A modular method for the modelling of health delivery systems
Item Type text; Thesis-Reproduction (electronic)
Authors Harding, William James, 1947-
Publisher The University of Arizona.
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Link to Item http://hdl.handle.net/10150/318374
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W illia m J a m e s H ard in g
A T h e s is S u b m itted to th e F a c u l t y of the DEPARTMENT OF SYSTEMS ENGINEERING In P a r tia l F u lfillm e n t of th e R eq u irem e n ts
For th e D e g re e of MASTER OF SCIENCE In th e G ra d u a te C o lle g e THE UNIVERSITY OF ARIZONA
1 9 7 0
STATEMENT BY AUTHOR
This t h e s i s h a s b e e n s u b m itte d in p a r t ia l f u lf illm e n t of r e q u ire m e n ts for a n a d v a n c e d d e g r e e a t The U n i v e r s i t y of A rizona and is d e p o s i t e d in th e U n i v e r s i t y Library to be m ade a v a i l a b l e to b o rro w ers u n d e r r u l e s of th e L i b r a r y .
Brief q u o t a t i o n s from t h i s t h e s i s are a llo w a b le w ith o u t s p e c i a l p e r m is s i o n , p ro vid e d t h a t a c c u r a t e a c k n o w le d g m e n t of s o u rc e i s m a d e . R e q u e s ts for p e r m is s io n for e x te n d e d q u o t a t i o n from or r e p ro d u c tio n of t h i s m a n u s c rip t in w h o le or in part m ay be g ra n te d by th e h e a d of th e m ajor d e p a rtm e n t or th e D e a n of the G r a d u a te C o lle g e w h en in h i s j u d g m ent th e p ro p o se d u s e of th e m a te r ia l is in th e i n t e r e s t s of s c h o l a r s h i p . In a ll o th e r i n s t a n c e s , h o w e v e r , p e r m is s io n m u st be o b ta in e d from th e a u th o r .
APPROVAL BY THESIS DIRECTOR T his t h e s i s h a s b e e n a p p ro v e d on th e d a te show n b elo w :
Robert L. Baker
A s s i s t a n t P r o fe s s o r of S y ste m s E n g in ee rin g
D a te
A s s i s t a n t P ro fe s so r o f S y ste m s E n g i n e e r i n g , for h i s c o n s i d e r a t i o n an d aid t o me during th e r e s e a r c h for t h i s t h e s i s . I am a l s o g r a te fu l to D r. Baker for s e rv in g a s my t h e s i s a d v i s o r .
I w i s h to e x te n d my t h a n k s a l s o t o D r. A. W . W y m o re, H e a d of th e S y s te m s E n g in ee rin g D e p a r tm e n t, an d D r. J. L. S a n d e r s , P ro fe s so r of S y ste m s E n g in e e rin g , for s e rv in g a s m o st h e lp f u l c o m m ittee m e m b e rs.
I w is h to e x p r e s s my a p p r e c i a t i o n to the N a tio n a l S c ie n c e F o u n d a tio n for th e T rain ee s h ip th a t m ade s tu d y for an a d v a n c e d d e g re e p o s s i b l e .
M y th a n k s go to L. J. M u lle n s for th e m any o c c a s i o n s w hen t h o u g h ts w ere e x c h a n g e d c o n c e rn in g th e r e s e a r c h p r e s e n t e d in th is t h e s i s .
TABLE OF CONTENTS
Page LIST OF ILLUSTRA TIONS... . v i LIST OF TABLES. . ... .... . . . . v i i ABSTRACT . . . . * . . . * «■• . . . . ■ » • . . . . .
I . INTRODUCTION AND REVIEW OF THE LITERATURE . . . 1
G e n e r a l D i s c u s s i o n ... 4
Review of th e L ite ra tu re . . . 6
G e n e r a l D e s c r i p t i o n of the M e th o d o lo g y . . . 13
II. .MACROSCOPIC DESCRIPTION OF THE METHODOLOGY. . . . . 16
P h y s i c a l R e p r e s e n ta tio n of th e S y stem ... 16
H e a lth N e e d G e n e r a tio n . . . 17
T r a n s p o rta tio n 19 T r e a t m e n t ... 19
S p e c i f ic a t io n of a Sam ple Area . . . 20
III. DESCRIPTION OF THE SIMULATION METHODOLOGY . '. . . . 28
M e th o d of S im u la tio n . . . 28
The G e n e r a tio n M o d u le . . . 30
The T ra n s p o rta tio n M o d u le . ... 34
The T reatm en t M o d u l e ... . 37
IV. - STATISTICAL M ETHODS... 43
The E x p o n e n tia l D is tr ib u tio n . . . 44
The E m p irical D i s t r i b u t i o n ... 45
The P o is s o n D i s t r i b u t i o n ... . 48
O ther D i s t r i b u t i o n s ... 49
M e th o d for Adding D is tr ib u tio n G e n e r a to r s . . . 50
iv
Page
V. • THE SIMULATION 5.2
S y stem D e s i g n ... 53
G e n e r a tio n M o d u le P a ra m e te rs . ... 53
T r a n s p o rta tio n M o d u le P a ra m e te rs ... 54
T reatm en t M o d u le P a ra m e te rs . . . 55
A. S im u latio n « . . . . . . . . . . . u 1 VI. EXTENSIONS OF THE METHODOLOGY AND CONCLUSIONS . . 61
M ic r o s c o p i c E x te n s io n s : ... 61
R ec o m m en d a tio n s for F u rth er S t u d y . ... 64
C o n c l u s i o n s . . . 67
APPENDIX A: DESCRIPTION OF THE INPUT DECK . . . . 68
APPENDIX B: SAMPLE OUTPUT . . . 75
REFERENCES. ... 125
LIST OF ILLUSTRATIONS
F igure . _ Page
1. P h y s i c a l R e p r e s e n ta tio n of th e Real H e a l t h D e liv e r y
S y stem ... 18
2 . Sam ple Area of Papago In d ia n R e s e r v a t i o n , Arizona an d an
E x te rn a l D i s t r i c t ... 22
3 . A P h y s ic a l R e p r e s e n ta tio n of th e O u tp a tie n t C lin ic a t
S e 11 s , z ona » . o . 2 5
4 . A P h y s ic a l R e p r e s e n ta tio n of th e O u tp a tie n t C lin ic a t
San X a v ie r, A rizona ... 27
5. M a c r o s c o p i c D e s c r i p t i o n of the S im u la tio n M o d e l 's
6. D e s c r i p t i o n of th e L o g ic a l Flow for th e G e n e r a tio n M o du le. . 33 7. D e s c r i p t i o n of the L o g ic a l Flow for th e T ra n s p o rta tio n
M o d u le . ... 38
8. D e s c r i p t i o n of th e L o g ic a l Flow for th e T rea tm en t M o d u le . . 42 9 . The D e n s i t y F u n c tio n and C u m u la tiv e D i s tr i b u t i o n for th e
E x p o n e n tia lly D i s tr i b u t e d Random V ariable X ... 46 10. • Exam ple of a F re q u e n c y D i s tr ib u tio n . . . 47
v i
1. D i s t r i c t s , G e n e r a tio n P o i n t s , an d T rea tm en t Points for a Sam ple M o d e l of the H e a lth D e liv e r y S y s t e m , P apago
I n d ia n R e s e r v a t i o n , Arizona. . . . . . . . . ... 23 2 . R e s u lts of th e V alid atio n of th e Random Number F u n c tio n ,
RANF (X). . . . . ... 44
3. An Example of a n E m p irical D i s tr i b u t i o n . . . 48
v ii
ABSTRACT
A m o d u lar r e p r e s e n t a t i o n of a h e a l t h d e l i v e r y s y s te m a llo w s a s im u la tio n m o d el to be c o n s tr u c t e d s o t h a t th e o p e ra tio n of th e s y s te m co m p o n e n ts c a n be i n v e s t i g a t e d . The h e a l t h d e l i v e r y s y s te m is d e c o m p o s e d in to a g e n e r a tio n m o d u l e , a t r a n s p o r t a t io n m o d u le , an d a tre a tm e n t m o d u l e ,
The g e n e r a tio n m odule i s a s im u la tio n of th e s y s t e m h e a l t h
l e v e l . The num ber of p e r s o n s t h a t co m p o se th e h e a lth l e v e l for a s in g le . d a y a re s im u la te d by s t a t i s t i c a l m e t h o d s . The tr a n s p o r t a t io n m odule i s a s im u la tio n of th e t r a n s p o r t a t io n s y s te m for th e h e a l t h d e l i v e r y s y s t e m . The d e c i s i o n p r o c e s s of c h o o s in g t r a n s p o r t a t io n for e a c h p e rso n w ho c o m p o s e s th e h e a l t h l e v e l i s s im u l a t e d . The tre a tm e n t m odule s im u l a t e s th e m ovem ent of a p a t i e n t w ith in a tre a tm e n t c e n t e r th a t i s in th e h e a l t h d e liv e r y s y s t e m .
The s im u la tio n m eth o d o lo g y d e v e lo p e d i s g e n e r a l and f l e x i b l e . It i s d e s ig n e d to h a n d le n um erous s y s te m c o n f i g u r a t i o n s .
