Jsun Yui Wong
Adapting to the computer in Wong [15], the following computer seeks to solve a k-parallel row ordering problem (k-prop) of 56 facilities. Each row of the first 6 rows has 7 facilities. The 7th row has 14 facilities. See Amara [5]. The flows of the matrix below are from Anjos [9]--see the n=49 case, the last 12 lines of the n=56 case, and the last 12 lines of the n=64 case of the J. Skorin-Kapov section of [9]. The lengths of line 17 through line 32 are the first 56 lengths of the n=60 case in Anjos [8]--see AnKeVa_2005_60dept_set5 of the "Data for medium and large instances" section [8].
One notes that here line 128 is 128 FOR I = 1 TO 2500.
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(59), J44(2002), J(99), AA(99), HR(59), HHR(59), Y(59), C(59), CC(59), RA(99)
3 DIM HS(59, 59)
4 DIM PE(59, 59)
5 DIM SD(59, 59)
17 HR(1) = 34: HR(2) = 40: HR(3) = 48: HR(4) = 25: HR(5) = 3: HR(6) = 12: HR(7) = 40: HR(8) = 3: HR(9) = 18
18 HR(10) = 7: HR(11) = 17: HR(12) = 59: HR(13) = 23: HR(14) = 33: HR(15) = 4: HR(16) = 59: HR(17) = 27: HR(18) = 33: HR(19) = 33: HR(20) = 19
29 HR(21) = 6: HR(22) = 24: HR(23) = 14
30 HR(24) = 38: HR(25) = 2: HR(26) = 59: HR(27) = 14: HR(28) = 22: HR(29) = 46: HR(30) = 6
31 HR(31) = 18: HR(32) = 27: HR(33) = 35: HR(34) = 33: HR(35) = 11: HR(36) = 16
32 HR(37) = 56: HR(38) = 18: HR(39) = 48: HR(40) = 2: HR(41) = 39: HR(42) = 3: HR(43) = 19: HR(44) = 33: HR(45) = 6: HR(46) = 49: HR(47) = 41: HR(48) = 5: HR(49) = 29: HR(50) = 8: HR(51) = 4: HR(52) = 55: HR(53) = 12: HR(54) = 53: HR(55) = 11: HR(56) = 13
33 FOR IL = 1 TO 56
34 FOR JL = 1 TO 56
35 READ HS(IL, JL)
36 NEXT JL
37 NEXT IL
41 DATA 99999,1,2,3,4,5,6,1,2,3,4,5,6,7,2,3,4,5,6,7,8,3,4,5,6,7,8,9,4,5,6,7,8,9,10,5,6,7,8,9,10,11,6,7,8,9,10,11,12,1,1,0,1,1,5,3
42 DATA 1,99999,1,2,3,4,5,2,1,2,3,4,5,6,3,2,3,4,5,6,7,4,3,4,5,6,7,8,5,4,5,6,7,8,9,6,5,6,7,8,9,10,7,6,7,8,9,10,11,5,0,0,0,3,10,0
43 DATA 2,1,99999,1,2,3,4,3,2,1,2,3,4,5,4,3,2,3,4,5,6,5,4,3,4,5,6,7,6,5,4,5,6,7,8,7,6,5,6,7,8,9,8,7,6,7,8,9,10,2,10,0,0,0,0,5
