Specialty care single and multi-period location–allocation models within the Veterans Health Administration

Socio-Economic Planning Sciences 46 (2012) 136e148

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Specialty care single and multi-period locationeallocation models within the Veterans Health Administration James C. Benneyan a, b, *, Hande Musdal a, Mehmet Erkan Ceyhan a, Brian Shiner b, c, Bradley V. Watts b, c a

Center for Health Organization Transformation, Northeastern University, Boston, MA, USA New England Veterans Engineering Resource Center, Boston, MA, USA c White River Junction VA Medical Center, White River Junction, VT, USA b

a r t i c l e i n f o

a b s t r a c t

Article history: Available online 8 January 2012

Optimal location of specialty care services within any healthcare network is increasingly important for balancing costs, access to care, and patient-centeredness. Typical long-range planning efforts attempt to address a myriad of quantitative and qualitative issues, including within-network access within reasonable travel distances, space capacity constraints, costs, politics, and community commitments. To help inform these decisions, single and multi-period mathematical integer programs were developed that minimize total procedure, travel, non-coverage, and start-up costs to increase network capacity subject to access constraints. These models have been used to help the Veterans Health Administration (VHA) explore relationships and tradeoffs between costs, coverage, service location, and capacity and to inform larger strategic planning discussions. Results indicate significant opportunity to simultaneously reduce total cost, reduce total travel distances, and increase within-network access, the latter being linked to better care continuity and outcomes. An application to planning short and long-term sleep apnea care across the VHA New England integrated network, for example, produced 10e15% improvements in each performance measure. As an example of further insight provided by these analyses, most optimal solutions increase the amount of outside-network care, contrary to current trends and policies to reduce external referrals.
2012 Elsevier Ltd. All rights reserved.

Keywords: Healthcare Specialty care Network planning Optimization

1. Introduction Over a decade ago, the Institute of Medicine (IOM) released two landmark reports outlining significant deficiencies in the quality and safety of medical care provided in the United States. To Err is Human (2000) [1] documented the nearly 100,000 lives lost each year due to systematic problems in the design and execution of healthcare delivery. Crossing the Quality Chasm (2001) [2] provided a broad vision of how health care could be effectively transformed and improved, and recommended the use of systems and industrial engineering techniques to assist with understanding and optimizing healthcare processes. In response to this call, the National Academy of Engineering (NAE) and the IOM initiated a study in 2002 to identify engineering tools and technologies that could help

* Corresponding author. Healthcare Systems Engineering Program, Northeastern University, 360 Huntington Ave., Boston, MA 02115, USA. Tel.: þ1 617 373 2975; fax: þ1 617 373 2921. E-mail address: [email protected] (J.C. Benneyan). URL: http://www.coe.neu.edu/healthcare 0038-0121/$ e see front matter
2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.seps.2011.12.005

the health system improve and deliver care that is safe, effective, timely, patient-centered, efficient, and equitable e the six health system aims defined in Crossing the Quality Chasm. The result of this study was published as Building a Better Delivery System (2005) [3], which concluded that the U.S. healthcare industry has neglected use of systems engineering methods and concepts that have revolutionized quality, productivity, and performance in many other industries, and that this “collective inattention” has contributed to serious consequences within health care e huge amounts of preventable harm and deaths, outdated procedures, an approximately half-trillion dollars wasted annually through inefficiency, costs rising at roughly three times the rate of inflation, and 43 million people uninsured. Today, health care is still an area of crucial concern in the United States, spending substantially more than any other developed country in the Organization for Economic Co-operation and Development (OECD). The use of healthcare services in the U.S., however, is below the OECD median by almost all measures, which means that Americans are receiving fewer real resources than people in over 50% of OECD countries. These facts suggest that the difference in spending is caused mostly by higher prices for the delivery of healthcare goods and services in

J.C. Benneyan et al. / Socio-Economic Planning Sciences 46 (2012) 136e148

the U.S. [4]. Rising costs and inadequate levels of care underscore the importance of making strategic decisions within this industry. The use of systems engineering models to help make decisions in many key areas, in fact can be very effective at helping design both cost-efficient and qualified healthcare services, especially in cases involving complex and competing considerations. Network planning is one of several areas that can be improved via systems engineering methods, with the optimal location of health services across geographic care networks having significant potential to improve costs, patient-centeredness, and care continuity (3 of the IOM dimensions). This paper describes recent experiences to use such models across a range of specialty care services within the Veterans Health Administration. The opportunity for significant improvements is illustrated for the case of sleep apnea specialty care services, a common injury among U.S. veterans. The remainder of this paper is organized as follows. Section 2 provides a general overview of locationeallocation models as they relate to health care. Section 3 describes the current state of VA sleep apnea services across the New England region. Section 4 describes the mathematical models and results for sleep apnea services, and Section 5 concludes with general implications, study limitations, and possible extensions. 2. Background Locationeallocation models seek to simultaneously determine optimal facility locations and the assignment of customers (here, patients) to facilities. These models have been applied widely in many industries to reduce costs and increase access, with examples spanning retail, telecommunication, energy, and manufacturing. In health care, poor location decisions also can result in increased mortality and morbidity, with optimal facility location therefore having even greater importance [5]. Historical healthcare applications have included locating ambulances [6,7] and hospitals in rural regions [8], trauma care resources [9], organ transplant services [10], blood facilities [11], emergency medical service vehicles [12], hospital networks [13], and specialized care services such as traumatic brain injury (TBI) treatment [14,15]. Models that account for transient populations who change their locations seasonally [16] and continuously changing nature of health systems [17] also have been developed for specific applications. From a modeling perspective, location problems can be classified as discrete and continuous. Discrete models assume a finite number of candidate locations exist at which facilities can be sited, whereas continuous models assume facilities can be located anywhere within a geographic area. All models aim simultaneously to determine both the best locations for facilities and the best assignment (“allocation”) of individuals to these facilities, where “best” usually is defined by some combination of total travel

