CATASTROPHIC BEHAVIOUR IN SYSTEM DYNAMICS MODELS
FOR BLOOD BANK MANAGEMENT
SHOUKATH ALI, K
RAMASWAMY.N
Department of Mechanical Engineering
Indian Institute of Technology, Bombay -400076, INDIA
ABSTRACT
This paper explores the advantages of System Dynamics as an enquiry method for analysis of
blood bank management systems which exhibit far reaching social implications. Causal loop
diagrams are developed connecting various system components. The integration of individual
causal loops is presented in the form of aninfluence diagram representing the ‘dynamics’ of ablood
bank.Simulation model is built on the basis of causal loop diagrams. The system response to
exogenous disturbances or policy changes are analyzed. The catastrophe model of blood bank
system is developed and the parameters forming the control surface and behaviour surface are
correlated with those of the System Dynamics model.
INTRODUCTION
For the past three decades blood bank management has been a formidable problem for all kinds
of system enquiry methods. The need for a simple and compact description technique is essential
for any approach to system enquiry especially when that system exhibits far reaching social
implications as in the case of blood transfusion services. Studies conducted in India by the authors
reveal that despite advancements in Immuno-Haematology and transfusion therapy there has
been little improvement in blood bank management techniques. The ever increasing gap between
demand and availability of blood, and the unique dependence of patient safety on transfusion
service in the face of alarming rise in seropositive detection of AIDS among donors further
aggravate the cause for concern.
The management problems in blood banking is chiefly due to the outdating of blood after its life
period. A major part of the literature published so far suggesting policies for blood bank
management is in reality mere academic exercises especially so under the present conditions of
sophistication and complexity. Though simulation techniques yield solutions to complex inventory
situations they ignore or fail to identify the time varying fluctuations in measures describing the
system states and the decisive roles of exogenous elements in the inter dependant back loops.
To cite an example the demand for blood originates outside the simulated system and hence
cannot be treated as an internally generated variable. It is purely exogenous and hence the
mechanism generating demand forblood is understood in a probabilisticsense only. ‘Replenishment’,
‘leadtime’, ‘ordering’ etc are conceptual parameters which are indiscriminately applied to blood
bank inventory models. In reality they are variables outside the inventory set up over which the
blood bank administrator has least control. Thus simulation studies confine themselves to
constructing and operating dynamic models either disregarding exogenous elements influencing
the system states or regarding them as controllable internal parameters. The generalizability of
these studies are limited too.
This article explores the usefulness of System Dynamics simulation modelling for the analysis of
blood bank inventory system. The problem.is looked upon from an integrated vantage point.
DYNAMICS OF A BLOOD BANK
Most systems are dynamic in nature i.e they change their states with time. Even systems normally
considered static turn out to be dynamic when perceived through a magnified time frame. System
Dynamics is primarily a philosophy, a way of looking at organizations and systems, a methodology
forthe study of complex systems and the interaction of system variables. Its conceptual frame work
integrates knowledge of the real world with the concept of how feed back structures cause
observed changes, through time.(Forrester,J.W.,1973).It focuses on policies and how policies
determine behavior.
The complexity of operations in a blood bank make the task of policy selections a formidable
problem.(England and Roberts.,1978).The policy issues to be considered are multi objective in
nature. Obviously an analytical model has to solve for several simultaneous equations with non
linearities arising from interaction of these objectives and variables.
The starting point of system modelling exercise is identification of objectives which arise from
an observed cause for concern of behaviour of one or more variables. Such a thinking towards
problem definition leads to causal loopdiagrams. The role of causal loop diagrams in representing
the structural relationships in a system is significant. ( Nancy Roberts et.al 1983 ).
Some SD practitioners prefer such causal loops introduced by Maruyama in 1963 for the display
“ASSIGNED
tNVENTORY
(CROSS_MATCHED)|
UNASSIGNED.
GUT VATED 4
INVENTORY i
|
COMPONENTS DEMAND,
INVENTORY USAGE!
FIG 1 MODIFIED BLOOD BANK INVENTORY MODEL
- 696 -
ASSIGNED BLOOD
INVENTORY
DESIRED
ASSIGNED
BLOOD RATE OF BLOOD
INVENTORY TRANSFUSION
OT
TIME CONSTANT
FIG.2. SIMPLE C-L DIAGRAM
of relationships between variables, while Forrester consistently opposed the use of such diagrams.
because he believed that they can give a misleading impression of the feed back properties of the
system. He suggested the well known flow diagramming approach based on providing clear cut
tules for development of system models.
While inagreementwith Forrester's reservations about causal loop diagrams itis to be remembered
that the reasonably large collection of meaningful operating data required for the causal loop
diagrams prevents erratic conclusions about feed back properties of the system. Besides,the
computer software tools of SD ranging from DYNAMO, DYSMAP, STELLA etc have a strong
affinity for information inputs in sizable quantities. Therefore in this work the authors have used
C-L diagrams as building blocks for the development of the cumbersome SD flow diagram.This
method adds to the modeller's insight into the behaviour exhibited by the system over a specified
length of time.
