Title of manuscript: Applying Analytical Modeling to the ... Willoughby/ORHC Homecare... · “Applying Analytical Modeling to the Decentralization of Health Homecare Services ...

Title of manuscript:

“Applying Analytical Modeling to the Decentralization of Health Homecare Services”

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ABSTRACT

The homecare program in the Saskatoon Health Region (Canada) is responsible for providing

healthcare services to elderly persons and patients recently discharged from acute care facilities.

At the beginning of their eight-hour shifts, each homecare worker reports to a central facility to

receive an assigned list of healthcare visits. These health professionals report back to this site at

shift end to complete required reports and return various medical supplies and equipment.

Homecare management has observed that workers are incurring lengthy travel distances

(annually in excess of 800,000 kilometres) while driving to client homes scattered throughout the

city. In an effort to demonstrate successful operational research (OR) practice, we develop an

optimization model to investigate the decentralization of homecare offices within this city. Our

analytical model informs managerial decision-making by prioritizing the candidate facilities and

demonstrating the impact of various cost factors on location planning.

Keywords: Homecare services; Integer programming; Location

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1. Introduction

The Saskatoon Health Region (SHR) is the largest health jurisdiction in the Canadian

province of Saskatchewan. As described on its website (www.saskatoonhealthregion.ca), it

serves roughly 300,000 individuals in more than 100 cities, towns, villages and First Nation

communities spread over 34,000 square kilometres. The health region operates in excess of 75

facilities and delivers a vast array of programs and services, including hospital and long term

care, public health and homecare, and mental health and addiction services. With nearly 900

physicians and over 13,000 nurses and other healthcare workers, it is the province’s largest

employer. Figure 1 provides a health region map. Saskatoon, the principal city within this

region, includes over 250,000 residents and is positioned towards the middle-left portion of

Figure 1.

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Figure 1: Saskatoon Health Region map

The health region’s homecare program is responsible for providing a variety of services

within Saskatoon, such as in-home respite, meal preparation, security calls, home management,

wound care and medication assistance. These services employ home health aides (HHA) and

nurses to deliver important assistance to elderly persons as well as patients (known as “clients”)

recently discharged from acute care facilities. Generally, nurses provide more medically complex

homecare services than those offered by HHAs.

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In order to more effectively manage homecare demand within Saskatoon, the city is

divided into four quadrants. Quadrant managers are tasked with the challenging assignment of

ensuring that limited homecare staff resources are efficiently deployed to meet client care needs.

To accomplish this, these managers scrutinize care plans to determine the prioritization of clients

receiving homecare services. Further, the managers build a more detailed care plan for each

individual that includes, among other features, client preferences for caregiver gender, ideal

times for homecare visits, required equipment for client services, and so forth.

At the beginning of their eight-hour shifts, each HHA or nurse reports to the Idylwyld

Centre, a two-story facility located close to Saskatoon’s downtown core. This facility serves as

the city’s homecare base. Upon reporting to the Idylwyld Centre, staff members are provided

with their assigned daily schedules. At the conclusion of their daily list of visits and service

calls, each HHA or nurse reports back to the Idylwyld Centre to complete required reports and

return various medical supplies and equipment.

Despite the best intentions of quadrant managers (who attempt to provide healthcare

workers with daily assignments that reduce travel burden), it is not entirely uncommon for staff

members to repeatedly travel across the city to fulfill their healthcare obligations. These

occurrences could arise due to staff unavailability (e.g. a nurse or HHA calls in sick), surges in

homecare demand, last-minute client cancellations, or particular services taking longer than

anticipated. With the city spanning an area roughly 25 kilometres (east to west) and about 20

kilometres (north to south), inefficient travelling intensifies staff anxiety, reduces available time

for providing homecare services, frustrates clients, and increases total system costs. Current

contractual agreements govern healthcare worker reimbursements for travel between consecutive

homecare appointments. For example, a HHA is paid a fixed amount of $3.50 for any distance

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traveled up to 9.1 kilometres and $0.38 per kilometre for any trips beyond this distance. Nurses

are paid a fixed amount of $4.50 for trips up to 11.4 kilometres and $0.40 per kilometre for

distances above this threshold.