137

distance, facility costs that include fixed locating and variable operating costs, and demand coverage. The work in this paper focuses on discrete location models, which also have been used more extensively in healthcare location problems [5], because typically the VHA has been interested in considering specific existing or candidate locations. Table 1 summarizes the three basic types of discrete facility location models and the performance measures they seek to optimize. The key concept in covering models is the notion of coverage, with a maximum acceptable travel distance specified such that a “demand node” (here, a patient’s 3-digit zip code home location) can be served only by a facility within this distance. Covering models have been studied within two major classes in the literature [18]. The first class is the location set covering problem (LSCP), introduced by Toregas (1970) [19], which aims to minimize the cost of facility location while ensuring that all demand nodes are covered. These models are useful for cases in which all demand must be covered and one wishes to minimize the total cost to accomplish this. The second class is the maximal covering location problem (MCLP), introduced by Church and ReVelle (1974) [20], which aims to maximize the level of coverage (i.e. the number of covered demand nodes) using only a specified number of facilities and a maximum acceptable travel distance. These models are useful in cases for which the cost of covering all demand nodes is prohibitive. Finally, P-median models [21] seek to minimize the average travel distance and are useful in cases for which a specific maximum acceptable distance is less clear [5]. Many single and multiple objective extensions of these three basic ideas have been developed over the past four decades to address particular problems specific in manufacturing [22], distribution networks [23], web services [24], and other contexts. It also should be noted that all of these types of models have continuous counterparts e for example planar LSCP and MCLP [25e27] and multi-source Weber formulations [28] e where facilities can be located anywhere in the plane. 3. VA New England sleep apnea services The VA New England healthcare system is one of 21 Veterans Integrated Service Networks (VISNs) within the Department of Veterans Affairs, with each VISN being regionally managed and operating as a somewhat autonomous decision-making system. The VA New England VISN (VISN 1) provides comprehensive medical services (including primary, mental health, specialty, and hospital-based care) to 235,000 veterans residing in any of the six New England states (Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, and Connecticut). With an annual operating budget of approximately $2.2 billion, VISN 1 has 8 medical centers, 40 community-based outpatient clinics, 6 nursing homes, and 2 domiciliaries e institutional houses for aged and disabled veterans.

Table 1 Representation of basic discrete facility location models. Model

Description

Assumptions

Decision variables

Performance measures

Location set covering model

Minimize total cost of providing service

- Specify potential facility locations - Specify maximum acceptable distance (S) - Iterate on S

Location, number

Cost (dollars)

Maximal covering location model

Maximize demand coverage

-

Location, number

Demand coverage (percent)

P-median model

Minimize total weighted travel distance

- Specify potential facility locations - Specify total number of facilities (P) - Iterate on P

Location

Travel distance (miles)

Specify potential facility locations Specify maximum acceptable distance (S) Specify total number of facilities (P) Iterate on S and P

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Nationwide, the VA spends more than $2.5 billion annually to provide specialty care services, of which $125 million spent by VISN 1 [29]. While the VA has strived to develop integrated and coordinated care, veterans who also are eligible for Medicare increasingly use non-VA specialty services, resulting in increased fragmentation in care continuity [30]. Better availability of specialty services within the VA could decrease this fragmentation as well as result in lower overall costs. New users of VA health care are predominantly Vietnam veterans in their 50s and 60s [31]. Given the high prevalence of sleep disorders in this age group [32,33], there has been an increased demand for testing and treatment services. The overwhelming majority of patients referred and treated in sleep medicine clinics suffer from sleep apnea [34]. Sleep apnea is a disorder characterized by abnormal pauses in breathing or instances of abnormally low breathing during sleep and has been linked with high blood pressure, heart problems, stroke, fatigue, headaches, snoring, daytime drowsiness, and memory problems [35,36]. These health problems occur at a much higher rate among veterans than in the general population due to long-term exposure to dust, smoke, chemicals, and other environments [37]. Up to 20% of all U.S. veterans currently suffer from sleep apnea, with an annual treatment cost of $225 million to the VA [29]. Fig. 1 summarizes the number of treated sleep apnea patients in VISN 1 by state, with the majority residing in Connecticut and Massachusetts as expected given greater overall populations. Since observed utilization is a function of capacity and may under- or over-represent true demand, also shown is an estimate of the greater true need over this time period, based on clinical input and patient-specific predictors, such as their body mass index (since it is well-known that the risk for sleep apnea is higher for people who are overweight [37]). Fig. 2 shows estimated demand by 3-digit zip code relative to VA facilities across VISN 1. A definitive diagnosis of sleep apnea is made through use of overnight polysomnographic testing that involves having a patient sleep in a polysomnogram bed (referred to as a “sleep bed”) with continuous monitoring of their blood oxygen levels, electroencephalogram, and vital signs. A general belief has been that inadequate access to overnight polysomnographic testing in VISN 1 is causing a large number of veterans to be referred to out-of-network providers. The fees for these out-of-network services are reimbursed by the VA (“fee basis” visits) and can represent large amounts of monies for some specialties. In the sleep apnea case, data between January 2009 and May 2010 shows that of 4712 tested patients from VISN 1, 3927 were tested in one of the VA facilities at a total operation and travel cost of $2,431,762, with 785 tested outside the network at a total cost of $667,250 or 9% of the overall cost. Currently, only four of eight VA medical centers in VISN 1 (West Haven, West Roxbury, Manchester, and Providence) have sleep laboratories that provide polysomnographic testing. Closing these 3178

Demand (number of visits)

3200

Observed utilization

2800

Estimated true need

2502

2400 2000

1774

1600

1640 1326 1120

1200

1023 723

800

566

455

455

400

136

0 CT

MA

NH

RI

ME

VT

State

Fig. 1. Sleep apnea care demand by state across VISN 1 (January 2009eMay 2010).

