Preventive healthcare facility location planning with quality-conscious clients

Abstract

Pursuing the overarching goal of saving both lives and healthcare costs, we introduce an approach to increase the expected participation in a preventive healthcare program, e.g., breast cancer screening. In contrast to sick people who need urgent medical attention, the clients in preventive healthcare decide whether to go to a specific facility (if this maximizes their utility) or not to take part in the program. We consider clients’ utility functions to include decision variables denoting the waiting time for an appointment and the quality of care. Both variables are defined as functions of a facility’s utilization. We employ a segmentation approach to formulate a mixed-integer linear program. Applying GAMS/CPLEX, we optimally solved instances with up to 400 demand nodes and 15 candidate locations based on both artificial data as well as in the context of a case study based on empirical data within one hour. We found that using a Benders decomposition of our problem decreases computational effort by more than 50%. We observe a nonlinear relationship between participation and the number of established facilities. The sensitivity analysis of the utility weights provides evidence on the optimal participation given a specific application (data set, empirical findings).

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Notes

  1. 1.

    https://github.com/Urwolfen/ORSP-Preventive-Healthcare-Facility-Location-Planning-with-Quality-Conscious-Clients.

  2. 2.

    https://github.com/Urwolfen/ORSP-Preventive-Healthcare-Facility-Location-Planning-with-Quality-Conscious-Clients.

References

  1. Anand KS, Paç MF, Veeraraghavan S (2011) Quality-speed conundrum: trade-offs in customer-intensive services. Manag Sci 57(1):40–56

    Article  Google Scholar 

  2. Aros-Vera F, Marianov V, Mitchell JE (2013) p-Hub approach for the optimal park-and-ride facility location problem. Eur J Oper Res 226(2):277–285

    Article  Google Scholar 

  3. Australian Bureau of Statistics (2011a) Greater Sydney (Statistical Area Level 1), Basic Community Profile, Excel spreadsheet 2011 Census B04 A+B New South Wales SA1, AGE BY SEX. Viewed May 16, 2018. http://www.abs.gov.au/websitedbs/censushome.nsf/home/census?opendocument&navpos=10

  4. Australian Bureau of Statistics (2011b) Statistical Area Level 1 (SA1) ASGS Ed 2011 Digital Boundaries in ESRI Shapefile Format. Viewed May 16, 2018. http://www.abs.gov.au/AUSSTATS/abs@.nsf/DetailsPage/1270.0.55.001July

  5. Ayer T, Alagoz O, Stout NK, Burnside ES (2016) Heterogeneity in women’s adherence and its role in optimal breast cancer screening policies. Manag Sci 62(5):1339–1362

    Article  Google Scholar 

  6. Baron O, Berman O, Krass D (2008) Facility location with stochastic demand and constraints on waiting time. Manuf Serv Oper Manag 10(3):484–505

    Article  Google Scholar 

  7. Batt RJ, Terwiesch C (2015) Waiting patiently: an empirical study of queue abandonment in an emergency department. Manag Sci 61(1):39–59

    Article  Google Scholar 

  8. Belloni A, Freund R, Selove M, Simester D (2008) Optimizing product line designs: efficient methods and comparisons. Manag Sci 54(9):1544–1552

    Article  Google Scholar 

  9. Benati S, Hansen P (2002) The maximum capture problem with random utilities: problem formulation and algorithms. Eur J Oper Res 143(3):518–530

    Article  Google Scholar 

  10. Besbes O, Sauré D (2016) Product assortment and price competition under multinomial logit demand. Prod Oper Manag 25(1):114–127

    Article  Google Scholar 

  11. Blankart CR (2012) Does healthcare infrastructure have an impact on delay in diagnosis and survival? Health Policy 105(2–3):128–137

    Article  Google Scholar 

  12. Blum K, Offermanns M (2004) Umverteilungswirkungen der Mindestmengenregelung. das Krankenhaus 96(10):787–790

    Google Scholar 

  13. BreastScreen Australia (2014) BreastScreen and you—information about mammography screening. Viewed May 16, 2018. http://cancerscreening.gov.au/internet/screening/publishing.nsf/Content/breastscreen-and-you

  14. BreastScreen Australia (2015) National Accreditation Handbook. Viewed May 16, 2018. http://www.cancerscreening.gov.au/internet/screening/publishing.nsf/Content/acc-hb-2015