44 DATA 3,2,1,99999,1,2,3,4,3,2,1,2,3,4,5,4,3,2,3,4,5,6,5,4,3,4,5,6,7,6,5,4,5,6,7,8,7,6,5,6,7,8,9,8,7,6,7,8,9,5,10,1,10,10,2,5
45 DATA 4,3,2,1,99999,1,2,5,4,3,2,1,2,3,6,5,4,3,2,3,4,7,6,5,4,3,4,5,8,7,6,5,4,5,6,9,8,7,6,5,6,7,10,9,8,7,6,7,8,10,3,2,0,5,1,5
46 DATA 5,4,3,2,1,99999,1,6,5,4,3,2,1,2,7,6,5,4,3,2,3,8,7,6,5,4,3,4,9,8,7,6,5,4,5,10,9,8,7,6,5,6,11,10,9,8,7,6,7,1,10,5,2,5,5,10
47 DATA 6,5,4,3,2,1,99999,7,6,5,4,3,2,1,8,7,6,5,4,3,2,9,8,7,6,5,4,3,10,9,8,7,6,5,4,11,10,9,8,7,6,5,12,11,10,9,8,7,6,0,0,0,0,1,5,5
48 DATA 1,2,3,4,5,6,7,99999,1,2,3,4,5,6,1,2,3,4,5,6,7,2,3,4,5,6,7,8,3,4,5,6,7,8,9,4,5,6,7,8,9,10,5,6,7,8,9,10,11,10,5,5,5,2,4,5
49 DATA 2,1,2,3,4,5,6,1,99999,1,2,3,4,5,2,1,2,3,4,5,6,3,2,3,4,5,6,7,4,3,4,5,6,7,8,5,4,5,6,7,8,9,6,5,6,7,8,9,10,5,2,0,0,0,0,2
50 DATA 3,2,1,2,3,4,5,2,1,99999,1,2,3,4,3,2,1,2,3,4,5,4,3,2,3,4,5,6,5,4,3,4,5,6,7,6,5,4,5,6,7,8,7,6,5,6,7,8,9,0,1,2,2,2,10,1
51 DATA 4,3,2,1,2,3,4,3,2,1,99999,1,2,3,4,3,2,1,2,3,4,5,4,3,2,3,4,5,6,5,4,3,4,5,6,7,6,5,4,5,6,7,8,7,6,5,6,7,8,5,4,1,2,1,0,1
52 DATA 5,4,3,2,1,2,3,4,3,2,1,99999,1,2,5,4,3,2,1,2,3,6,5,4,3,2,3,4,7,6,5,4,3,4,5,8,7,6,5,4,5,6,9,8,7,6,5,6,7,5,5,0,5,0,1,2
53 DATA 6,5,4,3,2,1,2,5,4,3,2,1,99999,1,6,5,4,3,2,1,2,7,6,5,4,3,2,3,8,7,6,5,4,3,4,9,8,7,6,5,4,5,10,9,8,7,6,5,6,10,5,0,1,10,0,0
54 DATA 7,6,5,4,3,2,1,6,5,4,3,2,1,99999,7,6,5,4,3,2,1,8,7,6,5,4,3,2,9,8,7,6,5,4,3,10,9,8,7,6,5,4,11,10,9,8,7,6,5,0,5,5,10,0,1,2
55 DATA 2,3,4,5,6,7,8,1,2,3,4,5,6,7,99999,1,2,3,4,5,6,1,2,3,4,5,6,7,2,3,4,5,6,7,8,3,4,5,6,7,8,9,4,5,6,7,8,9,10,1,1,5,0,1,0,2
56 DATA 3,2,3,4,5,6,7,2,1,2,3,4,5,6,1,99999,1,2,3,4,5,2,1,2,3,4,5,6,3,2,3,4,5,6,7,4,3,4,5,6,7,8,5,4,5,6,7,8,9,5,5,1,3,5,2,6
57 DATA 4,3,2,3,4,5,6,3,2,1,2,3,4,5,2,1,99999,1,2,3,4,3,2,1,2,3,4,5,4,3,2,3,4,5,6,5,4,3,4,5,6,7,6,5,4,5,6,7,8,0,0,2,1,5,1,5
58 DATA 5,4,3,2,3,4,5,4,3,2,1,2,3,4,3,2,1,99999,1,2,3,4,3,2,1,2,3,4,5,4,3,2,3,4,5,6,5,4,3,4,5,6,7,6,5,4,5,6,7,2,2,0,1,0,10,2
59 DATA 6,5,4,3,2,3,4,5,4,3,2,1,2,3,4,3,2,1,99999,1,2,5,4,3,2,1,2,3,6,5,4,3,2,3,4,7,6,5,4,3,4,5,8,7,6,5,4,5,6,1,5,10,2,5,5,5
60 DATA 7,6,5,4,3,2,3,6,5,4,3,2,1,2,5,4,3,2,1,99999,1,6,5,4,3,2,1,2,7,6,5,4,3,2,3,8,7,6,5,4,3,4,9,8,7,6,5,4,5,0,1,0,5,0,4,5
