Jsun Yui Wong
The complete computer program listed below seeks to solve an eight-department layout problem (Armour and Buffa, 1963). The departmment sizes for department 1 through department 8 are 25x20, 25x20, 35x30, 30x20, 35x20, 60x40, 40x10, and 20x10, respectively; the interdepartmental flows are shown in line 1624 through line 1647 of the following program. The sizes and flows of the first five departments are from Heragu (2008, page 220). Most of the other given flows are based on those of Amaral (2008, page 1032). In order to have integer solutions, these original lengths and widths are multiplied by 4; then these longer lengths and widths are used in line 291 through line 417 of the following program.
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),J(466),HS(99)
6 DIM T(11,11,5),TZ(11,11),TL(33)
65 FOR JJJJ=-32000 TO 32000
74 RANDOMIZE JJJJ
76 M=-1D+17
85 FOR I=1 TO 16
88 A(I)=FIX(RND*1000)
89 NEXT I
126 IMAR=10+FIX(RND*20000)
128 FOR I=1 TO IMAR
129 FOR KK=1 TO 16
131 X(KK)=A(KK)
132 NEXT KK
223 IJL=1+FIX(RND*16)
234 X(IJL)=FIX(RND*1000)
291 HS(1)=ABS(X(1)-X(2))-100
292 HS(2)=ABS(X(1)-X(3))-120
293 HS(3)=ABS(X(1)-X(4))-110
294 HS(4)=ABS(X(1)-X(5))-120
295 HS(5)=ABS(X(1)-X(6))-170
296 HS(6)=ABS(X(1)-X(7))-130
297 HS(7)=ABS(X(1)-X(8))-90
307 HS(8)=ABS(X(2)-X(3))-120
308 HS(9)=ABS(X(2)-X(4))-110
309 HS(10)=ABS(X(2)-X(5))-120
310 HS(11)=ABS(X(2)-X(6))-170
311 HS(12)=ABS(X(2)-X(7))-130
312 HS(13)=ABS(X(2)-X(8))-90
322 HS(14)=ABS(X(3)-X(4))-130
323 HS(15)=ABS(X(3)-X(5))-140
324 HS(16)=ABS(X(3)-X(6))-190
325 HS(17)=ABS(X(3)-X(7))-150
326 HS(18)=ABS(X(3)-X(8))-110
336 HS(19)=ABS(X(4)-X(5))-130
337 HS(20)=ABS(X(4)-X(6))-180
338 HS(21)=ABS(X(4)-X(7))-140
339 HS(22)=ABS(X(4)-X(8))-100
349 HS(23)=ABS(X(5)-X(6))-190
350 HS(24)=ABS(X(5)-X(7))-150
351 HS(25)=ABS(X(5)-X(8))-110
369 HS(26)=ABS(X(6)-X(7))-200
370 HS(27)=ABS(X(6)-X(8))-160
371 HS(28)=ABS(X(7)-X(8))-120
383 HS(29)=ABS(X(9)-X(10))-80
384 HS(30)=ABS(X(9)-X(11))-100
385 HS(31)=ABS(X(9)-X(12))-80
386 HS(32)=ABS(X(9)-X(13))-80
387 HS(33)=ABS(X(9)-X(14))-120
388 HS(34)=ABS(X(9)-X(15))-60
389 HS(35)=ABS(X(9)-X(16))-60
391 HS(36)=ABS(X(10)-X(11))-100
392 HS(37)=ABS(X(10)-X(12))-80
393 HS(38)=ABS(X(10)-X(13))-80
394 HS(39)=ABS(X(10)-X(14))-120
395 HS(40)=ABS(X(10)-X(15))-60
396 HS(41)=ABS(X(10)-X(16))-60
401 HS(42)=ABS(X(11)-X(12))-100
402 HS(43)=ABS(X(11)-X(13))-100
403 HS(44)=ABS(X(11)-X(14))-140
404 HS(45)=ABS(X(11)-X(15))-80
405 HS(46)=ABS(X(11)-X(16))-80
