Resource Scheduling w/ Nonstandard Temporal Constraints
/***************************************************************************/
/* */
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: clpe09 */
/* TITLE: Resource Scheduling w/ Nonstandard Temporal Constraints */
/* (clpe09) */
/* PRODUCT: OR */
/* SYSTEM: ALL */
/* KEYS: OR */
/* PROCS: CLP, GANTT, NETDRAW, SQL */
/* DATA: */
/* */
/* SUPPORT: UPDATE: */
/* REF: */
/* MISC: Example 9 from the CLP Procedure chapter of the */
/* Constraint Programming book. */
/* */
/***************************************************************************/
%macro drawPiling(center=49, operator=-, offset=4);
%let barWidth=0.8;
%let yStart=31;
%bar(%sysevalf(¢er &operator &offset), &yStart,
%sysevalf(¢er &operator &offset &operator &barWidth),
%sysevalf(&yStart - &barHeight), black, 0, SOLID);
%mend drawPiling;
%macro drawPilings(operator=-);
%let barHeight=10;
%drawPiling(operator=&operator);
%drawPiling(operator=&operator, offset=9.2);
%let barHeight=12;
%drawPiling(operator=&operator, offset=5.5);
%drawPiling(operator=&operator, offset=7.7);
%let x = 43.4;
%let y = 17;
%label(&x, &y, 'p1', black, 0, 0, 2.5, , 4);
%let x = 57.1;
%label(&x, &y, 'p2', black, 0, 0, 2.5, , 4);
%mend;
%macro drawClay(center=49, operator=-);
%let color = CXFFD090;
%let top = 76;
%poly(%sysevalf(¢er &operator ¢er &operator -1),
&top, &color, MSOLID, 1);
%polycont(%sysevalf(¢er &operator ¢er &operator -1), 5, &color);
%polycont(¢er, 5, &color);
%polycont(¢er, %sysevalf(&top/2.0 +2), &color);
%polycont(%sysevalf(¢er &operator (¢er/2.0) &operator 2),
%sysevalf(&top/2.0 + 2), &color);
%polycont(%sysevalf(¢er &operator (¢er/2.0) &operator 3),
%sysevalf(&top/2.0 + 12), &color);
%polycont(%sysevalf(¢er &operator (¢er/2.0) &operator 10),
%sysevalf(&top/2.0 + 12), &color);
%mend;
%macro drawBar(type=, drawBorder=1, drawFill=1, color=);
%bar(%sysevalf(&x+&xStart), &y,
%sysevalf(&x + &barWidth + &xStart),
%sysevalf(&y + &barHeight),
&color, 0, &type);
%mend drawBar;
%macro drawBars(color=, drawBorder=1, drawFill=1, pattern=MEMPTY,
hashColor=black);
%if &drawFill %then %do;
%drawBar(type=SOLID, drawFill=1, color=&color);
%end;
%if &drawBorder %then %do;
%drawQuad(
%sysevalf(&x+&xStart), &y,
%sysevalf(&x + &barWidth + &xStart), &y,
%sysevalf(&x + &barWidth + &xStart), %sysevalf(&y + &barHeight),
%sysevalf(&x+&xStart), %sysevalf(&y + &barHeight),
color=&color, pattern=&pattern, hashColor=&hashColor
);
%end;
%mend drawBars;
%macro drawLabel(char=, num=0);
%label(%sysevalf((&x + &barWidth)/2.0 * &xLabelFactor +
&xLabelOffset + &xStart),
%sysevalf((&y + &barHeight)/2.0 * &yLabelFactor),
"&char.&num", black, 0, 0, 2.5, , 4);
%mend drawLabel;
%macro drawBoxes(char=, count=, color=, drawBorder=1, drawFill=1,
pattern=MEMPTY, hashColor=black);
%do i = 1 %to &count;
%let x = &i * (&barWidth + &barSeparation);
%let y = &yStart;
%drawBars(color=&color, drawBorder=&drawBorder, drawFill=&drawFill,
pattern=&pattern, hashColor=&hashColor);
%if &char ne %then %do;
%drawLabel(char=&char, num=%eval(&i.+5-&count));
%end;
%end;
%mend;
%macro drawTri(x1, y1, x2, y2, x3, y3, color=);
%poly(&x1, &y1, &color, MSOLID, 1);
%polycont(&x2, &y2, &color);
%polycont(&x3, &y3, &color);
%poly(&x1, &y1, black, M5X45, 1);
%polycont(&x2, &y2, black);
%polycont(&x3, &y3, black);
%mend;
%macro drawQuad(x1, y1, x2, y2, x3, y3, x4, y4, color=, pattern=MEMPTY,
hashColor=black);
%poly(&x1, &y1, &color, MSOLID, 1);
%polycont(&x2, &y2, &color);