The dynamic behaviour within a system is essentially generated by two types of mechanisms,
namely positive feed back and negative feed back. The former promotes growth while the latter
is goal seeking tending to move the system towards a desired level of operation. The underlying
concept of this model building approach is based on the resource-state transformations in natural
dynamic systems.(Wolstenholme and Coyle,1983).The blood bank inventory model of Jennings
(Jennings, 1973 ) exhibits these resource-state transformation and can be considered as a
dynamic system. (Shoukath Ali and Ramaswamy, 1991). A modified version of this classical model
is given in Fig (1) with the addition of more state changes namely blood components and outdating.
Such state changes are affected either through natural processes or by human decisions.
The dynamics of the system are highlighted through time dependant variations of the quantities
and presence of substantial feed back relationships. Fig(2) is a simple causal feed back loop of
the second type.
RATE OF -
===>
PATIENTS
PATIENTS DEMAND FOR
NEEDING BLOOD TRANSFUSED
POPULATION BLOOD RATE OF PEOPLE
PHYSICIAN
RATE OF —==3\, REQUISITION
=> DISCARD DISCARD QTY
DISEASED AFTER TESTS
DONORS
nn RATE OF
WHOLE BLOOD
i na adsicneD RATE OF sarcroay TRANSFUSION
: FRESH CROSS MATCHING a
COLLECTION Loop INVENTORY
RATE COLLECTION
f *& RATE OF " SHORTAGE
iN SUPPLY h cor aetaa LEVEL
ts FROM OTHER TH "Sy a
Suruce HOSPITALS <@ntd
COMPONENTS
INVENTORY
“me TO OTHER RATE OF
OF NO OF
PEOPLE = HOSPITALS v
Aw SUPPLY
ary
REQUISIT
COLLECTION HOSPITALS aGeing__, OUTDATED ron hoon
CAMPAIGN RATE > QTY
FIG.3. BLOOD BANK DYNAMICS
- 698 -
The flow inthe system is triggered through positive or negative feedback loops. The model exhibits
a goal seeking behaviour tending to move the system to a desired level of operation. Thus
transfusion rate is proportional to the difference between the desired level and the actual level while
the rate over the time period determines the actual level. Thus the simple first order difference
equation for the causal loop is obtained as,
L.& fr *DT
R = (1/0T)*(L, - Ly)
Integrating the individual causal loops connecting various system components the entire structural
relationship may be obtained in the form of an influence diagram which represents the dynamics
of a blood bank.(Fig 3.)
SIMULATION MODEL
As causal loop diagrams do not use specific symbols for representing rates and levels care should
be taken while switching over to SD simulation flow diagrams. The simple causal loop of Fig (2)
may be redrawn using SD symbols as shown in fig (4).
La PATIENTS
AINV TRANSFUSED
vo RTRN
ys _ aa oT
/
2 >
FIG.4.SIMPLE SD SIMULATION FLOW DIAGRAM
The DYNAMO equations may be written as follows:,
L AINV.K = AINV.J + DT * (RCMB.JK- RTRN.JK),
NOTE Assigned INVentory (Units of blood),
N_ AINVN = AINVD,
NOTE Assigned !NVentory iNitial value,
R_ RTRN.KL = SHTGB.K DFPTDB,
NOTE Rate of TRansfusioN (Units of blood per day),
where,
RCMB = Rate of Cross Matching Blood(Units per day),
SHTGB = SHorTaGe of Blood (Units of blood),
DFPTDB = Delay in Filling PaTients’ Demand for Blood,
AINVD = Assigned !NVentory Desired.
The key elements considered in the simple flow diagram of fig (4) are assigned blood inventory
level,shortage level, rate of cross matching etc. Introducing the state changes of blood fromdonor
level to cross matched and components level,flow of requisitions for blood from other banks and
hospitals, and exogenous elements influencing the bank operations, the SD simulation flow
diagram for the whole system may be developed.
The conservative system part of the flow diagram has two major components namely flow of blood
fromthe donor base to the demand usage point and the flow of requisitions from physicians to the
donor base routed through the banks.
The nonconservative system part is constituted of the delays, constants and auxiliary variables
estimated from the data collected on the blood bank operations. Some of these estimates are
results of qualitative assessments made by the authors. Nevertheless the lack of precision that
may have to be tolerated does not in any way destroy the value of such studies (Gordon,1990).
The graphs shown in figures 5 and 6 are the plotted output from the simulation run of the model.