406 HS(47)=ABS(X(12)-X(13))-80
407 HS(48)=ABS(X(12)-X(14))-120
408 HS(49)=ABS(X(12)-X(15))-60
409 HS(50)=ABS(X(12)-X(16))-60
412 HS(51)=ABS(X(13)-X(14))-120
413 HS(52)=ABS(X(13)-X(15))-60
414 HS(53)=ABS(X(13)-X(16))-60
415 HS(54)=ABS(X(14)-X(15))-100
416 HS(55)=ABS(X(14)-X(16))-100
417 HS(56)=ABS(X(15)-X(16))-40
551 IF HS(1)<-.0001 AND HS(29)<-.0001 THEN TL(1)=999999! ELSE TL(1)=0
553 IF HS(2)<-.0001 AND HS(30)<-.0001 THEN TL(2)=999999! ELSE TL(2)=0
554 IF HS(3)<-.0001 AND HS(31)<-.0001 THEN TL(3)=999999! ELSE TL(3)=0
555 IF HS(4)<-.0001 AND HS(32)<-.0001 THEN TL(4)=999999! ELSE TL(4)=0
557 IF HS(5)<-.0001 AND HS(33)<-.0001 THEN TL(5)=999999! ELSE TL(5)=0
559 IF HS(6)<-.0001 AND HS(34)<-.0001 THEN TL(6)=999999! ELSE TL(6)=0
560 IF HS(7)<-.0001 AND HS(35)<-.0001 THEN TL(7)=999999! ELSE TL(7)=0
565 IF HS(8)<-.0001 AND HS(36)<-.0001 THEN TL(8)=999999! ELSE TL(8)=0
568 IF HS(9)<-.0001 AND HS(37)<-.0001 THEN TL(9)=999999! ELSE TL(9)=0
569 IF HS(10)<-.0001 AND HS(38)<-.0001 THEN TL(10)=999999! ELSE TL(10)=0
581 IF HS(11)<-.0001 AND HS(39)<-.0001 THEN TL(10)=999999! ELSE TL(11)=0
582 IF HS(12)<-.0001 AND HS(40)<-.0001 THEN TL(10)=999999! ELSE TL(12)=0
583 IF HS(13)<-.0001 AND HS(41)<-.0001 THEN TL(10)=999999! ELSE TL(13)=0
584 IF HS(14)<-.0001 AND HS(42)<-.0001 THEN TL(10)=999999! ELSE TL(14)=0
585 IF HS(15)<-.0001 AND HS(43)<-.0001 THEN TL(10)=999999! ELSE TL(15)=0
586 IF HS(16)<-.0001 AND HS(44)<-.0001 THEN TL(10)=999999! ELSE TL(16)=0
587 IF HS(17)<-.0001 AND HS(45)<-.0001 THEN TL(10)=999999! ELSE TL(17)=0
588 IF HS(18)<-.0001 AND HS(46)<-.0001 THEN TL(10)=999999! ELSE TL(18)=0
589 IF HS(19)<-.0001 AND HS(47)<-.0001 THEN TL(10)=999999! ELSE TL(19)=0
590 IF HS(20)<-.0001 AND HS(48)<-.0001 THEN TL(10)=999999! ELSE TL(20)=0
591 IF HS(21)<-.0001 AND HS(49)<-.0001 THEN TL(10)=999999! ELSE TL(21)=0
592 IF HS(22)<-.0001 AND HS(50)<-.0001 THEN TL(10)=999999! ELSE TL(22)=0
593 IF HS(23)<-.0001 AND HS(51)<-.0001 THEN TL(10)=999999! ELSE TL(23)=0
594 IF HS(24)<-.0001 AND HS(52)<-.0001 THEN TL(10)=999999! ELSE TL(24)=0
595 IF HS(25)<-.0001 AND HS(53)<-.0001 THEN TL(10)=999999! ELSE TL(25)=0
596 IF HS(26)<-.0001 AND HS(54)<-.0001 THEN TL(10)=999999! ELSE TL(26)=0
597 IF HS(27)<-.0001 AND HS(55)<-.0001 THEN TL(10)=999999! ELSE TL(27)=0
598 IF HS(28)<-.0001 AND HS(56)<-.0001 THEN TL(10)=999999! ELSE TL(28)=0
1611 SUMTL=0
1613 FOR IR=1 TO 28
1615 SUMTL=SUMTL+TL(IR)
1618 NEXT IR
1621 PR1=-10*ABS(X(1)-X(2))-15*ABS(X(1)-X(3))-20*ABS(X(1)-X(4))-0*ABS(X(1)-X(5))-17*ABS(X(1)-X(6))-0*ABS(X(1)-X(7))-6*ABS(X(1)-X(8))