In th e l a s t t h r e e hu nd red y e a r s th e p o p u la tio n of th e w orld h a s i n c r e a s e d a p p r o x im a te ly th re e an d o n e - h a l f t i m e s . Time an d th e i n c r e a s i n g p o p u la tio n h a v e w ro u g h t c h a n g e s in s o c i a l an d c u l t u r a l f a c t o r s in th e U n ite d S t a t e s , T o d a y 's s ta n d a rd of l i v i n g , group p r e s s u r e s , la b o r m a rk e t c h a n g e s , a d v a n c in g t e c h n o l o g y , an d a u to m a tio n are a l l a f f e c tin g th e c u l t u r a l s t a t u s of A m e r ic a . E d u c a tio n a l l e v e l s are m oving up r a p i d ly an d th e ag e c o m p o s itio n of th e i n c r e a s i n g p o p u la tio n i s s e e n to be
c h a n g in g . Due to th e tre m e n d o u s p o p u la tio n c h a n g e s in th e w o rld , a t t e n tio n h a s b e e n draw n to th e s c i e n t i f i c an d t e c h n o l o g i c a l a d v a n c e s a f f e c t i n g th e h e a l t h of a l l p eo p le . There h a v e b e e n m any t e c h n o l o g i c a l a d v a n c e s in th e a r e a of p u b lic h e a l t h b rin g in g n e w and im proved b i o l o g i c a l s , a n t i b i o t i c s , d r u g s , an d s a n i t a r y e q u ip m e n t. S o c io lo g ic a l c h a n g e s h a v e o c c u rre d in th e a r e a of p u b lic h e a l t h . a l s o . On th e w h o l e , a fa v o ra b le e co n om y in th e U n ite d S t a t e s h a s p ro d u c ed a r e l a t i v e l y h ig h l e v e l of in co m e an d s ta n d a r d of li v i n g . This f a v o ra b le ec o n o m ic l e v e l h a s had th e e f f e c t of d im in is h in g som e h e a l t h pro b lem s s u c h a s m a ln u tritio n due t o u n d e r f e e d i n g . At th e sam e t im e , b e c a u s e t h i s e c o n o m ic le v e l p ro d u c e s p eo p le w ho w a n t more t h i n g s , th e re m ay be d an g er of a n x i e t y an d s t r e s s
due to s tr iv in g for b e t t e r l e v e l s of l i v i n g . That i s , t h i s e c o n o m ic l e v e l p ro d u c e s a s o c i e t y t h a t h a s h ig h d e m a n d s for h e a l t h c a r e . Koos (15)x h a s show n t h a t th e u s e of m e d ic a l s e r v i c e s g o e s u p a s inco m e g o e s u p .
W ith th e num ber of c o n t i n u a l c h a n g e s of f a c t o r s a f f e c tin g p u b lic h e a l t h , th e p aram ount problem i s d e l i v e r in g th e h e a l t h s e r v i c e provided b y s o c i e t y (public or priv ate ) to t h o s e w ho n e e d i t . P u b lic h e a l t h c o u ld be d e f in e d a s "the s c i e n c e an d a rt of p r e v e n tin g d i s e a s e , prolonging l i f e , an d promoting p h y s i c a l an d m e n ta l h e a l t h and e f f i c i e n c y th ro u g h o rg a n iz e d co m m unity e f f o r t s " (5, 4 7 1 ). The im p le m e n ta tio n of a p u b lic h e a l t h program i s a c c o m p l i s h e d in h o s p i t a l s , g o v e rn m e n ta l h e a l t h d e p a r t m e n t s , an d v o lu n ta r y a g e n c i e s . To pro vid e th e p u b lic h e a l t h s e r v i c e , th e c o n c e p t of h e a l t h d e l i v e r y s y s t e m s h a s b e e n f o r m a liz e d .
The problem s of h e a l t h d e l i v e r y s y s t e m s h a v e b e co m e a m ajor c o n c e r n for e v e r y p e r s o n in some w a y r e l a t e d to health, s e r v i c e s . A d i s c u s s i o n of th e r e a s o n s for c o n c e r n a b o u t t h e s e problem s w a r ra n ts a d e f i n i tio n of th e s tr u c tu r e of a h e a l t h d e l i v e r y s y s te m j A h e a l t h d e liv e r y
s y s te m i s c o m p o se d of th e fo llo w in g b u ild in g b lo c k s : s y s te m c o m p o n e n ts , th e s y s te m c o n f ig u r a tio n , an d t r a n s f e r r a b l e a t t r i b u t e s (1). An e x p l a n a t i o n
of t h e s e b u ild in g b lo c k s d e f in e s th e s tr u c tu r e of a h e a l t h d e l i v e r y s y s t e m . The s y s te m s tr u c tu r e of a h e a l t h d e l i v e r y s y s te m i s s p e c i f i e d by f a c t o r s
*The s t y l e of th e c i t a t i o n s on th e fo llo w in g p a g e s i s t h a t of The. Journal of I n d u s t r ia l E n g i n e e r i n g .
n e e d " i s d e f in e d a s an i n d iv id u a l w ho r e q u i r e s th e u s e of a h e a l t h d e l i v e r y s y s te m , b ut he m ay or m ay n o t d em and s u c h u s e . The s e c o n d co m po n en t tr a n s p o r t s a h e a l t h d em and to a p la c e of tr e a tm e n t or b rin g s th e t r e a tm e n t to th e h e a l t h d e m a n d . The term " h e a lth d em an d " i s d e fin e d a s a h e a l t h n e e d t h a t d e m a n d s th e u s e of a h e a l t h d e l i v e r y s y s t e m . The a c t u a l tre a tm e n t of th e h e a l t h n e e d i s a d m in is te r e d in th e th ird com p o n e n t. The s y s te m i s a s e r i a l c o u p le of th e ab o v e c o m p o n e n ts in w h ic h th e tr a n s f e r r a b l e a t t r i b u t e s provide a r e l a t i o n s h i p b e tw e e n th e c o m p o n e n t s . For th e p u r p o s e s of t h i s d e f i n i t i o n , th e tr a n s f e r r a b l e a t t r i b u t e s r e p r e s e n t - t h e h e a l t h n e e d s an d c e r t a i n h e a l t h n e e d d e s c r i p t o r s g iv e n by e a c h s y s te m
co m p o n e n t.
For m any y e a r s th e h e a l t h d e l i v e r y s y s t e m s of th e w orld h a v e b e e n u n d er g r e a t p u b lic and i n t e r n a l p r e s s u r e . Some "of th e c o n trib u to rs to t h i s p r e s s u r e h a v e b e e n r i s i n g c o s t s , problem s b e tw e e n p h y s ic i a n s . and a d m in istra tio n ., s h o r t a g e s of k e y p r o f e s s i o n a l p e r s o n n e l , i n a d e q u a c y of p h y s ic a l p l a n t , i n e f f i c i e n c y and w a s t e , The num ber of problem s are e v e r - i n c r e a s i n g an d are a r e s u l t of th e s o c i a l an d t e c h n o l o g i c a l d e v e l o p m en ts of th e tw e n t i e t h c e n tu r y (10).
G e n e r a l D i s c u s s i o n
This t h e s i s w a s fo rm u la ted to provide an a id to th e p lan n in g p r o c e s s in th e d e s i g n of h e a l t h d e liv e r y s y s t e m s . M a n a g e m e n t and p lan n in g p e r s o n n e l in th e p a s t g e n e r a l l y h a v e n o t r e c o g n i z e d or u n d e r s to o d th e p r e d o m in a n tly s t o c h a s t i c and v a r i a b l e n a tu re of th e h e a l t h d e l i v e r y s y s t e m . P lan s for h e a l t h d e l i v e r y s y s t e m s h a v e b e e n b a s e d upon th e f ix e d e x p e r i e n c e of th e p la n n e r and h i s i n t u itio n a b o u t th e
s y s t e m . The s t e p s in s u c h a n i n t u i t i o n a l m eth od c o u ld b ec o m e p r o c e d u r- a l l y an d e c o n o m ic a lly c u m b e r s o m e . For e x a m p l e , f i r s t th e p lan n ing pro ble m s of th e s y ste m m u st be r e c o g n i z e d an d s e c o n d l y th e d e c i s i o n m ak er m u s t p r e s e n t an a d d itio n or a l t e r n a t i v e to p r e s e n t d e s i g n to s o lv e th e p ro b le m . T h ird ly , th e p ro p o se d s o lu tio n m u st be im p lem en te d an d r e s u l t s of th e c h a n g e m u s t be a n a l y s e d . O ften t h i s p r o c e s s m u st be r e p e a t e d to find th e d e s i r e d s o lu t i o n . '
To c a rry out t h i s p la n n in g p r o c e s s in th e p u b lic h e a l t h e n v ir o n m ent w o u ld d e f i n i t e l y p r e s e n t p r o b le m s . To c h a n g e som e a s p e c t of a h e a l t h d e l i v e r y s y s t e m , e . g . , th e num ber of d o c to r s t h a t g iv e tre a tm e n t t o h e a l t h n e e d s a t a tr e a tm e n t c e n t e r , w o u ld t a k e a c o n s i d e r a b l e am ount of tim e an d m oney to im p lem en t . There w o u ld be a l e n g t h y s t a b i l i z a t i o n period to v ie w th e r e s u l t s . If i t is found t h a t s u c h a c h a n g e i s not t h e proper m o v e , th e n th e e x p e n d e d time and m oney h a v e b e e n for n a u g h t.