61 DATA 8,7,6,5,4,3,2,7,6,5,4,3,2,1,6,5,4,3,2,1,99999,7,6,5,4,3,2,1,8,7,6,5,4,3,2,9,8,7,6,5,4,3,10,9,8,7,6,5,4,5,2,3,4,4,4,5
62 DATA 3,4,5,6,7,8,9,2,3,4,5,6,7,8,1,2,3,4,5,6,7,99999,1,2,3,4,5,6,1,2,3,4,5,6,7,2,3,4,5,6,7,8,3,4,5,6,7,8,9,2,2,0,10,0,5,10
63 DATA 4,3,4,5,6,7,8,3,2,3,4,5,6,7,2,1,2,3,4,5,6,1,99999,1,2,3,4,5,2,1,2,3,4,5,6,3,2,3,4,5,6,7,4,3,4,5,6,7,8,2,4,1,0,2,0,1
64 DATA 5,4,3,4,5,6,7,4,3,2,3,4,5,6,3,2,1,2,3,4,5,2,1,99999,1,2,3,4,3,2,1,2,3,4,5,4,3,2,3,4,5,6,5,4,3,4,5,6,7,5,10,10,1,2,1,5
65 DATA 6,5,4,3,4,5,6,5,4,3,2,3,4,5,4,3,2,1,2,3,4,3,2,1,99999,1,2,3,4,3,2,1,2,3,4,5,4,3,2,3,4,5,6,5,4,3,4,5,6,1,0,10,5,0,3,5
66 DATA 7,6,5,4,3,4,5,6,5,4,3,2,3,4,5,4,3,2,1,2,3,4,3,2,1,99999,1,2,5,4,3,2,1,2,3,6,5,4,3,2,3,4,7,6,5,4,3,4,5,2,2,2,3,5,5,2
67 DATA 8,7,6,5,4,3,4,7,6,5,4,3,2,3,6,5,4,3,2,1,2,5,4,3,2,1,99999,1,6,5,4,3,2,1,2,7,6,5,4,3,2,3,8,7,6,5,4,3,4,0,2,0,10,0,2,0
68 DATA 9,8,7,6,5,4,3,8,7,6,5,4,3,2,7,6,5,4,3,2,1,6,5,4,3,2,1,99999,7,6,5,4,3,2,1,8,7,6,5,4,3,2,9,8,7,6,5,4,3,5,2,0,0,0,1,10
69 DATA 4,5,6,7,8,9,10,3,4,5,6,7,8,9,2,3,4,5,6,7,8,1,2,3,4,5,6,7,99999,1,2,3,4,5,6,1,2,3,4,5,6,7,2,3,4,5,6,7,8,1,3,2,3,5,0,1
70 DATA 5,4,5,6,7,8,9,4,3,4,5,6,7,8,3,2,3,4,5,6,7,2,1,2,3,4,5,6,1,99999,1,2,3,4,5,2,1,2,3,4,5,6,3,2,3,4,5,6,7,5,1,1,0,10,3,2
71 DATA 6,5,4,5,6,7,8,5,4,3,4,5,6,7,4,3,2,3,4,5,6,3,2,1,2,3,4,5,2,1,99999,1,2,3,4,3,2,1,2,3,4,5,4,3,2,3,4,5,6,0,0,1,1,0,5,0
72 DATA 7,6,5,4,5,6,7,6,5,4,3,4,5,6,5,4,3,2,3,4,5,4,3,2,1,2,3,4,3,2,1,99999,1,2,3,4,3,2,1,2,3,4,5,4,3,2,3,4,5,0,5,1,4,2,0,2
73 DATA 8,7,6,5,4,5,6,7,6,5,4,3,4,5,6,5,4,3,2,3,4,5,4,3,2,1,2,3,4,3,2,1,99999,1,2,5,4,3,2,1,2,3,6,5,4,3,2,3,4,2,1,10,5,0,0,2
74 DATA 9,8,7,6,5,4,5,8,7,6,5,4,3,4,7,6,5,4,3,2,3,6,5,4,3,2,1,2,5,4,3,2,1,99999,1,6,5,4,3,2,1,2,7,6,5,4,3,2,3,0,4,1,6,0,6,1
75 DATA 10,9,8,7,6,5,4,9,8,7,6,5,4,3,8,7,6,5,4,3,2,7,6,5,4,3,2,1,6,5,4,3,2,1,99999,7,6,5,4,3,2,1,8,7,6,5,4,3,2,4,5,1,1,0,0,2
76 DATA 5,6,7,8,9,10,11,4,5,6,7,8,9,10,3,4,5,6,7,8,9,2,3,4,5,6,7,8,1,2,3,4,5,6,7,99999,1,2,3,4,5,6,1,2,3,4,5,6,7,5,0,5,10,10,0,2
