A Triplet-Based Exact Method for the Shift Minimisation Personnel Task Scheduling Problem

In this paper we describe a new approach for solving the shift minimisation personnel task scheduling problem. This variant of fixed job scheduling problems arises when tasks with fixed start and end times have to be assigned to personnel with shift time constraints. We present definitions, formulations and briefly discuss complexity results for the variant that focuses on minimising the number of machines (or workers) that are required to schedule all jobs. We first develop some mathematical properties of the problem and subsequently, the necessary and sufficient conditions for feasibility. These properties are used to develop a new branch and bound scheme, which is used in conjunction with two column generation based approaches and a heuristic algorithm to create an efficient solution procedure. We present extensive computational results for large instances and thereby, empirically demonstrate the effectiveness of our new approach.

[1]  André Rossi,et al.  A metaheuristic for the fixed job scheduling problem under spread time constraints , 2010, Comput. Oper. Res..

[2]  Deniz Türsel Eliiyi,et al.  Heuristics for operational fixed job scheduling problems with working and spread time constraints , 2011 .

[3]  Pieter Smet,et al.  A matheuristic approach to the shift minimisation personnel task scheduling problem , 2012 .

[4]  Sven Oliver Krumke,et al.  Interval scheduling on related machines , 2011, Comput. Oper. Res..

[5]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[6]  Leo G. Kroon,et al.  Exact and Approximation Algorithms for the Tactical Fixed Interval Scheduling Problem , 1997, Oper. Res..

[7]  Bo Chen,et al.  Tactical fixed job scheduling with spread-time constraints , 2014, Comput. Oper. Res..

[8]  Andreas T. Ernst,et al.  The Personnel Task Scheduling Problem , 2001 .

[9]  T. C. Edwin Cheng,et al.  Fixed interval scheduling: Models, applications, computational complexity and algorithms , 2007, Eur. J. Oper. Res..

[10]  Özgür Özpeynirci,et al.  Operational fixed job scheduling problem under spread time constraints: a branch-and-price algorithm , 2009 .

[11]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[12]  Joseph Y.-T. Leung,et al.  Efficient algorithms for interval graphs and circular-arc graphs , 1982, Networks.

[13]  Deniz Türsel Eliiyi,et al.  Working time constraints in operational fixed job scheduling , 2010 .

[14]  Shih-Wei Lin,et al.  Minimizing shifts for personnel task scheduling problems: A three-phase algorithm , 2014, Eur. J. Oper. Res..

[15]  Frits C. R. Spieksma,et al.  Interval scheduling: A survey , 2007 .

[16]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[17]  J. Desrosiers,et al.  A Primer in Column Generation , 2005 .

[18]  Matteo Fischetti,et al.  The Fixed Job Schedule Problem with Spread-Time Constraints , 1987, Oper. Res..

[19]  Pieter Smet,et al.  The shift minimisation personnel task scheduling problem: a new hybrid approach and computational insights , 2014 .

[20]  Andreas T. Ernst,et al.  Algorithms for large scale Shift Minimisation Personnel Task Scheduling Problems , 2012, Eur. J. Oper. Res..

[21]  Meral Azizoglu,et al.  Operational fixed interval scheduling problem on uniform parallel machines , 2008 .