Y et, if a co m p u ter s im u la tio n m odel w ere a v a i l a b l e t h a t c o u ld e m u la te
a f ifth s t e p c o u ld be a d d e d to s e l e c t th e p referred c o n f ig u ra tio n of th e s im u la te d s y s t e m an d im p lem en t it in th e r e a l s y s te m an d a n a l y s e th e r e s u l t s .
The m e th o d o lo g y p r e s e n t e d in t h i s t h e s i s i s fo rm u la te d for th e a b o v e p u r p o s e . The u s e r m u st be k n o w le d g e a b le a b o u t th e h e a l t h d e l i v e r y s y s te m to be s i m u l a t e d , for he m u s t s p e c i f y th e s im u la tio n p a r a m e t e r s .
C o n s i d e r th e fo llo w in g m o d u le s : 1. G e n e r a tio n m o d u l e .
2 . T r a n s p o rta tio n m o d u l e . 3. T reatm en t m o d u l e . ■
T h e se are th e s y s te m c o m p o n e n ts t h a t d e f in e th e s im u la tio n m e th o d o lo g y . P utting t h e s e c o m p o n e n ts t o g e th e r s p e c i f i e s th e s im u la tio n of th e h e a l t h
)
d e l i v e r y s y s t e m .
T his t h e s i s d e s c r i b e s a m o d u lar s im u la tio n m e th o d o lo g y for a h e a l t h d e l i v e r y s y s te m programmed in FORTRAN IV l a n g u a g e to run on th e C o n tro l D a ta C o rp o ra tio n 6400 C o m p u ter S y stem i n s t a l l e d a t The U n i
v e r s i t y of A riz o n a . The m e th o d o lo g y w i l l e n a b le a u s e r to d e s c r i b e a h e a l t h d e l i v e r y s y s te m s o t h a t i t s c h a r a c t e r i s t i c s m ay be s tu d i e d an d c h a n g e s i n v e s t i g a t e d in b a s i c s y s te m d e s i g n c o n c e rn in g h e a l t h n e e d
o c c u r r e n c e , dem and for h e a l t h s e r v i c e s , t r a n s p o r t a t i o n , an d h e a l t h n e e d - s e r v e r i n t e r a c t i o n a t a tre a tm e n t c e n t e r .
R eview of th e L ite ra tu re
The a v a i l a b l e lit e r a t u r e in th e f ie ld of o p e r a tio n s r e s e a r c h m e th o d s for h e a l t h d e l i v e r y s y s t e m s c o v e r s a w ide r a n g e of t o p i c s . This r e v ie w w ill c o n c e r n i t s e l f w ith th e fo llo w in g a r e a s :
1. M a th e m a ti c a l i n v e s t i g a t i o n s . 2 . S im u latio n m o d e ls t o in c lu d e :
a . H o s p i t a l s ta f f i n g .
- b . A d m issio n s y s te m m o d e l s .
c . O u t - p a t i e n t a p p o in tm e n t m o d e l s . . 3 . R ela te d w o rk .
The p u rp o se of t h i s d i s c u s s i o n i s to g iv e a n o v e r a ll v ie w of p rev io u s r e s e a r c h in h e a l t h d e l i v e r y s y s t e m s .
In th e a r e a of m a th e m a tic a l i n v e s t i g a t i o n s , a s i g n i f i c a n t d e v e l o p m en t to w a rd r e s e a r c h in h o s p i t a l m a n a g e m e n t to o k p la c e in th e summer of
1956 w ith th e fo rm atio n of a n O p e r a tio n s R e s e a r c h D i v i s i o n a t th e Johns H o p k in s H o s p i t a l (9). The o b je c tiv e of th e D iv is io n i s to p lan and e x e c u te a r e s e a r c h program w ith th e .g oal of b rin g in g a b o u t im p ro v em en ts i n h o s p i t a l o p e r a tio n s b y p r o v id i n g , th ro u g h r e s e a r c h and a n a l y s i s , f a c t u a l b a s e s to a id m an ag em en t d e c i s i o n s . This o b je c tiv e i s a p p r o a c h e d by
Johns H o p k in s H o s p i ta l e n c o m p a s s e d th re e m ajor problem a r e a s : s c h e d u lin g of s t a f f , e c o n o m ic b a l a n c e , and p e r s o n n e l t u r n o v e r . The p o l i c i e s t h a t d e te rm in e th e o p tim al s y s te m of s t a f f , f a c i l i t i e s , p r o c e d u r e s , an d c o o r d in a tio n w ith o th er d e p a r tm e n ts in th e s y s te m u n d er th e p r e s e n t t e c h n i c a l k n o w le d g e an d e c o n o m ic c o n d itio n s provide th e s o lu t i o n to th e a b o v e p r o b le m s . C u rre n t r e s e a r c h i s d i r e c t e d to w a rd i n - p a t i e n t an d o u t - p a t i e n t c a r e . The aim of t h e s e s t u d i e s i s t o d e te rm in e s y s t e m s w h ic h w ill r e d u c e th e s p a c e c o n g e s t e d b y w a i t i n g p a t i e n t s , a n d s t i l l a s s u r e th e p h y s ic i a n s an u n in te rr u p te d flo w of p a t i e n t s . The a n a l y t i c a l t o o l s u s e d in t h i s r e s e a r c h are t h o s e of q u e u in g th e o r y , w ork m e a s u r e m e n t, a n d a p p lie d s t a t i s t i c s . Gam e t h e o r y an d o th e r r e l a t e d t e c h n i q u e s h a v e b e e n u s e d to s tu d y
s y s t e m s in c o m p e titio n w ith one a n o t h e r , b u t t h e s e t e c h n i q u e s h a v e n o t b e e n found d i r e c t l y a p p l i c a b l e to th e i n v e s t i g a t i o n of h o s p i t a l o p e r a t i o n s .
Though th e p r e v io u s ly m e n tio n e d m o d els are l a r g e l y fo u n d ed up o n q u e u in g th e o r y , th e re are m an y h e a l t h d e l i v e r y s y s t e m s e n c o u n te r e d in th e r e a l w orld t h a t c a n n o t be m o d e lle d b y q u e u in g th e o r y . Singer (19) h a s d o ne som e s p e c i f i c w ork c o n c e r n in g s y s t e m s in w h ich n e w a r r i v a l s m u s t • be a c c e p t e d . S i n g e r 's r e s e a r c h i s c o n c e r n e d w ith f in i t e c a p a c i t y s y s t e m s t h a t h a v e p o t e n t i a l l y i n f i n i t e p o p u la tio n s .
F la g le (8) d e s c r i b e s a d e c i s i o n p r o c e s s u s in g c l a s s i c a l e c o nom ic a n a l y s i s for i n v e s t i g a t i o n of h e a l t h d e l i v e r y s y s te m c a p a c i t y
p l a n n i n g . The m eth o d i n c r e a s e s c a p a c i t y u n til th e c o s t of ad d in g a n o th e r u n it of c a p a c i t y i s n o lo n g e r r e c o v e r e d i n th e v a lu e of a v o id in g e x p e c t e d s h o r t a g e . A n a l y t i c a l l y , c a p a c i t y i s e s t a b l i s h e d a t a po int s u c h t h a t th e p r o b a b ility t h a t dem and e x c e e d s t h i s e s t a b l i s h e d po in t i s h e ld b elo w som e l e v e l . That i s , g iv e n a random v a r i a b l e X r e p r e s e n t i n g p o p u l a t i o n , k i s c a p a c i t y , c^Ck) i s th e d a i l y c o s t of pro v id in g th e k th u n i t , and Cp
i s th e c o s t of e a c h s h o rta g e on a g iv e n d a y , w h e re c^(k) i s a s s u m e d to be l i n e a r l y r e l a t e d t o k an d C p i s a c o n s t a n t . The d e c i s i o n ru le for c a p a c i t y k i s to c h o o s e k s u c h t h a t
s y s t e m a t i c c l i n i c a l tr e a tm e n t e v a l u a t i o n a n d e m p h a s iz e s the im p o rta n c e of e l e c t r o n i c co m p u te r a i d s to problem s o l u t i o n s . The m a th e m a tic a l m e th o d s d i s c u s s e d are th e u s e of d y n am ic programming in th e fo rm u la tio n
of th e d i a g n o s t i c t r e a t m e n t c y c l e and B a y e 's theorem i s a p p l i e d a s an a id t o th e c o l l e c t i o n of t r e a t m e n t - e v a l u a t i o n d a t a . The im p o rta n c e of th e co m p u ter i s b a s e d upon th re e im p o rta n t a d v a n t a g e s . F i r s t , the co m p u ter c a n m ake the e x t e n s i v e c o l l e c t i o n of d a ta f e a s i b l e . S e c o n d , p rev io u s problem s of in f o r m a t i o n - s t o r a g e an d in f o r m a t i o n - r e t r i e v a l a s s o c i a t e d w ith
X
•X=X=kL e d le y (16) d i s c u s s e s p r e c i s e m a th e m a tic a l fo rm u la tio n s of
p le x c a l c u l a t i o n s n e c e s s a r y in th e a n a l y s i s of h e a l t h d e l i v e r y s y s t e m s . M u ch of th e w ork in th e a r e a of h o s p i t a l s im u la tio n m o d e llin g i s c u r r e n tly b e in g done by F e tte r an d Thom pson of Yale U n i v e r s i t y (7). As w ith th e m a jo rity of s im u la tio n m o d e l s , th e o b j e c t i v e of th e m o d e ls d e s ig n e d by F e tte r and Thom pson i s to provide h o s p i t a l a d m i n i s t r a t o r s w ith t o o l s t h a t w ill g iv e them th e a b i l i t y t o p r e d ic t th e o p e r a t i o n a l c o n s e
q u e n c e s of a l t e r n a t i v e d e c i s i o n s . F e t t e r a n d T h o m p so n .h av e c o n c e n t r a t e d th e i r w ork on th e d e s i g n of a s e t of s im u la tio n m o d e ls t h a t are d e s c r i p t i v e of v a r io u s s u b - s y s t e m s in a h o s p i t a l . The m o d e ls c o m p le te d are th o se, of a m a te r n ity s u i t e , a n o u t - p a t i e n t c l i n i c , an d a s u r g i c a l p a v ilio n . T h ese m o d e ls h a v e b e e n d e s i g n e d in a g e n e r a l n a tu r e to a llo w maximum f l e x i b i l i t y . C u rre n t w ork i s c o n c e n t r a t e d on th e d e v e lo p m e n t of a m odel of a c l i n i c a l la b o r a to r y , a g e n e r a l m o d el to p r e d ic t th e e f f e c t of v a r io u s room a r ra n g e m e n ts on e co n o m y of o p e r a t i o n s , a n d a g e n e r a l m o d el to p re d ic t th e ec o n o m ic and t e c h n i c a l c o n s e q u e n c e s , of a n y s c h e m e of p a tie n t o r g a n i z a t i o n . •
D unn an d H in d ie (6) d i s c u s s a s im u la tio n m o del to i n v e s t i g a t e th e e f f e c t of m an ag em en t d e c i s i o n s on h o s p i t a l r e s o u r c e s . The m odel h a s b e e n u s e d to s tu d y th e e f f e c t of h o s p i t a l i n - p a t i e n t s u s in g th e o u t - p a t i e n t f a c i l i t i e s of a h o s p i t a l .
