Exercises in causal loop diagrams (CLD s) 1 Room hea A room is heaed by an elecrical heaer. Explain how he in he room is changed by he elecrical heaer using a causal loop diagram. Reference mode: Draw a hypohesized reference mode of how room adjus o he desired, assuming he room was iniially 10 degrees below desired room. Variables :, room heaing, desired ( seing for hermosa) CLD: 2 Room hea II There may be some more imporan facors ha influence he of he room. Asume he room is surrounded by oudoor walls. How does he oudoor affec he indoor? Include he oudoor in your CLD, and include oher variables if necessary. You have probably included hea losses o he surroundings in your diagram. Suppose he hea losses are higher han he room heaing from he? (The hea loss rae is greaer han he room heaing rae) How does his aler he possible behaviour of he sysem? 3 Room hea III Suppose here are people living in his room, and ha hey keep adjusing he hermomeer according o heir comfor. How would you include his process in your CLD? 1
Soluions o exercises 1 Room heaing I The hypohesized ime developmen of an in room is shown below: Desired room = 25 C Iniial T=10 C We know ha an increase in room heaing by he elecrical heaer, increases he room, ceeris paribus (everyhing else he same) : Furhermore, if here is a big gap beween desired room (defined by he hermosa seing a, for insance 25 C), he heaer will increase he hea in he room o increase he. Thus an increase in gap (where desired > is defined as a posiive gap) increases room heaing from : If we assume ha he desired is iniially higher han acual, an increase in will decrease he gap. Thus : gap seing Noe he negaive polariy of he from o gap. Now his makes up a balancing (goal seeking)informaion feedback process, and i explains he hypohesized behavior of he reference mode. The gap beween desired and acual makes he heaer swich on and increase he room hea, which increases he in he room. The is coninuously moniored by he hermosa, and when he room equals desired, he heaer is swiched off. B Room adjusmen gap seing gap 2 Room heaing II o he surroundings occur, if he oudoor is lower han he room. This occurs hrough convecion and conducion of hea hrough he walls, windows and venilaion. We inroduce he addiional explanaory variables: Hea loss gap Insulaion hickness. A firs aemp o capure hese causal relaionships are shown in he figure below. An increase in oudoor 2
decrease hea loss. An increase in hea loss, decrease room. Hea loss B Room adjusmen gap seing This seems reasonable, and he causal relaionships sounds correc, bu wha if boh oudoor and room increases simulaneously, and by he same amoun? Wouldn hea losses also depend on he room, or raher he difference beween oudoor and indoor? The figure below shows how hea losses are proporional o he gap beween oudoor and indoor. An increase in increases he oudoor gap (assuming indoor >oudoor ). An increase in oudoor gap increases hea losses. An increase in hea losses decrease, forming anoher balancing feedback loop, B2. B2 hea loss gap B1 Room seing gap be driven owards he oudoor, raher han he seing. Iniial T=10 C = 2 C Room heaing (energy) is an exensive propery, while is an inensive propery. The hea capaciy of he room is imporan for how fas he room can be heaed by he. A large room needs a lo of heaing o change he. Thus an increase in he he room hea capaciy reduces he. Concerning hea losses, o he surroundings, his very much depends on he insulaion hickness of he walls, and of how well he windows are insulaed. We include hese facors in our diagram, bu i does no change he srucure of he causal loop diagram in he sense hese facors (hea capaciy and insulaion hickness) are reaed as consans. Insulaion hickness B2 hea loss gap Room hea capaciy B1 Room seing gap We could, of course go furher ino deails, for insance concerning he hermosa of he elecrical heaer. You ve maybe heard he on and off clicking of your heaer a home when he relay swiches on and off. There is a cerain hreshold for he relay o swich on and off, causing a ime delay here. This delay is no very large, however, bu i If hea losses are greaer han he room heaing from elecriciy, he room will coninued o drop. In fac, he B2 loop dominaes, and he room will 3
causes he heaer o oscillae over and under he desired, because of he ime delay involved: Desired room = 25 C Iniial T=10 C 3 Room heaing III We define he following variables: Comfor Perceived gap If he room deviaes significanly from our comfor, we ry o reduce he perceived gap according by adjusing he hermosa seing: Insulaion hickness B2 hea loss gap Perceived Room hea gap capaciy B1 Room B3 Comfor gap seing This inroduces a hird balancing loop B3. An increase in perceived gap, resuls in an increase in he hermosa seing, which increases he gap observed by he hermosa, which resuls in increasedri heaing and herefore higher room, which gives he hermosa new informaion on which i can make new decisions of wheher o swich on or off he heaing. Similarily, he people occupying he room feels he new, and make new decisions abou wheher o adjus he hermosa or no. We could of course, coninue o add loops here. On a longer ime perspecive, oher facors are more relevan han he hermosa conrol. Perhaps people ake noice of heir elecriciy bill, and ries o find ways o cu heir coss by reducing heir comfor (a feedback loop Comfor formed by, energy consumpion, elecriciy bills and comfor, which adjuss ), or even consider alernaive ways of cuing coss, such as increasing he insulaion hickness of he walls, changing windows, ec. To illusrae his, les inroduce Coss of elecriciy, Desire o save energy and Insulaion hickness. As shown in he below CLD, his forms anoher balancing loop (B5) denoed Energy efficiency invesmens. Furhermore a quicker response could be o reduce Comfor driven by he Desire o save energy. gap Room hea capaciy B2 hea loss B1 Room Insulaion hickness gap Comfor Perceived gap seing 4 Some general observaions There is some general feaures o his process, namely he way decisions are made according o goals. Sae B decision process The elecrical heaer observed he and according o he hermosa seing, is policy was o swich he heaer on if he was lower han he desired, or swich i off if he gap was sufficienly small (or perhaps negaive). The decisions are made coninuously, or a each poin in ime on he basis of new informaion abou. Similarily, he people living in he room aced in he same way. Their goal of keeping room was compared wih heir perceived room. If here B3 Comfor B5 Energy efficiency invesmen Coss of elecriciy informaion abou sae correcive acion discrepancy decisions B4 Say cold Desire o save energy goal 4
was a discrepancy beween he room and heir comfor, heir policy is o adjus he hermosa seing in order o achiveve heir comforable. Some hours laer, hey perhaps perceive he room oo high, and ake new correcive acions. In he longer run, when he elecriciy bill arrive in heir mail, hey migh realise an excessively expensive energy consumpion. To do somehing abou heir bills, hey migh consider reducing heir comfor, or a leas make sure o urn down he hermosa during he nigh or when hey leave for work (loop B4) In he even longer run, hey migh decide ha invesing in more insulaion will be worhwile, if i pays off (loop B5). We make our decisions on he basis of informaion available o us. Seemingly, we use all sors of informaion o make very complex decisions. In fac, a he decision poin, we are only able o make use of a few relaionships a a ime, when we make he acual decision, because he human mind is no adaped o keep more han wo or hree houghs in mind simulaneously (as has been shown by cogniive psychologiss). By capuring he essenial decision rules governing decisions in organisaions, i.e. invesmen decisions, pricing decisions, rading sraegies, consumer behaviour ec, i is possible o sudy he consequences of hese for he oal sysem. 5