laboratories or decreasing their capacities is not feasible within the VA given policy and other considerations. Table 2 summarizes the number of sleep beds and visits at each facility. The West Haven medical center generated outside-network fee visits over this time period, even though it has sleep beds, due to demand at times exceeding capacity as shown in Fig. 3. However, a relatively large number of fee type visits occurred in months in which utilization (measured as the percent of capacity usage) was low. Fee type utilization associated with other facilities with sleep beds suggests regional demand does not exceed regional capacities, as shown in Fig. 4. Due to the fact that patient records are based on billing rather than visit dates, utilizations in some months are over 100%, which may not reflect actual utilization levels. Those observations underscore data inaccuracies and idiosyncracies, the need for sensitivity analyses, and the value of working in an integrated analysteclinician research team. Fig. 5 summarizes the distances patients traveled to receive within-network care over the same time period, with a mean of 44.5 miles but a high variability ranging from 2 to 420 miles. Approximately 70% of patients traveled more than 30 miles and 25% more than 60 miles, typical acceptable distance thresholds. Roughly 5% of patients traveled more than 100 miles. Travel distances exceeding 30 miles are fully reimbursed by the VA at a current rate of $0.70 per mile to cover gas, maintenance, vehicle depreciation, and inconvenience. 4. Methodology 4.1. Model overview and assumptions The below models determine the optimal sleep bed capacity in each existing VISN 1 VHA facility that minimizes overall total costs over a single or multiple periods, relative to geographic demand. The single-period model is useful for short term planning or for cases in which future demand is unlikely to change, whereas the multi-period model is important in cases for which demand or patient volume may significantly change over time, as can be the case with veteran populations. Both models specify a maximum acceptable travel distance (S) to a VA facility, beyond which a patient is directed to an out-ofnetwork provider at the VA’s expense. Patients at demand nodes (3-digit zip codes) assigned to an available VA facility within this acceptable distance are referred to as in-house type visits and incur procedure costs as well as travel costs, as described above. Other model assumptions include (1) Each patient receives his care at the facility to which he is assigned and spends one night there, (2) Annual capacity of a sleep bed is equal to the number of working days in a year, (3) Facilities that currently provide this care continue to do so, (4) Procedure costs include overhead independent from a patient’s health state, (5) Demand is deterministic, equally distributed over time, and with no seasonality effects, and (6) Care cost variations between medical centers and geographic regions are negligible. The first four assumptions reflect the current circumstances of the VA sleep apnea testing services. The fifth and sixth assumptions also are realistic since seasonality is not indicated in the literature as a major factor in sleep apnea cases and there is not a significant cost variation between VISN 1 facilities all of which operate under the same local administration. These two assumptions, in fact, decrease the complexity of the model.

J.C. Benneyan et al. / Socio-Economic Planning Sciences 46 (2012) 136e148

139

Fig. 2. Estimated sleep apnea care demand by 3-digit zip code and all VA facilities across VISN 1 (January 2009eMay 2010).

The multi-period model considers an n-year planning horizon, with a user-specified maximum number of facilities P that can be added each year (assumed the same for each period). An underutilization cost is included in the multi-period model since expansion decisions may produce over capacity in some following years. Facilities in which service is added or expanded also are Table 2 Number of sleep beds, within-network and outside-network sleep apnea patients in VISN 1 (January 2009eMay 2010). Facilities

Current # of sleep beds

# of within-network visits

# of outside-network visits

West Haven, CT West Roxbury, MA Manchester, NH Providence, RI Togus, MEa White River Junction (WRJ), VT

4 6 4 2 e e

1738 1119 476 434 97a e

255 e e e 286 204

Total

16

3767

745

a

In 2009, there were two sleep beds in Togus.

assumed to continue to operate at this capacity level over the remainder of the planning horizon. 4.2. Single-period model The following notation and input parameters are used in the single-period model, with i ¼ index of geographic demand nodes, j ¼ index of facilities, hi ¼ total number of sleep apnea patients at demand node i, P ¼ maximum number of additional facilities to be located, S ¼ maximum acceptable travel distance, C1 ¼ in-house procedure cost per patient, C2 ¼ travel cost per mile, C3 ¼ non-coverage cost per patient, C4 ¼ cost of adding a sleep bed, Kj ¼ maximum capacity of facility j, tij ¼ distance between demand node i and facility j, fj ¼ initial number of beds in facility j, T ¼ total number of days in the given period,

140

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a

32 28

Number of fee-type visits Utilization

24

22

160% 140% 20

20

16

16

16 13

12

12

13

120%

20

100%

16

13

80%

13

12 10

12

60%

9

6

8

Utilization

Number of fee-type visits

32

40%

4

20%

0

0%

Month

b

70 House-type

59

63

Fee-type

60 Number of visits

50 45

50 39 40

34

30

36 31

26

24 24 18

20 10

31

25 23

22 24 23 21 20

13 5

3

2

2

2

2

3

2

4

3

6

5

3

8

6

5

3

2

4

4

3

0

Week Fig. 3. Fee visits for West Haven, (a) number of fee visits versus monthly utilization (months with relatively low utilization (<50%) and high fee visits are circled), (b) weekly fee visits versus in-house visits.

O ¼ set of facilities that provide service currently, D ¼ total demand in the corresponding planning horizon, dij ¼ reimbursed travel distance, equal to tij if tij > 30, and 0 otherwise, and M ¼ a positive constant whose value is sufficiently large.

aj ¼ number of additional sleep beds to add in facility j. Using the above notation, an integer programming mathemat1 0 1 ical model0can be written as

Minimize@

The decision variables are

þ C4

160% 140% 120%

i

100% 100% 80% 60% 40% 20% 0%

j

i

j

aj

Subject to 50%

West Haven West Roxbury Manchester Providence Togus

XX   Yij hi C1 þ dij C2 A þ C3 @D  Yij hi A

j

Percent of patients

Within-network capacity utilization

Xj ¼ 1 if facility j provides sleep apnea service and 0 otherwise, Yij ¼ 1 if patients in demand node i are treated at facility j and 0 otherwise, and

X

XX

44.80%

40% 31.58%

30% 17.74%

20% 10%

3.44%

2.44%

91-120

>120

0% Month

0-30

31-60

61-90

Travel distance (miles) Fig. 4. Utilization of sleep apnea capacity by medical center over time (utilizations over 100% are circled).

Fig. 5. Travel distance distribution, VISN 1 (January 2009eMay 2010).

J.C. Benneyan et al. / Socio-Economic Planning Sciences 46 (2012) 136e148

X

Xj  P

(3)

Xtj ¼ 1 if facility j provides sleep apnea service during period t, and 0 otherwise, Yijt ¼ 1 if demand node i is covered by facility j during period t, and 0 otherwise, atj ¼ number of additional sleep beds in facility j during period t, and btj ¼ number of total sleep beds in facility j at the beginning of period t (an auxiliary decision variable).

(4)

The mathematical model then extends to

(1)

j;O

X

Yij  1

ci

(2)

j

    Xj tij  S  1  M 1  Yij  1 X

  Yij hi  T fi þ aj

ci; j

cj

141

i

X

0 Yij hi  Kj

cj

(5)

i

Minimize @

XXX t

Xj ¼ 1

cj˛0

Xj ˛f0; 1g

cj;0

i

(6)

ci; j

(8)

aj integer

cj

(9)

1  C1 þ dij C2 A

j

t

(7)

Yij ˛f0; 1g



0 1 X XX XX @Dt  þ C3 Yijt hti A þ C4 aj þ C5

i

XX t

t

j





T btj þ atj 

j

X

!

j

Yijt hti

i

Subject to

The objective function minimizes the total of in-house, fee, and set-up cost for additional beds. In the first term of the objective function, treatment and travel costs are calculated for the patients who receive in-house type service. The second term represents the fee type service cost calculated for the remaining patients that are not covered by any VA facility. The weighted sum of non-covered demand nodes is multiplied by the fixed external visit cost to calculate the total cost of fee type visits. It should be noted that the term “C3D” in the fee type cost equation could be excluded from the objective function since it is constant and non-optimizable, but is included here for completeness. Finally, the last term multiplies the total number of additional sleep beds in all facilities by a fixed bed set-up cost. Constraint (1) requires that service is added to at most P additional facilities, while constraint (2) assigns every demand node to at most one VA facility (those unassigned receive their care outside the network). Constraint (3) ensures that a demand node can be assigned to a facility if and only if this facility provides this type of care service and the travel distance is less than or equal to the acceptable maximum. The number of additional beds at each facility is determined by constraint (4). Constraint (5) ensures that the capacity of each facility is not exceeded. Constraint (6) ensures that all facilities currently providing service remain open. Constraints (7) through (9) define the location (Xj), allocation (Yij), and capacity expansion (aj) decision variables to be binary or nonnegative integers.

4.3. Multi-period model The multi-period model expands the above to include the additional notation and parameters, with most inputs and decision variables now having a time period index t ¼ index of period, hti ¼ total number of patients at demand node i during period t, C5 ¼ unused sleep bed cost per day, and Dt ¼ total demand during period t, with the decision variables now being

Yijt hti

X

Xjt  P

ct

(10)

j;O

Xjt  Xjt1 b1j ¼ fj

c; t˛f2; 3; 4; 5; 6g

cj

(12)

btj ¼ bt1 þ at1 j j X

(11)

ct˛f2; 3; 4; 5; 6g

  Yijt hti  T btj þ atj

cj; t

(13) (14)

i

X

Yijt  1

ci; t

(15)

j

    Xjt tij  S  1  M 1  Yijt  1 X

Yijt hti  Kj

cj; t

ci; j; t

(16) (17)

i

Xjt ¼ 1

cj˛0; t

(18)

Xjt ˛f0; 1g

cj;0; t

(19)

Yijt ˛f0; 1g

ci; j; t

(20)

atj integer

cj; t

(21)

The objective function now includes a fourth term that represents the total underutilization cost, where the number of empty beds at each facility is the difference between its total capacity and total allocated patients. Constraint (10) ensures that at most P number of sleep laboratories can be located in each period. Closing a service over the remaining planning horizon per VISN 1 policy is prevented by constraint (11), although this could be considered in future models. Constraints (12) and (13) calculate the number of

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beds in each facility at the beginning of each period, and constraint (14) determines the number of needed beds in each facility at each period. Constraints (15e21) function much as their counterparts in the single-period model (constraints (2e3 and 5e9)).

Table 3 Cost parameters used in mathematical models.

5. Application and results 5.1. Application details The above models were solved using both the observed and predicted geographic demand patterns described earlier. Future demand for the next five years was estimated via the VA’s veteran population projections (http://www.va.gov/VETDATA/ Demographics/Demographics.asp), summarized in Fig. 6, with significant estimated decreases over the next 20 years due to aging veteran populations and smaller modern military sizes. The implication of these trends is that in the short term it may be optimal to source a large percent of care outside the network so as to not overbuild long-term excess capacity. These future annual demand estimates were geographically distributed across the 59 zip code demand nodes based on the current relative proportions. Based on discussions with VISN 1 leadership, for both types of models three sets of facilities were considered for expansion:  Case 1: All seven existing VA medical centers in New England,  Case 2: All seven existing VA medical centers and the five largest outpatient clinics (Burlington VT, Springfield MA, Worcester MA, Portland ME, Bangor ME),  Case 3: All seven existing VA medical centers and all 45 outpatient clinics across New England, regardless of size.

Notation

Explanation

Cost ($)

C1 C2 C3 C4 C5

In-house procedure cost per patient Travel cost per mile Non-coverage cost per patient Cost of adding a sleep bed (capacity expansion) Unused sleep bed (underutilization) cost per day

588 0.70 850 21,000 385

additional facilities. Also shown is the current situation for comparison, which has a 2.3% higher cost and 4.5% lower access than even the “zero” case with no added capacity nor facilities, due to sub-optimal patient-to-facility allocation. Increasing the number of new facilities to three (P ¼ 3) would result in a savings of $145,188 (4.7%) given the same access coverage, a roughly 50% reduction in maximum driving distance to 50 miles given the same cost, or any pairwise costedistance point on the shown curve. After three new facilities, the cost-access tradeoff starts to become negligible, indicating expansion beyond P > 3 facilities may not be useful for practical purposes. Table 5 summarizes general results and savings for the singleperiod model assuming estimated true demands and based on a 60 mile maximum travel distance, showing the costs of fee and inhouse visits. The rows with P ¼ 0 correspond to the cases of modified capacities in existing facilities but not additional sleep care anywhere else.

Table 4 Multi-period model solution times based on different scenarios for cases 1, 2, and 3.

Cost parameters provided by VISN 1 are summarized in Table 3. The mathematical models were solved using the LINGO 11 software on a Dell desktop computer with 3 GB of RAM running a 1.8 GHz Intel Core 2 Duo processor. Both models were run for almost 100 scenarios in order to examine different coverage distance policies (S), numbers of allowable additional facilities (P), and candidate locations. With larger coverage distances or candidate locations, the feasible region and thus run times significantly increase (up to 44 min), as illustrated in Table 4 for the multi-period model.

Case

Acceptable travel distance (S) (miles)

1 1 1 4 15

1 1 2 8 19

2 (12 candidate locations)

20 30 40 50 60

1 2 3 5 23

1 2 3 5 381

1 3 3 3 214

3 (52 candidate locations)

20 30 40 50 60

2 8 16 13 73

4 10 12 9 464

5 13 29 22 2597

Total estimated demand (number of patients)

9,878 9,574 9,277 8,991

9,000

8,714

8,500 8,000 7,500 2010

2011

P¼3

1 1 2 4 8

10,187

9,500

P¼2

20 30 40 50 60

For the single-period model, Fig. 7 summarizes the optimized tradeoff between maximum acceptable driving distance, total minimal cost, and access assuming current observed demands and that sleep apnea care can be added at zero through five

10,000

P¼1

1 (7 candidate locations)

5.2. Single-period results

10,500

Solution times (in seconds)

2012 2013 Year

2014

2015

Fig. 6. Total projected sleep apnea demand by year for entire VISN 1 (New England).

J.C. Benneyan et al. / Socio-Economic Planning Sciences 46 (2012) 136e148

a

$3,800

P=0 P=1 P=2 P=3 P=4 P=5 Current

Cost (x1000 dollars)

$3,650 $3,500 $3,350

Table 7 summarizes the corresponding “allocation” results; that is, the assignment of patients to facilities (or fee basis) based on home zip code. As shown, even though the optimal locations change for each scenario, zip codes are clustered in similar manners; that is, similar groups of demand nodes are assigned to the same facilities. Most patients living in Vermont also become fee type visits, which follow intuition given that demand is relatively low in Vermont as compared to other regions. Fig. 9 visualizes the demand nodes covered within-network (in-house type) and outside-network (fee type) as well as the VA facility locations that provide service assuming a 60 mile acceptable maximum travel distance and the candidate facilities given by case 3.

Current approximate 95 travel distance percentile

$3,200 Current cost

$3,050 $2,900 20

30

40

50

60

70

80

90

143

100

Maximum accetable travel distance (S) (miles)

5.3. Multi-period results

b

100% 90%

Current

80% Coverage

70% 60%

Current approximate 95 travel distance percentile

P=0 P=1 P=2 P=3 P=4 P=5 Current

50% 40% 30% 20% 10% 20

30

40

50

60

70

80

90

100

Maximum acceptable travel distance (S) (miles)

Fig. 7. Optimized tradeoff between acceptable distance and (a) total cost, and (b) coverage percentage for single-period model assuming current observed demands and case 3.

Fig. 8 illustrates similar information and conclusions now using the estimated true demands. Table 6 further summarizes optimal locations and their corresponding capacities, using true demand, for 27 different scenarios based on coverage policy, additional number of facilities, and set of candidates. Patterns in this table provided important insight for decision makers. For example, capacity expansion at the current sleep laboratory in Providence always is suggested in all scenarios, removing most debate about the accuracy of various assumptions and demand estimates. Several other candidates also are frequently suggested as optimal expansion facilities, namely Newington, Togus, Northampton, and Springfield.

The multi-period model was solved for five, ten, and twentyfive year planning horizons. For the 5 year case, Table 8 summarizes general results, again assuming a 60 mile acceptable maximum travel distance. Since demand is expected to decrease over time, the optimal solution adds additional facilities only in the first year, although this must not necessarily be the case in general. As above, Fig. 10 shows the tradeoff frontier between acceptable travel distance, average annual cost, and coverage percentage assuming sleep beds can be added to zero through four additional facilities and the candidate facilities given by case 3. Due to excessive computational times, the multi-period model was solved only for maximum coverage distances of 60 miles or less. Similar to the single-period results, the current situation also is shown for comparison. Even with the “zero” case, an improvement of 3.5% in annual cost and 27.9% in access is possible. Increasing the number of new facilities in which sleep beds could be added to three could result in a savings of $965,849 (12.9%) given the same access coverage, a reduction in maximum driving distance to 42 miles given the same cost, or any pairwise costedistance point on the shown curve. After service capacity is added in three new facilities, again, the cost-access tradeoff starts to become negligible. Table 9 summarizes the optimal locations and their corresponding capacities for 27 different scenarios as previously. Similar to the single-period case, capacity expansion at the current Providence sleep laboratory always is suggested regardless of assumptions about acceptable travel distances (greater than 20 miles), with facilities Newington, Togus, Bedford, and Springfield again

Table 5 Results for single-period model with 60 mile maximum acceptable travel distance. Case

# of add. facilities (P)

Total cost

In-house type visit cost

Fee type visit cost

% in-house type visits

Optimal facility locations (total # of beds)b

Savings

1 (7 candidate locations)

Est. obs.a 0 1 2 3

$7,455,189 $7,274,793 $7,020,768 $6,874,504 $6,810,171

$3,252,421 $3,494,030 $4,342,393 $4,896,599 $5,102,943

$4,202,768 $3,759,762 $2,573,375 $1,809,905 $1,518,228

51 53 70 79 82

e e Northampton (4) Togus (3)eNorthampton (4) Togus (3)eNorthampton (4)eWRJ (1)

e $110,085 $434,421 $580,685 $645,018

2 (12 candidate locations)

Est. obs.a 0 1 2 3

$7,455,189 $7,274,793 $7,007,062 $6,860,798 $6,775,736

$3,252,421 $3,494,030 $4,296,089 $4,850,296 $5,134,086

$4,202,768 $3,759,762 $2,605,972 $1,842,502 $1,452,650

51 53 70 79 83

e e Springfield (4) Togus (3)eSpringfield (4) Togus (3)eSpringfield (4)ePortland (2)

e $110,085 $448,127 $594,391 $679,453

3 (52 candidate locations)

Est. obs.a 0 1 2 3

$7,455,189 $7,274,793 $7,007,062 $6,860,798 $6,774,937

$3,252,421 $3,494,030 $4,296,089 $4,850,296 $5,153,385

$4,202,768 $3,759,762 $2,605,972 $1,842,502 $1,411,553

51 53 70 79 84

e e Springfield (4) Togus (3)eSpringfield (4) Togus (3)eSpringfield (4)eSaco (2)

e $110,085 $448,127 $594,391 $680,252

a b

Estimated observed case. For all cases, optimum solution also requires a capacity expansion of one bed at the current facility in Providence.

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a $8,250

P=0 P=1 P=2 P=3 P=4

Cost (x1000 dollars)

$8,000 $7,750

Current approximate 95 travel distance percentile

S ¼ 60

Case 1

$7,250

$6,750 $6,500 30

40

50

60

70

Assigned demand node 3-digit zip codes

West Haven Togus West Roxbury

064-065-066-067-068-069 (CT) 041-042-043-045-048-049 (CT) 015-016-017-019-020-021-022-023-024-027 (MA), 029 (RI) 060-061 (CT), 010-011-012-013-053 (MA) 014-018 (MA), 030-031-032-033-034 (NH), 039 (ME) 062-063 (CT), 028 (MA) 037 (NH), 050-051-057 (VT) 025-026 (MA), 035-036-038 (NH), 040-044-046-047 (ME) 052-054-056-058-059 (VT)

Northampton Manchester Providence WRJ Fee type

$7,000

20

Facilities

P¼3

Current cost

$7,500

Table 7 Allocation of demand nodes to facilities for single-period model.

80

90

100

Maximum acceptable travel distance (S) (miles)

Case 2

b 100% P=0 P=1 P=2 P=3 P=4

90%

Coverage

80% 70%

Manchester Providence Springfield Portland Fee type

Current approximate 95 travel distance percentile

60% Current

50% 40%

West Haven Togus West Roxbury

Case 3

30%

West Haven Togus West Roxbury

20% 20

30

40

50

60

70

80

90

100

Manchester Providence Springfield Saco Fee type

Maximum acceptable travel distance (S) (miles)

Fig. 8. Optimized tradeoff between acceptable distance and (a) total cost, and (b) coverage percentage for single-period model assuming estimated true demand and candidate facilities under case 3.

being common additional expansion candidates. The broad similarity of these results under a variety of assumptions and to those of the single-period model has been useful for management to better understand obvious and robust decisions. Table 10 summarizes patient-facility assignments (based on home zip code) for the multi-period case, which again are very similar to those for the single-period model. One noticeable difference is that the capacity expansions in the multi-period model are relatively lower than those in the single-period model, which makes intuitive sense given shrinking veteran population

064-065-066-067-068-069 (CT) 042-045-048-049 (ME) 015-016-017-019-020-021-022-023-024-027 (MA), 029 (RI) 014-018 (MA), 030-031-032-033-034 (NH) 062-063 (CT), 028 (RI) 060-061 (CT), 010-011-012-013 (RI) 038-039-040-044 (ME) 025-026 (MA), 035-036-037 (NH), 041-044-046-047 (ME), 050-051-052-053-054-056-057-058-059 (VT) 064-065-066-067-068-069 (CT) 042-043-045-048-049 (ME) 015-016-017-019-020-021-022-023-024-027 (MA), 029 (RI) 014-018 (MA), 030-031-032-033-034 (NH) 062-063 (CT), 028 (MA) 060-061 (CT), 010-011-012-013 (MA) 038-039-040-041 (ME) 025-026 (MA), 035-036-037 (NH), 044-046-047 (ME), 050-051-052-053-054-056-057-058-059 (VT)

projections. This also results in the optimal number of patients that receive fee type service being higher especially in earlier years, contrary to current policy, with more patients who live outside of Vermont now also being sent to non-VA facilities. In addition to the 5 year planning horizon, 10 and 25 year horizons also were considered. To reduce execution times for the 10 and 25 year horizon cases, increments of two-year and five-year periods were employed respectively, with the projected demand for each n-year period aggregated accordingly (that is, each model

Table 6 Optimal facility locations for single-period model based on estimated true demand (numbers in parentheses represent the number of additional beds in corresponding facilities). S (miles)

P

30

1 2 3

60

1 2 3

90

1 2 3

Case 1

Case 2

Case 3

Facility

Beds

Capacity expansion

Facility

Beds

Capacity expansion

Facility

Beds

Capacity expansion

Newington Newington Northampton Newington Jamaica Plain Northampton

4 4 2 4 1 2

Providence (þ2) Providence (þ2)

Newington Newington Northampton Newington Northampton Worcester

4 4 2 4 2 2

Providence (þ2) Providence (þ2)

Newington Newington Northampton Newington Northampton Haverhill

4 4 2 4 2 2

Providence (þ2) Providence (þ2)

Newington Togus Northampton Togus Northampton WRJ

4 3 4 3 4 1

Providence (þ1) Providence (þ1)

Springfield Togus Springfield Togus Springfield Portland

4 3 4 2 4 2

Providence (þ1) Providence (þ1)

Springfield Togus Springfield Togus Springfield Saco

4 3 4 3 4 2

Providence (þ1) Providence (þ1)

Northampton Togus Northampton Togus Northampton WRJ

4 3 4 3 4 1

Providence (þ2) Providence (þ2)

Springfield Togus Springfield Togus Springfield Burlington

4 3 4 3 4 2

Providence (þ2) Providence (þ2)

Springfield Togus Springfield Springfield Bangor Littleton

4 3 4 4 3 4

Providence (þ2) Providence (þ2)

Providence (þ2)

Providence (þ1)

Providence (þ2)

Providence (þ2)

Providence (þ1)

Providence (þ2)

Providence (þ2)

Providence (þ1)

Providence (þ1)

J.C. Benneyan et al. / Socio-Economic Planning Sciences 46 (2012) 136e148

145

Fig. 9. Demand nodes covered within-network and outside-network and VA facilities that provide service for single-period model assuming a 60 mile acceptable maximum distance and candidate facilities under case 3.

