access to long-term care: the true cause of hospital congestion?

Access to Long-Term Care: The True Causeof Hospital Congestion?

Jonathan PatrickUniversity of Ottawa, Ottawa, Ontario K1N 6N5, Canada, [email protected]

Much attention has been paid to lengthy wait times in emergency departments (EDs) and much research has sought toimprove ED performance. However, ED congestion is often caused by the inability to move patients into the wards

while the wards in turn are often congested primarily due to patients waiting for a bed in a long-term care (LTC) facility. Thescheduling of clients to LTC is a complex problem that is compounded by the variety of LTC beds (different facilities androom accommodations), the presence of client choice and the competing demands of the hospital and community popu-lations. We present a Markov decision process (MDP) model that determines the required access in order for the census ofpatients waiting for LTC in the hospitals to remain below a given threshold. We further present a simulation model thatincorporates both hospital and community demand for LTC in order to predict the impact of implementing the policy derivedfrom the MDP on the community client wait times and to aid in capacity planning for the future. We test the MDP policy vs.current practice as well as against a number of other proposed policy changes.

Key words: health care; long-term care; Markov decision processes; scheduling; simulation health careHistory: Received: December 2008; Accepted: August 2010, after 2 revisions.

1. IntroductionThe management of long-term care (LTC) has becomeincreasingly important within Canada as the impactof insufficient planning has progressively hamperedthe ability of hospitals to function efficiently. Hospi-tals are often faced with over 100% occupancy with asmuch as 15–20% of that congestion due to so-called‘‘alternate level of care’’ (ALC) patients. The termALC refers to patients who remain in acute care be-yond the medically recommended time due to ashortage of capacity available in a more appropriatefacility—primarily a LTC facility. The president of theOntario Hospital Association cited the backlog of ALCpatients as the most serious problem facing hospitalsin the province while many who work within thehospitals believe that much of the current congestioncrisis could be alleviated by removing this backlog ofALC patients.

Compounding the problem is the presence of sig-nificant demand for LTC arriving directly from thecommunity. While the impact of ALC patients onhospital congestion is obvious, the impact of excessivewait times in the community is more subtle but none-theless crucial. Excessive wait times result in addedstress on the family of the LTC client who are forced tominister to someone who has been deemed to require24 hour supervision.

While strictly speaking anyone over 18 who haschronic health needs that cannot be met by any com-bination of home care or community care is eligible

for LTC, it is almost exclusively the elderly who findthemselves on the wait list. Clients often enter thewait list from the hospital following an incident (oftena fall) that has sufficiently debilitated them that theyare no longer capable of returning home. Alterna-tively, clients may enter the wait list by requestingan in-home assessment done by the local healthauthority.

A scan of major operations research journals dem-onstrates that an impressive amount of effort has goneinto improving the day-to-day management of emer-gency departments (EDs) (see for instance Carter andLapierre 2001, Cochran and Roche 2009). In contrast,there is next to nothing regarding the question of LTCplanning. This is somewhat surprising as it is quiteclear that improving the efficiency of an upstreamprocess is of limited use if there is a significant back-log downstream. Forster et al. (2003) performed anobservational study that demonstrated a clear in-crease in ED wait times as hospital occupancyincreased, with a marked increase once occupancyexceeded 90%. Similarly, Green and Nguyen (2000)used a queuing approach to demonstrate a markeddecrease in hospital admittance delays with a reduc-tion in the hospital length of stay (LOS). A recentpaper by Thompson et al. (2009) uses a Markov de-cision model to attempt ward-to-ward re-allocation ofpatients in order to alleviate ED congestion but doesnot deal with the issue of blocked beds due to patientswho are unable to transfer out of the hospital. Two

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PRODUCTION AND OPERATIONS MANAGEMENTVol. 20, No. 3, May–June 2011, pp. 347–358ISSN 1059-1478|EISSN 1937-5956|11|2003|0347

POMSDOI 10.1111/J.1937-5956.2011.01229.X

r 2011 Production and Operations Management Society

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papers that do deal specifically with blocked beds area paper by Weiss and McClain (1987) that uses aqueuing analytic approach to describe the processfrom being labeled as ALC to exiting the hospital anda paper by Koizumi et al. (2005) that models move-ment between mental health facilities using a queuingapproach with blocking to model downstream con-gestion. Both papers provide some interestinganalytical results of the impact of ALC patients onhospital congestion but neither go beyond the hospitalto look at means of improving the flow of patients outof the hospital to more appropriate facilities.

