Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
Article

ONLINE CAPACITY PLANNING FOR REHABILITATION TREATMENTS: AN APPROXIMATE DYNAMIC PROGRAMMING APPROACH

  • Ingeborg A. Bikker (a1), Martijn R.K. Mes (a2), Antoine Sauré (a3) and Richard J. Boucherie (a4)

Abstract

We study an online capacity planning problem in which arriving patients require a series of appointments at several departments, within a certain access time target.

This research is motivated by a study of rehabilitation planning practices at the Sint Maartenskliniek hospital (the Netherlands). In practice, the prescribed treatments and activities are typically booked starting in the first available week, leaving no space for urgent patients who require a series of appointments at a short notice. This leads to the rescheduling of appointments or long access times for urgent patients, which has a negative effect on the quality of care and on patient satisfaction.

We propose an approach for allocating capacity to patients at the moment of their arrival, in such a way that the total number of requests booked within their corresponding access time targets is maximized. The model considers online decision making regarding multi-priority, multi-appointment, and multi-resource capacity allocation. We formulate this problem as a Markov decision process (MDP) that takes into account the current patient schedule, and future arrivals. We develop an approximate dynamic programming (ADP) algorithm to obtain approximate optimal capacity allocation policies. We provide insights into the characteristics of the optimal policies and evaluate the performance of the resulting policies using simulation.