77 DATA 6,5,6,7,8,9,10,5,4,5,6,7,8,9,4,3,4,5,6,7,8,3,2,3,4,5,6,7,2,1,2,3,4,5,6,1,99999,1,2,3,4,5,2,1,2,3,4,5,6,1,2,2,5,0,1,0
78 DATA 7,6,5,6,7,8,9,6,5,4,5,6,7,8,5,4,3,4,5,6,7,4,3,2,3,4,5,6,3,2,1,2,3,4,5,2,1,99999,1,2,3,4,3,2,1,2,3,4,5,1,5,3,10,4,1,3
79 DATA 8,7,6,5,6,7,8,7,6,5,4,5,6,7,6,5,4,3,4,5,6,5,4,3,2,3,4,5,4,3,2,1,2,3,4,3,2,1,99999,1,2,3,4,3,2,1,2,3,4,5,5,0,0,5,0,4
80 DATA 9,8,7,6,5,6,7,8,7,6,5,4,5,6,7,6,5,4,3,4,5,6,5,4,3,2,3,4,5,4,3,2,1,2,3,4,3,2,1,99999,1,2,5,4,3,2,1,2,3,0,0,2,5,0,0,5
81 DATA 10,9,8,7,6,5,6,9,8,7,6,5,4,5,8,7,6,5,4,3,4,7,6,5,4,3,2,3,6,5,4,3,2,1,2,5,4,3,2,1,99999,1,6,5,4,3,2,1,2,0,1,3,0,1,0,0
82 DATA 11,10,9,8,7,6,5,10,9,8,7,6,5,4,9,8,7,6,5,4,3,8,7,6,5,4,3,2,7,6,5,4,3,2,1,6,5,4,3,2,1,99999,7,6,5,4,3,2,1,10,5,2,5,10,5,0
83 DATA 6,7,8,9,10,11,12,5,6,7,8,9,10,11,4,5,6,7,8,9,10,3,4,5,6,7,8,9,2,3,4,5,6,7,8,1,2,3,4,5,6,,7,99999,1,2,3,4,5,6,3,10,2,0,0,2,1
84 DATA 7,6,7,8,9,10,11,6,5,6,7,8,9,10,5,4,5,6,7,8,9,4,3,4,5,6,7,8,3,2,3,4,5,6,7,2,1,2,3,4,5,6,1,99999,1,2,3,4,5,2,2,0,0,10,1,2
85 DATA 8,7,6,7,8,9,10,7,6,5,6,7,8,9,6,5,4,5,6,7,8,5,4,3,4,5,6,7,4,3,2,3,4,5,6,3,2,1,2,3,4,5,2,1,99999,1,2,3,4,10,0,3,5,10,1,0
86 DATA 9,8,7,6,7,8,9,8,7,6,5,6,7,8,7,6,5,4,5,6,7,6,5,4,3,4,5,6,5,4,3,2,3,4,5,4,3,2,1,2,3,4,3,2,1,99999,1,2,3,2,1,5,0,2,5,1
87 DATA 10,9,8,7,6,7,8,9,8,7,6,5,6,7,8,7,6,5,4,5,6,7,6,5,4,3,4,5,6,5,4,3,2,3,4,5,4,3,2,1,2,3,4,3,2,1,99999,1,2,1,1,0,0,2,0,1
88 DATA 11,10,9,8,7,6,7,10,9,8,7,6,5,6,9,8,7,6,5,4,5,8,7,6,5,4,3,4,7,6,5,4,3,2,3,6,5,4,3,2,1,2,5,4,3,2,1,99999,1,0,0,5,0,0,0,1
89 DATA 12,11,10,9,8,7,6,11,10,9,8,7,6,5,10,9,8,7,6,5,4,9,8,7,6,5,4,3,8,7,6,5,4,3,2,7,6,5,4,3,2,1,6,5,4,3,2,1,99999,5,0,0,4,1,10,0
90 DATA 1,5,2,5,10,1,0,10,5,0,5,5,10,0,1,5,0,2,1,0,5,2,2,5,1,2,0,5,1,5,0,0,2,0,4,5,1,1,5,0,0,10,3,2,10,2,1,0,5,99999,5,0,6,0,2,1
91 DATA 1,0,10,10,3,10,0,5,2,1,4,5,5,5,1,5,0,2,5,1,2,2,4,10,0,2,2,2,3,1,0,5,1,4,5,0,2,5,5,0,1,5,10,2,0,1,1,0,0,5,99999,4,2,5,5,2
92 DATA 0,0,0,1,2,5,0,5,0,2,1,0,0,5,5,1,2,0,10,0,3,0,1,10,10,2,0,0,2,1,1,1,10,1,1,5,2,3,0,2,3,2,2,0,3,5,0,5,0,0,4,99999,2,5,5,1