Table 8 Results for multi-period model with 60 mile maximum acceptable travel distance. Case

# of add. facilities (P)

Average annual cost

In-house type visit cost

Fee type visit cost

% in-house type visits

Optimal facility locations (total # of beds)b

Savings

1 (7 candidate locations)

Est. obs.a 0 1 2 3

$7,455,189 $6,960,730 $6,734,157 $6,587,880 $6,517,772

$3,252,421 $3,305,465 $3,929,943 $4,360,938 $4,562,840

$4,202,768 $3,392,237 $2,513,087 $1,920,172 $1,635,157

51 58 69 76 80

e e Northampton (3) Togus (2)eNorthampton (3) Togus (2)eNorthampton (3)eWRJ (1)

e $494,459 $721,032 $867,309 $937,417

2 (12 candidate locations)

Est. obs.a 0 1 2 3

$7,455,189 $6,960,730 $6,723,166 $6,576,890 $6,489,340

$3,252,421 $3,305,465 $3,914,317 $4,345,313 $4,709,745

$4,202,768 $3,392,237 $2,516,278 $1,923,362 $1,416,678

51 58 69 76 82

e e Springfield (3) Togus (2)eSpringfield (3) Togus (2)eSpringfield (3)ePortland (2)

e $494,459 $732,023 $878,299 $965,849

3 (52 candidate locations)

Est. obs.a 0 1 2 3

$7,455,189 $6,960,730 $6,723,166 $6,574,090 $6,489,340

$3,252,421 $3,305,465 $3,914,317 $4,346,015 $4,709,745

$4,202,768 $3,392,237 $2,516,278 $1,920,952 $1,416,678

51 58 69 76 82

e e Springfield (3) Togus (2)eSpringfield (3) Togus (2)eSpringfield (3)ePortland (2)

e $494,459 $732,023 $878,299 $965,849

a b

Estimated observed case. For all cases, optimum solution also requires a capacity expansion of one bed at the current facility in Providence.

146

a

J.C. Benneyan et al. / Socio-Economic Planning Sciences 46 (2012) 136e148

$9,200 P=0 P=1 P=2 P=3 P=4

Cost (x1000 dollars)

$8,850 $8,500 $8,150 $7,800 Current cost

$7,450 $7,100 $6,750 $6,400 20

30

40

50

60

Maximum acceptable travel distance (S) (miles)

b

100%

P=0 P=1 P=2 P=3 P=4

90% 80% Coverage

70% 60%

Current

50% 40% 30% 20% 10% 0% 20

30

40

50

60

Maximum acceptable travel distance (S) (miles) Fig. 10. Optimized tradeoff between acceptable distance and (a) average annual cost, and (b) coverage percentage for multi-period model assuming case 3.

still used 5 periods, for example with the 25 year model treating the first 5 years as one period, the second 5 years as a second period, and so on). The average annual cost and coverage percentage for each planning horizon are shown in Fig. 11. Of note, as the planning horizon increases the average annual cost decreases, primarily because of long-term decreases in demand. 6. Discussion As the U.S. veteran population ages, effective delivery of health services becomes more important in terms of optimal within-

network coverage at minimum total cost and travel distance. This study investigated the optimal short and long-term location of specialty care services across New England VA facilities, using sleep apnea as a case study. Results indicate that significant cost savings and improvements in patient-centeredness can be achieved simply by optimizing capacity in existing VA facilities. These potential savings demonstrate this is a useful approach to help decision makers make more deliberate and tactical healthcare service location and capacity optimization decisions. In this particular application, significant savings are possible by opening an additional sleep laboratory to serve unmet need in northern Connecticut and western Massachusetts. If closing or relocating underutilized facilities were allowed, even greater improvements could be achieved, especially in the multi-period case. These results also have implications on the optimal amount of out-of-network “fee” care that run contrary to current practice and beliefs. Counter to the VA’s desire to eliminate almost all fee basis care, in almost all specialty care applications and scenarios examined to-date, roughly 10e25% of all care is optimal to occur outside of the VA network. To better understand the costs of out-of-network care, the above models were modified to require that all patients must be covered by VA facilities, resulting in a 34% increase in average travel distance while decreasing the total cost only by 4% (versus roughly 5% when compared with the S ¼ 60 and P ¼ 3 case). While these results do not consider the potential for reduced care continuity, they do suggest the savings possible by network redesign versus the significant cost and travel increase from fee reduction mandates. Similar analyses have been conducted for colonoscopy and post-traumatic stress disorder (PTSD), with preliminary results similarly indicating 15e22% potential cost savings. Crudely extrapolating these results across all VA networks and specialty care services conservatively suggests potential savings of several hundred million dollars annually. Possible limitations of this study include the assumption that out-of-network capacity always is available within desired distances, which may not reflect the actual market. Additional savings might be achieved by adding or relocating existing facilities. Expansion of the system is perhaps less disruptive than facility relocation, the latter potentially forcing staff to relocate or find work elsewhere. Since the disruptive nature of change may limit a health system’s ability to immediately implement an optimized network design, some thought might be put into multi-period transition or minimally disruptive models.