%polycont(&x3, &y3, &color);
%polycont(&x4, &y4, &color);
%poly(&x1, &y1, &hashColor, &pattern, 1);
%polycont(&x2, &y2, black);
%polycont(&x3, &y3, black);
%polycont(&x4, &y4, black);
%mend;
%macro drawQuads(count=, color=, pattern=);
%let y = 40;
%do i = &count %to 1 %by -1;
%let x = %eval(&i * 14);
%drawQuad(%sysevalf(&x + 8.5), &y,
%sysevalf(&x + 19.5), &y,
%sysevalf(&x + 18.5), %sysevalf(&y - 9),
%sysevalf(&x + 9.5), %sysevalf(&y - 9),
color=&color, pattern=&pattern);
%end;
%mend;
%macro drawSide(center=49, textCenter=42.3, operator=-, num1=1, num2=1);
/* draw V1 */
%let y=75.9;
%drawTri(%sysevalf(¢er &operator 30), &y,
%sysevalf(¢er &operator 48), &y,
%sysevalf(¢er &operator 38), %sysevalf(&y-25.9),
color=&sand
);
%let y = %sysevalf(&y - 17.9);
%let x = %sysevalf(&textCenter &operator 45);
%drawLabel(char=v, num=&num1);
/* draw B1 */
%let y = 58;
%drawQuad(%sysevalf(¢er &operator 29), &y,
%sysevalf(¢er &operator 38), &y,
%sysevalf(¢er &operator 38), %sysevalf(&y - 8),
%sysevalf(¢er &operator 29), %sysevalf(&y - 8),
color=CXA0A0A0
);
%let x = %sysevalf(&textCenter &operator 33.5);
%let y = %sysevalf(&y - 6);
%drawLabel(char=b, num=&num2);
%let y = %sysevalf(&y - 3);
%drawLabel(char=s, num=&num2);
/* draw M1 */
%let y = 70;
%drawQuad(%sysevalf(¢er &operator 30), &y,
%sysevalf(¢er &operator 35), &y,
%sysevalf(¢er &operator 37), %sysevalf(&y - 12),
%sysevalf(¢er &operator 30), %sysevalf(&y - 12),
color=ltgray, pattern=M1L0, hashColor=CXD0D0D0
);
%let x = %sysevalf(&textCenter &operator 33);
%let y = %sysevalf(&y - 10);
%drawLabel(char=m, num=&num2);
/* label A1-A6 */
%let x = %sysevalf(&textCenter &operator 33.5);
%let y = %sysevalf(&y - 15.7);
%drawLabel(char=a, num=&num2);
%let x = %sysevalf(&textCenter &operator 21.0);
%let y = %sysevalf(&y - 19.5);
%drawLabel(char=a, num=%eval(&num2 &operator -1));
%let x = %sysevalf(&textCenter &operator 13.0);
%drawLabel(char=a, num=%eval(&num2 &operator -2));
%mend drawSide;
%macro drawSky;
%bar(1, 10, 97, 100, white, 0, SOLID);
%bar(0.85, 4.7, 97.15, 100, black, 0, EMPTY);
%mend drawSky;
%macro drawBridge;
%annomac;
data anno_bridge;
%dclanno;
%system(3,3,3);
%drawSky;
%drawClay;
%drawClay(operator=+);
%drawPilings;
%drawPilings(operator=+);
%let barWidth = 14;
%let barHeight = 6;
%let yLabelFactor = 1.93;
%let xLabelFactor = 2.0;
%let xLabelOffset = -6;
%let yStart = 70;
%let xStart = 0;
%let barSeparation = 0;
%let sand = CXF8EABF;
%drawSide;
%drawSide(operator=+, num1=2, num2=6);
/* draw sand buckets */
%drawQuads(color=&sand, count=4, pattern=M5X45);
/* draw T1-T5 */
%drawBoxes(char=t, count=5, color=CX80A0DF);
%let barWidth = 4;
%let barHeight = 30;
%let yLabelFactor = 1.6;
%let xLabelFactor = 2.0;
%let xLabelOffset = -0.6;
%let yStart = 40;
%let barSeparation = 10;
%let xStart = 12;
/* draw M2-M5 */
%drawBoxes(char=m, count=4, color=ltgray, pattern=M1L0,
hashColor=CXD0D0D0);
%let barWidth = 6;
%let yLabelFactor = 1.8;
%let xLabelFactor = 2.0;
%let xLabelOffset = -1.8;
%let yStart = 31;
%let barSeparation = 8;
%let xStart = 11;
%let barHeight = 7.5;
/* draw B2-B5 */
%drawBoxes(char=s, count=4, color=CXA0A0A0, drawBorder=0);
%let barHeight = 11;
%drawBoxes(char=b, count=4, color=CX000000, drawBorder=0, drawFill=0);
%let barHeight = 9;
%drawBoxes(char=, count=4, color=CXA0A0A0);
run;
proc ganno annotate=anno_bridge;
run;
quit;
%mend drawBridge;
option nodate nonumber;
%drawBridge;
data bridge;
format _ACTIVITY_ $3. _DESC_ $34. _RESOURCE_ $14.