At the equilibrium state the model is initialized with,
AINV= 50 units of blood,
UAINV= 100 units of blood and
RPTDB= 50 units of blood (Rate of PaTients’ Demand for Blood)
On the 15th day a sudden hike in RPTDB (might be due to accidents etc.) for 100 units occurs.
This hike is injected into the model in the form of a PULSE function. The system responds with
transient fluctuations which are characteristic of such systems. A sudden catastrophic rise in
shortage level is observed.
When a STEP input is injected similar transients are generated. The system steadies itself after
aperiod of about 100 days. The second graph shows the effect of sudden rise in blood collection
injected as a PULSE function, on outdating quantity, OUTQ. An initial value of zero is assumed for
OUT and this suddenly rises upto 20 units or more.A STEP input also produces similar pattern
of outdating.
One of the significant weakness of DYNAMO is the primitive and less precise integration scheme
ie Euler's method. Even so modelling of complex information feed back systems can effectively
be done with fair accuracy and precision. The process by which the SD equation structure is
obtained is rather different and on the whole superior to most other modelling methods (Sharp and
Price,1984).
- 700 -
288.
468.
158.
388.
188.
268.
s8.
188.
oa
RPIDBC8. ,268.)
UATHUCB. , 488.)
SHTCE(B., 488.)
i j i
1
|
FIG. 5
% i !
& i |
a ; i
qt iL\ |
a
<a SHTAI !
| |
8. 18. 28. 38. 48. 58. 9.999 69.999 79.99989.999188
————- _ABCOL(8.,288.)
OUTQ(B.,2B.)
TINE
UATHY CE. 468.)
FIG. 6
RBcoL
TAIN
Daw
28.
38.
40.
se. 59.999 69.999 79.99989.999188.
TIHE
CATASTROPHIC BEHAVIOUR
System Dynamics and Catastrophe theory deal with nonlinear dynamic systems and it is natural
that one resembles the other in many ways.
in 1974, Thorm, R classified elementary catastrophes describing discontinuities and cataclysmic
changes in nature into seven groups, each of which is controlled by not more than four factors
controlling the processes. The mathematical equations associated with these archetype forms
along with their proof are presented by Golubitsky (1978).
The cusp Catastrophe model of a blood bank system is shown in fig (7). Inblood banking the most
significant elements over which the administrator has least contro! and thatinfluence the optimum
operating conditions, are outdating and shortage. The system swings between these two
behavioural states.
PLASMA FRACTIONATION
AND COMPONENTS
OUTDATING
SUPPLY FROM
OTHER HOSPITALS
| LEAST LIKELY
BEHAVIOUR
a4
BLOOD
INVENTORY
LeveL
DEMAND COLLECTION
RATE RATE
‘BIFURCE iTON:
FIG.7. CATASTROPHE MODE! OF BLOOD BANK INVENTORY
SYSTEM.
me 702
The single dimension which characterizes the behaviour surface is the blood inventory level. The
parameters forming the control surface are demand rate and fresh blood collection rate. The
behaviour surface is in fact a plot of points where the first derivative of the energy function is equal
to zero. The unstable middle plate and the inflection points where catastrophes occut are formed
by the maxima and the stable top and bottom sheets are formed by the minima. (Zeeman,1976).
Itcan be seen from the diagram that normal inventory levels are associated with mild catastrophes
while large stock levels end up in severe catastrophes as indicated by the lines A-A-A and B-B-
B respectively. Blood donation campaigns quite often yield good results in raising the inventory
levels of blood banks. But as canbe seen from the figure, if the collection rate is not rationally fixed
basedon shortage and preservation limitations large quantities of blood get outdated catastrophically.
Acute shortage of blood is felt during times of major accidents, wars etc. Such unforeseen and
sudden hikes in demand rate result in shortage catastrophes, the degree of which vary depending
on the urgency of the requisitions for blood.
The bimodality of the model is indicated by an increase in the normal inventory level resulting in
either shortage or outdating. This constitutes the bifurcation set of the model.
CONCLUSION
Ascientific computer based model developmentis suggested for policy making inthe management
of blood banks. The set of DYNAMO equations developed for the conservative and non
conservative systems were initialized using data collected through a survey conducted by the
authors in 1991 on blood banking operations in India.
The survey revealed that out of about 1000 small and large blood banks in India only less than 150
banks are operating under licensing regulations stipulated by authorities. In the year 1990, there
was a shortage of blood to the tune of 3.5 million units. in all the 1000 and odd banks the total
quantity of blood collected was 19.5 million units against a demand for about 23 million units. This
shortfall is reflected world wide. Donation campaigns alone do not serve the purpose because
despite elaborate screening procedures as many as 10% recipients of transfusion developed
Hepatitis virus C and about 1000 donors were detected as seropositive for AIDS.
The simulation results presented bring forth these points in a revealing manner and upholds the
need for major changes in the management style of blood banks in India.
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