  15. BreastScreen New South Wales (2015) Viewed August 18, 2015. http://www.bsnsw.org.au/

  16. Castillo I, Ingolfsson A, Sim T (2009) Social optimal location of facilities with fixed servers, stochastic demand, and congestion. Prod Oper Manag 18(6):721–736

    Article  Google Scholar 

  17. Chen H, Qian Q, Zhang A (2015) Would allowing privately funded health care reduce public waiting time? Theory and empirical evidence from Canadian joint replacement surgery data. Prod Oper Manag 24(4):605–618

    Article  Google Scholar 

  18. Codato G, Fischetti M (2006) Combinatorial Benders’ cuts for mixed-integer linear programming. Oper Res 54(4):756–766

    Article  Google Scholar 

  19. Cordeau J-F, Furini F, Ljubic I (2019) Benders decomposition for very large scale partial set covering and maximal covering location problems. Eur J Oper Res 275(3):882–896

    Article  Google Scholar 

  20. Dan T, Marcotte P (2019) Competitive facility location with selfish users and queues. Oper Res 67:479–497

    Google Scholar 

  21. de Bekker-Grob EW, Ryan M, Gerard K (2012) Discrete choice experiments in health economics: a review of the literature. Health Econ 21(2):145–172

    Google Scholar 

  22. Elhedhli S (2006) Service system design with immobile servers, stochastic demand, and congestion. Manuf Serv Oper Manag 8(1):92–97

    Google Scholar 

  23. Espinoza Garcia JC, Alfandari L (2018) Robust location of new housing developments using a choice model. Ann Oper Res 271:527–550

    Google Scholar 

  24. Feldman J, Liu N, Topaloglu H, Ziya S (2014) Appointment scheduling under patient preference and no-show behavior. Oper Res 62(4):794–811

    Article  Google Scholar 

  25. Freire AS, Moreno E, Yushimito WF (2016) A branch-and-bound algorithm for the maximum capture problem with random utilities. Eur J Oper Res 252(1):204–212

    Article  Google Scholar 

  26. Gallego G, Topaloglu H (2014) Constrained assortment optimization for the nested logit model. Manag Sci 60(10):2583–2601

    Article  Google Scholar 

  27. GAMS Development Corporation (2017) General Algebraic Modeling System (GAMS) Release 24.8.4. GAMS Development Corporation, Washington, DC, USA

  28. Gerard K, Shanahan M, Louviere J (2003) Using stated preference discrete choice modelling to inform health care decision-making: a pilot study of breast screening participation. Appl Econ 35(9):1073–1085

    Article  Google Scholar 

  29. Gerard K, Shanahan M, Louviere J (2008) Using discrete choice modelling to investigate breast screening participation. In: Ryan M, Gerard K, Amaya-Amaya M (eds) Using discrete choice experiments to value health and health care, volume 11 of the economics of non-market goods and resources. Springer, Dordrecht, pp 117–137

    Google Scholar 

  30. Güneş ED, Chick SE, Akşin OZ (2004) Breast cancer screening services: trade-offs in quality, capacity, outreach, and centralization. Health Care Manag Sci 7(4):291–303

    Article  Google Scholar 

  31. Güneş ED, Örmeci EL, Kunduzcu D (2015) Preventing and diagnosing colorectal cancer with a limited colonoscopy resource. Prod Oper Manag 24(1):1–20

    Article  Google Scholar 

  32. Haase K (2009) Discrete location planning. Technical Report WP-09-07, Institute of Transport and Logistics Studies, University of Sydney

  33. Haase K, Müller S (2013) Management of school locations allowing for free school choice. Omega 41(5):847–855

    Article  Google Scholar 

  34. Haase K, Müller S (2014) A comparison of linear reformulations for multinomial logit choice probabilities in facility location models. Eur J Oper Res 232(3):689–691

    Article  Google Scholar 

  35. Haase K, Müller S (2015) Insights into clients’ choice in preventive health care facility location planning. OR Spectr 37(1):273–291

