Jsun Yui Wong
The computer program listed below seeks to solve the hospital layout problem in Elshafei (1977).
0 DEFSNG A-Z
3 DEFINT I,J,K
4 DIM X(466),A(466),L(466),K(466),P(466),B(466),S(466),T(111)
6 DIM TBM(33,33)
11 TBM(1,1)=999:TBM(1,2)=12:TBM(1,3)=36:TBM(1,4)=28:TBM(1,5)=52:TBM(1,6)=44:TBM(1,7)=110:TBM(1,8)=126:TBM(1,9)=94:TBM(1,10)=63
12 TBM(1,11)=130:TBM(1,12)=102:TBM(1,13)=65:TBM(1,14)=98:TBM(1,15)=132:TBM(1,16)=132:TBM(1,17)=126:TBM(1,18)=120:TBM(1,19)=126
13 TBM(2,1)=12:TBM(2,2)=999:TBM(2,3)=24:TBM(2,4)=75:TBM(2,5)=82:TBM(2,6)=75:TBM(2,7)=108:TBM(2,8)=70:TBM(2,9)=124:TBM(2,10)=86
14 TBM(2,11)=93:TBM(2,12)=106:TBM(2,13)=58:TBM(2,14)=124:TBM(2,15)=161:TBM(2,16)=161:TBM(2,17)=70:TBM(2,18)=64:TBM(2,19)=70
15 TBM(3,1)=36:TBM(3,2)=24:TBM(3,3)=999:TBM(3,4)=47:TBM(3,5)=71:TBM(3,6)=47:TBM(3,7)=110:TBM(3,8)=73:TBM(3,9)=126:TBM(3,10)=71
16 TBM(3,11)=95:TBM(3,12)=110:TBM(3,13)=46:TBM(3,14)=127:TBM(3,15)=163:TBM(3,16)=163:TBM(3,17)=73:TBM(3,18)=67:TBM(3,19)=73
17 TBM(4,1)=28:TBM(4,2)=75:TBM(4,3)=47:TBM(4,4)=999:TBM(4,5)=42:TBM(4,6)=34:TBM(4,7)=148:TBM(4,8)=111:TBM(4,9)=160:TBM(4,10)=52
18 TBM(4,11)=94:TBM(4,12)=148:TBM(4,13)=49:TBM(4,14)=117:TBM(4,15)=104:TBM(4,16)=109:TBM(4,17)=111:TBM(4,18)=105:TBM(4,19)=111
19 TBM(5,1)=52:TBM(5,2)=82:TBM(5,3)=71:TBM(5,4)=42:TBM(5,5)=999:TBM(5,6)=42:TBM(5,7)=125:TBM(5,8)=136:TBM(5,9)=102:TBM(5,10)=22
20 TBM(5,11)=73:TBM(5,12)=125:TBM(5,13)=32:TBM(5,14)=94:TBM(5,15)=130:TBM(5,16)=130:TBM(5,17)=136:TBM(5,18)=130:TBM(5,19)=136
21 TBM(6,1)=44:TBM(6,2)=75:TBM(6,3)=47:TBM(6,4)=34:TBM(6,5)=42:TBM(6,6)=999:TBM(6,7)=148:TBM(6,8)=111:TBM(6,9)=162:TBM(6,10)=52
22 TBM(6,11)=96:TBM(6,12)=148:TBM(6,13)=49:TBM(6,14)=117:TBM(6,15)=152:TBM(6,16)=152:TBM(6,17)=111:TBM(6,18)=105:TBM(6,19)=111
23 TBM(7,1)=110:TBM(7,2)=108:TBM(7,3)=110:TBM(7,4)=148:TBM(7,5)=125:TBM(7,6)=148:TBM(7,7)=999:TBM(7,8)=46:TBM(7,9)=46:TBM(7,10)=136
24 TBM(7,11)=47:TBM(7,12)=30:TBM(7,13)=108:TBM(7,14)=51:TBM(7,15)=79:TBM(7,16)=79:TBM(7,17)=46:TBM(7,18)=47:TBM(7,19)=41
25 TBM(8,1)=126:TBM(8,2)=70:TBM(8,3)=73:TBM(8,4)=111:TBM(8,5)=136:TBM(8,6)=111:TBM(8,7)=46:TBM(8,8)=999:TBM(8,9)=69:TBM(8,10)=141
26 TBM(8,11)=63:TBM(8,12)=46:TBM(8,13)=119:TBM(8,14)=68:TBM(8,15)=121:TBM(8,16)=121:TBM(8,17)=27:TBM(8,18)=24:TBM(8,19)=36