This research was first motivated by conversationswith a local hospital. The hospital is the largest in theregion with over 1000 beds. However, it is invariablyfunctioning at less than capacity due to the presenceof up to 150 ALC patients. In the last year, almost 600surgeries were canceled due to hospital congestion,largely attributed to high numbers of ALC patients.Consequently, management is looking to determinethe necessary LTC access in order to insure that thecensus of ALC patients in the hospital does not exceeda given threshold. In conjunction with the hospital, wehave worked closely with the Continuing Care AccessCenter (CCAC) whose role it is to determine thescheduling of clients to LTC. All empirical data wereprovided by the CCAC.

We present in this paper a model that determinesthe necessary access to LTC for a hospital in order tomaintain the ALC census below a pre-specifiedthreshold. We demonstrate that, in all instances ofthe problem we have solved to date, a policy thatseeks to return the ALC census as close as possible toa level significantly below the desired threshold isoptimal. Further, we demonstrate through a full-scalesimulation of the scheduling of clients (both from thehospital and from the community) to LTC, that cur-rent capacity is insufficient to both maintain thehospital census below a reasonable threshold andcommunity wait times below the current wait timetarget of 90 days. Finally, in light of the current policyemphasis on increasing home services in order to de-lay entry into LTC, we demonstrate that a 33%reduction in the average LOS in LTC is required inorder to reduce the wait times to close to the targetunder the current capacity constraints. While our em-pirical results are based on the local setting, theproblem of insufficient access to LTC causing hospitalcongestion is endemic across Canada and most likelyelsewhere as well. Both the Markov decision process(MDP) model and the simulation presented below canbe easily transferred to other health regions facingsimilar problems.

The rest of the paper proceeds as follows. Section 2presents the scheduling challenge that we address.Section 3 presents an MDP model that determines the

appropriate policy for hospital placements in orderto maintain the ALC census below a pre-specifiedthreshold. Finally, section 4 presents the simulationmodel that compares the policy derived from theMDP with the current practice and assesses the im-pact of two major policy changes proposed by theministry of health.

2. The Scheduling ChallengeEach new LTC client designates up to three preferredLTC facilities as potential destinations as well as whatbed type (private, semi-private, or ward) s/he desires.Current regulations require that each facility offer 40%of their capacity at the ward rate. While the cost ofward beds is covered by the government, clients mustpay an additional fee if they desire a private or semi-private room. Clients are placed in the queue andserved on a first-come-first-served basis. If the condi-tion of a client in the community deterioratessufficiently then s/he is upgraded to an urgent cat-egory and jumps to the front of the queue. Initially,hospital clients were never upgraded to the urgentcategory as they were deemed to already be receivingadequate (if inappropriate) care. This policy proved tobe unworkable for the hospitals as it led to a signifi-cant backlog of ALC patients. Thus, in April 2006, apolicy was introduced that dictated that all hospitalclients be upgraded to the urgent category for 2 dayseach week. While this has helped to mitigate the im-pact of ALC patients on hospital congestion, itremains a somewhat arbitrary solution. Part of themotivation behind this research is to provide a moreevidence-based policy for hospital placements whileat the same time being able to predict the impact ofthis policy on the wait times for community clients.

Two other aspects of current practice are worthmentioning. First, the current practice is that both ur-gent clients and hospitals clients are required to takethe first available bed even if it is not on their list ofpreferred facilities. However, all clients who are notplaced in their top facility choice have the option ofremaining on the wait list for their preferred choice(s)once they have been placed. This ‘‘first available bed’’policy is strictly speaking contrary to ministry regu-lations but has been in place for many years. One ofthe changes we examine in this paper is the impact ofremoving this policy. Second, each client is given a‘‘level of care’’ score and facilities do have the right torefuse a client placement if they deem that they can-not adequately meet that ‘‘level of care.’’ Theserefusals are not a regular occurrence and usually re-sult in negotiations between the CCAC and the facilitythat result in the client eventually being placed.

The size of this scheduling problem makes solvingthe complete model analytically extremely challeng-

Patrick: Access to Long-Term Care348 Production and Operations Management 20(3), pp. 347–358, r 2011 Production and Operations Management Society

ing. The region under study has 28 facilities. Thus,even if all hospitals are considered as one entity andsemi-private rooms are ignored, there are already over600,000 different demand categories (based on28�27�26 facility preference triplets, 28 facilitiesand three wait list locations and two bed types).Thus, in this paper, we first present a model that an-swers the partial question of hospital access to LTCand then build a simulation model to assess the im-pact of granting this access.

Our model simplifies somewhat from reality in anumber of respects. For the hospital model, we ignorethe non-homogeneity of LTC beds. Ignoring facilitypreference reflects the ‘‘first available bed’’ policycurrently in place and is therefore a reflection of cur-rent practice. We also ignore bed type preference,which is contrary to current practice. However, as thehospital census invariably contains a mixture of pri-vate and ward demand and as the goal is to maintainthe census below a certain threshold (rather thanminimizing individual wait times), this added sim-plification does not greatly impact the policy.Moreover, for equity reasons, when a bed becomesavailable to the hospital it is offered to the client withthe longest wait time who is willing to take the bed(i.e., a ward client cannot be offered a private bed).Thus, it is straightforward to adapt a policy that doesnot differentiate between private and ward clients tothe reality where one must. In the simulation model,we incorporate both bed type and facility preferencebut in both the MDP and the simulation we ignore the‘‘level of care’’ of the client.

A crucial factor that is incorporated into both mod-els is that a portion of clients exit the wait list withoutbeing placed. The primary reason for such exits isdeath but there are other reasons—especially amongthe community clients. Other reasons include place-ment in a different region, the decision to remain in aprivate retirement home instead, or an improvementin the client’s condition. These ‘‘exits without place-ment’’ are modeled slightly differently in the MDP vs.the simulation. In the MDP model, the probability ofan ‘‘exit without placement’’ is modeled as a functionof the size of the wait list (because wait times are nottracked), whereas in the simulation model this prob-ability is modeled as a function of the wait time.

In the next section, we describe the MDP model forhospital placements.

3. The Hospital ModelDecisions regarding the placement of hospital patientsare taken at regular intervals. The CCAC determineswhich of the available beds are offered to the hospitaland, in consultation with the hospital, which patientsshould receive them. Currently those decisions are

made independent of the census of ALC patients inthe hospitals. We seek to address this deficiency bycausing the policy to depend both on the hospitalcensus and on the number of LTC beds available.Thus, the state space is represented by a vector ~s ¼ðh; bÞ where h represents the difference between thepre-specified threshold and the current ALC censusand b represents the number of LTC beds available.The reason for letting h represent the difference ratherthan the actual census is to more easily motivate arelationship between classical inventory managementproblems and the scheduling problem modeled here.

The action, a, represents the number of availablebeds to assign to hospital demand. Actions are con-strained so that assignments never exceed supply ordemand and are always positive and integer. The ac-tion set can therefore be defined as

Að~sÞ ¼ faja � minðT � h; bÞ; a 2 Zg; ð1Þ

where T is the pre-specified threshold for the ALCcensus in the hospital.

We impose two costs on the system. First, there is acost, f1(a), for placements representing the ‘‘loss’’ ofcapacity for community requests. Second, there is acongestion cost, f2(h), for every patient over the pre-specified threshold, T, in the hospital. The cost iswritten as

rð~s; aÞ ¼ f1ðaÞ þ f2ðhÞ: ð2Þ

The placement costs can reasonably be assumed to belinear in a while the the congestion costs could take ona number of forms. One option is to allow f2(h) to bezero for positive h and convex for negative h (that is,the higher the congestion the greater the cost). Thiswould reflect the current situation where a certainnumber of beds have been set aside for ALC patientsso that hospital function is only impacted when thecapacity of these wards is exceeded.

The actual values of both f1( � ) and f2( � ) are clearlysubjective. The cost of placement for instance dependson what cost one associates to LTC clients waiting inthe home. The cost of congestion can perhaps be moreeasily quantified by taking the difference betweenservicing an acute patient in the ED as opposed toon the wards but this fails to capture the other costsof congestion such as patients being placed in non-ideal wards, being exposed to sicker patients, and thelack of beds causing surgical cancelations. Thus, dueto this subjective nature, we have varied the ratio ofthe costs quite dramatically in order to determine theimpact.