    Article  Google Scholar 

  36. Harewood GC (2005) Relationship of colonoscopy completion rates and endoscopist features. Dig Dis Sci 50(1):47–51

    Article  Google Scholar 

  37. Harper PR, Shahani AK, Gallagher JE, Bowie C (2005) Planning health services with explicit geographical considerations: a stochastic location-allocation approach. Omega 33(2):141–152

    Article  Google Scholar 

  38. Hol L, de Bekker-Grob EW, van Dam L, Donkers B, Kuipers EJ, Habbema JDF, Steyerberg EW, van Leerdam ME, Essink-Bot M-L (2010) Preferences for colorectal cancer screening strategies: a discrete choice experiment. Br J Cancer 102(6):972–980

    Article  Google Scholar 

  39. Killaspy H, Banerjee S, King M, Lloyd M (2000) Prospective controlled study of psychiatric out-patient non-attendance. Br J Psychiatry 176(2):160–165

    Article  Google Scholar 

  40. Koppelman FS, Bhat C (2006) A self instructing course in mode choice modeling: multinomial and nested logit models. US Department of Transportation, Federal Transit Administration

  41. Lacy NL, Paulman A, Reuter MD, Lovejoy B (2004) Why we don’t come: patient perceptions on no-shows. Ann Fam Med 2(6):541–545

    Article  Google Scholar 

  42. Lancsar E, Louviere J (2008) Conducting discrete choice experiments to inform healthcare decision making. PharmacoEconomics 26(8):661–677

    Article  Google Scholar 

  43. Liu N, Finkelstein SR, Kruk ME, Rosenthal D (2018) When waiting to see a doctor is less irritating: understanding patient preferences and choice behavior in appointment scheduling. Manag Sci 64(5):1975–1996

    Article  Google Scholar 

  44. Ljubić I, Moreno E (2018) Outer approximation and submodular cuts for maximum capture facility location problems with random utilities. Eur J Oper Res 266(1):46–56

    Article  Google Scholar 

  45. Madadi M, Zhang S, Henderson LM (2015) Evaluation of breast cancer mammography screening policies considering adherence behavior. Eur J Oper Res 247(2):630–640

    Article  Google Scholar 

  46. Marianov V, Ríos M, Icaza MJ (2008) Facility location for market capture when users rank facilities by shorter travel and waiting times. Eur J Oper Res 191(1):32–44

    Article  Google Scholar 

  47. McFadden D (2001) Economic choices. Am Econ Rev 91(3):351–378

    Article  Google Scholar 

  48. Moscelli G, Siciliani L, Gutacker N, Gravelle H (2016) Location, quality and choice of hospital: evidence from England 2002–2013. Reg Sci Urban Econ 60:112–124

    Article  Google Scholar 

  49. Müller S, Haase K (2014) Customer segmentation in retail facility location planning. Bus Res 7(2):235–261

    Article  Google Scholar 

  50. Müller S, Haase K (2016) On the product portfolio planning problem with customer-engineering interaction. Oper Res Lett 44(3):390–393

    Article  Google Scholar 

  51. Osadchiy N, Diwas K (2017) Are patients patient? The role of time to appointment in patient flow. Prod Oper Manag 26(3):469–490

    Article  Google Scholar 

  52. QGIS Development Team (2015). QGIS Geographic Information System. Open Source Geospatial Foundation Project

  53. R Core Team (2017) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria

  54. Rahmaniani R, Crainic TG, Gendreau M, Rei W (2017) The benders decomposition algorithm: a literature review. Eur J Oper Res 259(3):801–817

    Article  Google Scholar 

  55. Rusmevichientong P, Shmoys D, Tong C, Topaloglu H (2014) Assortment optimization under the multinomial logit model with random choice parameters. Prod Oper Manag 23(11):2023–2039

    Article  Google Scholar 

  56. Ryan M, Gerard K, Amaya-Amaya M (2008a) Discrete choice experiments in a nutshell. In: Ryan M, Gerard K, Amaya-Amaya M (eds) Using discrete choice experiments to value health and health care, volume 11 of the economics of non-market goods and resources. Springer, Dordrecht, pp 13–46

    Google Scholar 

  57. Ryan M, Gerard K, Watson V, Street DJ, Burgess L (2008b) Practical issues in conducting a discrete choice experiment. In: Ryan M, Gerard K, Amaya-Amaya M (eds) Using discrete choice experiments to value health and health care, volume 11 of the economics of non-market goods and resources. Springer, Dordrecht, pp 73–97