27 TBM(9,1)=94:TBM(9,2)=124:TBM(9,3)=126:TBM(9,4)=160:TBM(9,5)=102:TBM(9,6)=162:TBM(9,7)=46:TBM(9,8)=69:TBM(9,9)=999:TBM(9,10)=102
28 TBM(9,11)=34:TBM(9,12)=45:TBM(9,13)=84:TBM(9,14)=23:TBM(9,15)=80:TBM(9,16)=80:TBM(9,17)=69:TBM(9,18)=64:TBM(9,19)=51
29 TBM(10,1)=63:TBM(10,2)=86:TBM(10,3)=71:TBM(10,4)=52:TBM(10,5)=22:TBM(10,6)=52:TBM(10,7)=136:TBM(10,8)=141:TBM(10,9)=102:TBM(10,10)=999
30 TBM(10,11)=64:TBM(10,12)=118:TBM(10,13)=29:TBM(10,14)=95:TBM(10,15)=131:TBM(10,16)=131:TBM(10,17)=141:TBM(10,18)=135:TBM(10,19)=141
31 TBM(11,1)=130:TBM(11,2)=93:TBM(11,3)=95:TBM(11,4)=94:TBM(11,5)=73:TBM(11,6)=96:TBM(11,7)=47:TBM(11,8)=63:TBM(11,9)=34:TBM(11,10)=64
32 TBM(11,11)=999:TBM(11,12)=47:TBM(11,13)=56:TBM(11,14)=54:TBM(11,15)=94:TBM(11,16)=94:TBM(11,17)=63:TBM(11,18)=46:TBM(11,19)=24
33 TBM(12,1)=102:TBM(12,2)=106:TBM(12,3)=110:TBM(12,4)=148:TBM(12,5)=125:TBM(12,6)=148:TBM(12,7)=30:TBM(12,8)=46:TBM(12,9)=45:TBM(12,10)=118
34 TBM(12,11)=47:TBM(12,12)=999:TBM(12,13)=100:TBM(12,14)=51:TBM(12,15)=89:TBM(12,16)=89:TBM(12,17)=46:TBM(12,18)=40:TBM(12,19)=36
35 TBM(13,1)=659:TBM(13,2)=58:TBM(13,3)=46:TBM(13,4)=49:TBM(13,5)=32:TBM(13,6)=49:TBM(13,7)=108:TBM(13,8)=119:TBM(13,9)=84:TBM(13,10)=29
36 TBM(13,11)=56:TBM(13,12)=100:TBM(13,13)=999:TBM(13,14)=77:TBM(13,15)=113:TBM(13,16)=113:TBM(13,17)=119:TBM(13,18)=113:TBM(13,19)=119
37 TBM(14,1)=98:TBM(14,2)=124:TBM(14,3)=127:TBM(14,4)=117:TBM(14,5)=94:TBM(14,6)=117:TBM(14,7)=51:TBM(14,8)=68:TBM(14,9)=23:TBM(14,10)=95
38 TBM(14,11)=54:TBM(14,12)=51:TBM(14,13)=77:TBM(14,14)=999:TBM(14,15)=79:TBM(14,16)=79:TBM(14,17)=68:TBM(14,18)=62:TBM(14,19)=51
39 TBM(15,1)=132:TBM(15,2)=161:TBM(15,3)=163:TBM(15,4)=104:TBM(15,5)=130:TBM(15,6)=152:TBM(15,7)=79:TBM(15,8)=121:TBM(15,9)=80:TBM(15,10)=131
40 TBM(15,11)=94:TBM(15,12)=89:TBM(15,13)=113:TBM(15,14)=79:TBM(15,15)=999:TBM(15,16)=10:TBM(15,17)=113:TBM(15,18)=107:TBM(15,19)=119
41 TBM(16,1)=132:TBM(16,2)=161:TBM(16,3)=163:TBM(16,4)=109:TBM(16,5)=130:TBM(16,6)=152:TBM(16,7)=79:TBM(16,8)=121:TBM(16,9)=80:TBM(16,10)=131
42 TBM(16,11)=94:TBM(16,12)=89:TBM(16,13)=113:TBM(16,14)=79:TBM(16,15)=10:TBM(16,16)=999:TBM(16,17)=113:TBM(16,18)=107:TBM(16,19)=119
43 TBM(17,1)=126:TBM(17,2)=70:TBM(17,3)=73:TBM(17,4)=111:TBM(17,5)=136:TBM(17,6)=111:TBM(17,7)=46:TBM(17,8)=27:TBM(17,9)=69:TBM(17,10)=141