Once a decision is made, the transition to the nextstate involves a number of stochastic processes—newly arrived demand, newly vacated LTC beds, andexits without placement. We assume that any beds notassigned to the hospital demand are used to reduce

Patrick: Access to Long-Term CareProduction and Operations Management 20(3), pp. 347–358, r 2011 Production and Operations Management Society 349

the community wait list and thus do not carry over totomorrow. Thus, we write the transition as

ðh; bÞ ! ðhþ a� ðD� EÞ;BÞ; ð3Þ

where D, B, and E are random variables representingnewly designated ALC patients waiting for LTC, va-cated LTC beds, and clients exiting the hospitalwithout placement, respectively. We let D, B, and E

represent the set of possible instances of new demand,newly vacated beds, and exits without placement, re-spectively. The optimality equation is written as

vð~sÞ ¼ mina2Að~sÞ

(f1ðaÞ þ f2ðhÞ þ g

Xd 2 D; b0 2 B

e 2 E

pdðdÞpbðb0Þ

� peðejhþ aÞvðhþ a� ðd� eÞ; b0Þ);

ð4Þ

where g is the discount factor and pd, pb, and pe are theprobability functions for new hospital demand, bedavailability, and hospital exits without placement,respectively.

The reason for using the difference between thethreshold and the current census is that one can thenthink of the state as inventory and congestion as backorders. Placements equate to new orders where thehospital ‘‘buys’’ additional capacity. Thus, the aboveformulation turns out to be an inventory managementproblem with back orders, no fixed set-up cost, noholding cost, stochastic capacity limitations on supply,and state-dependent demand (due to exits withoutplacement).

If we were to simplify by assuming no exits withoutplacement and unlimited supply of LTC beds, thenthis becomes a standard inventory management prob-lem where a base stock policy is optimal provided thatcosts are convex (Arrow et al. 1959). A base stockpolicy always seeks to return the post-decision state toas close to a pre-specified inventory level as possible.Federgruen and Zipkin (1986a, b) demonstrate that abase stock policy remains optimal for a fixed capacitylimitation on supply and i.i.d. demand under fairlystandard conditions of convexity on the holding/stock out costs and assuming that the average de-mand is less than the capacity limitation on demand.Gayen and Pal (2009) as well as others (Gupta andVrat 1986) have explored the impact of stock-depen-dent demand, again demonstrating that a base stockpolicy often remains optimal. Though our modelcombines the two and has a stochastic cap on supply,the above research does suggest that a base stock pol-icy would remain optimal. While we have not provedthis conjecture, it has held true in all instances of theproblem that we have solved to date.

3.1. Data AnalysisFor input into the model, we obtained data on allhospital demand arriving to the CCAC from April 1,2006 to May 15, 2009. To determine supply and de-mand distributions we assumed a 5 day work week aso1% of demand was registered on the weekend ando3% of placements occurred on the weekend. Thus,we fit a distribution to the weekday data to find thetype of distribution and include the weekend data incalculating the rates or averages of the distribution.The average demand was 3.21 new patients per dayand the average number of available LTC beds perday was 5.1. Thus, the cap on supply was not overlyrestrictive. Figure 1 demonstrates a reasonable Pois-son fit for the hospital demand.

Supply would appear to be more problematic tomodel as the region has added capacity from 2000 to2005 and thus we see a steady increase in daily bedvacancies over the last 3 years. Nonetheless, a histo-gram of weekday supply shows a nice Poisson fit(Figure 2). Because, all facilities are invariably runningat or very near to full capacity and as newly vacatedbeds rarely remain empty for long, it is reasonable toassume an exponential LOS in LTC. The ministry ofhealth publishes the average LOS in LTC but the ac-tual data were not made available.

Interestingly, the number of exits without place-ment did not exhibit a proportional increase with thesize of the wait list. That is, though it was certainlytrue that the number of exits without placementincreased with the census, the rate of increase dimin-ished as the census grew. This was true both in thecommunity and in the hospital with a more markedeffect in the hospital. For the community, the intuitiveexplanation is that, as the wait list gets longer, mem-bers in the community apply for LTC sooner (as theyknow the wait times are very long) and therefore thecomposition of the wait list represents a healthier

20%

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Daily Demand Total0 1 2 3 4 5 6 7 8 9 10 11 12

Figure 1 Histogram of Hospital Demand


population. For hospital patients it is not quite so ob-vious and probably indicates that the hospitalsometimes holds on to sicker clients who they feelmay deteriorate soon in an effort to avoid re-hospi-talizations. Daily ‘‘exits without placement’’ aremodeled as a binomial distribution with the samplesize being the current census and the probability ofexit depending on the census level.

3.2. The Optimal PolicyTo determine the form of the resulting policy, we builta simulation model (not to be confused with the largersimulation model described later) that randomly gen-erates new demand, exits without placement, andvacated LTC beds and uses the arg max of the right-hand side of Equation (4) from the MDP to determinethe appropriate action each day. We ran the simula-tion for 20,000 days, collecting the statistics after thefirst 5000. We varied the threshold above which thecongestion costs are incurred (see Figure 3) and therelative cost of placement vs. congestion (see Figure4). In all scenarios that we ran in the simulation, theoptimal policy is a base stock policy that returns thepost-decision census as close as possible to the samevalue, S, each day (the 451 angle of the line in Figures3 and 4 reflects the base stock policy). If the number ofavailable beds is insufficient to reduce the census to Sthen all beds that day are allocated to the hospital. Thevalue of S is significantly lower than the actualthreshold due to the stochastic nature of supply.How much lower is dependent on the ratio of thecosts chosen. Note however that even with the cost ofplacement being twice the cost of congestion, the op-timal policy still has the same form and still returnsthe post-decision census to a value well below thethreshold. Moreover, even varying the ratio of thecosts 10-fold only shifts the optimal post-decisioncensus from 33 to 39 (see Figure 4) when the thresholdis 50. The intuitive explanation for this is that there is

very little benefit to exceeding the threshold as it in-variably merely delays the necessity of offering LTCbeds to hospital clients. The only gain is that as clientsstay longer in the hospital (due to allowing the censusto grow), they have a greater chance of dying while inthe hospital and thus slightly fewer LTC beds are re-quired.

4. Simulation Model IncorporatingCommunity Demand

Incorporating community demand into the modelgreatly increases the complexity primarily due to thepresence of client choice. In the region under study,there are 28 different facilities with a total of 4530beds. If clients are allowed to specify up to three fa-cility choices, this creates almost 20,000 differentdemands classes without even incorporating bedtype preferences, the location of the patient, or theurgency of placement. The presence of exits withoutplacement and transitions between priority classes

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Figure 4 Impact of the Ratio of Costs on the Optimal Policy

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Figure 3 Impact of Threshold Value on the Optimal Policy


merely compounds the complexity. Finally, in thecommunity, the objective is not to keep the wait listsmall but to insure that no client waits longer than thespecified wait time target. Thus, any model wouldhave to track wait times that would cause the statespace to explode even further. Thus, due to the size ofthe problem, analytic solutions (whether via an MDPmodel or through a queueing model) become intrac-table. While future research will look to solve an MDPmodel through approximate dynamic programming(ADP), here we present a simulation model, usingARENA, that determines the impact on communitydemand resulting from an implementation of theMDP policy.

The MDP policy works as follows. If any urgentcommunity clients (with the appropriate bed type pref-erence) are waiting then available beds are allocated tothose clients first. Otherwise, the simulation only allo-cates beds to hospital patients if the current hospitalcensus is above the value, S, determined by the MDP. Ifthe census is below S then any available beds areoffered to the community clients with the longest waitfor whom the current bed is acceptable (i.e., matchesbed type and any of the facility preferences). For illus-trative purposes we have arbitrarily set the value of S at50 and 100 in the comparisons given below.

The current policy offers clients available bedson a first-come-first-served basis within each priorityclass. Hospital patients are deemed to be equivalent tonon-urgent community clients (i.e., wait in thesame wait list and are offered a bed only if they havethe longest wait time) except for 2 days of the weekwhen they are considered equal to urgent communityclients.

The simulation model incorporates Poisson arrivalsfrom both the hospital and the community. Demand isbroken down into three bed type preferences—pri-vate, ward, or either. Under both the MDP policy andthe current policy, hospital and urgent communityclients are required to take the first available bed ofthe appropriate bed type. If clients are placed in afacility other than their first choice then they remainon the wait list until they are transferred to their topchoice (or they exit the system). Clients already placedare considered to be equivalent in priority to non-urgent community clients and therefore will get pre-cedence only if they have been on the wait list for alonger time.

The breakdown of bed type preferences, as shownin Table 1, is significantly different between hospitaland community clients. Facility preferences, on theother hand, are fairly similar. Figure 5 demonstratesthe marked discrepancy between the first choice pref-erences of clients and actual placements. It is clear thatcurrently there are a number of facilities that act asholding bays for urgent and hospital demand untilclients are transferred to one of the preferred facilities.The probability of the second choice facility is mod-eled as a function of the first choice and theprobability of the third choice facility as a functionof the first two. The probability of exiting without

Table 1 Percentage Breakdown of Demand Based on Bed Type Preference

Private Ward Either

Community 52 31 12

Hospital 30 39 30

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Figure 5 First Choice Facility Preferences vs. Actual Initial Placements


placement and the probability of being upgraded tothe urgent priority class are modeled as functions of aclient’s wait time.