    Google Scholar 

  58. Ryan M, Skåtun D, Major K (2008c) Using discrete choice experiments to go beyond clinical outcomes when evaluating clinical practice. In: Ryan M, Gerard K, Amaya-Amaya M (eds) Using discrete choice experiments to value health and health care, volume 11 of the economics of non-market goods and resources. Springer, Dordrecht, pp 101–116

    Google Scholar 

  59. Schrag D, Cramer LD, Bach PB, Cohen AM, Warren JL, Begg CB (2000) Influence of hospital procedure volume on outcomes following surgery for colon cancer. JAMA 284(23):3028–3035

    Article  Google Scholar 

  60. Street DJ, Burgess L (2007) The construction of optimal stated choice experiments: theory and methods. Wiley, Hoboken

    Google Scholar 

  61. Street DJ, Burgess L, Viney R, Louviere J (2008) Designing discrete choice experiments for health care. In: Ryan M, Gerard K, Amaya-Amaya M (eds) Using discrete choice experiments to value health and health care, volume 11 of the economics of non-market goods and resources. Springer, Dordrecht, pp 47–72

    Google Scholar 

  62. Tiwari V, Heese HS (2009) Specialization and competition in healthcare delivery networks. Health Care Manag Sci 12(3):306–324

    Google Scholar 

  63. Train KE (2009) Discrete choice methods with simulation, 2nd edn. Cambridge University Press, Cambridge

    Google Scholar 

  64. Truong V-A (2015) Optimal advance scheduling. Manag Sci 61(7):1584–1597

    Google Scholar 

  65. van Dam L, Hol L, de Bekker-Grob EW, Steyerberg EW, Kuipers EJ, Habbema JDF, Essink-Bot M-L, van Leerdam ME (2010) What determines individuals’ preferences for colorectal cancer screening programmes? A discrete choice experiment. Eur J Cancer 46(1):150–159

    Google Scholar 

  66. van der Pol M, Currie G, Kromm S, Ryan M (2014) Specification of the utility function in discrete choice experiments. Value Health 17(2):297–301

    Google Scholar 

  67. Verter V, Lapierre SD (2002) Location of preventive health care facilities. Ann Oper Res 110(1–4):123–132

    Google Scholar 

  68. Vidyarthi N, Kuzgunkaya O (2015) The impact of directed choice on the design of preventive healthcare facility network under congestion. Health Care Manag Sci 18(4):459–474

    Article  Google Scholar 

  69. Viiala CH, Tang KW, Lawrance IC, Murray K, Olynyk JK (2007) Waiting times for colonoscopy and colorectal cancer diagnosis. Med J Aust 186(6):282–285

    Article  Google Scholar 

  70. Viney R, Lancsar E, Louviere J (2002) Discrete choice experiments to measure consumer preferences for health and healthcare. Expert Rev Pharmacoecon Outcomes Res 2(4):319–326

    Article  Google Scholar 

  71. Wang R, Wang Z (2017) Consumer choice models with endogenous network effects. Manag Sci 63(11):3944–3960

    Article  Google Scholar 

  72. Wang Q, Batta R, Rump CM (2002) Algorithms for a facility location problem with stochastic customer demand and immobile servers. Ann Oper Res 111(1–4):17–34

    Article  Google Scholar 

  73. Wang D, Morrice DJ, Muthuraman K, Bard JF, Leykum LK, Noorily SH (2018) Coordinated scheduling for a multi-server network in outpatient pre-operative care. Prod Oper Manag 27(3):458–479

    Article  Google Scholar 

  74. Zhang Y, Berman O, Verter V (2009) Incorporating congestion in preventive healthcare facility network design. Eur J Oper Res 198(3):922–935

    Article  Google Scholar 

  75. Zhang Y, Berman O, Marcotte P, Verter V (2010) A bilevel model for preventive healthcare facility network design with congestion. IIE Trans 42(12):865–880

    Article  Google Scholar 

  76. Zhang Y, Berman O, Verter V (2012) The impact of client choice on preventive healthcare facility network design. OR Spectr 34(2):349–370