93 DATA 1,0,0,10,0,2,0,5,0,2,2,5,1,10,0,3,1,1,2,5,4,10,0,5,1,3,10,0,3,0,1,4,5,6,1,10,5,10,0,5,0,5,0,0,5,0,0,0,4,6,2,2,99999,2,0,3
94 DATA 1,3,0,10,5,5,1,2,0,2,1,0,10,0,1,5,5,0,5,0,4,0,2,2,0,5,0,0,5,10,0,2,0,0,0,10,0,4,5,0,1,10,0,10,10,2,2,0,1,0,5,5,2,99999,0,3
95 DATA 5,10,0,2,1,5,5,4,0,10,0,1,0,1,0,2,1,10,5,4,4,5,0,1,3,5,2,1,0,3,5,0,0,6,0,0,1,1,0,0,0,5,2,1,1,5,0,0,10,2,5,5,0,0,99999,2
96 DATA 3,0,5,5,5,10,5,5,2,1,1,2,0,2,2,6,5,2,5,5,5,10,1,5,5,2,0,10,1,2,0,2,2,1,2,2,0,3,4,5,0,0,1,2,0,1,1,1,0,1,2,1,3,3,2,99999
99 FOR JJJJ = -32000 TO 32000
116 RANDOMIZE JJJJ
117 M = -1D+37
118 FOR J44 = 1 TO 56
119 A(J44) = J44
120 NEXT J44
128 FOR I = 1 TO 2500
129 FOR KKQQ = 1 TO 56
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 III = 1 + FIX(RND * 56)
134 JJJ = 1 + FIX(RND * 56)
137 X(III) = A(JJJ)
139 X(JJJ) = A(III)
231 FOR J44 = 1 TO 56
233 FOR J45 = 1 TO 56
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 6
253 FOR ISE20 = (RN - 1) * 7 + 1 TO RN * 7
254 C(ISE20) = .5 * HHR(Y(ISE20))
258 FOR ISE2000 = ISE20 + 1 TO RN * 7
259 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))
263 NEXT ISE2000
269 NEXT ISE20
355 NEXT RN
453 FOR ISE20 = 43 TO 56
454 C(ISE20) = .5 * HHR(Y(ISE20))
458 FOR ISE2000 = ISE20 + 1 TO 56
459 C(ISE20) = C(ISE20) + HHR(Y(ISE2000))
463 NEXT ISE2000
469 NEXT ISE20
499 NEXT J44
555 FOR RN = 1 TO 6
601 FOR J77 = (RN - 1) * 7 + 1 TO RN * 7
605 IF X(J77) > RN * 7 THEN 1670
609 NEXT J77
610 NEXT RN
621 FOR J77 = 43 TO 56
625 IF X(J77) > 56 THEN 1670
629 NEXT J77
811 PROD = 0
812 FOR J44 = 1 TO 56
813 FOR J45 = J44 + 1 TO 56
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 56
1454 CC(KLX) = C(KLX)
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1657 GOTO 128
1670 NEXT I
1889 REM IF M < -9999999 THEN 1999
1911 FOR J49 = 1 TO 51 STEP 5
1922 PRINT A(J49), A(J49 + 1), A(J49 + 2), A(J49 + 3), A(J49 + 4)
1933 NEXT J49
1944 PRINT A(56), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [14]. Selected candidate solutions through JJJJ=-23650 are shown below:
2 1 7 5 3
4 6 10 9 11
8 14 12 13 18
21 19 15 20 16
17 22 24 27 25
28 26 23 34 32
30 33 35 29 31
40 42 37 36 38
