A two-stage stochastic programming approach for multi-activity tour scheduling

This paper addresses a discontinuous multi-activity tour scheduling problem under demand uncertainty and when employees have identical skills. The problem is formulated as a two-stage stochastic programming model, where first-stage decisions correspond to the assignment of employees to weekly tours, while second-stage decisions are related to the allocation of work activities and breaks to daily shifts. A multi-cut L-shaped method is presented as a solution approach. Computational results on real-based and randomly generated instances show that the use of the stochastic model helps to reduce understaffing and overstaffing costs, when compared with the expected-value problem solutions.

[1]  T. Aykin.  Optimal Shift Scheduling with Multiple Break Windows , 1996 .

[2]  Louis-Martin Rousseau,et al.  Combining Benders decomposition and column generation for multi-activity tour scheduling , 2018, Comput. Oper. Res..

[3]  Andreas T. Ernst,et al.  An Annotated Bibliography of Personnel Scheduling and Rostering , 2004, Ann. Oper. Res..

[4]  Colin N. Jones,et al.  A two-stage stochastic programming approach to employee scheduling in retail outlets with uncertain demand , 2015 .

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

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

[7]  Donald F. Rossin,et al.  A Stochastic Goal Program for Employee Scheduling , 1996 .

[8]  GendronBernard,et al.  A branch-and-price algorithm for the multi-activity multi-task shift scheduling problem , 2014 .

[9]  Nikolaos Papadakos,et al.  Practical enhancements to the Magnanti-Wong method , 2008, Oper. Res. Lett..

[10]  Stephen E. Bechtold,et al.  A METHODOLOGY FOR LABOR SCHEDULING IN A SERVICE OPERATING SYSTEM , 1987 .

[11]  Hesham K. Alfares,et al.  Survey, Categorization, and Comparison of Recent Tour Scheduling Literature , 2004, Ann. Oper. Res..

[12]  Louis-Martin Rousseau,et al.  Grammar-Based Column Generation for Personalized Multi-Activity Shift Scheduling , 2013, INFORMS J. Comput..

[13]  Louis-Martin Rousseau,et al.  Branch-and-Price for Personalized Multi-Activity Tour Scheduling , 2015 .

[14]  Monia Rekik,et al.  Solving multi-activity multi-day shift scheduling problems with a hybrid heuristic , 2015, J. Sched..

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

[16]  Louis-Martin Rousseau,et al.  Grammar-Based Integer Programming Models for Multiactivity Shift Scheduling , 2009, Manag. Sci..

[17]  Nashat Mansour,et al.  A distributed genetic algorithm for deterministic and stochastic labor scheduling problems , 1999, Eur. J. Oper. Res..

[18]  Laurent Péridy,et al.  Cut generation for an employee timetabling problem , 2009, Eur. J. Oper. Res..

[19]  Larry P. Ritzman,et al.  The Disaggregation of Aggregate Manpower Plans , 1976 .

[20]  Andrés L. Medaglia,et al.  Constrained network-based column generation for the multi-activity shift scheduling problem ☆ , 2012 .

[21]  François Soumis,et al.  Shift scheduling under stochastic demand , 2014 .

[22]  Louis-Martin Rousseau,et al.  A large neighbourhood search approach to the  multi-activity shift scheduling problem , 2010, J. Heuristics.

[23]  Hanif D. Sherali,et al.  Two-stage workforce planning under demand fluctuations and uncertainty , 2009, J. Oper. Res. Soc..

[24]  Toby Walsh,et al.  Decomposing Global Grammar Constraints , 2007, CP.

[25]  Thomas L. Magnanti,et al.  Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria , 1981, Oper. Res..

[26]  Huei Chuen Huang,et al.  A successive convex approximation method for multistage workforce capacity planning problem with turnover , 2008, Eur. J. Oper. Res..

[27]  Louis-Martin Rousseau,et al.  A branch-and-price algorithm for the multi-activity multi-task shift scheduling problem , 2014, J. Sched..

[28]  Prattana Punnakitikashem,et al.  A stochastic programming approach for integrated nurse staffing and assignment , 2013 .

[29]  Guy Desaulniers,et al.  Assigning multiple activities to work shifts , 2009, J. Sched..

[30]  Jonathan F. Bard,et al.  Workforce planning at USPS mail processing and distribution centers using stochastic optimization , 2007, Ann. Oper. Res..

[31]  Sanjay Mehrotra,et al.  A Two-Stage Stochastic Integer Programming Approach to Integrated Staffing and Scheduling with Application to Nurse Management , 2015, Oper. Res..

[32]  R. Wets,et al.  L-SHAPED LINEAR PROGRAMS WITH APPLICATIONS TO OPTIMAL CONTROL AND STOCHASTIC PROGRAMMING. , 1969 .

[33]  J. Birge,et al.  A multicut algorithm for two-stage stochastic linear programs , 1988 .

[34]  G. Shedler,et al.  Simulation of Nonhomogeneous Poisson Processes by Thinning , 1979 .

[35]  Tallys H. Yunes,et al.  Modeling with Metaconstraints and Semantic Typing of Variables , 2016, INFORMS J. Comput..

[36]  G. M. Campbell,et al.  A two-stage stochastic program for scheduling and allocating cross-trained workers , 2011, J. Oper. Res. Soc..

[37]  M. D. Devine,et al.  A Modified Benders' Partitioning Algorithm for Mixed Integer Programming , 1977 .

[38]  Terry P. Harrison,et al.  A stochastic programming model for scheduling call centers with global Service Level Agreements , 2010, Eur. J. Oper. Res..

[39]  Erik Demeulemeester,et al.  Workforce Planning Incorporating Skills: State of the Art , 2014, Eur. J. Oper. Res..

[40]  Louis-Martin Rousseau,et al.  Branch-and-Price for Personalized Multiactivity Tour Scheduling , 2016, INFORMS J. Comput..

[41]  Louis-Martin Rousseau,et al.  Formal languages for integer programming modeling of shift scheduling problems , 2009, Constraints.

[42]  Gilles Pesant,et al.  A Cost-Regular Based Hybrid Column Generation Approach , 2006, Constraints.