Multiskilled personnel assignment problem under uncertain demand: A benchmarking analysis

César Augusto Henao; Ana Batista; Andrés Felipe Porto; Virginia I. González; César Augusto Henao; Ana Batista; Andrés Felipe Porto; Virginia I. González

doi:10.3934/mbe.2022232

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 5: 4946-4975. doi: 10.3934/mbe.2022232

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Multiskilled personnel assignment problem under uncertain demand: A benchmarking analysis

1.
Department of Industrial Engineering, Universidad del Norte, Km. 5 Vía Puerto Colombia, Barranquilla, Colombia
2.
Industrial and Systems Engineering Department, Pontificia Universidad Católica de Chile, Santiago, Chile
3.
Department of Industrial Engineering, Corporación Universitaria Americana, Barranquilla, Colombia

Received: 15 December 2021 Revised: 14 February 2022 Accepted: 14 February 2022 Published: 15 March 2022

The personnel assignment problem in different service industries aims to minimize the staff surplus/shortage costs. However, uncertainty in the staff demand challenges the accomplishment of that objective. This research studies the personnel assignment problem considering uncertain demand and multiskilled workforce configured through a 2-chaining strategy. We develop a two-stage stochastic optimization (TSSO) approach to calculate the multiskilling requirements that minimize the training costs and the expected costs of staff surplus/shortage. Later, we evaluate and compare the performance of the TSSO approach solutions with the solutions of two alternative optimization approaches under uncertainty - robust optimization (RO) and closed-form equation (CF). These two alternative approaches were published in Henao et al. ^[1] and Henao et al. ^[2], respectively. In addition, we compare the performance of the TSSO approach solutions with the solution of the deterministic (DT) approach and the solutions of myopic multiskilling approaches. To make performance comparisons between the different approaches, we used both real and simulated data derived from a retail store operating in Chile. The results show that, for different demand variability levels, TSSO, RO, and CF always belong to the set of approaches with the lowest average total cost. That is, in this group, there are no statistical differences from one approach to another, so these approaches are the most cost-effective. We also provide insights to retail decision-makers for addressing two key aspects. First, the methodology allows to address two fundamental multiskilling issues: how much multiskilling to add and how it should be added. Second, it is provided understanding on how to select the most suitable approach according to the balance between the conservatism and the reliability associated with the solutions delivered by each approach. Finally, we identify some methodological challenges for future research, such as the evaluation of k-chaining strategies with $ k\ge 2 $.
- workforce flexibility,
- multiskilling,
- cross-training,
- 2-chaining,
- stochastic optimization,
- robust optimization,
- retail
Citation: César Augusto Henao, Ana Batista, Andrés Felipe Porto, Virginia I. González. Multiskilled personnel assignment problem under uncertain demand: A benchmarking analysis[J]. Mathematical Biosciences and Engineering, 2022, 19(5): 4946-4975. doi: 10.3934/mbe.2022232

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Abstract

The personnel assignment problem in different service industries aims to minimize the staff surplus/shortage costs. However, uncertainty in the staff demand challenges the accomplishment of that objective. This research studies the personnel assignment problem considering uncertain demand and multiskilled workforce configured through a 2-chaining strategy. We develop a two-stage stochastic optimization (TSSO) approach to calculate the multiskilling requirements that minimize the training costs and the expected costs of staff surplus/shortage. Later, we evaluate and compare the performance of the TSSO approach solutions with the solutions of two alternative optimization approaches under uncertainty - robust optimization (RO) and closed-form equation (CF). These two alternative approaches were published in Henao et al. ^[1] and Henao et al. ^[2], respectively. In addition, we compare the performance of the TSSO approach solutions with the solution of the deterministic (DT) approach and the solutions of myopic multiskilling approaches. To make performance comparisons between the different approaches, we used both real and simulated data derived from a retail store operating in Chile. The results show that, for different demand variability levels, TSSO, RO, and CF always belong to the set of approaches with the lowest average total cost. That is, in this group, there are no statistical differences from one approach to another, so these approaches are the most cost-effective. We also provide insights to retail decision-makers for addressing two key aspects. First, the methodology allows to address two fundamental multiskilling issues: how much multiskilling to add and how it should be added. Second, it is provided understanding on how to select the most suitable approach according to the balance between the conservatism and the reliability associated with the solutions delivered by each approach. Finally, we identify some methodological challenges for future research, such as the evaluation of k-chaining strategies with $ k\ge 2 $.