41 39 52 47 46
44 45 49 50 51
53 56 55 54 48
43 -2.773173E+07 -32000
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.
.
3 1 7 2 4
5 6 10 12 11
13 14 9 8 18
21 20 16 15 19
17 23 25 22 24
28 26 27 35 31
33 30 29 34 32
40 36 37 42 39
41 38 56 55 54
53 52 51 50 49
48 47 46 45 44
43 -429428 -31811
.
.
.
3 1 7 2 4
5 6 10 12 11
13 14 9 8 18
21 20 16 15 19
17 23 25 22 24
28 26 27 35 31
33 30 29 34 32
40 36 37 42 39
41 38 56 55 54
53 52 51 50 49
48 47 46 45 44
43 -429428 -31405
.
.
.
3 1 7 2 4
5 6 10 12 11
13 14 9 8 18
21 20 16 15 19
17 23 25 22 24
28 26 27 35 31
33 30 29 34 32
40 36 37 42 39
41 38 56 55 54
53 52 51 50 49
48 47 46 45 44
43 -429428 -27559
.
.
.
3 1 7 2 4
5 6 10 12 11
13 14 9 8 18
21 20 16 15 19
17 23 25 22 24
28 26 27 35 31
33 30 29 34 32
40 36 37 42 39
41 38 56 55 54
53 52 51 50 49
48 47 46 45 44
43 -429428 -26253
.
.
.
3 1 7 2 4
5 6 10 12 11
13 14 9 8 18
21 20 16 15 19
17 23 25 22 24
28 26 27 35 31
33 30 29 34 32
40 36 37 42 39
41 38 56 55 54
53 52 51 50 49
48 47 46 45 44
43 -429428 -25733
.
.
.
3 1 7 2 4
5 6 10 12 11
13 14 9 8 18
21 20 16 15 19
17 23 25 22 24
28 26 27 35 31
33 30 29 34 32
40 36 37 42 39
41 38 56 55 54
53 52 51 50 49
48 47 46 45 44
43 -429428 -23899
.
.
.
3 1 7 2 4
5 6 10 12 11
13 14 9 8 18
21 20 16 15 19
17 23 25 22 24
28 26 27 35 31
33 30 29 34 32
40 36 37 42 39
41 38 56 55 54
53 52 51 50 49
48 47 46 45 44
43 -429428 -23650
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 [14], the wall-clock time for obtaining the output through JJJJ=-23650 was 25 hours.
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] S. S. Heragu, A. Kusiak. Efficient Models for the Facility Layout Problem. European Journal of Operational Research 53 (1), 1991, pp. 1-13.
[11] 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
[12] 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.
[13] 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.
[14] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64
[15] 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/
[16] 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