10 A m o d el of a com m unity i n - p a t i e n t h o s p i t a l s y s te m w a s d e v e lo p e d b y H o w lan d (12). The m odel e s t a b l i s h e s d i s t i n g u i s h i n g l e v e l s of the
d e c i s i o n p r o c e s s and i n v e s t i g a t e s th e i n t e r a c t io n b e tw e e n d e c i s i o n m ak er and p a t i e n t a t e a c h l e v e l .
H o s p i t a l s ta f f in g m o d els h a v e b e e n u n d er s tu d y for more th a n th re e y e a r s by th e H o s p i t a l S y ste m s R e s e a r c h G roup of th e U n i v e r s i t y of M ic h i g a n 's D e p a rtm e n t of I n d u s t r ia l E n g in ee rin g (11). The o b je c tiv e of t h e group i s to d e v e lo p m e th o d s for d e te rm in in g s ta f f in g re q u ire m e n ts in h o s p i t a l s and for more e f f e c t i v e u t i l i z a t i o n of p e r s o n n e l . C u rren t r e s e a r c h i s b ein g c o n d u c te d w ith t h e fo llo w in g g o a l s :
1. To d e te rm in e th e e x i s t i n g n e e d s for s ta ffin g 2 . To f o r e c a s t t e c h n i q u e s for fu tu re s ta f f i n g .
3. To e v a l u a t e a l t e r n a t i v e s y s t e m s for im pro v ed u t i l i z a t i o n in s a t i s f y i n g d e m a n d s .
The fo rm u latio n of t h e s e h o s p i t a l s ta f f in g m o d e ls f o llo w e d a p r e s c r ib e d s e q u e n c e of s t e p s . The f i r s t s t e p w a s to d e v e l o p a g e n e r a l m o d el of th e h o s p i t a l . N e x t, th e h o s p i t a l w a s d iv id e d in to f u n c t i o n s , e a c h w ith i t s c o rre s p o n d in g a c t i v i t i e s . At t h i s p o in t, a g e n e r a l m odel of e a c h fu n c tio n w a s f o rm u la te d . The m e th o d s of m o d ellin g w e re d e fin e d and d a ta w a s t a k e n . The m e th o d s w ere th e n t e s t e d and a n a l y s e d for v a l i d i t y . N e x t , th e m odel in p u ts c a n be a d j u s t e d to d e te rm in e future r e q u i r e m e n t s . Two m o d e ls of t h i s ty p e are c u r re n tly u t i l i z i n g t h e s e
B ith ell (4) of th e U n i v e r s i t y of Oxford h a s d e v e lo p e d a c l a s s of m o d e ls for h o s p i t a l a d m i s s i o n s y s t e m s . A ssum ing m o d e ls of h o s p i t a l a d m i s s i o n s y s t e m s c a n be b a s e d in d i s c r e t e t i m e , th e a n a l y t i c a l t e c h n i q u e s of M ark o v c h a in th e o r y are u s e d to d e v e lo p t h e s e m o d e l s . The s t a t e s of th e s y s te m c o r re s p o n d to th e num ber of p a t i e n t s p r e s e n t and th e tim e u n it is one d a y . T h is c l a s s of m o d e ls i s b e l i e v e d t o h o ld r e a l
prom ise for th e s tu d y of v a r i e d a n d c o m p le x s im u la tio n s of h o s p i t a l a d m i s s i o n s c o n t r o l .
V isits to o u t - p a t i e n t d e p a r tm e n ts in th e U n ite d S t a t e s t o t a l ab o u t 120 m illio n per y e a r . This la rg e num ber i n d i c a t e s th e im p o rta n c e of th e e f f i c i e n c y of th e a p p o in tm e n t s y s t e m s t h a t s c h e d u l e t h e s e p a t i e n t s . Some w ork in t h i s a r e a h a s b e e n done b y B a iley (2) w ith W e lc h and Katz (14).
W e lc h an d B a iley fo rm u la te d th e W e l c h - B a i l e y m eth o d of i n d iv id u a l a p p o i n t m en t s y s t e m s . The m eth od s t a r t s th e s e r v i c e i n te r v a l w ith tw o p a t i e n t s a n d s c h e d u l e s e v e r y o th er p a t i e n t X tim e u n i t s a p a r t w h e re X i s th e m ean s e r v i c e tim e for th e s e r v e r . In l a t e r s t u d i e s Katz v e r i f i e d t h i s m ethod for o p tim iz in g a p p o in tm e n t s y s t e m s .
The m ajor c o n tr ib u tio n of Katz (14) i s a n e x p e r im e n ta l s im u la tio n program t h a t e n a b l e s th e u s e r to e v a l u a t e th e e f f e c t i v e n e s s of a l t e r n a t i v e a p p o in tm e n t s y s t e m s in a g iv e n c l i n i c a l e n v iro n m e n t. The program i s w r itte n in FORTRAN and o ffers th e fo llo w in g c a p a b i l i t i e s :
12
■ 1, The u s e r m ay s im u la te b o th in d iv id u a l an d b lo c k type a p p o i n t m ent s y s t e m s .
2 . C lin ic s e r v i c e s o th er th a n t h o s e of p h y s i c i a n s are s i m u l a t e d . 3 . There n e e d n o t be a o n e - t o - o n e r e l a t i o n s h i p b e tw e e n p a tie n t
q u e u e s and c l i n i c p h y s i c i a n s .
The s im u la to r w a s fo rm u la ted to be g e n e r a l e n o u g h to h a n d le th e e v a l u a tio n of s u c h n ew d e v e lo p m e n ts a s r e a l - t i m e co m p u te r a d m in is te r e d a p p o in tm e n t s y s t e m s .
R e la te d w ork in th e f ie ld of h e a l t h d e l i v e r y S y ste m s h a s show n t h a t th e r e i s a c o n c e r t e d effo rt to d e r iv e c o n c r e t e m e th o d o lo g ie s for th e e s t a b l i s h m e n t of o p tim al d e c i s i o n r u l e s for prob le m s e n c o u n t e r e d ,
H o w lan d (13) an d h i s a s s o c i a t e s a t th e Ohio S ta te U n i v e r s i t y E n g in ee rin g E x p e rim e n ta l S ta tio n h a v e d e m o n s tr a te d th e common i n t e r d i s c i p l i n a r y n a tu r e of th e h o s p i t a l . Their s e a r c h for a m e th o d o lo g y for e v a l u a t i n g th e q u a l i t y of p a tie n t c a r e i s a p e r tin e n t and b a s i c s tu d y w h ic h d r a m a t iz e s th e i n a b i l i t y of th e s o c i a l s c i e n c e s to d a y to m e a s u re
one m a n 's ju d g e m e n t a g a i n s t t h a t of a n o th e r . This p o in ts to th e f a c t t h a t d e c i s i o n s are m ade from d a y to d a y a n d th e im p lic a tio n i s t h a t in a m a jo r it y .o f c a s e s , i n t u i t i o n a l ju d g e m e n t w a s u s e d a s a d e c i s i o n r u le r a t h e r th a n m e a s u re d r a t i o n a l i z a t i o n .
