Petroleum Distributor's Decision Problem
/**************************************************************/
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: DTREEE06 */
/* TITLE: Petroleum Distributor's Decision Problem */
/* (dtreee06) */
/* PRODUCT: OR */
/* SYSTEM: ALL */
/* KEYS: OR GRAPHICS PATTERN SYMBOL */
/* PROCS: DTREE PRINT GPLOT */
/* DATA: */
/* */
/* SUPPORT: UPDATE: */
/* REF: Example 6 from the DTREE chapter */
/* MISC: */
/* */
/**************************************************************/
goptions hpos=80 vpos=32;
goptions cback=ligr ctext=black;
/* -- create the STAGEIN= data set -- */
data Stage7;
format _OUTCOM1 $14. _OUTCOM2 $14. ;
input _STNAME_ $ _STTYPE_ $ _OUTCOM1 $
_SUCC1 $ _OUTCOM2 $ _SUCC2 $ ;
datalines;
Action D Invoking Response Not_Invoking .
Response C Accept . Refuse Lawsuit
Lawsuit C Press_Issue . Settle .
. . Sue Last . .
Last C 3_Years Result 4_Years Result
. . 5_Years Result . .
Result C No_Damages . Normal_Damages .
. . Double_Damages . . .
;
/* -- create the PROBIN= data set -- */
data Prob7;
format _EVENT1_ _EVENT2_ $14.;
input _EVENT1_ $ _PROB1_ _EVENT2_ $ _PROB2_ ;
datalines;
Accept 0.1 Refuse 0.9
Press_Issue 0.1 Settle 0.45
Sue 0.45 . .
3_Years 0.3 4_Years 0.4
5_Years 0.3 . .
No_Damages 0.15 Normal_Damages 0.65
Double_Damages 0.20 . .
;
/* -- create the PAYOFFS= data set -- */
data Payoff7(drop=i j k D PCOST);
length _ACTION_ _STATE1-_STATE4 $16;
/* possible outcomes for the case last */
array YEARS{3} $16. _TEMPORARY_ ('3_Years',
'4_Years',
'5_Years' );
/* numerical values for the case last */
array Y{3} _TEMPORARY_ (3, 4, 5);
/* possible outcomes for the size of judgment */
array DAMAGES{3} $16. _TEMPORARY_ ('No_Damages',
'Normal_Damages',
'Double_Damages' );
/* numerical values for the size of judgment */
array C{3} _TEMPORARY_ (0, 1500, 3000);
D=0.1; /* discount rate */
/* payoff for the scenario which the */
/* 10 percent clause is not invoked */
_ACTION_='Not_Invoking'; _VALUE_=-450; output;
/* the clause is invoked */
_ACTION_='Invoking';
/* payoffs for scenarios which the clause is */
/* invoked and the customer accepts the */
/* invocation */
_STATE1='Accept'; _VALUE_=600; output;
/* the customer refuses the invocation */
_STATE1='Refuse';
/* payoffs for scenarios which the clause is */
/* invoked and the customer refuses the */
/* invocation but decline to press the issue */
_STATE2='Press_Issue'; _VALUE_=500; output;
/* payoffs for scenarios which the clause is */
/* invoked and the customer refuses the */
/* invocation but willing to settle out of */
/* court for 900K */
_STATE2='Settle'; _VALUE_=500-900; output;
/* the customer will sue for damages */
_STATE2='Sue';
do i=1 to 3;
_STATE3=YEARS{i};
/* determine the cost of proceedings */
PCOST=30; /* initial cost of the proceedings */
/* additional cost for every years in */
/* in present value */
do k=1 to Y{i};
PCOST=PCOST+(20/((1+D)**k));
end;
/* loop for all poss. of the lawsuit result */
do j=1 to 3;
_STATE4=DAMAGES{j}; /* the damage have to paid */
/* compute the net return in present value */
_VALUE_=500-PCOST-(C{j}/((1+D)**Y{i}));
/* output an observation for the payoffs */
/* of this scenario */
output;
end;
end;
run;
/* -- print the payoff table -- */
title "Petroleum Distributor's Decision";
title3 "Payoff Table";
proc print;
run;
/* -- define graphics options -- */
goptions colors=(green red blue);
goptions hsize=8 in vsize=8.4 in;
/* -- define title -- */
title h=2.5 "Petroleum Distributor's Decision";
/* -- PROC DTREE statements -- */
proc dtree stagein=Stage7 probin=Prob7 payoffs=Payoff7;
evaluate / summary;
treeplot / graphics compress nolg name="dt6p1" ftext='Cumberland AMT'
ybetween=1 cell lwidth=2 lwidthb=3 hsymbol=3;
quit;
/* -- create data set for decision diagram -- */
data Data7(drop=i);
P=0.0; /* initialize P */
/* loop for all possible values of P */
do i=1 to 21;
/* determine the corresponding Q */
Q=(86-(1136*P))/(1036*(1.0-P));
if Q < 0.0 then Q=0.0;
/* output this data point */
output;
/* set next possible value of P */
P=P+0.005;
end;
run;
/* create the ANNOTATE= data set for labels of */
/* decision diagram */
data label;
length FUNCTION STYLE COLOR $8;
length XSYS YSYS $1;
length WHEN POSITION $1;
length X Y 8;
length SIZE ROTATE 8;
WHEN = 'A';
POSITION='0';
XSYS='2';
YSYS='2';
input FUNCTION $ X Y STYLE $ SIZE COLOR $
ROTATE TEXT $ & 16.;
datalines;
label 0.01 0.04 centx 2 black . Do Not
label 0.01 0.03 centx 2 black . Invoke
label 0.01 0.02 centx 2 black . The Clause
label 0.06 0.06 centx 2 black . Invoke The
label 0.06 0.05 centx 2 black . Clause
;
/* -- define symbol characteristics for boundary -- */
symbol1 i=joint v=NONE l=1 ci=black;
/* -- define pattern for area fill -- */
pattern1 value=msolid color=cyan;
pattern2 value=msolid color=green;
/* -- define axis characteristics -- */
axis1 label=('Pr(Accept the Invocation)')
order=(0 to 0.1 by 0.01) minor=none;
axis2 label=(angle=90 'Pr(Press the Issue)')
order=(0 to 0.1 by 0.01) minor=none;
/* -- plot decision diagram -- */
title h=2.5 "Petroleum Distributor's Decision";
proc gplot data=Data7 ;
plot Q*P=1 / haxis=axis1
vaxis=axis2
annotate=label
name="dt6p2"
frame
areas=2;
run;
quit;