Health region management has recognized that requiring each homecare worker to report

to the Idylwyld Centre at the beginning and conclusion of their shifts may engender system

inefficiencies. For example, it may be preferable for SHR to consider a network of homecare

offices distributed throughout the Saskatoon metropolitan area. Under this proposed

decentralized configuration, homecare workers could report to an office closer to their residence.

Although homecare workers are not reimbursed for travel prior to or after their shifts, such a

move would most likely increase staff satisfaction. Further, having multiple offices located

within Saskatoon may provide greater opportunity for homecare professionals to be associated

with and provide service to specific city zones, thereby reducing total distance travelled and

decreasing system expenditures.

This paper, which describes the development of a cost-effective decentralized network of

homecare offices, is an account of an actual OR project. Management’s motivation to

analytically explore this location problem stems from a variety of reasons. As depicted above,

an optimal configuration would lead to travel distance and cost savings. Currently, these

homecare workers are annually travelling in excess of 800,000 kilometres. Since the

government reimburses homecare travel through taxation revenues, cost savings would reduce

the burden on the public purse.

Secondly, reducing travel times would permit more time for direct care. Within the

current system, homecare workers provide actual client care for roughly 50% of their typical

working day. The remaining half is absorbed with driving to client homes, finding parking spots,

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and negotiating travel through congested urban streets. Moreover, the demand for nurse and

HHA services increased by nearly 20% and 15%, respectively, in a recent three-year stretch.

This augmentation of homecare demand – accompanied by the ubiquitous problem of staff

recruitment - fuels the need to identify a solution in which medical professionals devote less of

their day to traveling.

An additional impetus for a location analysis involves the city of Saskatoon’s plan to

expand the roadway near the Idylwyld Centre. This would curtail the available office space in

this building, thereby reducing the amount of medical equipment and supplies that could be

stored. Further, it would limit the number of staff members that could report there for duty at the

beginning and end of their shifts.

As an aside, we note that one could model this situation as a vehicle routing problem in

which care givers were provided optimal tours for visiting a daily client roster. However, it was

felt that showcasing any benefits of network decentralization would provide sufficient

managerial insights into how the system could improve its efficiency.

Our paper proceeds as follows. The next section provides a brief literature summary.

We then explain the development of our analytical optimization model, after which we describe

various homecare office location results. We conclude the paper with some summary remarks.

2. Literature summary

The determination of the optimal number, size and location of facilities to serve a base of

customers is one of a well-studied class of problems known as location-allocation analysis.

Researchers from several academic disciplines including economics, engineering, mathematics

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and operational research have studied these problems. Cooper [4] was an early contributor.

Love, Morris and Wesolowsky [12] provided a seminal treatment.

Academics and practitioners have explored a vast array of health service areas.

Moreover, researchers have investigated healthcare facility location within a myriad of regions

and countries, thus demonstrating the global appeal of this particular topic.

Daskin and Dean [5] provided a principal piece in this specific stream of research. They

illustrated that healthcare facilities should be situated in locations that optimize accessibility,

adaptability and availability of required services. Within the context of in-patient facilities,

Davies [6] also postulated the prime importance of ease of access.