_SUCCESSOR_ $3. _LAG_ $3. ;
input _ACTIVITY_ & _DESC_ & _DURATION_ _RESOURCE_ &
_SUCCESSOR_ & _LAG_ & _LAGDUR_;
_QTY_ = 1;
datalines;
a1 excavation (abutment 1) 4 excavator s1 . .
a2 excavation (pillar 1) 2 excavator s2 . .
a3 excavation (pillar 2) 2 excavator p1 . .
a4 excavation (pillar 3) 2 excavator p2 . .
a5 excavation (pillar 4) 2 excavator s5 . .
a6 excavation (abutment 2) 5 excavator s6 . .
ab1 concrete setting time (abutment 1) 1 . m1 . .
ab2 concrete setting time (pillar 1) 1 . m2 . .
ab3 concrete setting time (pillar 2) 1 . m3 . .
ab4 concrete setting time (pillar 3) 1 . m4 . .
ab5 concrete setting time (pillar 4) 1 . m5 . .
ab6 concrete setting time (abutment 2) 1 . m6 . .
b1 concrete foundation (abutment 1) 1 concrete mixer ab1 . .
b1 concrete foundation (abutment 1) 1 concrete mixer s1 ff -4
b2 concrete foundation (pillar 1) 1 concrete mixer ab2 . .
b2 concrete foundation (pillar 1) 1 concrete mixer s2 ff -4
b3 concrete foundation (pillar 2) 1 concrete mixer ab3 . .
b3 concrete foundation (pillar 2) 1 concrete mixer s3 ff -4
b4 concrete foundation (pillar 3) 1 concrete mixer ab4 . .
b4 concrete foundation (pillar 3) 1 concrete mixer s4 ff -4
b5 concrete foundation (pillar 4) 1 concrete mixer ab5 . .
b5 concrete foundation (pillar 4) 1 concrete mixer s5 ff -4
b6 concrete foundation (abutment 2) 1 concrete mixer ab6 . .
b6 concrete foundation (abutment 2) 1 concrete mixer s6 ff -4
l delivery of the preformed bearers 2 crane t1 . .
l delivery of the preformed bearers 2 crane t2 . .
l delivery of the preformed bearers 2 crane t3 . .
l delivery of the preformed bearers 2 crane t4 . .
l delivery of the preformed bearers 2 crane t5 . .
m1 masonry work (abutment 1) 16 bricklaying t1 . .
m1 masonry work (abutment 1) 16 bricklaying ua fs -2
m2 masonry work (pillar 1) 8 bricklaying t1 . .
m2 masonry work (pillar 1) 8 bricklaying t2 . .
m2 masonry work (pillar 1) 8 bricklaying ua fs -2
m3 masonry work (pillar 2) 8 bricklaying t2 . .
m3 masonry work (pillar 2) 8 bricklaying t3 . .
m3 masonry work (pillar 2) 8 bricklaying ua fs -2
m4 masonry work (pillar 3) 8 bricklaying t3 . .
m4 masonry work (pillar 3) 8 bricklaying t4 . .
m4 masonry work (pillar 3) 8 bricklaying ua fs -2
m5 masonry work (pillar 4) 8 bricklaying t4 . .
m5 masonry work (pillar 4) 8 bricklaying t5 . .
m5 masonry work (pillar 4) 8 bricklaying ua fs -2
m6 masonry work (abutment 2) 20 bricklaying t5 . .