Community demand is additionally characterizedby a priority class—urgent or regular. In actual prac-tice, community demand is divided into five prioritycategories. Two of these are very small (o5% of totaldemand) and represent spousal re-unifications andculturally appropriate placements (there is a signifi-cant French speaking population in the region). Thesecategories are subsumed in our model into the regularcategory as their facility preferences dictate theseplacement restrictions. The other category of commu-nity demand that is ignored represents clients who areeligible but can wait. These clients rarely get placedwithout being first upgraded to the ‘‘regular’’ cate-gory. Unfortunately there is no data available onpriority changes as the data set only reflects a client’scurrent priority. Thus, we are forced to make two as-sumptions. First, we assume that urgent clients do notwait very long for placement and therefore urgentplacements are a reasonable proxy for upgradesfrom ‘‘regular’’ to ‘‘urgent’’ (minus urgent arrivals).Second, we assume that the arrival rate of the ‘‘eligiblebut can wait’’ category is roughly equivalent tothe rate at which these clients are upgraded to‘‘regular.’’ Thus, in our model almost all communityclients enter the system as ‘‘regular’’ clients (only 1%arrive as urgent cases) but may require upgradingat a later stage (based on their length of wait) to the‘‘urgent’’ category.

One of the challenges in assessing the potentialimpact of a policy change is that available dataare often influenced by the current policy. The mostobvious potential danger of this, in the currentexample, is patient choice. Facility preference maybe impacted by perceived wait times for the variousfacilities. It is possible that a policy change thatalters the frequency with which various facilitieshave vacancies may result in different probabilitydistributions of facility preference. However, thecurrent facility preference distributions are almosta worst-case scenario. Ideally, one would like allfacilities to be equally desired whereas currently cer-tain facilities are dramatically more popular thanothers. Any changes therefore would most likely im-prove the results rather than exacerbate them.Increased hospital access may also have the impactof altering the bed type preference distribution as thepopulation mix in the hospital will undoubtedly bedifferent. All these, and potentially other unforeseenconsequences, are an obvious caution to taking anymodeling results as absolutely accurate. However,there is little reason to believe that changes to clientpreferences will be so drastic as to significantly alterthe conclusions.

4.1. ValidationTo validate the model, we determined the initial waitlists as of April 1, 2006 and fed those directly into thesimulation. We ran 10 runs of the simulation for 811days representing the number of weekdays betweenApril 1, 2006 and May 15, 2009 and compared thesimulation with the data set in terms of the evolutionof the wait lists as well as in terms of the number ofarrivals, placements, and exits. We also modeledchanges in capacity that occurred over the 3-year pe-riod as one facility closed some beds and anotheropened up new ones. However, we assumed that allavailable beds were in full circulation whereas in re-ality, some of the beds added in 2005 were probablynot into the regular turnover cycle initially and thusthe simulation does place a few more clients than inreality. Figure 6 compares the simulated and the ac-tual evolution of the wait lists for both communityand hospital demand. The simulation mirrors the dataextremely well for most of the length of the simulationrun but begins to deviate near the end—overestimat-ing the hospital census and underestimating thecommunity census (though the total census remainsaccurate).

The reason for this discrepancy has to do with adeficiency in the data set that does not track transfersfrom the community wait list to the hospital (the re-verse is rare). The data capture the entry date and thecurrent wait list (hospital or community) but does notallow us to know whether and on what date some ofthose clients may have transferred from the commu-nity to the hospital. Thus, the further removed fromthe date the data were pulled, the more the hospitalcensus includes clients who in fact were still in thecommunity and only transferred to the hospital at alater date. Thus, the initial wait list as of April 2006 isan overestimate of the hospital census and an under-estimate of the community wait list. The assumptionin the simulation is that hospital demand (whethernew or transferred from the community) will remainconstant regardless of the size of the community waitlist. The simulation therefore maintains what is anoverestimate in the initial hospital census (as takenfrom the data set) while the data set begins to moreclosely mirror reality as one nears the date when thedata were pulled. This is less of an issue in the policyanalysis that follows as all simulation runs begin withan empty wait list and full LTC facilities. It has noimpact on the comparisons as the same arrival ratesare used in all simulation runs.

Table 2 gives the comparison of the other statisticsproviding the mean plus or minus the standard de-viation and demonstrating only minor deviationsfrom the data set. The presence of ‘‘unknown’’ de-mand is due to the fact that for some placed clients, itwas no longer known whether they originated from


the hospital or the community. Most likely the major-ity of these clients were community clients and thuswere modeled in the simulation as such.