The notion of patient accessibility is synonymous with coverage; namely, determining the

specific percentage of patients “covered” by a healthcare facility located within particular travel

limits. For instance, Radiah-Shariff, Hasnah-Moin and Omar [17] studied healthcare facility

location planning in Malaysia. They incorporated the limited capacity of facilities and

determined the percentage of the population residing within allowable distance targets of any

health service site. In a novel application, Chan et al. [2] explored cardiac arrests in Toronto,

Canada. The authors geographically plotted all public location cardiac incidents over a five-year

period as well as all automated external defibrillator (AED) locations. They quantified coverage

as the percentage of such arrests occurring within 100 metres of an AED. By using AEDs

positioned at 30 best locations, nearly one-third of all arrests would have happened within the

distance target. This represented improvement over the current deployment method. Marianov

and Taborga [14] determined the best location for public health centres that operated in

competition with private entities. In this environment, public centres provided paid services to

prosperous patients and subsidized care to low-income groups. Therefore, the number of public

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centres that could be constructed would depend on the number of visits from wealthier patients,

since the revenue from these affluent patients at public centres would be used to defray the costs

of treating lower-income individuals.

Bowers, Mould and Marshall [1] specified that a relocation of healthcare services may

improve access, but could result in negatively impacting other system features (such as waiting

times). With careful planning, the authors illustrated how more patient care could be delivered

locally. Exploring data from the Department of Veterans Affairs, Syam and Cote [20] developed

a location-allocation model for such services as rehabilitation for traumatic brain injuries. They

investigated the degree of service centralization through a determination of the optimal

assignment of admission districts to treatment units.

Graber-Naidich, Carter and Verter [8] explored the location of different types of primary

care facilities. Some of these centres involved remuneration through fee-for-service

arrangements while others were salary-based. Their mathematical model, subsequently applied

to a specific Canadian city, sought to determine the impact on accessibility of provided care

offered through a particular facility location scheme. Gu, Wang and McGregor [9] investigated

the best location for breast cancer screening programs in the Canadian province of Alberta.

Increasing patients’ participation in this program was imperative since it promoted enhanced

quality of life. Therefore, the authors sought to increase the accessibility of these preventive

services. Verter and Lapierre [21] also analyzed the location of precautionary healthcare

facilities. The main objective of their research was to maximize participation, defined as the

probability that a patient requiring preventive healthcare services would select the closest facility

location.

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Malczewski and Ogryczak [13] employed an interactive approach to find best locations

for a pediatric hospital in Warsaw. They deployed a multi-objective analysis to minimize such

factors as travel cost, investment cost, operating cost and the hospital’s environmental pollution.

Further, they maximized users’ satisfaction. Rahman and Smith [18] used quantitative models to

find the best locations of hospitals in developing countries such as Bangladesh. Ndiaye and

Alfares [15] analyzed the location of public services for particular populations (e.g., nomadic

groups) that seasonally relocate. Their integer programming model determined the best number

and location of health units to serve the resulting seasonal demand, and was successfully applied

to a network of 17 Middle East nomadic groups. Ghaderi and Jabalameli [7] studied the

accessibility of Iranian healthcare facilities. They determined best locations for sites in

conjunction with a budget constraint on facility construction costs. Ultimately, they proposed a

pair of heuristic approaches to address the problem. Through an exploration of Turkish primary

care facility systems, Gunes, Yaman, Cekyay and Verter [10] considered physician incentives in

the planning portions of the study. The author’s case study demonstrated the impact of focusing

on patient or physician preferences.

Rajagopalan, Saydam and Xiao [19] explored the dynamic redeployment of ambulances.

In this case, ambulance demand fluctuated during the week and throughout the day. The authors

determined the minimum number of ambulances and their concomitant locations. Investigating a

situation in which demands were stochastic, Chan et al. [3] formulated a stochastic location-

routing problem for a medical-evacuation case study of the United States Air Force. Jia,

Ordonez and Dessouky [11] used different facility location models to plan the location of

emergency medical services for large-scale crises such as terrorist attacks, hurricanes and

earthquakes in the Los Angeles, California area. Since these events rarely occur but have huge

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influence on medical service demand, the authors adopted an objective of minimizing the loss of

life. They determined that facilitating access to multiple highways and being safe from crisis

damage are important criteria in selecting locations. Exploring an actual Quebec City case,

Price, Turcotte and Hebert [16] studied the relocation of a blood bank. Due to population

increases, blood demand was expected to rise. The authors gathered data related to mobile

clinics, blood deliveries and donors who travel to clinic centres, and performed a series of

gravity models to optimize location options.