1622 PR2=-30*ABS(X(2)-X(3))-35*ABS(X(2)-X(4))-10*ABS(X(2)-X(5))-32*ABS(X(2)-X(6))-10*ABS(X(2)-X(7))-2*ABS(X(2)-X(8))
1631 PR3=-10*ABS(X(3)-X(4))-20*ABS(X(3)-X(5))-26*ABS(X(3)-X(6))-0*ABS(X(3)-X(7))-10*ABS(X(3)-X(8))
1632 PR4=-15*ABS(X(4)-X(5))-13*ABS(X(4)-X(6))-10*ABS(X(4)-X(7))-10*ABS(X(4)-X(8))
1633 PR5=-19*ABS(X(5)-X(6))-4*ABS(X(5)-X(7))-10*ABS(X(5)-X(8))-20*ABS(X(6)-X(7))-0*ABS(X(6)-X(8))-0*ABS(X(7)-X(8))
1636 REM
1643 PR8=-10*ABS(X(9)-X(10))-15*ABS(X(9)-X(11))-20*ABS(X(9)-X(12))-0*ABS(X(9)-X(13))-17*ABS(X(9)-X(14))-0*ABS(X(9)-X(15))-6*ABS(X(9)-X(16))
1644 PR9=-30*ABS(X(10)-X(11))-35*ABS(X(10)-X(12))-10*ABS(X(10)-X(13))-32*ABS(X(10)-X(14))-10*ABS(X(10)-X(15))-2*ABS(X(10)-X(16))
1645 PR10=-10*ABS(X(11)-X(12))-20*ABS(X(11)-X(13))-26*ABS(X(11)-X(14))-0*ABS(X(11)-X(15))-10*ABS(X(11)-X(16))
1646 PR11=-15*ABS(X(12)-X(13))-13*ABS(X(12)-X(14))-10*ABS(X(12)-X(15))-10*ABS(X(12)-X(16))
1647 PR12=-19*ABS(X(13)-X(14))-4*ABS(X(13)-X(15))-10*ABS(X(13)-X(16))-20*ABS(X(14)-X(15))-0*ABS(X(14)-X(16))-0*ABS(X(15)-X(16))
1650 P=PR1+PR2+PR3+PR4+PR5+PR8+PR9+PR10+PR11+PR12-999*SUMTL
1651 IF P<=M THEN 1670
1657 FOR KEW=1 TO 16
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1662 MM=PR1+PR2+PR3+PR4+PR5+PR7+PR8+PR9+PR10+PR11+PR12
1666 GOTO 128
1670 NEXT I
1890 IF M>-63333! THEN 1912 ELSE 1999
1912 PRINT A(1),A(2),A(3),A(4),A(5)
1914 PRINT A(6),A(7),A(8),A(9),A(10)
1915 PRINT A(11),A(12),A(13),A(14)
1916 PRINT A(15),A(16),MM,M,JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with Microsoft's GW BASIC 3.11 interpreter, and the output through sixteen hours of running is presented below. What immediately follows is a manual copy from the computer screen.
951 851 863 741 723
851 851 741 293 293
393 293 374 133
233 434 -63142 -63142 -29900
283 383 346 493 486
383 383 486 345 345
245 345 265 465
565 205 -62945 -62945 -26755
Interpreted in accordance with line 1912 through line 1916, this output was produced through sixteen hours of running on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter, which is not a compiler.
References
G. C. Armour and E. S. Buffa, "A Heuristic Algorithm and Simulation Approach to Relative Location of Facilities," Management Science 9, 294-309 (1963).
S. S. Heragu. Facilities Design, Third Edition. Boca Raton, Florida: CRC Press, 2008.
A. R. S. Amaral, "An Exact Approach to the One-Dimensional Facility Layout Problem," Operations Research 56, 1026-1033 (2008).