P e lle tie r and Thom pson (18) h a v e d e m o n s tr a te d w a y s for p r e d ic tin g th e num ber of in p u ts n e c e s s a r y for d e c i s i o n m a k in g . Their s t u d i e s
A num ber Of s t u d i e s of h o s p i t a l s p a c e a l l o c a t i o n for d e p a r tm e n ta l u s e h a v e d e s c r i b e d th e g r o s s v a r i a t io n in A m erican h o s p i t a l e x p e r i e n c e . Souder (20) s u b s e q u e n t l y s u g g e s t e d a m eth o d for p r e d ic tin g s p a c e d e m a n d s fo r g e n e r a l h o s p i t a l s b u t did n o t d e r iv e m e a n s for e v a l u a t i n g th e m e rits of th e d e m a n d s .
G e n e r a l D e s c r i p t i o n of th e M e th o d o lo g y
This t h e s i s d e s c r i b e s a m o du lar s im u la tio n m eth o d o lo g y for th e g e n e r a l h e a l t h d e l i v e r y s y s te m d e f in e d on page 2 . The p u rp o se of th e m e th o d o lo g y i s to g iv e s y s te m m a n a g e m e n t an a id to m ak ing m e a n in g fu l d e c i s i o n s .
As w ith a l l s im u la tio n m o d e l s , for th e m o d el t o be u s e f u l the u s e r m u s t be c o m p le te ly f a m ilia r w ith th e r e a l s y s te m h e w i s h e s to m od el an d h e m u st fo llo w a s p e c i f i c s e q u e n c e of s t e p s in m o d e l fo rm u la tio n . T h e se s t e p s a re :
S te p 1, D efin e th e r e a l s y s t e m , i t s c o m p o n e n t s , i t s t r a n s - f e rr a b le a t t r i b u t e s , an d m e th o d s for c o l l e c t i n g d a t a . S te p 2. ' C o l l e c t and r e d u c e d a t a .
S te p 3. S p e c if y th e m odel p a r a m e te rs to s im u la te th e r e a l s y s t e m .
S te p 4 . M ak e t e s t ru n of th e s im u l a t i o n .
S te p 5. V alid ate th e s im u la tio n m o d e l.
S te p 6, At t h i s p o in t the m odel c a n be u s e d t o a p p ro x im a te r e s u l t s of c h a n g e s in th e r e a l s y s te m b y e s ti m a t i n g c o r re s p o n d in g c h a n g e s in m od el p a ra m e te rs and s tu d y in g t h e r e s u l t s .
The o b j e c t i v e of t h i s t h e s i s i s to d e v e lo p a s im u la tio n m e th o d o lo g y t h a t c a n be u s e d to d e v e lo p a s im u la tio n m o d e l . The d i f f e r e n t i a t i o n b e tw e e n th e m e th o d o lo g y d e v e lo p e d in t h i s p ap er and th e d e v e lo p m e n t of a m od el i s due to th e o m is s io n of th e d e f in itio n of m e th o d s for d a ta c o l l e c t i o n an d a v a l i d a t i o n of th e m e th o d o lo g y for a r e a l h e a l t h d e liv e r y s y s tem from t h i s p a p e r . The u s e r i s le f t w ith th e r e s p o n s i b i l i t y to fo rm u late t h o s e p o rtio n s of th e m o d el t h a t th e m e th o d o lo g y d o e s n o t s u p p ly . A v e r y good e x a m p le of a n e c e s s a r y p o rtion of a m o d el of a h e a l t h d e l i v e r y s y s te m t h a t th e u s e r m u s t fo rm u la te i s a m o d el t h a t d e f i n e s th e r e l a t i o n s h i p b e tw e e n th e h e a l t h n e e d s t h a t are g e n e r a t e d from th e s y s te m an d th o s e h e a l t h n e e d s t h a t b eco m e h e a l t h d e m a n d s . This n e c e s s a r y portion of a m o del w ill be d i s c u s s e d a g a i n in C h a p te r III.
The m e th o d o lo g y p r e s e n te d in t h i s t h e s i s i s f o rm u la te d in to th re e m o d u le s : t h e y a r e ; a h e a l t h n e e d g e n e r a tio n m o d u l e , a t r a n s p o r t a t i o n m o d u l e , a n d a tr e a tm e n t m o d u le . The b a s i c id e a of th e m e th o d o lo g y i s to n o te th e o ccurrence, of a h e a l t h n e e d an d t r a c e him th ro u g h th e s y s tem n o tin g th e f a c t o r s t h a t d e te rm in e h i s m o v em en t. T h e se f a c t o r s are
n e e d from some lo c a t i o n w ith in th e a r e a b e in g s i m u l a t e d . There are a num ber of d i s e a s e t y p e s p o s s i b l e for th e h e a l t h n e e d ; t h e s e are s p e c i f i e d by th e u s e r .
If th e h e a l t h n e e d c a l l s for t r a n s p o r t a t i o n , he b e c o m e s a h e a l t h dem an d an d e x p e r i e n c e s a num ber of p r o b a b i li s t i c t e s t s to a s s i g n him a mode of t r a n s p o r t a t io n to a tre a tm e n t c e n t e r . In g e n e r a l th o u g h , the
tre a tm e n t c e n t e r c o u ld com e to the p a t i e n t . From th e t r a n s p o r t a t io n m odule th e h e a l t h dem an d i s g iv e n a d e s c r i p t o r for h i s m ode of t r a n s p o r t a t io n a n d an in d i c a t o r for h i s t r a v e l tim e b e tw e e n g e n e r a tio n an d a r r i v a l a t (or of) th e tre a tm e n t c e n t e r . The tre a tm e n t m odule i s a s im u la tio n of th e h e a l t h n e e d 's m ovem ent w ith in th e tre a tm e n t c e n t e r . D e s c r i p t o r s of t h i s m o v e m ent are r e c o r d e d d u rin g h is s t a y in th e tre a tm e n t m o d u l e . The s im u - • l a t i o n i s b a s e d upon a t w e n t y - f o u r - h o u r d a y for h e a l t h n e e d s to e n te r an d e x i t th e s y s t e m .
CHAPTER II
MACROSCOPIC DESCRIPTION OF THE METHODOLOGY
The prim ary c o n c e r n of t h i s c h a p t e r i s to o u tlin e th e co m p o
s it i o n of a r e a l s y s te m t h a t c a n be m o d e lle d by th e m e th o d s of t h i s t h e s i s . It i s v e r y im p o rta n t t h a t th e m o d el d e s i g n e r u n d e r s t a n d s th e s y s te m he i n t e n d s to m o d e l. This c o n c e p t i s e v e r - p r e s e n t in th e a p p l i c a t i o n of th e m e th o d s of t h i s t h e s i s , for th e a c c u r a c y of a s im u la tio n m o d e l i s no
b e t t e r th a n th e d e fin in g p a ra m e te rs g iv e n i t by th e u s e r . H e n c e , a th o ro u g h s tu d y of th e r e a l s y s te m m u st be perform ed b efo re th e m o d e llin g p r o c e s s
/ ' .
i s b e g u n . '
P h y s i c a l R e p r e s e n ta tio n of th e S ystem
An e x a m in a tio n of th e r e a l s y s te m m u s t a llo w i t to be r e p r e
s e n te d b y c e r t a i n d i s t i n c t c h a r a c t e r i s t i c s , There m u s t b e a d e f in a b le a r e a of c o n s i d e r a t i o n by w h ic h th e m o d el c a n be b o u n d e d . P h y s i c a l l y , t h i s a r e a c o u ld c o r re s p o n d t o th e g e o g r a p h i c a l r e g io n h o ld in g th e r e s i d e n t p o p u la tio n of th e h e a l t h d e l i v e r y s y s t e m . An ex am p le of s u c h an a r e a , to be d i s c u s s e d more th o ro u g h ly l a t e r , i s c o n t a i n e d in th e b o u n d a r ie s of th e Papago I n d ia n R e s e r v a t i o n , A rizo n a. A nother e x am p le of a n a r e a i s t h a t of th e p h y s i c a l b o u n d a r ie s of a h o s p i t a l . W ith in t h i s a r e a th e re m u st e x i s t a fin ite num ber of d i s t i n c t g e n e r a t i o n p o in ts from w h ic h th e h e a lth
16
m u st be a v a i l a b l e a t a f in ite number of t r e a t m e n t p o in ts w ith in th e a r e a . T h e se tr e a tm e n t p o in ts m ay or m ay not be g e n e r a t i o n p o i n t s . The g e n e r a tio n an d tre a tm e n t p o in ts m u st be s e p a r a b l e in to d i s t r i c t s . An ex am p le of th e r e a l s y s te m c o n f ig u ra tio n is sh o w n in F igu re 1. The term s for e s t a b l i s h m e n t of d i s t r i c t s w ill be e x p l a i n e d l a t e r . The n e x t to p ic to c o n s id e r i s th e r e p r e s e n t a t i o n s of th e s y s te m c o m p o n e n ts in th e r e a l s y s t e m .
