Jsun Yui Wong
The computer program listed below seeks to solve the example in Gavett and Plyter (1966) and in Pierce and Crowston (1971).
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)
6 DIM TBM(11,11)
11 TBM(1,1)=999:TBM(1,2)=6:TBM(1,3)=7:TBM(1,4)=2
12 TBM(2,1)=6:TBM(2,2)=999:TBM(2,3)=5:TBM(2,4)=6
13 TBM(3,1)=7:TBM(3,2)=5:TBM(3,3)=999:TBM(3,4)=1
14 TBM(4,1)=2:TBM(4,2)=6:TBM(4,3)=1:TBM(4,4)=999
51 A(1)=1
52 A(2)=2
53 A(3)=3
54 A(4)=4
65 FOR JJJJ=-32000 TO 32000
74 RANDOMIZE JJJJ
76 M=-1D+17
126 IMAR=10+FIX(RND*0)
128 FOR I=1 TO IMAR
129 FOR KK=1 TO 4
131 X(KK)=A(KK)
132 NEXT KK
330 IJM=1+FIX(RND*4)
331 IJN=1+FIX(RND*4)
333 X(IJM)=A(IJN):X(IJN)=A(IJM)
401 T(1)=28*TBM(X(1),X(2))
402 T(2)=25*TBM(X(1),X(3))
403 T(3)=13*TBM(X(1),X(4))
404 T(4)=15*TBM(X(2),X(3))
405 T(5)=4*TBM(X(2),X(4))
406 T(6)=23*TBM(X(3),X(4))
1589 P=-T(1)-T(2)-T(3)-T(4)-T(5)-T(6)
1651 IF P<=M THEN 1670
1657 FOR KEW=1 TO 4
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1666 GOTO 128
1670 NEXT I
1890 IF M>-417 THEN 1912 ELSE 1999
1912 PRINT A(1),A(2),A(3),A(4)
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 second of running is presented below. (What immediately follows is a manual copy from the computer screen.)
3 2 4 1
-416 -31998
4 1 3 2
-403 -31996
4 1 3 2
-403 -31995
Interpreted in accordance with line 1912 through line 1927, the output through JJJJ=-31995 was produced during the first second of running on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter.
References
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).
