Mixed integer programming based heuristics for the Patient Admission Scheduling problem

Abstract The Patient Admission Scheduling (PAS) problem is a combinatorial optimization problem where elective patients are automatically assigned to beds for the duration of their stay considering not only the medical necessity but also the patient preferences. Due to its combinatorial nature, solving the previously published problem instances to optimality is a difficult task. In this paper, we present two Mixed Integer Programming (MIP) based heuristics namely Fix-and-Relax (F&R) and Fix-and-Optimize (F&O) where PAS problem instances are decomposed into sub-problems and then the sub-problems are optimized. Our approach uses patient decomposition considering patient length-of-Stay (LoS), room preference, admission date, specialism choice, and age, as well as time decomposition considering different optimization window sizes. Quick solutions generated by F&R heuristic are used as an input to the F&O heuristic and are improved in an iterative nature. Main goal of the study is to provide high quality solutions in shorter run times. Computational findings show that the proposed heuristics provide promising results towards the solution of the problem in faster CPU times than the previously reported values where less than 15 percent gap from the best known solutions is achieved for most of the test instances, and as low as 5 percent gap for some of the sample data.

[1]  Canrong Zhang,et al.  An informative column generation and decomposition method for a production planning and facility location problem , 2015 .

[2]  Jing Xiao,et al.  A hybrid Lagrangian-simulated annealing-based heuristic for the parallel-machine capacitated lot-sizing and scheduling problem with sequence-dependent setup times , 2015, Comput. Oper. Res..

[3]  Wu Zhang,et al.  On practical resource allocation for production planning and scheduling with period overlapping setups , 1994 .

[4]  John L. Mann,et al.  Flowsheet decomposition heuristic for scheduling: a relax-and-fix method , 2004, Comput. Chem. Eng..

[5]  Alfredo Moreno,et al.  Heuristic approaches for the multiperiod location-transportation problem with reuse of vehicles in emergency logistics , 2016, Comput. Oper. Res..

[6]  Diego Klabjan,et al.  Pricing, relaxing and fixing under lot sizing and scheduling , 2013, Eur. J. Oper. Res..

[7]  Mohamad Saeed Jabalameli,et al.  Modeling the budget-constrained dynamic uncapacitated facility location-network design problem and solving it via two efficient heuristics: A case study of health care , 2013, Math. Comput. Model..

[8]  Patrick De Causmaecker,et al.  A hybrid tabu search algorithm for automatically assigning patients to beds , 2010, Artif. Intell. Medicine.

[9]  Yves Pochet,et al.  A tighter continuous time formulation for the cyclic scheduling of a mixed plant , 2008, Comput. Chem. Eng..

[10]  Laureano F. Escudero,et al.  On solving the multi-period single-sourcing problem under uncertainty , 2006, Comput. Manag. Sci..

[11]  Jesper Larsen,et al.  A column generation approach for solving the patient admission scheduling problem , 2014, Eur. J. Oper. Res..

[12]  Claudio Fabiano Motta Toledo,et al.  A relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems , 2015, Journal of Heuristics.

[13]  Hartmut Stadtler,et al.  Multilevel Lot Sizing with Setup Times and Multiple Constrained Resources: Internally Rolling Schedules with Lot-Sizing Windows , 2003, Oper. Res..

[14]  Sara Ceschia,et al.  Local search and lower bounds for the patient admission scheduling problem , 2011, Comput. Oper. Res..

[15]  Leena Suhl,et al.  Solving large multiple-depot multiple-vehicle-type bus scheduling problems in practice , 2005, OR Spectr..

[16]  Sara Ceschia,et al.  Modeling and solving the dynamic patient admission scheduling problem under uncertainty , 2012, Artif. Intell. Medicine.

[17]  Bernardo Almada-Lobo,et al.  Tactical production and distribution planning with dependency issues on the production process , 2017 .

[18]  Marte Fodstad,et al.  Using and extending fix-and-relax to solve maritime inventory routing problems , 2013 .

[19]  Horst Tempelmeier,et al.  Solving a multi-level capacitated lot sizing problem with multi-period setup carry-over via a fix-and-optimize heuristic , 2009, Comput. Oper. Res..

[20]  Safia Kedad-Sidhoum,et al.  MIP-based heuristics for multi-item capacitated lot-sizing problem with setup times and shortage costs , 2007, RAIRO Oper. Res..

[21]  Bernardo Almada-Lobo,et al.  A long-haul freight transportation problem: Synchronizing resources to deliver requests passing through multiple transshipment locations , 2016, Eur. J. Oper. Res..

[22]  Herbert Meyr,et al.  Combining the principles of variable neighborhood decomposition search and the fix&optimize heuristic to solve multi-level lot-sizing and scheduling problems , 2013, Comput. Oper. Res..

[23]  Patrick De Causmaecker,et al.  A Hyper-heuristic Approach to the Patient Admission Scheduling Problem , 2009 .

[24]  Sara Ceschia,et al.  Dynamic patient admission scheduling with operating room constraints, flexible horizons, and patient delays , 2014, J. Sched..

[25]  Bilge Bilgen,et al.  Hybrid simulation and MIP based heuristic algorithm for the production and distribution planning in the soft drink industry , 2014 .

[26]  Semra Tunali,et al.  A hybrid approach for the capacitated lot sizing problem with setup carryover , 2012 .

[27]  Mustapha Ouhimmou,et al.  Furniture supply chain tactical planning optimization using a time decomposition approach , 2008, Eur. J. Oper. Res..

[28]  Stefan Helber,et al.  A Fix-and-Optimize Approach for the Multi-Level Capacitated Lot Sizing Problems , 2010 .

[29]  Li Zheng,et al.  MIP-based fix-and-optimise algorithms for the parallel machine capacitated lot-sizing and scheduling problem , 2013 .

[30]  Hartmut Stadtler,et al.  A lot-sizing and scheduling model for multi-stage flow lines with zero lead times , 2013, Eur. J. Oper. Res..

[31]  Awi Federgruen,et al.  Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems , 2007, Oper. Res..

[32]  Eduardo Camponogara,et al.  A MILP model for planning the trips of dynamic positioned tankers with variable travel time , 2016 .

[33]  Claudio Fabiano Motta Toledo,et al.  Mathematical programming-based approaches for multi-facility glass container production planning , 2016, Comput. Oper. Res..

[34]  Peter Demeester,et al.  One hyper-heuristic approach to two timetabling problems in health care , 2012, J. Heuristics.

[35]  Luciana S. Buriol,et al.  A fix-and-optimize heuristic for the high school timetabling problem , 2014, Comput. Oper. Res..

[36]  Edmund K. Burke,et al.  Surgical scheduling with simultaneous employment of specialised human resources , 2015, Eur. J. Oper. Res..

[37]  Ross J. W. James,et al.  Single and parallel machine capacitated lotsizing and scheduling: New iterative MIP-based neighborhood search heuristics , 2011, Comput. Oper. Res..

[38]  Kerem Akartunali,et al.  A heuristic approach for big bucket multi-level production planning problems , 2009, Eur. J. Oper. Res..

[39]  Guoqing Zhang,et al.  An integrated strategy for a production planning and warehouse layout problem: Modeling and solution approaches , 2017 .

[40]  Franklina Maria Bragion Toledo,et al.  HOPS - Hamming-Oriented Partition Search for production planning in the spinning industry , 2014, Eur. J. Oper. Res..

[41]  Alistair R. Clark,et al.  Joint rolling-horizon scheduling of materials processing and lot-sizing with sequence-dependent setups , 2007, J. Heuristics.