H e a lth N eed G e n e r a tio n
The r e a l s y s te m i n t e r p r e t a t i o n of h e a l t h n eed g e n e r a tio n i s a
s im p le c o n c e p t . G iv e n t h a t the r e a l s y s t e m c o n f ig u ra tio n h a s b e e n d e f i n e d , a t some tim e du rin g th e d a y a n in d iv id u a l b e c o m e s i l l a t some g e n e r a tio n p o in t ( v il l a g e , e t c . ) w ith some d i s e a s e or i l l n e s s . At th e tim e a p e rso n b e c o m e s a h e a l t h n e e d , he h a s m ade no d em a n d s on th e s y s t e m . There are c h a r a c t e r i s t i c s of th e s y s te m th a t w ill d e te rm in e a h e a l t h n e e d 's d e s i r e to d em and s e r v i c e from th e s y s t e m . P erh a p s an in a d e q u a t e tr a n s p o r t a t io n s y s te m or a la rg e p a t i e n t w a itin g tim e a t a tre a tm e n t c e n t e r w i l l in flu e n c e a p e r s o n 's d e c i s i o n n o t to s e e k s e r v i c e from th e h e a l t h d e l i v e r y s y s t e m . If th e h e a l t h n e e d d e c i d e s to d em and s e r v i c e , he lo o k s for t r a n s p o r t a t i o n . If th e h e a l t h n e e d d e c i d e s n o t to d em and s e r v i c e , he w ill e i t h e r re m a in a t home or s e e k s e r v i c e o u ts id e th e s y s t e m .
Area Boundary
G e n e r a tio n Point
T reatm en t Point
D i s t r i c t Boundary
F ig . 1. P h y s ic a l R e p r e s e n ta tio n of the Real H e a lth D e liv e r y System
a re : a v a i l a b l e p e r s o n a l t r a n s p o r t a t io n ( in d i v i d u a l 's c a r , borrow ed c a r , t a x i , e t c . ) , common c a r r ie r t r a n s p o r t a t io n s u c h a s a b u s , a m b u la n c e s c a l l e d from th e tre a tm e n t c e n t e r , and w a lk in g for t h o s e h e a l t h n e e d s w ith in w a lk in g d i s t a n c e of th e tre a tm e n t c e n t e r . Though th e p re c e d in g m o des of t r a n s p o r t a t io n are n o t a l l i n c l u s i v e , t h e y do r e p r e s e n t th e
m a jo rity of m e a n s for an in d iv id u a l to r e a c h a tre a tm e n t c e n t e r . There is one c l a s s of i n d i v i d u a l s n o t d i s c u s s e d ab o v e t h a t d e s e r v e s c o n s i d e r
a t i o n . This c l a s s of in d iv id u a ls i n c l u d e s t h o s e h e a l t h d e m a n d s t h a t co u ld n o t find t r a n s p o r t a t io n to a tr e a tm e n t c e n t e r . T h e se i n d i v i d u a l s are
c l a s s i f i e d a s " h e a lth .d e m a n d s u n a b le to r e a c h a tre a tm e n t c e n t e r . "
T reatm ent
A tre a tm e n t c e n t e r in a h e a l t h d e l i v e r y s y s te m i s e x tre m e ly v a r i a b l e in i t s d e s i g n . The norm al c o n f ig u ra tio n for a tr e a tm e n t c e n te r c o n s i s t s of some ty p e of r e c e i v i n g point w ith in th e c e n t e r , s u c h a s a w a itin g r o o m , a n d a num ber of tr e a tm e n t s t a t i o n s . A fe w common s t a t i o n s found in tre a tm e n t c e n t e r s are : a n u r s e ' s o f f i c e , a n u r s e ' s w o rk ro o m , a d o c t o r 's o f f i c e , a d e n t i s t ' s o f f i c e , a la b o r a t o r y , an X -ra y la b o r a to ry , a p h a rm a c y , and an o p e ra tin g r o o m . The tre a tm e n t c e n te r m ay c o n ta in o nly a d o c to r a n d a minimum am ount of e q u ip m e n t or it m ay be a f u lly s ta f f e d
20 a n d e q u ip p e d c l i n i c . Each h e a l t h d e l i v e r y s y s te m h a s a tr e a tm e n t c e n t e r • w ith a d iff e r e n t c o n f ig u r a tio n .
O nce a h e a l t h dem and a r r iv e s a t a tre a tm e n t c e n t e r , he b e c o m e s a p a tie n t of th e tre a tm e n t c e n t e r . The m ovem ent of th e p a t i e n t w ith in th e tr e a tm e n t c e n t e r is a prim ary c o n s id e r a t i o n for a n i n v e s t i g a t i o n of the o p e r a tio n of th is c o m p o n e n t of the s y s t e m . The f i r s t e n c o u n te r t h a t th e p a t i e n t h a s w ith t h i s co m p o n en t i s to r e p o rt to some i n i t i a l s t a t i o n , n o t n e c e s s a r i l y th e r e c e i v i n g p o i n t . After he i s in tro d u c e d in to th e tre a tm e n t co m p o n e n t, th e p a t i e n t v i s i t s t h o s e s t a t i o n s t h a t are r e q u ir e d to s a t i s f y h is d em and for u s e of th e h e a l t h d e l i v e r y s y s t e m „ Some e x a m p le s of
v i s i t s are for r e g u la r m e d ic a l c h e c k u p s , m e d ic a l d i a g n o s i s , i l l n e s s c h e c k u p s , e t c . After t h i s d em and h a s b e e n s a t i s f i e d , th e in d iv id u a l l e a v e s th e tre a tm e n t c o m p o n en t to r e tu rn h o m e .
S p e c i f ic a t io n of a Sam ple Area
A field, of c u rre n t r e s e a r c h b e in g c o n d u c te d a t The U n i v e r s i t y of Arizona c o n c e r n s th e a p p l i c a t i o n of s im u la tio n m o d els in P u blic H e a lth S e rv ic e h e a l t h d e liv e r y s y s t e m s . The i n i t i a l a p p l i c a t i o n h a s b e e n to s tu d y th e h e a l t h d e l i v e r y s y s te m on the Papago I n d ia n R e s e r v a t i o n , A rizo n a. It i s from t h i s s o u rc e t h a t a sam p le a r e a w ill be ta k e n to be u s e d in i l l u s tr a ti o n of the a p p l i c a t i o n s of th e m e th o d o lo g y d i s c u s s e d in t h i s t h e s i s . The p u rp o se of t h i s sam p le a r e a i s s t r i c t l y to provide a n e x a m p le of th e
th e c u rre n t c h a p t e r . The a r e a b o u n d a r ie s are t h o s e of th e Papago In d ia n R e s e r v a tio n and an e x t e r n a l r e g io n h o ld in g th e to w n s of T u c s o n , Ajo, and C a s a G r a n d e , A rizona a s show n in F igure 2 . The r e s e r v a t i o n i s s e p a r a t e d in to e l e v e n i n t e r n a l d i s t r i c t s an d th e o f f - r e s e r v a t i o n r e g io n forms a
tw e lf th d i s t r i c t . W ith in t h e s e tw e lv e d i s t r i c t s th e r e are f if ty - f o u r g e n e r a tio n p o in ts w h ic h a re m ajor v i l l a g e s an d to w n s w ith in th e s y s te m a r e a . The e l e v e n d i s t r i c t s i n t e r n a l to th e .P a p a g o I n d ia n R e s e r v a tio n are r e p r e
s e n t a t i o n s of th e a c t u a l d i s t r i c t s on th e r e s e r v a t i o n . . Of th e f if ty - fo u r g e n e r a tio n p o i n t s , tw o w i l l be d e n o te d a s tr e a tm e n t p o i n t s . L is te d in T able 1 are th e d i s t r i c t s and g e n e r a tio n p o in ts for th e a r e a w ith th e t r e a t m en t po int u n d e r lin e d .
The g e n e r a tio n of h e a l t h n e e d s o c c u r s a t e a c h g e n e r a tio n p o in t (villag e) and to i l l u s t r a t e th e u s e of d i s e a s e t y p e s , th e r e w ill be a p o s s i b i l i t y of four d i s e a s e t y p e s (in t h i s e x a m p le d i s e a s e ty p e r e f e r s to an i l l n e s s c a t e g o r y ) , for a n y h e a l t h n e e d : e m e r g e n c y , c r i t i c a l , g e n e r a l , or o th e r . The u s e of d i s e a s e ty p e s for t h i s ex a m p le d o e s n o t a s s u m e d i a g n o s i s a t g en era tio n ., r a t h e r th e h e a l t h n e e d s are s e p a r a t e d in to four g e n e r a l c a t e g o r i e s for i l l u s t r a t i v e p u r p o s e s . The c a te g o r y of e m e rg e n c y d o e s
22 G ila Bend
D i s t r i c t C a s a G ran de
O f f- R e s e r v a tio n D i s t r i c t
Sif O idak D i s t r i c t
H ic k iw a n D i s t r i c t
Schuk Toak
D i s t r i c t / T u cso n
Ajo
San X avier D i s t r i c t Gu Vo
D i s t r i c t
P isin im o D i s t r i c t
S e lls D i s t r i c t C h u k u t Kuk
D i s t r i c t Baboquivari
D i s tr i c t MEXICO
F ig . 2 . Sam ple Area of Papago In d ia n R e s e r v a t i o n , Arizona an d an E x tern al D i s tr i c t *
*Not to s c a l e .