The analytical model presented in this case study differs from other literature in the

following ways. First, we note that our approach involves determining locations from which

healthcare professionals are daily deployed to serve a client base as opposed to positioning sites

to which patients will visit. The latter approach - that of locating facilities such as hospitals or

care centres that draw patients- seems to be especially predominant within the cited research.

Our model addresses accessibility from the perspective of healthcare professionals.

Secondly, a direct connection exists between our modeling efforts and lean process

improvement investigations. To wit, we are combining practical OR with lean process analysis.

Within the field of lean, researchers and other decision-makers identify opportunities to reduce

the sources of waste or non-value added activities. In the present homecare context, we have

observed that healthcare professionals are devoting roughly half of their daily shift time to

activities such as driving through congested streets and securing parking spots. Since they fail to

add direct value to the patient, these activities epitomize waste. Reducing travel time (through a

decentralization arrangement that provides homecare offices more proximate to the patients) will

provide enhanced system capacity for patient care, thus helping the overall process to become

more efficient.

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Thirdly, to the best of our knowledge, our study represents the initial attempt to

mathematically model the essential area of homecare health operations.

Finally, since the particular jurisdiction in this case study reimburses homecare travel

through taxation monies, any system improvements resulting from our optimization model would

reduce the financial encumbrance on the provincial citizenry. This differentiates our work from

those investigations that have explored privately-funded healthcare systems.

3. Model

Recall that the Idylwyld Centre is the health region’s current homecare office. Using the

knowledge and judgments of health region senior management, this group identified five

potential office locations distributed throughout the city of Saskatoon. Each of the proposed

locations is situated near a major thoroughfare or a commercial real estate area. Figure 2

provides shows much of the city’s road network along with the Idylwyld Centre (dark dot), five

candidate locations (numbered circles) and Saskatoon’s three hospitals (white stars). The

candidate facilities involve office space in the following areas, with the numbers representing

particular circles on the map:

Lawson Heights Mall (1)

Confederation Park Mall (2)

University Heights Square (3)

Market Mall (4)

Avenue H South (5)

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Figure 2: Current and potential homecare office locations

Our analytical facility location model determines the optimal set of sites that leads to

overall cost minimization. We consider factors such as new facility lease costs, as well as the

travel expenditures associated with meeting homecare demand. Using information from

Saskatoon commercial real estate data, we obtained the total lease cost for office space of

suitable capacity at or near each proposed site. Besides determining the best number and

location of homecare offices, it is desirable to establish the size of each facility in terms of the

number of healthcare professionals assigned to each site.

In order to proceed with finding the best set of locations, we segmented the city of

Saskatoon into 64 residential neighborhoods. Using Google map, we computed the distance

travelled between the set of locations (either current facility or proposed sites) and the centre of

each neighborhood. This assumes, of course, that each area’s demand originates at each

neighborhood’s hub. Nonetheless, we felt that such an aggregated approach would still provide

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realistic travel distances. Health region management concurred with this tactic. Moreover, this

method was deemed preferable to calculating travel distances from all locations to individual

homecare clients. Since the set of clients displays some variation over time (some patients may

no longer require service, with new clients being routinely added to the homecare roster), it

would be an extremely challenging task to calculate actual distances at the level of the individual

client.

We also required each neighborhood’s demand for homecare services. Homecare

managers provided this information in terms of the annual number of visits for either HHAs or

nurses. We note that the region’s roster currently includes 128 HHAs and 83 nurses available for

delivering homecare services.