m6 masonry work (abutment 2) 20 bricklaying ua fs -2
p1 foundation piles 2 20 pile driver s3 . .
p2 foundation piles 3 13 pile driver s4 . .
pa beginning of project 0 . a1 . .
pa beginning of project 0 . a2 . .
pa beginning of project 0 . a3 . .
pa beginning of project 0 . a4 . .
pa beginning of project 0 . a5 . .
pa beginning of project 0 . a6 . .
pa beginning of project 0 . l fse 30
pa beginning of project 0 . ue . .
pe end of project 0 . . . .
s1 formwork (abutment 1) 8 carpentry b1 . .
s1 formwork (abutment 1) 8 carpentry a1 sf -3
s2 formwork (pillar 1) 4 carpentry b2 . .
s2 formwork (pillar 1) 4 carpentry a2 sf -3
s3 formwork (pillar 2) 4 carpentry b3 . .
s3 formwork (pillar 2) 4 carpentry p1 sf -3
s4 formwork (pillar 3) 4 carpentry b4 . .
s4 formwork (pillar 3) 4 carpentry p2 sf -3
s5 formwork (pillar 4) 4 carpentry b5 . .
s5 formwork (pillar 4) 4 carpentry a5 sf -3
s6 formwork (abutment 2) 10 carpentry b6 . .
s6 formwork (abutment 2) 10 carpentry a6 sf -3
t1 positioning (preformed bearer 1) 12 crane v1 . .
t2 positioning (preformed bearer 2) 12 crane pe . .
t3 positioning (preformed bearer 3) 12 crane pe . .
t4 positioning (preformed bearer 4) 12 crane pe . .
t5 positioning (preformed bearer 5) 12 crane v2 . .
ua removal of the temporary housing 10 . pe . .
ue erection of temporary housing 10 . . . .
ue erection of temporary housing 10 . s1 ss 6
ue erection of temporary housing 10 . s2 ss 6
ue erection of temporary housing 10 . s3 ss 6
ue erection of temporary housing 10 . s4 ss 6
ue erection of temporary housing 10 . s5 ss 6
ue erection of temporary housing 10 . s6 ss 6
v1 filling 1 15 caterpillar pe . .
v2 filling 2 10 caterpillar pe . .
;
/* invoke PROC CLP */
proc clp actdata=bridge schedtime=schedtime_bridge;
schedule finish=104;
run;
/* Create Consolidated Schedule */
proc sql;
create table bridge_info as
select distinct _ACTIVITY_ as ACTIVITY format $3. length 3,
_DESC_ as DESCRIPTION, _RESOURCE_ as RESOURCE from bridge;
proc sort data=schedtime_bridge;
by ACTIVITY;
run;
data schedtime_bridge;
merge bridge_info schedtime_bridge;
by ACTIVITY;
run;
proc sort data=schedtime_bridge;
by START FINISH;
run;
proc print data=schedtime_bridge noobs width=min;;
title 'Bridge Construction Schedule';
run;
/* start to prepare a schedule for PROC GANTT */
/* extract the project data set with ONLY precedence constraints */
data bridge_c;
drop _lag_;
set bridge(where=(_lag_=''));
run;
/***************************************************************/
/* Define Utility Macros for Graphical Output */
/***************************************************************/
/* %colorIdex creates resource-pattern-color mapping */
/* %fnLegend uses footnote to add legends according to the mapping */
/* %setPatterns executes pattern statements according to the mapping */
%macro colorIdex(res_var=, proj=, palette=, out=);
proc sql;
create table &out as
select distinct(&res_var) from &proj;
quit;
data &out;
set &out;
drop name_tr color_ct;
format color $10.;
retain _pattern 1;
retain color_ct 1;
name_tr=lowcase(strip(&res_var));
if name_tr eq 'n/a' or name_tr eq '' then color='red';
else do;
color=scan(&palette, color_ct);
color_ct=color_ct+1;
end;
output;
_pattern=_pattern+1;
run;
%mend colorIdex;
/* macro %fnLegend uses footnote to add legends */
/* Title */
/* */
/* color bar 11 text ... color bar 1n text */
/* color bar m1 text ... color bar mn text */
%macro fnLegend(tfact=1.75,h=10,xStart=5,rhs=100,nCol=,nRow=,
title='Resource Used',map=,font='Albany AMT',var=_RESOURCE_);
%let rH = %sysevalf(&h/(&nRow+2)); /* row height */