D i s t r i c t G e n e r a tio n P oints a n d / o r T rea tm en t Points S e lls C o w lik , Gu O id a k , N o l i a , San L u is , S e lls B aboquivari Ali C hu ck s o n , C h o a l i c , Supe O id a k , Komelik,
T o p a w a , A rte sa
C h u k u t Kuk San M ig u e l , Vamori, Kots Kut, N ew F i e l d s , Tatkum Vo, C h u k u t Kut
Gu Achi San S e r a f in , S an ta R o s a , Ko Vaya, M a is h V a y a , Q u i j o t o a , Ak C h i n , Sikul H im atk
Gu Vo Ali C h u k , Gu Vo
H ic k iw a n S c h u c h u li, H ic k e w a n , H o ta s o n Vo, K aka, V e n ta n a , Vaya C h in
P isin im o Chuw uk M u rk , Kom Vo, Tatk Kam Vo, P isin im o ,
San Simon
Schuk Toak N a v a n a N a k y a , C o m o b a b i , . Pan T ak , Sil N a k y a , San P edro, S a n ta R osa R an ch , C h ia w u li Tak Sif O id ak A negam , C h u ic h u , K ohatk, V a iv a v o , Tat M om uli
San X avier San X avier
G ila Bend G ila Bend /
O ff-Re s e r v a tio n T u c s o n , Ajo, C a s a G ran d e
24 h o ld a d i s t i n c t r e a s o n for p r e s e n c e for t h i s i s th e on ly d i s e a s e ty p e th a t i s s e n t to a tre a tm e n t c e n t e r (clinic) b y a m b u la n c e .
The m o d es of t r a n s p o r t a t io n a v a i l a b l e to a h e a l t h d em and in th e sa m p le a r e a are a s f o llo w s : w alk ( a p p lic a b le only to a h e a l t h dem and a t a tre a tm e n t p o in t), c a r , b u s p ro v id ed by tre a tm e n t c e n t e r , or e m e rg e n c y a m b u l a n c e . The u s e of a c a r for t r a n s p o r t a t io n s i g n i f i e s t h a t th e h e a l t h d em and owned a c a r or c o u ld find s im ila r t r a n s p o r t a t i o n . As m e n tio n e d in t h e p re c e d in g p a ra g ra p h th e a m b u la n c e i s d i s p a t c h e d o n ly for t h o s e p e r s o n s w ho h a v e th e d i s e a s e ty p e " e m e r g e n c y . " . -
N o ted in T able 1, th e r e are tr e a tm e n t c e n t e r s (c lin ic s ) a t S e l l s , A rizona an d San X a v ie r, A rizo n a . A d e s c r i p t i o n of e a c h of t h e s e c l i n i c s i s to f o llo w . Both c l i n i c s f i t . t h e g e n e r a l d e s c r i p t i o n of a tr e a tm e n t c e n te r found e a r l i e r in t h i s c h a p t e r , i . e . , b o th c l i n i c s h a v e a r e c e p t i o n room a n d a num ber of tre a tm e n t s t a t i o n s . The c l i n i c s a re a l s o i d e n t i c a l in th e f a c t . t h a t a p a tie n t r e p o rtin g to e i t h e r c l i n i c m u s t r e p o rt to th e r e c e p t i o n room a t a r r iv a l a t th e c l i n i c .
The c l i n i c a t S e l l s , A r i z o n a , to be in c o r p o ra te d in to th e e x a m p le i s an o u t - p a t i e n t c l i n i c s e r v i c i n g th e P ap ag o I n d i a n s . The s t a t i o n s a t th e c l i n i c a re : a w a itin g room (re c e p tio n room) , a n u r s e 's s t a t i o n , four d o c t o r 's o f f i c e s , a n u r s e ' s w orkroom , a d e n t i s t ' s o f f i c e , a p h a rm a c y , a l a b o r a
t o r y , and a n X -ra y room . A p h y s i c a l r e p r e s e n t a t i o n of th e c l i n i c i s show n in F igure 3 . The c h a r a c t e r i z a t i o n of th e m ovem ent of a p a t i e n t w ith in th e
L a b o rato ry
* X -ra y P harm acy
W a itin g Room
D o c t o r 's O ffic e 4
D o c t o r 's O ffice 3 D e n t i s t ' s O ffice
D o c t o r 's O ffice 2 N u r s e 's
S ta tio n N u r s e 's
Workroom D o c t o r 's O ffice 1
F ig . 3. A P h y s ic a l R e p r e s e n ta tio n of th e O u tp a tie n t C lin ic a t S e l l s , Arizona*
*Not to s c a l e .
26 c l i n i c i s g iv e n by t r a n s i t i o n s t h a t h e m a k e s b e tw e e n th e s t a t i o n s . E ach s t a t i o n i s c h a r a c t e r i z e d by p a t i e n t s w a itin g to be s e r v e d an d p a t i e n t s b e in g s e r v e d . The m e th o d s u s e d to s im u la te t h i s p r o c e s s w ill be d i s c u s s e d in C h a p te r III. The c l i n i c a t S e l l s s u p p o rts a b u s s c h e d u l e on T u e s d a y s to th e fo llo w in g v i l l a g e s on th e r e s e r v a t i o n : C o w li c , Gu O id a k , All C h u c k s o n , C h o a l i c , Supi O i d a k , K om elik, San M i g u e l , Q u i j o t o a ,
Chuw uk M u rk , Pan T a k , a n d Sil N akya „
The c l i n i c a t San X a v ie r, A rizona i s a n o u t - p a t i e n t c l i n i c a l s o s e r v ic in g th e Papago I n d i a n s . The s t a t i o n s a t th e c l i n i c a re : m e d ic a l r e c o r d s ( re c e p tio n r o o m ) , a n u r s e ' s s t a t i o n , th re e d o c t o r 's o f f i c e s , a
p h a rm a c y , a la b o r a t o r y , an d a n X -ra y r o o m . A p h y s ic a l r e p r e s e n t a t i o n of t h i s c l i n i c i s sh ow n in F ig ure 4 . As a t th e c l i n i c a t S e l l s , the m ovem ent of a p a tie n t w ith in th e c l i n i c i s c h a r a c t e r i z e d by t r a n s i t i o n s b e tw e e n th e s t a t i o n s . Each' s t a t i o n i s c h a r a c t e r i z e d b y p a t i e n t s w a itin g to be s e rv e d a n d p a t i e n t s b e in g s e r v e d . There i s no b u s s e r v i c e from th e c l i n i c a t San X a v ie r .
The d i s c u s s i o n in t h i s s e c t i o n i s a g e n e r a l d e f i n it i o n of th e in fo rm atio n n e c e s s a r y t o m o d el a h e a l t h d e l i v e r y s y s te m b y th e m odular m eth o d t r e a t e d in t h i s t h e s i s . The d e s c r i p t i o n of th e s a m p le a re a i s n o t c o m p l e t e , b u t i t p ro v id e s a n e x am p le of th e u s e of th e m e th o d o lo g y t r e a t e d in t h i s p a p e r . A more d e t a i l e d 't r e a t m e n t of d a ta n e c e s s a r y to m odel a.
h e a l t h d e l i v e r y s y s te m w i l l be d i s c u s s e d in C h a p te r V.
\
L a b o ra to ry
7
N u r s e 's S ta tio n
D o c t o r 's O ffice 1
W a itin g Room
\
D o c t o r 's O ffic e 3
D o c t o r 's O ffic e 2
M e d ic a l
R ecords
\
X -ra y
Pharm acy
F i g . 4 . A P h y s ic a l R e p r e s e n ta tio n of th e O u tp a tie n t C lin ic a t San X av ier, Arizona*
Not to s c a l e .
CHAPTER III
' DESCRIPTION OF THE SIMULATION METHODOLOGY
The s im u la tio n m e th o d o lo g y p r e s e n t e d in t h is t h e s i s i s d e s ig n e d to provide i t s u s e r w ith a to o l for m akin g m a n a g e m e n t d e c i s i o n s r e g a rd in g h e a l t h d e l i v e r y s y s t e m s „ The u s e r w ho d e v e l o p s a m o d el from t h is m e th o d o lo g y c a n i n v e s t i g a t e th e e f f e c t t h a t c e r t a i n c h a n g e s in th e s y ste m p ro d u ce on th e h e a l t h d e l i v e r y s y s t e m . E x a m p les of som e c h a n g e s a r e : an e p i d em ic w ith in th e system ., c h a n g e s in th e c o n f ig u ra tio n of th e t r a n s p o r t a t i o n sy stem , s e r v i c i n g th e h e a l t h d e l i v e r y s y s t e m , or c h a n g e s in th e
d e s i g n of a tr e a tm e n t c e n t e r , e . g . , th e a d d i t i o n of a d o c to r a t th e t r e a tm e n t c e n t e r . The m e th o d o lo g y h a s b e e n d e v e lo p e d to s im u la te a w id e v a r i e t y of s i t u a t i o n s and s y s te m c o n f i g u r a t i o n s . The k e y t o i t s f l e x i b i l i t y i s th e g e n e r a l i t y of i t s d e s i g n a n d th e e a s e , w ith w h ic h a d d i t i o n s c a n be m a d e . The r e s e a r c h a s s o c i a t e d w ith th e o r ig in a tio n of t h i s m e th o d o lo g y h a s u n c o v e r e d a num ber of d iff e r e n t u s e s , s u c h a s a s im u la tio n of a s y s te m a s s p e c i f i e d b y th e sa m p le a re a g iv e n in C h a p te r I I, or a s im u la tio n of a h o s p i t a l a s d i s c u s s e d in C h a p te r VI.
