Polynomially solvable personnel rostering problems

Personnel rostering is a personnel scheduling problem in which shifts are assigned to employees, subject to complex organisational and contractual time-related constraints. Academic advances in this domain mainly focus on solving specific variants of this problem using intricate exact or (meta)heuristic algorithms, while little attention has been devoted to studying the underlying structure of the problems. The general assumption is that these problems, even in their most simplified form, are NP-hard. However, such claims are rarely supported with a proof for the problem under study. The present paper refutes this assumption by presenting minimum cost network flow formulations for several personnel rostering problems. Additionally, these problems are situated among the existing academic literature to obtain insights into what makes personnel rostering hard.

[1]  Ravindra K. Ahuja,et al.  Network Flows , 2011 .

[2]  Alain Billionnet.  Integer programming to schedule a hierarchical workforce with variable demands , 1999, Eur. J. Oper. Res..

[3]  Maria Antónia Carravilla,et al.  Cyclic staff scheduling: optimization models for some real-life problems , 2013, J. Sched..

[4]  Jonathan F. Bard,et al.  Bounded flexibility in days-on and days-off scheduling , 2013 .

[5]  Jeffrey H. Kingston,et al.  An XML format for benchmarks in High School Timetabling , 2010, Ann. Oper. Res..

[6]  Michael W. Carter,et al.  Work Force Size and Single Shift Schedules with Variable Demands , 1985 .

[7]  Jonathan F. Bard,et al.  Preference scheduling for nurses using column generation , 2005, Eur. J. Oper. Res..

[8]  Patrick De Causmaecker,et al.  The first international nurse rostering competition 2010 , 2010, Ann. Oper. Res..

[9]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[10]  Andreas T. Ernst,et al.  Staff scheduling and rostering: A review of applications, methods and models , 2004, Eur. J. Oper. Res..

[11]  Hoong Chuin Lau,et al.  On the complexity of manpower shift scheduling , 1996, Comput. Oper. Res..

[12]  H. C. Lau.  On the complexity of manpower shift scheduling , 1996 .

[13]  Patrick De Causmaecker,et al.  Modelling and evaluation issues in nurse rostering , 2014, Ann. Oper. Res..

[14]  Mario Vanhoucke,et al.  NSPLib: a Nurse Scheduling Problem Library: a tool to evaluate (meta-)heuristic procedures , 2007 .

[15]  Hoong Chuin Lau,et al.  COMBINATORIAL APPROACHES FOR HARD PROBLEMS IN MANPOWER SCHEDULING , 1996 .

[16]  Edmund K. Burke,et al.  A shift sequence based approach for nurse scheduling and a new benchmark dataset , 2010, J. Heuristics.

[17]  Rudy Hung.  Single-shift off-day scheduling of a hierarchical workforce with variable demands , 1994 .

[18]  Hiroshi Imai,et al.  Classification of Various Neighborhood Operations for the Nurse Scheduling Problem , 2000, ISAAC.

[19]  Edmund K. Burke,et al.  A Time Predefined Variable Depth Search for Nurse Rostering , 2013, INFORMS J. Comput..

[20]  Erik Demeulemeester,et al.  Personnel scheduling: A literature review , 2013, Eur. J. Oper. Res..

[21]  Peter Brucker,et al.  Personnel scheduling: Models and complexity , 2011, Eur. J. Oper. Res..

[22]  David W. Pentico,et al.  Assignment problems: A golden anniversary survey , 2007, Eur. J. Oper. Res..