44 TBM(17,11)=63:TBM(17,12)=46:TBM(17,13)=119:TBM(17,14)=68:TBM(17,15)=113:TBM(17,16)=113:TBM(17,17)=999:TBM(17,18)=6:TBM(17,19)=24
45 TBM(18,1)=120:TBM(18,2)=64:TBM(18,3)=67:TBM(18,4)=105:TBM(18,5)=130:TBM(18,6)=105:TBM(18,7)=47:TBM(18,8)=24:TBM(18,9)=64:TBM(18,10)=135
46 TBM(18,11)=46:TBM(18,12)=40:TBM(18,13)=113:TBM(18,14)=62:TBM(18,15)=107:TBM(18,16)=107:TBM(18,17)=6:TBM(18,18)=999:TBM(18,19)=12
47 TBM(19,1)=126:TBM(19,2)=70:TBM(19,3)=73:TBM(19,4)=111:TBM(19,5)=136:TBM(19,6)=111:TBM(19,7)=41:TBM(19,8)=36:TBM(19,9)=51:TBM(19,10)=141
48 TBM(19,11)=24:TBM(19,12)=36:TBM(19,13)=119:TBM(19,14)=51:TBM(19,15)=119:TBM(19,16)=119:TBM(19,17)=24:TBM(19,18)=12:TBM(19,19)=999
65 FOR JJJJ=-32000 TO 32000
74 RANDOMIZE JJJJ
76 M=-1D+17
81 A(1)=1:A(2)=2:A(3)=3:A(4)=4:A(5)=5:A(6)=6:A(7)=7:A(8)=8:A(9)=9:A(10)=10
82 A(11)=11:A(12)=12:A(13)=13:A(14)=14:A(15)=15:A(16)=16:A(17)=17:A(18)=18:A(19)=19
126 IMAR=10+FIX(RND*3000)
128 FOR I=1 TO IMAR
129 FOR KK=1 TO 19
131 X(KK)=A(KK)
132 NEXT KK
330 IJM=1+FIX(RND*19)
331 IJN=1+FIX(RND*19)
333 X(IJM)=A(IJN):X(IJN)=A(IJM)
401 T(1)=76687!*TBM(X(1),X(2))
402 T(2)=415*TBM(X(1),X(4))
403 T(3)=545*TBM(X(1),X(5))
404 T(4)=819*TBM(X(1),X(6))
405 T(5)=135*TBM(X(1),X(7))
406 T(6)=1368*TBM(X(1),X(8))
407 T(7)=819*TBM(X(1),X(9))
408 T(8)=5630*TBM(X(1),X(10))
409 T(9)=3432*TBM(X(1),X(12))
410 T(10)=9082*TBM(X(1),X(13))
411 T(11)=1503*TBM(X(1),X(14))
412 T(12)=13732*TBM(X(1),X(17))
413 T(13)=1368*TBM(X(1),X(18))
414 T(14)=1783*TBM(X(1),X(19))
415 T(15)=40951!*TBM(X(2),X(3))
416 T(16)=4118*TBM(X(2),X(4))
417 T(17)=5767*TBM(X(2),X(5))
418 T(18)=2055*TBM(X(2),X(6))
419 T(19)=1917*TBM(X(2),X(7))
420 T(20)=2746*TBM(X(2),X(8))
421 T(21)=1097*TBM(X(2),X(9))
422 T(22)=5712*TBM(X(2),X(10))
423 T(23)=268*TBM(X(2),X(14))
424 T(24)=1373*TBM(X(2),X(16))
425 T(25)=268*TBM(X(2),X(17))
426 T(26)=3848*TBM(X(3),X(4))
427 T(27)=2524*TBM(X(3),X(5))
428 T(28)=3213*TBM(X(3),X(6))
429 T(29)=2072*TBM(X(3),X(7))
430 T(30)=4225*TBM(X(3),X(8))
431 T(31)=566*TBM(X(3),X(9))
432 T(32)=404*TBM(X(3),X(12))
433 T(33)=9372*TBM(X(3),X(13))
434 T(34)=972*TBM(X(3),X(15))
435 T(35)=13538*TBM(X(3),X(17))
436 T(36)=1368*TBM(X(3),X(18))
437 T(37)=256*TBM(X(4),X(5))
438 T(38)=829*TBM(X(4),X(10))
439 T(39)=128*TBM(X(4),X(11))