M e th o d of S im u la tio n
The m e th o d s in c o r p o ra te d in th e d e s i g n of t h i s s im u la tio n m e th o d o lo g y are b a s e d upon s im ila r m eth o d s d e v e lo p e d by Robert L. Baker (3)
28
.m an y v e h i c l e s , th o u g h h i s m o d el f o llo w s o n ly one v e h i c l e th rou g h t h e s y s te m a t a t i m e . T h e se v e h i c l e s w ill h a v e v a r io u s i n t e r a c t i o n s a s t h e y p ro c e e d th rou g h th e s y s t e m „ Baker (3) h a s s h o w n , a s s u m in g t h e s e i n t e r a c t i o n s c o u ld be r e p r e s e n t e d by m a th e m a tic a l e q u a t i o n s , s t a t i s t i c a l d i s t r ib u tio n s , or in d iv id u a l s im u la tio n m o d e l s , t h a t e a c h v e h i c l e c ou ld be ta k e n th ro u g h th e s y s te m by i t s e l f and th e r e s u l t s , a f te r a l l v e h i c l e s h ad g o ne th ro u g h th e s y s t e m , pro v id ed an a c c u r a t e m e a s u re of s y s t e m p e r fo rm an ce . B a k e r's m e th o d s are a p p lie d in th e m o d u lar s im u la tio n m e th o d o lo g y d e s c r i b e d b y t h i s t h e s i s w ith th e h e a l t h n e e d s in a h e a l t h d e l i v e r y s y s te m c o r re s p o n d in g to th e v e h i c l e s . The m e th o d o lo g y d e s c r i b e d by t h i s p ap e r i s more g e n e r a l in t h a t i t i s d e s i g n e d to in c o r p o r a te m eth o d s for i n v e s t i g a t i n g some of th e i n t e r a c t i o n s b e tw e e n h e a l t h n e e d s and c o m -
p o n e n ts of th e s y s t e m . T h e se m e th o d s are im p le m e n te d in th e tre a tm e n t m odule an d w ill be d i s c u s s e d l a t e r . In t h i s r e s p e c t th e m e th o d o lo g y b e c o m e s f le x ib l e to a d d i t i o n s and c h a n g e s .
The m ethod of s im u la tio n f o llo w s th e h e a l t h n e e d through th e s y s te m in th r e e d i s t i n c t p h a s e s . P h ase 1 i s c o n c e r n e d w ith th e g e n e r a tio n of th e h e a l t h n e e d . At t h i s point a d e c i s i o n is m ade by th e s im u la to r s p e c if y in g w h ic h h e a l t h n e e d s w ill dem an d s e r v i c e from th e s y s t e m . P h ase 2 f o llo w s e a c h h e a l t h d em and from g e n e r a tio n t o a r r i v a l a t a
30
t r e a t m e n t c e n t e r . P h a se 3 f o llo w s th e h e a l t h d em and (p atien t) th ro u g h th e tr e a tm e n t c e n t e r . At th e c o m p le tio n of e a c h p h a s e , th e h e a l t h n e e d s a re c o l l e c t e d and s e n t to th e n e x t p h a s e . F o llo w in g th e d e v e lo p m e n t of th e m e th o d o lo g y t o t h i s p o in t,, i t sh o u ld b e c l e a r t h a t th e g e n e r a tio n m odule e x e c u t e s p h a s e 1, th e t r a n s p o r t a t io n m odule e x e c u t e s p h a s e 2, and p h a s e 3 i s a c c o m p l i s h e d b y th e tr e a tm e n t m o d u l e .
The e x e c u t i o n of t h e s e th re e p h a s e s c o n s t i t u t e s th e s im u la tio n of a s in g l e r e a l tim e d a y . The s im u la tio n m e th o d o lo g y a llo w s t h i s p r o c e s s t o r e p e a t i t s e l f for a num ber of d a y s s p e c i f i e d by th e u s e r . A m a c r o s c o p ic d e s c r i p t i o n of th e flo w of lo g ic i s show n in F ig u re 5.
The G e n e r a tio n M o dule
The .g e n e ra tio n m odule i s a s im u la tio n of th e r e a l s y s te m p r o c e s s in w h ic h p e r s o n s in th e s y s te m b e co m e h e a l t h n e e d s . . T h e m eth o d o lo g y a llo w s th e u s e r to s p e c i f y the p o s s i b i l i t y of d iff e r e n t d i s e a s e ty p e s for th e h e a l t h n e e d s . E ach g e n e r a tio n po in t h a s a p r o b a b ility d is t r i b u t i o n for t h e t o t a l num ber of h e a l t h n e e d s g e n e r a t e d t h e r e . E ach d i s e a s e ty p e h a s an e x p e c t e d per c e n t of th e t o t a l d i s e a s e p o p u la tio n for e a c h g e n e r a tio n p o in t b e in g s i m u l a t e d .
The g e n e r a t i o n p r o c e s s i s a sim p le o n e . Each g e n e r a t i o n po in t i s c o n s id e r e d by i t s e l f . A random v a r i a t e i s t a k e n from th e p ro b a b ility d i s t r i b u t i o n for th e o c c u r re n c e of h e a l t h n e e d s a t th e g e n e r a t i o n po int b y th e m e th o d s d i s c u s s e d in .the n e x t c h a p t e r . This g iv e s th e g e n e r a tio n
Number of T reatm en t . c e n t e r s _ NOT EQUAL
* EQUAL
Number of d a y s ^ to be s im u la te d
NOT EQUAL
EQUAL STOP
DAY=1
j=J + l
DAY=DAY+1 G e n e r a tio n M o d u le:
G e n e r a te a n u m b e r , K, of h e a l t h n e e d s from the g e n e r a t i o n p o in ts
______________ in th e mo d e l____________
T rea tm e n t M o d u le : The kj p a t i e n t s a re fo llo w e d th ro u g h th e jth t r e a tm e n t c e n t e r
b e in g m o d e lle d T r a n s p o rta tio n M o d u le:
E a ch of th e h e a lth n e e d s is a s s i g n e d a mode of t r a n s p o r t a t io n to a t r e a tm e n t c e n t e r ,
w ith kj h e a l t h n e e d s go in g to th e jth tre a tm e n t c e n t e r , _______for j = l , 2 , . . . , num ber of tre a tm e n t c e n t e r s _____
F i g . 5. M a c r o s c o p i c D e s c r i p t i o n of the Si m ulation M o d e l ' s Logic
32 po in t k h e a l t h n e e d s w ith no t a g s a s to d i s e a s e t y p e . The d i s e a s e ty p e for e a c h h e a l t h n e e d i s found by t a k i n g a random v a r i a t e from th e c u m u l a t i v e d is t r i b u t i o n for th e e x p e c t e d per c e n t of e a c h d i s e a s e ty p e of th e t o t a l d i s e a s e p o p u la tio n . This random v a r i a t e c h o o s e s one of th e p o s s i b le d i s e a s e c a t e g o r i e s and t h i s c a t e g o r y i s a s s i g n e d t o th e h e a l t h n e e d . The h e a l t h n e e d s t h a t h a v e b e e n g e n e r a t e d for th e g e n e r a t i o n po in t are e a c h a s s i g n e d a . g e n e r a t i o n t i m e . T his tim e i s b a s e d upon a p ro b a b ility d i s t r i b u t i o n for th e o c c u r re n c e of h e a l t h n e e d s by hour of th e d a y . The o c c u r re n c e tim e i s p l a c e d w ith in th e hour b y a uniform d i s t r i b u t i o n over th e h o u r . The p re c e d in g p r o c e s s i s r e p e a t e d for e v e ry g e n e r a tio n p o in t.
The r e s u l t of th e e n tire p r o c e s s i s th e g e n e r a t i o n of K h e a l t h n e e d s for th e s y ste m ., e a c h w ith th e fo llo w in g d e s c r i p t o r s : a d i s e a s e t y p e , a l o c a t i o n (g e n e ra tio n p o i n t ) , an d a tim e of o c c u r r e n c e . After th e a re a h e a l t h l e v e l h a s b e e n s im u la te d by th e a b o v e p r o c e s s , a g e n e r a tio n su m m ary i s o u tp u t g iv in g t a l l y s of w h ere th e h e a l t h n e e d s w ere l o c a t e d . The program l i s t i n g i s on f il e a t th e S y ste m s E n g in e e rin g D e p a r tm e n t, U n i
v e r s i t y of A riz o n a . A d e s c r i p t i o n of th e flo w of lo g ic for th e g e n e r a tio n m odule i s show n in F ig u re 6. Sam ple o u tp u t for th e s a m p le s im u la tio n in tro d u c e d in C h a p te r II i s show n in A p pendix B.
To u s e th e g e n e r a t i o n m odule i t must, be a s s u m e d t h a t e a c h . g e n e r a t i o n p o i n t 's h e a l t h l e v e l c a n be s im u la te d b y .so m e d i s t r i b u t i o n u s a b l e by th e s t a t i s t i c a l m e th o d s d i s c u s s e d in th e n e x t c h a p t e r . It is