Nonlinear Integer/Continuous/Discrete Programming Solver: May 2017

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/