Table 9 Optimal facility locations for multi-period model (numbers in parentheses represent the number of additional beds in corresponding facilities). S (miles)

P

20

1 2 3

40

1 2 3

60

1 2 3

Case 1

Case 2

Case 3

Facility

Beds

Capacity expansion

Facility

Beds

Capacity expansion

Facility

Beds

Capacity expansion

Newington Newington Bedford Newington Bedford Northampton

2 2 1 2 1 1

e e

Newington Newington Bedford Newington Bedford Springfield

2 2 1 2 1 2

e e

Newington Newington Bedford Newington Bedford Springfield

2 2 1 2 1 2

e e

Newington Newington Bedford Newington Bedford Northampton

4 4 1 2 1 2

Providence (þ1) Providence (þ1)

Newington Newington Springfield Newington Bedford Springfield

4 2 3 2 1 3

Providence (þ1) Providence (þ1)

Newington Springfield Togus Springfield Fitchburg Togus

4 3 3 3 1 3

Providence (þ1) Providence (þ1)

Northampton Togus Northampton Togus Northampton WRJ

3 2 3 2 3 1

Springfield Togus Springfield Togus Springfield Portland

3 2 3 2 3 2

Springfield Togus Springfield Togus Springfield Portland

3 2 3 2 3 2

e

Providence (þ1) Newington (þ1) (year 2) Providence (þ1) Providence (þ1) Providence (þ1)

e

Providence (þ1)

Providence (þ1) Providence (þ1) Providence (þ1)

e

Providence (þ1)

Providence (þ1) Providence (þ1) Providence (þ1)

J.C. Benneyan et al. / Socio-Economic Planning Sciences 46 (2012) 136e148

Facilities

3-digit zip codes that assigned to each facility

West Haven Togus West Roxbury

061-064-065-066-067-068-069 (CT) 041-042-043-045-048-049 (ME) 015-016 (year 1e3)-017-018 (year 5e6)-019-020-021-022-023-024-027 (MA); 029 (RI) 010-011-012-013 (MA); 053 (VT); 060 (CT) 014-018 (year 1e4) (MA); 030-031-032-033-034 (NH); 039 (ME) 016 (year 4e6) (MA); 028 (RI); 062-063 (CT) 036-037 (NH); 050-051-057 (VT) 025-026 (MA); 035-038 (NH); 040-044-046-047 (ME); 052-054-056-058-059 (VT)

P¼3 Case 1

Northampton Manchester Providence WRJ Fee type Case 2

West Haven Togus West Roxbury

Manchester Providence Springfield Portland Fee type Case 3

West Haven Togus West Roxbury

Manchester Providence Springfield Portland Fee type

060 (year 3)-061-064 (year 1e2,4e6)-065-066-067-068-069 (CT) 042-043 (year 4e6)-045 (year 1e3)-048-049 (ME) 015-016 (year 1e3)-017-018 (year 5e6)-019-020-021-022-023-024-027 (MA); 029 (RI) 014-018 (year 1e4) (MA); 030-031-032-033-034 (NH); 039 (year 2) (ME) 016 (year 4e6) (MA); 028 (RI); 062-063 (CT) 010-011-012-013 (MA); 060 (year 1e2,4e6)-064 (year 3) (CT) 038 (NH); 039 (year 1,3e6)-040-041-043 (year 1e3)-045 (year 4e6) (ME) 025-026 (MA); 035-036-037 (NH); 044-046-047 (ME); 050-051-052-053-054-056-057-058-059 (VT) 060 (year 3)-061-064 (year 1e2,4e6)-065-066-067-068-069 (CT) 042-043 (year 4e6)-045 (year 1e3)-048-049 (ME) 015-016 (year 1e3)-017-018 (year 5e6)-019-020-021-022-023-024-027 (MA); 029 (RI) 014-018 (year 1e4) (MA); 030-031-032-033-034 (NH); 039 (year 2) (ME) 016 (year 4e6) (MA); 028 (RI); 062-063 (CT) 010-011-012-013 (MA); 060 (year 1e2,4e6)-064 (CT) 038 (NH); 039 (year 1,3e6)-040-041-043 (year 1e3)-045 (year 4e6) (ME) 025-026 (MA); 035-036-037 (NH); 044-046-047 (ME); 050-051-052-053-054-056-057-058-059 (VT)

A related potential limitation is poor “trialability”, especially given that healthcare practitioners have become more accustomed to gradual iterative PDSA improvement cycles than to instantaneous reengineering. Small cycles of change allow process improvement personnel to obtain safe feedback to minor changes before proceeding with broader implementation. Solutions such as those in this paper, conversely, may require more of a leap of faith. Unfortunately, since few healthcare practitioners and leaders understand modeling, simulation, and locationeallocation methods, it may be difficult for them to fully trust in results and make disruptive changes. Some thought thus may be useful into smaller, less disruptive initial changes to build initial acceptance of these methods. The development of graphical, interactive, or computer simulation also may be useful for building understanding, support and trust. These models also could be expanded in several manners. These include accounting for demand variability naturally occurring over time and future veteran population uncertainty due to such things as the unpredictability of future military conflicts. Stochastic modeling approaches might be appropriate here, such as recourse, chance-constraint, and dependent-chance programs. Multi-period capacity scale-down models also might be considered, although

Cost per year (x1000 dollars)

S ¼ 60

a

$9,000 5 year planning horizon 10 year planning horizon 25 year planning horizon

$8,500 $8,000 $7,500 $7,000 $6,500 $6,000 20

30

40

50

60

Maximum acceptable travel distance (S) (miles)

b

90% 80% 70% Coverage

Table 10 Allocation of demand nodes to facilities for multi-period model.

147

60% 50% 5 year planning horizon 10 year planning horizon 25 year planning horizon

40% 30% 20% 20

30

40

50

60

Maximum acceptable travel distance (S) (miles) Fig. 11. Optimal (a) annual cost and (b) coverage percentages considering different planning horizons.

implementation initially may be limited by “permanent” contracts and the ability to retrain staff. Finally, implementation of these models in user-friendly decision support tools also would be useful to enable decision makers to explore what-if scenarios more readily.

Acknowledgments This work was funded in part by the Center for Health Organization Transformation (National Science Foundation grant IIP10341990) and the VISN 1 Veterans Engineering Resource Center (grant VA 241-P-1772). Any views expressed here are those of the authors and do not necessarily reflect those of the National Science Foundation nor the Department of Veterans Affairs. We thank Dr. Michael Mayo-Smith, the VA New England healthcare system network director, for his valuable feedback and Seda Sinangil for her valuable modeling and analysis assistance.

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