For the most recent fiscal year, annual homecare travel was 820,155 kilometres. This

travel distance necessitated a reimbursement of $377,883. Therefore, we can evaluate our

analytical model’s performance in terms of reducing this overall cost amount. Using the

subscript i to represent locations and j to denote neighborhoods, our optimization model is as

follows:

MINIMIZE ∑ ∑{𝐶𝑖𝑗𝐻𝐻𝐴𝑆𝑖𝑗

𝐻𝐻𝐴 + 𝐶𝑖𝑗𝑅𝑁𝑆𝑖𝑗

𝑅𝑁} x 365 + ∑ 𝐿𝑖𝑋𝑖

6

𝑖=1

64

𝑗=1

6

𝑖=1

Subject to:

∑ 𝑆𝑖𝑗𝐻𝐻𝐴 ≥ 𝑑𝑗

𝐻𝐻𝐴 ∀ 𝑗 ∈ 𝐽

6

𝑖=1

[1]

∑ 𝑆𝑖𝑗𝑅𝑁 ≥ 𝑑𝑗

𝑅𝑁 ∀ 𝑗 ∈ 𝐽

6

𝑖=1

[2]

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15 𝑋𝑖 ≤ ∑ 𝑆𝑖𝑗𝐻𝐻𝐴 ≤ 128 𝑋𝑖 ∀ 𝑗 ∈ 𝐽

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𝑖=1

[3]

10 𝑋𝑖 ≤ ∑ 𝑆𝑖𝑗𝑅𝑁 ≤ 83 𝑋𝑖 ∀ 𝑗 ∈ 𝐽

6

𝑖=1

[4]

∑ ∑ 𝑆𝑖𝑗𝐻𝐻𝐴

64

𝑗=1

6

𝑖=1

≤ 128

[5]

∑ ∑ 𝑆𝑖𝑗𝑅𝑁

64

𝑗=1

6

𝑖=1

≤ 83

[6]

𝑆𝑖𝑗𝐻𝐻𝐴 ∈ 𝑁0 ∀ 𝑖 ∈ 𝐼; 𝑗 ∈ 𝐽 [7]

𝑆𝑖𝑗𝑅𝑁 ∈ 𝑁0 ∀ 𝑖 ∈ 𝐼; 𝑗 ∈ 𝐽 [8]

𝑋𝑖 ∈ {0, 1} ∀ 𝑖 ∈ 𝐼 [9]

Our analytical model deployed the following parameters:

𝐶𝑖𝑗𝐻𝐻𝐴: Daily cost of travelling from location i to neighborhood j for a HHA

𝐶𝑖𝑗𝑅𝑁: Daily cost of travelling from location i to neighborhood j for a registered nurse

𝐿𝑖 : Annual lease cost associated with location i

𝑑𝑗𝐻𝐻𝐴

: Daily demand for HHAs from neighborhood j

𝑑𝑗𝑅𝑁

: Daily demand for RNs from neighborhood j

We adopted the following variable definitions:

𝑆𝑖𝑗𝐻𝐻𝐴: Number of HHAs sent from location i to neighborhood j

𝑆𝑖𝑗𝑅𝑁: Number of registered nurses sent from location i to neighborhood j

𝑋𝑖 = 1: if facility is placed at location i; else, 0

The objective function tabulates the annual travel cost as well as lease costs for new

facilities. Constraints [1] and [2] ensure that the number of homecare professionals assigned

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from all open locations to each neighborhood is such that the demand of that neighborhood is

fully covered.

In constraints [3] and [4], we prevent assigning a neighborhood’s demand to an unopened

site. The maximum amount corresponds to the number of available HHAs or nurses. Officials

were careful to consider candidate locations that had sufficient office space to house, if needed,

the entire allotment of homecare workers. The minimum numbers refer to the lowest possible

assignment of staff that would still make a location suitable. It would be rather inefficient to

open an office location within the city and only assign one or two homecare professionals to it.

Even though HHAs or nurses spend nearly all of their shift time “out of the office”, homecare

management desired a certain minimum allocation so that resources ascribed to leased spaces

were appropriately deployed. They related that the minimum values of 15 (HHA) and 10

(nurses) were reasonably suitable minima. Constraints [5] and [6] limit the total number of

HHAs and nurses sent from all open locations to all neighborhoods. Finally, constraints [7]

through [9] feature numerical bounds on various variables.

