5)

1906 PRINT CC(6), CC(7), CC(8), CC(9)

1919 PRINT M, JJJJ, IIMAX, A(1), A(2)

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [11]. The complete output through JJJJ=-31973 is shown below:

1 4 2 3 22
8 15 21 12 13
16 7 11 5 9
10 23 19 20 6
14 17 18
-18725 -31996 4 1 4

1 4 2 3 22
8 15 17 12 13
18 7 11 5 9
10 23 21 16 6
14 19 20
-18619 -31988 4 1 4

1 4 2 3 22
8 15 17 12 13
18 7 11 5 9
10 23 21 16 6
14 19 20
-18619 -31973 4 1 4

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 [11], the wall-clock time for obtaining the output through JJJJ=-31973 was one minute.

Acknowledgment

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

References

[1] Andre R. S. Amaral (2006), On the Exact Solution of a Facility Layout Problem. European Journal of Operational Research 173 (2006), pp. 508-518.

[2] Andre R. S. Amaral (2008), An Exact Approach to the One-Dimensional Facility Layout Problem. Operations Research, Vol. 56, No. 4 (July-August, 2008), pp. 1026-1033.

[3] Andre R. S. Amaral (2011), Optimal Solutions for the Double Row Layout Problem. Optimization Letters, DOI 10.1007/s11590-011-0426-8, published on line 30 November 2011, Springer-Verlag 2011.

[4] Andre R. S. Amaral (2012), The Corridor Allocation Problem. Computers and Operations Research 39 (2012), pp. 3325-3330.

[5] Andre R. S. Amaral (2013), A Parallel Ordering Problem in Facilities Layout. Computers and Operations Research, Vol. 40, Issue 12, December 2013, pp. 2930-2939.

[6] Miguel F. Anjos, Anthony Vannelli, Computing Globally Optimal Solutions for Single-Row Layout Problems Using Semidefinite Programming and Cutting Planes. INFORMS Journal on Computing, Vol. 20, No. 4, Fall 2008, pp. 611-617.

[7] Miguel F. Anjos (2012), FLPLIB--Facility Layout Database. Retrieved on September 25 2012 from www.gerad.ca/files/Sites/Anjos/indexFR.html

[8] Miguel F. Anjos, FLPLIB--Facility Layout Database. www.miguelanjos.com.

[9] Philipp Hungerlaender, Miguel F. Anjos (January 2012), A Semidefinite Optimization Approach to Free-Space Multi-Row Facility Layout. Les Cahiers du GERAD. Retrieved from www.gerad.ca/fichiers/cahiers/G-2012-03.pdf

[10] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

[11] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64

[12] Jsun Yui Wong (2012, September 17). A General Nonlinear Integer/Discrete/Continuous Programming Solver Applied to the Corridor Allocation Problem with Eleven Facilities, Third Edition. https://myblogsubstance.typepad.com/substance/2012/09/index.html/