440 T(40)=47*TBM(X(5),X(9))
441 T(41)=1655*TBM(X(5),X(10))
442 T(42)=287*TBM(X(5),X(11))
443 T(43)=42*TBM(X(5),X(13))
444 T(44)=226*TBM(X(5),X(17))
445 T(45)=926*TBM(X(6),X(10))
446 T(46)=161*TBM(X(6),X(11))
447 T(47)=196*TBM(X(7),X(9))
448 T(48)=1538*TBM(X(7),X(10))
449 T(49)=196*TBM(X(7),X(11))
450 T(50)=301*TBM(X(8),X(11))
451 T(51)=1954*TBM(X(9),X(10))
452 T(52)=418*TBM(X(9),X(11))
453 T(53)=282*TBM(X(10),X(12))
454 T(54)=1686*TBM(X(11),X(12))
455 T(55)=226*TBM(X(11),X(17))
456 T(56)=99999!*TBM(X(15),X(16))
651 P1NEW=0
652 FOR KAU7=1 TO 56
653 P1NEW=P1NEW+T(KAU7)
654 NEXT KAU7
750 P=-P1NEW
1651 IF P<=M THEN 1670
1657 FOR KEW=1 TO 19
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1666 GOTO 128
1670 NEXT I
1890 IF M>-8700000! THEN 1912 ELSE 1999
1912 PRINT A(1),A(2),A(3),A(4),A(5)
1913 PRINT A(6),A(7),A(8),A(9),A(10)
1914 PRINT A(11),A(12),A(13),A(14),A(15)
1915 PRINT A(16),A(17),A(18),A(19)
1927 PRINT M,JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with the IBM basica/D interpreter, and the output produced during the first 5 minutes of running is presented below. (What immediately follows is a manual copy from the computer screen.)
17 18 19 11 12
9 3 14 1 2
10 13 7 5 15
16 8 6 4
-8606274 -31653
17 18 19 11 12
3 4 14 1 2
10 13 7 5 15
16 8 9 6
-8679132 -31568
17 18 19 11 3
14 4 7 1 2
10 13 12 5 15
16 8 9 6
-8679132 -31563
17 18 19 11 12
9 3 14 1 2
10 13 7 5 15
16 8 4 6
-8606274 -31559
Interpreted in accordance with line 1912 through line 1927, the output through JJJJ=-31559 was produced during the first 5 minutes of running on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter.
References
Elshafei, A. N., "Hospital Layout as a Quadratic Assignment Problem," Operational Research Quarterly 28, 167-179 (1977).
Gavett. J. W. and N. V. Plyter, "The Optimal Assignment of Facilities to Locations by Branch and Bound," Operations Research 14, 210-232 (Mar.-Apr. 1966).
Heragu, S. S. Facilities Design, Third Edition. Boca Raton, Florida: CRC Press, 2008.
Land, A. H., "A Problem of Assignment with Inter-Related Costs," Operational Research Quarterly 14, 185-199 (June 1963).
Pierce, J. F. and W. B. Crowston, "Tree-Search Algorithms for Quadratic Assignment Problems," Naval Research Logistics Quarterly, 18, 1-36 (1971).