4.2. Policy AnalysisTo compare the MDP policy vs. current practice, weset the initial system as full but with zero clients in thequeue and ran 5 runs of the simulation for 5000 dayseach. The objective measures for comparison are ‘‘thehospital census,’’ ‘‘the time to first placement,’’ ‘‘thetime to preferred placement,’’ and ‘‘the proportion ofclients exiting from their first choice facility.’’ Figure 7represents the evolution of the hospital census com-paring the current policy vs. MDP policies with 50and 100 as the post-decision preferred states. Notsurprisingly the MDP policies keep the hospital cen-sus around the threshold while the current policylevels out at a significantly higher level. The currentpolicy demonstrates significant variability so we haveincluded the lines 2 standard deviations above andbelow the average. For ease of viewing, we have notdone so for the MDP policy as the results for each runwere essentially identical.

Clearly, there is a cost associated with maintainingpredictable hospital wait lists and that cost manifestsitself in the length of wait for community clients.Figure 8 presents the expected increase in communitywait times when running the MDP policy vs. the cur-rent policy. We have omitted the variation both forease of viewing and because the variation betweensimulation runs was not substantial. The wait timesshown represent clients who arrived between day1000 and day 4000. Wait times tend to tail off near theend of the simulation due to the fact that those whosewait is substantial have yet to be placed and thereforedo not yet show up in the average wait time.

Urgent community clients are marginally affected(because even under the MDP policy they receivepriority placement) but regular community clients ex-perience a substantial increase in wait time—especially if the post-decision preferred state is keptas low as 50. However, under the MDP policy, ahigher proportion of placed clients reach their pre-ferred facility before death (see Figure 9) and thedifference between the current policy and the MDPpolicy in the length of time to reach the preferred

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Hosp Mean -2SD Comm Mean -2SD COMM (May 09) HOSP (May 09)

Hosp Mean Comm Mean Hosp Mean + 2SD Comm Mean + 2SD

Figure 6 Evolution of Hospital and Community Wait Lists in the Data Set and in the Simulation

Table 2 Validation of Simulation Model

Actual Simulation

Community Hospital Unknown Total Community Hospital Total Difference (%)

Arrivals 4326 2957 138 7421 4339 � 117 3001 � 89 7340 � 140 � 1.1

Exits 1514 924 0 2438 1527 � 56 842 � 41 2369 � 95 � 2.8

Placements 1958 2079 156 4193 2200 � 59 2139 � 69 4340 � 69 3.5

Final census 1770 237 0 2007 1483 � 24 395 � 46 1878 � 54 � 6.5


facility is much less pronounced (see Figure 10). It isnot clear to the author why this is so.

4.3. Reduced LOS in LTCFrom this analysis, it is clear that the CCAC simplydoes not have sufficient capacity to both reduce hos-pital census levels to the targets preferred by thehospitals while at the same time keeping the commu-nity wait times within the wait time target of 90 days.Even under the current policy, community wait timeswill continue to increase before leveling out wellabove the desired target. Nor is there much chance of

an increase in bed capacity in the near future. Thus,attention has shifted toward demand reduction or atleast demand postponement. Any delay in the place-ment of clients in LTC does have the potential forreducing the client’s LOS in LTC thus effectively in-creasing capacity. Significant resources are beingchanneled toward increasing home care so that cli-ents are more capable of remaining at home for alonger time period.

The current average LOS in LTC is 3 years. To gaugethe potential of this policy decision, we ran the sim-ulation (with the same length and number of runs)

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Figure 7 Evolution of the Hospital Census for Current Policy vs. Markov Decision Process (MDP) Policy

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Figure 8 Evolution of Community Wait Times


using the MDP policy with a threshold of 100and with the LOS in LTC reduced to 2.5 and 2 years.Figure 11 demonstrates that it is only when the LOSreaches 2 years that the current capacity is sufficient tocome close to meeting the community wait time tar-gets currently in place.