Copyright

COPYRIGHT: © Cambridge University Press 2018 

References

Hide All
1.Baharian, G. & Jacobson, S.H. (2013). Stochastic sequential assignment problem with threshold criteria. Probability in the Engineering and Informational Sciences 27(3): 277–296.
2.Boucherie, R.J. & van Dijk, N.M. (eds.), (2017). International Series in Operations Research and Management Science: Markov decision processes in Practice. Cham, Switzerland: Springer.
3.Braaksma, A., Kortbeek, N., Post, G.F. & Nollet, F. (2014). Integral multidisciplinary rehabilitation treatment planning. Operations Research for Health Care 3(3): 145–159.
4.Cayirli, T. & Veral, E. (2003). Outpatient scheduling in health care: a review of literature. Production and Operations Management 12(4): 519–549.
5.Dafoe, W., Arthur, H., Stokes, H., Morrin, L. & Beaton, L. (2006). Universal access: but when? Treating the right patient at the right time: access to cardiac rehabilitation. Canadian Journal of Cardiology 22: 905–911.
6.De Farias, D. P. & Van Roy, B. (2003). The linear programming approach to approximate dynamic programming. Operations Research 51(6): 850–865.
7.De Farias, D.P. & Van Roy, B. (2004). On constraint sampling in the linear programming approach to approximate dynamic programming. Mathematics of operations research 29(3): 462–478.
8.Desaulniers, G., Desrosiers, J. & Solomon, M.M. (eds.), (2006). Column generation, vol. 5, New York, NY, USA: Springer Science & Business Media.
9.Erdelyi, A. & Topaloglu, H. (2010). Approximate dynamic programming for dynamic capacity allocation with multiple priority levels. IIE Transactions 43: 129–142.
10.Fan, J. & Li, R. (2006). Statistical challenges with high dimensionality: feature selection in knowledge discovery. arXiv preprint math/0602133.
11.Gocgun, Y. & Ghate, A. (2012). Lagrangian relaxation and constraint generation for allocation and advanced scheduling. Computers & Operations Research 39: 2323–2336.
12.Gocgun, Y. & Puterman, M.L. (2014). Dynamic scheduling with due dates and time windows: an application to chemotherapy patient appointment booking. Health Care Management Science 17: 60–76.
13.Grötschel, M. & Holland, O. (1991). Solution of large-scale symmetric travelling salesman problems. Mathematical Programming 51: 141–202.
14.Guestrin, C., Koller, D. & Parr, R. (2001). Max-norm projections for factored MDPs. In Seventeenth International Joint Conference on Artificial Intelligence, vol. 1, pp. 673–682.
15.Gupta, D. & Denton, B. (2008). Appointment scheduling in health care: Challenges and opportunities. IIE transactions 40(9): 800–819.
16.Hulshof, P.J.H., Mes, M.R.K., Boucherie, R.J. & Hans, E.W. (2016). Patient admission planning using approximate dynamic programming. Flexible Services and Manufacturing 28: 30–61.
17.Leeftink, A.G., Bikker, I.A., Vliegen, I.M.H. & Boucherie, R.J. (2018). Multi-disciplinary planning in health care: a review. Health Systems 1–24.
18.Master, N., Chan, C.W. & Bambos, N. (2018). Myopic policies for non-preemptive scheduling of jobs with decaying value. Probability in the Engineering and Informational Sciences 32(1): 1–36.
19.Maxwell, M.S., Restrepo, M., Henderson, S.G. & Topaloglu, H. (2010). Approximate dynamic programming for ambulance redeployment. INFORMS Journal on Computing 22: 266–281.
20.Mes, M. & Pérez Rivera, A. (2017). Approximate dynamic programming by practical examples. In Boucherie, R.J. & van Dijk, N.M. (eds.), Markov Decision Processes in Practice, chapter 3, Cham, Switzerland: Springer, pp. 61–101.
21.Patrick, J. & Puterman, M.L. (2007). Improving resource utilization for diagnostic services through flexible inpatient scheduling: a method for improving resource utilization. Journal of the Operational Research Society 58: 235–245.
22.Patrick, J., Puterman, M.L. & Queyranne, M. (2008). Dynamic multipriority patient scheduling for a diagnostic resource. Operations Research 56: 1507–1525.
23.Powell, W.B. (2011). Approximate Dynamic Programming: solving the curses of dimensionality, 2nd ed., Wiley Series in Probability and Statistics. New York, NY, USA: John Wiley & Sons. Inc.
24.Pruhs, K., Sgall, J. & Torng, E. (2004). Online scheduling. In Leung, J.Y.-T. (ed.), Handbook of Scheduling: Algorithms, Models, and Performance Analysis. Boca Raton, FL: CRC Press, pp. 15-1–15-39.
25.Puterman, M.L. (2014). Markov decision processes: discrete stochastic dynamic programming. Hoboken, New Jersey, USA: John Wiley & Sons.
26. Revalidatie Nederland (Rehabilitation Sector Association The Netherlands), retr. Deccember 20, 2017. Utrecht, the Netherlands: Revalidatie Nederland. Available from http://www.revalidatie.nl/revalideren/home-r.
27.Roubos, D. & Bhulai, S. (2012). Approximate dynamic programming techniques for skill-based routing in call centers. Probability in the Engineering and Informational Sciences 26(4): 581–591.
28.Sauré, A., Patrick, J., Tyldesley, S. & Puterman, M.L. (2012). Dynamic multi-appointment patient scheduling for radiation therapy. European Journal of Operational Research 223: 573–584.
29.Scheer, J., Kroll, T., Neri, M.T. & Beatty, P. (2003). Access barriers for persons with disabilities. Journal of Disability Policy Studies 13: 221–230.
30.Schimmelpfeng, K., Helber, S. & Kasper, S. (2012). Decision support for rehabilitation hospital scheduling. OR spectrum 34: 461–489.
31.Schmid, V. (2012). Solving the dynamic ambulance relocation and dispatching problem using approximate dynamic programming. European Journal of Operational Research 219: 611–621.
32.Schütz, H.J. & Kolisch, R. (2012). Approximate dynamic programming for capacity allocation in the service industry. European Journal of Operational Research 218: 239–250.
33.Schütz, H.J. & Kolisch, R. (2013). Capacity allocation for demand of different customer-product-combinations with cancellations, no-shows, and overbooking when there is a sequential delivery of service. Annals of operations research 206: 401–423.
34.Sgall, J. (1998). On-line scheduling. In Fiat, A. & Woeginger, G. (eds.), Online Algorithms, vol. 1442 of Lecture Notes in Computer Science, Berlin Heidelberg: Springer, pp. 196–231.
35.Simao, H. & Powell, W.B. (2009). Approximate dynamic programming for management of high-value spare parts. Journal of Manufacturing Technology Management 20: 147–160.
36.Topaloglu, H. & Powell, W.B. (2006). Dynamic-programming approximations for stochastic time-staged integer multicommodity-flow problems. INFORMS Journal on Computing 18: 31–42.
37.Tsitsiklis, J.N. & van Roy, B. (1996). Feature-based methods for large scale dynamic programming. Machine Learning 22(1–3): 59–94.

Keywords

ONLINE CAPACITY PLANNING FOR REHABILITATION TREATMENTS: AN APPROXIMATE DYNAMIC PROGRAMMING APPROACH

  • Ingeborg A. Bikker (a1), Martijn R.K. Mes (a2), Antoine Sauré (a3) and Richard J. Boucherie (a4)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed