Operating room scheduling with Generalized Disjunctive Programming

This paper addresses the short-term scheduling problem involved in the selection of a subset of elective surgeries from a large waiting list. In order to overcome the combinatorial complexity, a decomposition algorithm is proposed that relies on two continuous-time Generalized Disjunctive Programming (GDP) models. More specifically, there is an upper-level planning model to select surgical assignments to operating rooms and a lower-level constrained scheduling model to synchronize surgeons operating in different rooms on a given day. The GDP models are reformulated using standard convex hull and big-M techniques so as to generate the most efficient set of integer or mixed-integer linear programming constraints. Through the solution of a set of real-life instances from the literature, we show that the new algorithm outperforms a full-space discrete-time formulation and a genetic algorithm, improving the total surgical time as well as the number of performed surgeries by 5%. New MILP-based algorithm for scheduling elective surgeries.Upper level assigns surgeries to operating rooms and working days.Lower level sequences surgeries so as to avoid conflicts.Real-life case study from a university hospital.Up to 700 surgeries scheduled from a waiting list of over 2000.

[1]  Luis Puigjaner,et al.  MIP-based decomposition strategies for large-scale scheduling problems in multiproduct multistage batch plants: A benchmark scheduling problem of the pharmaceutical industry , 2010, Eur. J. Oper. Res..

[2]  Fouad Riane,et al.  Scheduling an operating theatre under human resource constraints , 2010, Comput. Ind. Eng..

[3]  R. Raman,et al.  Modelling and computational techniques for logic based integer programming , 1994 .

[4]  I. Grossmann,et al.  A decomposition approach for the scheduling of a steel plant production , 2001 .

[5]  Alain Guinet,et al.  Operating theatre planning. , 2003, Nursing mirror and midwives journal.

[6]  I. Grossmann,et al.  Optimal short-term scheduling of large-scale multistage batch plants , 2009 .

[7]  Pedro M. Castro,et al.  Generalized Disjunctive Programming as a Systematic Modeling Framework to Derive Scheduling Formulations , 2012 .

[8]  Philipp Baumann,et al.  A hybrid method for large-scale short-term scheduling of make-and-pack production processes , 2014, Eur. J. Oper. Res..

[9]  F. Guerriero,et al.  Operational research in the management of the operating theatre: a survey , 2011, Health care management science.

[10]  Yuehwern Yih,et al.  An elective surgery scheduling problem considering patient priority , 2010, Comput. Oper. Res..

[11]  Chengbin Chu,et al.  Solving a tactical operating room planning problem by a column-generation-based heuristic procedure with four criteria , 2009, Ann. Oper. Res..

[12]  Z. Przasnyski.  Operating room scheduling. A literature review. , 1986, AORN journal.

[13]  I. Grossmann,et al.  Modeling issues and implementation of language for disjunctive programming , 2000 .

[14]  Iiro Harjunkoski,et al.  Solving a large-scale industrial scheduling problem using MILP combined with a heuristic procedure , 2002, Eur. J. Oper. Res..

[15]  Jaime Cerdá,et al.  An MILP continuous-time approach to short-term scheduling of resource-constrained multistage flowshop batch facilities , 2001 .

[16]  Erik Demeulemeester,et al.  Sequencing surgical cases in a day-care environment: An exact branch-and-price approach , 2009, Comput. Oper. Res..

[17]  Pedro M. Castro,et al.  Optimal maintenance scheduling of a gas engine power plant using generalized disjunctive programming , 2014 .

[18]  R. Sargent,et al.  A general algorithm for short-term scheduling of batch operations—II. Computational issues , 1993 .

[19]  Erik Demeulemeester,et al.  Operating room planning and scheduling: A literature review , 2010, Eur. J. Oper. Res..

[20]  E. Balas.  Disjunctive programming and a hierarchy of relaxations for discrete optimization problems , 1985 .

[21]  Chengbin Chu,et al.  A planning and scheduling problem for an operating theatre using an open scheduling strategy , 2010, Comput. Ind. Eng..

[22]  Iftekhar A. Karimi,et al.  An MILP Approach to Automated Wet-Etch Station Scheduling , 2003 .

[23]  Edmund K. Burke,et al.  Local search for the surgery admission planning problem , 2011, J. Heuristics.

[24]  Pedro M. Castro,et al.  Hybrid time slots sequencing model for a class of scheduling problems , 2012 .

[25]  Elena Tànfani,et al.  Tactical and operational decisions for operating room planning: Efficiency and welfare implications , 2009, Health care management science.

[26]  Pedro M. Castro,et al.  Cyclic Scheduling of Pulp Digesters with Integrated Heating Tasks , 2014 .

[27]  Pedro M. Castro,et al.  Scope for industrial applications of production scheduling models and solution methods , 2014, Comput. Chem. Eng..

[28]  C. Chu,et al.  Solving surgical cases assignment problem by a branch-and-price approach ☆ , 2008 .

[29]  Vipul Jain,et al.  Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems , 2001, INFORMS J. Comput..

[30]  Elena Tanfani,et al.  A three-phase approach for operating theatre schedules , 2007, Health care management science.

[31]  M. V. Pato,et al.  Scheduling elective surgeries in a Portuguese hospital using a genetic heuristic , 2014 .

[32]  Margarida Vaz Pato,et al.  An integer programming approach to elective surgery scheduling , 2012, OR Spectr..

[33]  I. Grossmann,et al.  Systematic modeling of discrete-continuous optimization models through generalized disjunctive programming , 2013 .

[34]  Egon Balas.  Disjunctive Programming , 2010, 50 Years of Integer Programming.

[35]  Pierre Ladet,et al.  OPERATING ROOMS SCHEDULING , 2006 .

[36]  R. Sargent,et al.  A general algorithm for short-term scheduling of batch operations */I , 1993 .