    Article  Google Scholar 

Download references

Acknowledgements

The authors are very grateful for the very helpful suggestions of two anonymous reviewers to improve the paper’s quality.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ralf Krohn.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix 1: Tighter bounds on variables

We can improve the upper bound for \(X_{i,j,m}\) in (25): If it is certain that r facilities will exist, we do not need to do the calculation as if (jm) was the only facility, but we can assume that \(r-1\) other facilities will be established as well. We replace \(p_{i,j,m}\) and get

$$\begin{aligned} X_{i,j,m}&\le \frac{\mathrm {e}^{v_{i,j,m}}}{\mathrm {e}^{v_{i,\mathrm {no}}} + \mathrm {e}^{v_{i,j,m}} + \sum _{k \in \mathscr {J}_i^{\text {min}}} \mathrm {e}^{v_{i,k,\check{m}}}} \cdot Y_{j,m}&\forall \; i \in \mathscr {I}; j \in \mathscr {J}; m \in \mathscr {M} \end{aligned}$$
(34)

where \(\mathscr {J}_i^{\text {min}}\) is the set of the \(r-1\) least attractive other facility locations for demand node i and \(\check{m}\) represents the globally least attractive mode. This change reduces solution times remarkably—a finding that is also discussed in Freire et al. (2016).

It is also helpful to determine bounds for the no-choice probability variables \(Z_i\). They can be easily computed by assuming worst case or best case scenarios. Let \(\mathscr {J}_i^{\text {worst}}\) and \(\mathscr {J}_i^{\text {best}}\) be the sets of the r least or most attractive alternatives j for demand node i, and \(\hat{m}\) the most attractive mode. Then we get upper bounds \(Z_i^{\text {UB}}\) and lower bounds \(Z_i^{\text {LB}}\):

$$\begin{aligned} Z_i^{\text {UB}}&= \frac{\mathrm {e}^{v_{i,\mathrm {no}}}}{\mathrm {e}^{v_{i,\mathrm {no}}} + \sum _{k \in \mathscr {J}_i^{\text {worst}}} \mathrm {e}^{v_{i,k,\check{m}}}}, \end{aligned}$$
(35)
$$\begin{aligned} Z_i^{\text {LB}}&= \frac{\mathrm {e}^{v_{i,\mathrm {no}}}}{\mathrm {e}^{v_{i,\mathrm {no}}} + \sum _{k \in \mathscr {J}_i^{\text {best}}} \mathrm {e}^{v_{i,k,\hat{m}}}}. \end{aligned}$$
(36)

If we also decided about the number of established facilities r with a variation of (30) to

$$\begin{aligned} \sum _{j \in \mathscr {J}} \sum _{m \in \mathscr {M}} Y_{j,m} \le r, \end{aligned}$$
(37)

our model is harder to solve and (34) and (35) would not be applicable.

Appendix 2: Modeling framework to derive a lower bound

Since it may take a long time to find a first integer solution within the solving process, it is expedient to determine a lower bound for our linear model PHCFLPP (23)–(33). We present three models that altogether yield a lower bound. This approach is basically introduced in Haase and Müller (2015). It relies on the constant part of individuals’ utility functions, which mainly depends on distances.

Step I

With the first auxiliary model the highest choice probabilities for each single demand node are chosen. I.e., the most attractive facilities for them are identified. We continue our nomenclature:

Additional variables

\(\Upsilon _{i,j,m}\):

= 1 if demand node i is assigned to location j in mode m; 0, otherwise

\(F^{\mathrm {I}}\):

Objective function value of Model Step I (cumulated r highest choice probabilities)

$$\begin{aligned} \mathrm {Maximize} \quad F^{\mathrm {I}} = \sum _{i \in \mathscr {I}} \sum _{j \in \mathscr {J}} \sum _{m \in \mathscr {M}} p_{i,j,m} \cdot {\Upsilon _{i,j,m}} \end{aligned}$$
(38)

subject to

$$\begin{aligned} \sum _{j \in \mathscr {J}} \sum _{m \in \mathscr {M}} {\Upsilon _{i,j,m}}&\le r&\forall \; i \in \mathscr {I} \end{aligned}$$
(39)
$$\begin{aligned} \sum _{m \in \mathscr {M}} {\Upsilon _{i,j,m}}&\le 1&\forall \; i \in \mathscr {I}; j \in \mathscr {J} \end{aligned}$$
(40)
$$\begin{aligned} {\Upsilon _{i,j,m}}&\in \{0;1\}&\forall \; i \in \mathscr {I}; j \in \mathscr {J}; m \in \mathscr {M} \end{aligned}$$
(41)

The objective function (38) maximizes the cumulated chosen choice probabilities subject to (39), which means that the at most r highest choice probabilities for each demand node i are selected. (40) ensures that a facility can only be demanded in exactly one mode m.