4.4. Removing the ‘‘First Available Bed’’ PolicyAs was mentioned earlier, the current practice re-quires that clients on the urgent wait list or in thehospital take the first bed that becomes available, re-gardless of whether it is one of their preferred

facilities. In reality, no patient can be forced to accepta bed s/he does not want but what would be theimpact if the hospitals were no longer able to stronglyencourage patients to do so? We looked at both acomplete removal of the first available bed policy aswell as scenarios where a portion of hospital patientsagreed to accept the first available bed while a portionchose to remain in the hospital until one of their pref-erences was offered to them. The main factor behindpatients potentially refusing the first available bed isthe fear that, once placed, they will lose their spot inthe queue for their preferred facilities. This is in fact

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Figure 9 Proportion of Clients Exiting from Preferred Placement

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Figure 10 Evolution of Time to Preferred Placement


not the case as placed clients still have priority basedon their date of entry to the wait list. Figure 12presents the hospital census under the current policybased on 0%, 50%, and 100% (current practice) ofhospital and urgent clients accepting the first avail-able bed. It is clear that hospitals would be severelyhampered by the removal of the ‘‘first available bed’’policy if all clients were to refuse to take a non-pre-ferred placement. However, even if only half theclients were willing to take a non-preferred place-ment, the impact would be minimal.

4.5. Priority to Internal TransfersThere has also been some discussion at the CCAC asto whether internal transfers should have priority onthe grounds that it is good practice to get clients intotheir preferred facility as quickly as possible. How-ever, as the simulation demonstrates, given currentfacility preference trends such a policy would be di-sastrous for community demand. In fact, after 1000days, the community wait list is already close to 1700(an increase of 300 from the base case) while the hos-pital wait list is almost zero. The reasoning is fairly

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Figure 11 Impact of Reduced Length of Stay in Long-Term Care

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intuitive. The ‘‘first available bed’’ policy for hospitalpatients means that they are most often placed inthose facilities for which there is little demand. How-ever, their preferred choices are similar to other clientsand thus, with priority given to internal transfers,these hospital clients jump the queue and get firstpriority on the high demand beds and once again freeup those beds that only hospital patients are willing togo into. It is clear from Figure 5 that currently thereare a few facilities that have very little demand andthus act as holding bays for urgent clients and hos-pital clients. However, if it was made known thatinternal transfers received priority then there wouldbe a high incentive for clients to be more flexible intheir willingness to be initially placed in any facility. Itmight even be sufficient motivation to create a defacto ‘‘first available bed’’ policy for all clients. Thismight therefore be a clear example of how the imple-mented policy may influence the data.

5. ConclusionCurrently, the scarcity of LTC beds is creating twoproblems—congestion in the hospital and long waitsin the community. The MDP policy presented hereprovides a solution to the congestion insuring thathospitals function with a predictable population ofALC patients. However, the consequence is an exac-erbation of the wait times in the community. Currentefforts at delaying entry into LTC by providing betterhome care services may help mitigate these impactsby reducing the LOS of clients in LTC. However, asubstantial reduction in the average LOS from 3 yearsto 2 years is required if the current wait time targetsare to be met.

This work was recently presented to the local healthauthority where it was concluded that each of thehospitals in the region should determine an appro-priate threshold. Once these are agreed upon, theMDP policy can be implemented for each hospitalthus establishing the primary goal of this research thatwas to provide the hospitals with a policy that guar-anteed predictable levels of ALC patients.

Although the demand rate for LTC was fairly stableover the last 3 years, there is good reason to believethat over the long term there may be greater volatility.In future work, we look to develop a detailed fore-casting tool for LTC in the region. Long-term planningfor LTC is complicated as there is an undeniable agingof the population currently occurring which onewould assume will lead to greater LTC demand.However, as the population imbalance currently ex-perienced due to plummeting birth rates levels itselfout again, it is possible that we will then see a reduc-tion in LTC demand and thus massive expenditureson infrastructure may turn out to be a poor invest-

ment in the long term. The key will be determiningmethods for dealing with the coming ‘‘bulge’’ in theover 75 population while having the flexibility to re-duce capacity once that ‘‘bulge’’ is passed.

In addition, though the simulation provides an ex-cellent scenario analysis tool, it does not provide anoptimal policy. When is it optimal to offer a secondarychoice to a client? When is it optimal to withhold award bed, as the scarcer resource, from a client who iswilling to take either bed type? In short, what is theoptimal scheduling policy for LTC? These are ques-tions to which the simulation can only hint at answersthrough scenario analysis. It would be better if wewere able to provide a model that at least pointedtoward an optimal solution. Although the size of thescheduling problem makes any MDP model intracta-ble, there are a number of methods that have gainedtraction of late for approaching an optimal solutionthrough ADP. Thus, a second line of future researchwill look to build an ADP model that will incorporateboth hospital and community demand and providesome insights into a near optimal scheduling policy.

AcknowledgmentsThis work was funded in part by a research grant fromNational Science and Engineering Research Council. Thiswork was done in partnership with the Champlain Com-munity Care Access Center.

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access to long-term care: the true cause of hospital congestion?

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