An Integrated Approach for Shift Scheduling and Rostering Problems with Break Times for Inbound Call Centers

Table 1

(a) Literature summary: some characteristics of workforce scheduling studies in call centers.

Reviewed literature	Year	Considered subproblems				Break(s)
		Call forecasting	Staffing	Shift scheduling	Rostering	M	R
Alfares [25]	2007		✓		✓	✓
Ásgeirsson& Sigurðardóttir [26]	2014		✓		✓
Atlason et al. [27]	2008		✓	✓
Atlason et al. [21]	2004			✓
Avradimis et al. [28]	2008		✓	✓
Avramidis et al. [29]	2009		✓
Bhulai et al. [5]	2008		✓	✓
Canon [13]	2007		✓	✓	✓	✓
Castillo et al. [30]	2009		✓	✓		✓	✓
Cezik&L’Ecuyer [31]	2008		✓
Defraeye et al. [32]	2016			✓
Dietz [3]	2011		✓		✓	✓
Dudin et al. [33]	2013		✓
Ertogral&Bamuqabel [34]	2008		✓		✓
Excoffier [35]	2016			✓
Gong et al. [17]	2015		✓
Green et al. [36]	2007		✓
Helber&Henken [37]	2010		✓	✓
Hojati [38]	2010				✓	✓
Ibrahim&L'Ecuyer [39]	2013	✓
Ingolfsson et al. [40]	2010		✓		✓	✓	✓
Koole&van der Sluis [19]	2003		✓	✓
Kyngäs et al. [41]	2012				✓
Liao et al. [42]	2009		✓
Liu et al. [43]	2018				✓
Mattia et al. [44]	2017		✓	✓
Millán-Ruiz&Hidalgo [45]	2013	✓
Nah&Kim [46]	2013		✓		✓	✓	✓
Örmeci et al. [47]	2014				✓
Pot et al. [48]	2008		✓
Restrepo [49]	2017				✓	✓	✓
Robbins&Harrison [50]	2008		✓	✓
Robbins&Harrison [51]	2010		✓
Taskiran&Zhang [52]	2017				✓	✓
Wallace&Whitt [53]	2005		✓
Weinberg et al. [54]	2007	✓

✓: defined, otherwise undefined, M: meal break, R: relief break(s).

(b) Literature summary: modeling approaches of workforce scheduling studies in call centers.

Reviewed literature	LP	IP	MIP	Queuing	Constructive heuristic	Other heuristic	Simulation	CP	Others
Alfares [25]		✓		✓
Ásgeirsson& Sigurðardóttir [26]			✓
Atlason et al. [27]			✓			✓	✓
Atlason et al. [21]			✓				✓
Avradimis et al. [28]			✓				✓
Avramidis et al. [29]			✓			✓	✓
Bhulai et al. [5]			✓			✓	✓
Canon [13]			✓			✓		✓
Castillo et al. [30]				✓	✓		✓		DEA
Cezik&L’Ecuyer [31]	✓					✓	✓
Defraeye et al. [32]					✓
Dietz [3]				✓
Dudin et al. [33]				✓
Ertogral&Bamuqabel [34]		✓		✓			✓		AHP
Excoffier [35]			✓						SP
Gong et al. [17]				✓
Green et al. [36]				✓		✓	✓
Helber&Henken [37]			✓				✓
Hojati [38]					✓
Ibrahim&L'Ecuyer [39]									RM
Ingolfsson et al. [40]			✓	✓		✓
Koole&van der Sluis [19]				✓	✓
Kyngäs et al. [41]						✓
Liao et al. [42]		✓					✓		SP
Liu et al. [43]		✓				✓
Mattia et al. [44]		✓			✓
Millán-Ruiz&Hidalgo [45]									NN
Nah&Kim [46]			✓
Örmeci et al. [47]			✓
Pot et al. [48]			✓			✓
Restrepo [49]									SP
Robbins&Harrison [50]					✓	✓	✓
Robbins&Harrison [51]			✓			✓	✓		SP
Taskiran&Zhang [52]		✓
Wallace&Whitt [53]				✓			✓
Weinberg et al. [54]									BF

✓: defined otherwise undefined, LP: linear programming, IP: integer programming, MIP: mixed integer programming, CP: constraint programming, DEA: data envelopment analysis, AHP: analytic hierarchy process, SP-stochastic programming, NN: neural network, RM: regression models, BF: bayesian forecasting.