Step II

In the second auxiliary model, the r overall most attractive facilities are established. The specific mode is not of interest here and the best one is always chosen. The decision is based on the remaining influences, mainly the distance between demand and supply nodes. An additional parameter that makes use of the solution to Step I sums up for how many demand nodes a certain facility belongs to the most attractive ones. The more demand nodes assigned to a facility the higher its attraction by this definition. We further extend our nomenclature:

Additional parameter

\(b_{j,m}\) :

Attractiveness value for each facility at location j in mode m with \(b_{j,m} = \sum _{i \in \mathscr {I}} {\Upsilon _{i,j,m}^{*}}\) where \({\Upsilon _{i,j,m}^{*}}\) is the optimal solution to Step I

Additional variables

\(\tilde{Y}_{j,m}\):

= 1 if facility at location j is specified to offer healthcare service in mode m; 0, otherwise

\(F^{\mathrm {II}}\):

Objective function value of Model Step II (attractiveness of located facilities)

$$\begin{aligned} \mathrm {Maximize} \quad F^{\mathrm {II}} = \sum _{j \in \mathscr {J}} \sum _{m \in \mathscr {M}} b_{j,m} \cdot {\tilde{Y}_{j,m}} \end{aligned}$$
(42)

subject to

$$\begin{aligned} \sum _{j \in \mathscr {J}} \sum _{m \in \mathscr {M}} {\tilde{Y}_{j,m}}&= r \end{aligned}$$
(43)
$$\begin{aligned} {\tilde{Y}_{j,m}}&\in \{0;1\}&\forall \; j \in \mathscr {J}; m \in \mathscr {M} \end{aligned}$$
(44)

The objective function (42) maximizes the cumulated overall attractiveness and thereby chooses the r most demanded facilities according to (43). The result represents a solution that depends on the individuals’ constant part of their deterministic utility function disregarding capacities.

Step III

The last auxiliary model is used to determine the final modes for the facility locations previously identified in Step II. We consider

Additional parameter

\(\tilde{Y}_{j,m}^{*}\) :

optimal solution to Step II

Additional variable

LB:

objective function value of Model Step III (a lower bound for PHCFLPP)

$$\begin{aligned} \mathrm {Maximize} \quad LB = \sum _{i \in \mathscr {I}} g_i \cdot \sum _{j \in \mathscr {J}} \sum _{m \in \mathscr {M}} {X_{i,j,m}} \end{aligned}$$
(45)

subject to (24)–(28), (31)–(33) as well as

$$\begin{aligned} \sum _{m \in \mathscr {M}} {Y_{j,m}}&= \sum _{m \in \mathscr {M}} \tilde{Y}_{j,m}^{*}&\forall \; j \in \mathscr {J}. \end{aligned}$$
(46)

The first restriction blocks are in fact PHCFLPP without two redundant constraints of which information is already included in Step I and Step II. The information is that only one mode per facility can be present as well as that r facilities are established. (45) maximizes the expected participation by now selecting the final modes of the predestined facility locations via (46). The objective function value is a lower bound for PHCFLPP as it is a feasible integer solution to it. It is allowed to add up the pre-defined locations on the right hand side of (46), because at most one value can equal 1 due to (40). Thus, (46) is a substitute for (29) and a linking constraint in addition. Those constraints can be left out in Step III, as well as (30), because of (43). So we can perform a MIP start with PHCFLPP after solving the Steps I, II and III in a row.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Krohn, R., Müller, S. & Haase, K. Preventive healthcare facility location planning with quality-conscious clients. OR Spectrum (2020). https://doi.org/10.1007/s00291-020-00605-w

Download citation

Keywords

  • Discrete choice
  • Healthcare
  • Random utility
  • Configurations of facilities
  • Facility location
  • Benders