4. Results

We optimized our analytical model by using Premium Solver on a Lenovo Thinkpad

T430 laptop with an Intel Core i5-3320M processor. This software package determined the best

set of locations, as well as the number of HHAs and nurses that should be dispatched from any

site to each neighborhood. Generally, the model solved to optimality within seconds. The speed

with which the software addressed the problem intensified management’s appreciation of the

methodology’s ability to identify least-cost location-allocation arrangements.

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Table 1 reports model results for instances in which we forced the optimizer to select a

certain number of open sites. It lists the annual travelling and lease costs associated with each

solution. We provide the results for 1 through 5 open sites. Obviously, when we selected 6 as

the desired number of locations, the model retained the current Idylwyld Centre and opened each

new candidate location.

As per our expectations, the annual transportation costs drop and the overall lease costs

climb as we increase the number of open facilities. With more facilities in operation, homecare

professionals are located closer to each neighborhood thus reducing travel distances. However,

additional open facilities necessitate greater total lease costs. Total annual costs increase

monotonically as we escalate the number of open facilities.

Table 1: Optimization model results

Number of open

facilities

Annual

transportation cost

Annual lease cost Total annual cost

1 $377,883

$0 $377,883

2 $373,517

$122,429 $495,945

3 $324,905

$242,827 $567,732

4 $319,450 $271,680 $591,130

5 $317,863 $330,387 $648,250

If healthcare planners wanted to minimize overall costs, the best system configuration

would be a one-facility network. In fact, this particular location would be the current Idylwyld

Centre because the optimal result for a one-location case (as given in Table 1) involves zero

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lease costs. Since the health region owns Idylwyld Centre, they do not incur any lease costs for

its operation.

Moreover, Table 1 demonstrates that the reduced transportation costs associated with

facility expansions are outweighed by the resulting lease cost increases. Undoubtedly, health

region management made a correct assertion that driving expenditures would drop with

decentralized operations. Nonetheless, in this particular instance, shortened transportation times

produce insufficient savings. Reduced travel times increase available client care capacity, but

the concomitant cost opening of more facilities increases total costs. Indeed, centralization

offers cost advantages within the current configuration. If management did want to proceed with

decentralized sites, it would need to identify opportunities to lower overall lease costs (perhaps

by pinpointing potential locations unexplored in the current optimization model that could yield

rental advantages).

Despite the fact that a centralized network offers optimal cost performance, health region

management was particularly interested in the relative ranking of the candidate locations, since

this offers an opportunity to assess decentralization merits. This can be understood by observing

the order in which each location entered the optimal network configuration. We provide these

details in Table 2. The number after each location refers to its symbol provided in the Figure 2

map. No matter the number of facilities that are required to be open, the Idylwyld Centre is

always one of the best sites to use. After the Idylwyld Centre, the Avenue H South location is

the second best choice. This outcome was influenced by this particular location’s relatively low

lease costs. The third best place for a new facility is the Market Mall location due to the high

demand for homecare services in the particular neighborhoods surrounding this site. To wit, this

facility is situated near a conglomeration of senior citizen apartment buildings. The

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Confederation Mall and Lawson Heights Mall locations are the next to enter the optimal

solution. The University Heights Square location is not listed in Table 2, thus suggesting that it

is the least preferred site. We note that it did not become part of any optimal solution until we

forced the model to open all six locations.

Table 2: Optimal locations

Proposed locations Number of facilities to open

1 2 3 4 5

Idylwyld Centre

Avenue H South (5)

Market Mall (4)

Confederation Mall (2)

Lawson Heights Mall (1)

Tables 3 and 4 provide the number of HHAs and nurses, respectively, assigned to each

office location. One may interpret these results as depicting the capacities of the various sites.

Table 3: HHA assignments

Proposed locations Number of facilities to open

1 2 3 4 5

Idylwyld Centre

128 73 35 28 21

Avenue H South (5)

55 44 30 21

Market Mall (4)

49 49 44

Confederation Mall (2)

21 21

Lawson Heights Mall (1)

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Table 4: Nurse assignments

Proposed locations Number of facilities to open

1 2 3 4 5

Idylwyld Centre

83 30 14 14 14

Avenue H South (5)

53 42 28 18

Market Mall (4)

27 27 23

Confederation Mall (2)

14 14

Lawson Heights Mall (1)

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To provide additional insight to homecare management, we analyzed the location-

allocation impact of various scenarios. We report on a few of them in this paper. For instance,

we explored a scenario to determine the best set of locations if one assumed there were no lease

costs. In this particular situation, the only relevant costs are the travel expenditures. This is akin

to a “greenfield” situation in which planners would have the luxury of starting afresh with a

brand-new location configuration. If one could start all over again, where would the homecare

offices be located in the city of Saskatoon?

We offer these results in Table 5. This analysis demonstrates that Idylwyld Centre is

again the best location for a one-facility homecare system. Thus, we have further evidence that

system centralization provides overall benefits for homecare office location. There is a certain

cost-effectiveness associated with the Idylwyld Centre location, certainly attributed to its pivotal

position close to the centre of the homecare network. It was featured in all but one of the Table 5

model instances. We note that, except for 2 or 3 open facilities, the best set locations remained

the same as those discovered earlier. When only two facilities are required to be open, the best

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locations were Idylwyld Centre and University Heights Square. For three facility locations, we

found that Market Mall, Confederation Mall and Lawson Heights Mall were chosen as the best

sites.

Table 5: Greenfield locations

Proposed locations Number of facilities to open

1 2 3 4 5

Idylwyld Centre

Avenue H South (5)

Market Mall (4)

Confederation Mall (2)

Lawson Heights Mall (1)

University Heights Square (3)

Notwithstanding the finding that the Idylwyld Centre produced cost efficiencies, we

modeled a scenario in which homecare management forced the closure of the Idylwyld Centre.

If one were to do this and restrict the number of open facilities to one, the best location would be

the Avenue H South site. However, we found that the annual transportation cost would rise to

$414,389, an increase of over $36,000 from the one-site transportation costs reported in Table 1.

This solution also incurred lease costs of $122,429, meaning that the total system costs would

definitely increase by using Avenue H South as the one-facility alternative instead of Idylwyld

Centre. This further underscores the importance of the current office location in the city’s

homecare network.

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5. Conclusions

In this paper, we have explored the application of analytical modeling to the

decentralization of homecare offices for the Saskatoon Health Region. This health jurisdiction

currently includes a sole facility located at the Idylwyld Centre, close to the city’s downtown

core. Challenging circumstances involve lengthy travel distances for its highly-trained homecare

staff, thus precipitating a reduction in the amount of client care time these professionals can

provide throughout the day. The city is experiencing growth in homecare demand. Further, a

roadway expansion near the present location may reduce available office space, thereby forcing

the health region to consider an alternative location scheme.

We used a model that minimized total annual costs subject to a set of constraints. Based

on homecare management suggestions, we studied five possible candidate locations. Our model

results reported the optimal number, location and size of homecare offices under a variety of

particular scenarios. System centralization offers superior cost performance. The preferred

locations are (in descending order) Idylwyld Centre, Avenue H South, Market Mall,

Confederation Mall, Lawson Heights Mall and University Heights Square.

In terms of possible limitations, we did assume that homecare staff would pick the

shortest route (the ones computed with Google map) when travelling between consecutive

appointments. In reality, it is conceivable that staff would select a different (longer) route

according to individual preferences, or on days involving high traffic or construction along the

pre-determined shortest route. Notwithstanding this assumption, we feel that our model results

can inform homecare management decision-making. It analytically demonstrates the impact of

various cost factors on location planning, prioritizes a list of candidate facilities, and illustrates

the current advantages of system centralization.

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