%let cW = %sysevalf((&rhs-2*&xStart)/&nCol); /* column width */
%let rowsH = %sysevalf(&rH*&nRow); /* height of all legend rows */
%let barH = %sysevalf(&rH*0.35); /* height of legend (colored bars) */
%let rTextH = %sysevalf(&barH*&tfact); /* height of text in legend rows */
%let tiTextH = %sysevalf(&rTextH*1.2); /* height of text in title row */
footnote;
data _null_;
call execute('footnote1 f='||"&font"||' j=c h='||put(&tiTextH.,best.)||
'pct '||'"'||&title||'";');
call execute('footnote2 f='||"&font"||' h='||put(&rH.,best.)||'pct " ";');
run;
data _null_;
set &map end=finish;
retain count 0;
idxRow = int(count/&nCol);
idxCol = count - idxRow*&nCol;
x = &xStart + idxCol*&cW;
y = &rowsH - idxRow*&rH;
_fnlStr_=strip(&var);
if _fnlStr_ eq '' then _fnlStr_='N/A';
if count eq 0 then
call execute('footnote3 h='||put(&rowsH.,best.)||'pct " "');
if lowcase(strip(color)) eq 'red' then
call execute(catx(' ','f=',"&font",'h=',&barH,'pct', 'm=(',x,',',y,
') pct','c=',color,
'box=1 bs=0 pct " "'));
else
call execute(catx(' ','f=',"&font",'h=',&barH,'pct', 'm=(',x,',',y,
') pct','c=',color,'bc=',color,
'box=1 bs=0 pct " "'));
call execute(catx(' ','f=',"&font",'h=',&rTextH,'pct', 'm=(+0.5,',y,
') pct','c=black')||' " '||_fnlStr_||'"');
count=count+1;
if finish then call execute(';');
run;
%mend fnLegend;
%macro setPatterns(map);
data _null_;
set ↦
cstr=lowcase(strip(color));
if cstr eq 'red' then
call execute('pattern'||strip(put(_pattern,best.))||' v=e color='||
cstr||' repeat=1;');
else
call execute('pattern'||strip(put(_pattern,best.))||' v=s color='||
cstr||' repeat=1;');
run;
%mend setPatterns;
/***************************************************************/
/* End Macro Definitions */
/***************************************************************/
/* restore precedence information, add pattern */
%let _palette='blue yellow orange cyan brown black gray green';
%colorIdex(res_var=_RESOURCE_,proj=bridge,palette=&_palette,
out=res_col_patn);
proc sql;
create table sched_gantt_ex1 as
select a._SUCCESSOR_ as SUCCESSOR, b.*, c._pattern
from bridge_c a, schedtime_bridge b, res_col_patn c
where a._ACTIVITY_ = b.ACTIVITY and a._RESOURCE_=c._RESOURCE_;
quit;
/* draw the Gantt chart */
%setPatterns(res_col_patn);
title1 j=c h=3pct 'PROC CLP - Solution to Bridge Problem:104 days (optimal)';
%fnLegend(xStart=10,h=12,map=res_col_patn,nCol=4,nRow=2,rhs=110);
proc gantt data=sched_gantt_ex1;
id activity start finish;
label activity='Act';
label start='Start';
label finish='Finish';
chart /
ref=0 to 110 by 10, 100 to 105 by 1
dur=duration
cprec=gray
es=start /* start time */
ef=finish /* finish time */
mindate=0
maxdate=105
increment=5
scale=2.8
height=2.7
between=1
skip=2
compress /* compresses chart onto a single page */
nojobnum
nolegend
font='Albany AMT'
act=activity
succ=successor
;
run;
/* start to output a net diagram for the bridge project */
proc netdraw data=bridge_c out=bridge1 nodisplay;
actnet / act = _activity_ succ = _successor_;
run;
proc sql;
create table act2zone as
select distinct _activity_, max(2, min(9,_y_)) as _zone_
from bridge1
where _pattern=1;
create table bridge_zones as
select a._zone_, b.*
from act2zone a, bridge_c b
where a._activity_=b._activity_;
quit;
pattern1 v=e c=green;
title1 j=c h=3.7pct 'Bridge Construction Project';
footnote;
proc netdraw data=bridge_zones out=bridge2;
actnet /
act = _activity_
succ = _successor_
compress
id = ( _activity_ _desc_ _duration_ _resource_)
nolabel
nodefaultid
boxwidth = 8
xbetween = 12
ybetween = 1
centerid
htext=1.2
arrowhead=2
separatearcs
zone=_zone_
nozonelabel
;
run;