References

[1]	C. A. Henao, J. C. Ferrer, J. C. Muñoz, J. A. Vera, Multiskilling with closed chains in the service sector: a robust optimization approach, Int. J. Prod. Econ., 179 (2016), 166–178. https://doi.org/10.1016/j.ijpe.2016.06.013 doi: 10.1016/j.ijpe.2016.06.013
[2]	C. A. Henao, J. C. Muñoz, J. C. Ferrer, Multiskilled workforce management by utilizing closed chains under uncertain demand: a retail industry case, Comput. Ind. Eng., 127 (2019), 74–88. https://doi.org/10.1016/j.cie.2018.11.061 doi: 10.1016/j.cie.2018.11.061
[3]	M. A. Abello, N. M. Ospina, J. M. De la Ossa, C. A. Henao, V. I. González, Using the k-chaining approach to solve a stochastic days-off-scheduling problem in a retail store, in Production Research: ICPR-Americas 2020, Communications in Computer and Information Science (eds. D. A. Rossit, F. Tohmé and G. Mejía Delgadillo), Springer, Cham, 1407 (2021), 156–170. https://doi.org/10.1007/978-3-030-76307-7_12
[4]	R. Muñoz, J. C. Muñoz, J. C. Ferrer, V. I. González, C. A. Henao, When should shelf stocking be done at night? A workforce management optimization approach for retailers, Work in progress.
[5]	C. A. Henao, Diseño de una fuerza laboral polifuncional para el sector servicios: caso aplicado a la industria del retail, (Tesis Doctoral, Pontificia Universidad Católica de Chile, Santiago, Chile), 2015.[Online]. Available from: https://repositorio.uc.cl/handle/11534/11764
[6]	A. F. Porto, C. A. Henao, H. López-Ospina, E. R. González, Hybrid flexibility strategic on personnel scheduling: retail case study, Comput. Ind. Eng., 133 (2019), 220–230. https://doi.org/10.1016/j.cie.2019.04.049 doi: 10.1016/j.cie.2019.04.049
[7]	E. Álvarez, J. C. Ferrer, J. C. Muñoz, C. A. Henao, Efficient shift scheduling with multiple breaks for full-time employees: A retail industry case, Comput. Ind. Eng., 150 (2020), 106884. https://doi.org/10.1016/j.cie.2020.106884 doi: 10.1016/j.cie.2020.106884
[8]	M. Mac-Vicar, J. C. Ferrer, J. C. Muñoz, C. A. Henao, Real-time recovering strategies on personnel scheduling in the retail industry, Comput. Ind. Eng., 113 (2017), 589–601. https://doi.org/10.1016/j.cie.2017.09.045 doi: 10.1016/j.cie.2017.09.045
[9]	C. A. Henao, J. C. Muñoz, J. C. Ferrer, The impact of multi–skilling on personnel scheduling in the service sector: a retail industry case, J. Oper. Res. Soc., 66 (2015), 1949–1959. https://doi.org/10.1057/jors.2015.9 doi: 10.1057/jors.2015.9
[10]	Y. Wang, J. Tang, Optimized skill configuration for the seru production system under an uncertain demand, Ann. Oper. Res., 2020 (2020), 1-21. https://doi.org/10.1007/s10479-020-03805-3 doi: 10.1007/s10479-020-03805-3
[11]	Y. A. Mercado, C. A. Henao, Benefits of multiskilling in the retail industry: K-chaining approach with uncertain demand, in Production Research: ICPR-Americas 2020, Communications in Computer and Information Science (eds. D. A. Rossit, F. Tohmé and G. Mejía Delgadillo), Springer, Cham, 1407 (2021), 126–141. https://doi.org/10.1007/978-3-030-76307-7_10
[12]	S. Vergara, J. Del Villar, J. Masson, N. Pérez, C. A. Henao, V. I. González, Impact of labor productivity and multiskilling on staff management: A retail industry case, in Production Research: ICPR-Americas 2020, Communications in Computer and Information Science (eds. D. A. Rossit, F. Tohmé and G. Mejía Delgadillo), Springer, Cham, 1408 (2021), 223–237. https://doi.org/10.1007/978-3-030-76310-7_18
[13]	C. Liu, Z. Li, J. Tang, X. Wang, M. J. Yao, How SERU production system improves manufacturing flexibility and firm performance: an empirical study in China, Ann. Oper. Res., 2021 (2021), 1–26. https://doi.org/10.1007/s10479-020-03850-y doi: 10.1007/s10479-020-03850-y
[14]	Y. A. Mercado, C. A. Henao, V. I. González, A two-stage stochastic optimization model for the retail multiskilled personnel scheduling problem: A k-chaining policy with k≥2, Math. Biosci. Eng., 19 (2022), 892–917. https://doi.org/10.3934/mbe.2022041 doi: 10.3934/mbe.2022041
[15]	W. C. Jordan, S. C. Graves, Principles on the benefits of manufacturing process flexibility, Manag. Sci., 41 (1995), 577–594. https://doi.org/10.1287/mnsc.41.4.577 doi: 10.1287/mnsc.41.4.577
[16]	M. J. Brusco, T. R. Johns, Staffing a multiskilled workforce with varying levels of productivity: An analysis of cross-training policies, Decision Sci., 29 (1998), 499–515. https://doi.org/10.1111/j.1540-5915.1998.tb01586.x doi: 10.1111/j.1540-5915.1998.tb01586.x
[17]	G. K. Taskiran, X. Zhang, Mathematical models and solution approach for cross-training staff scheduling at call centers, Comput. Oper. Res., 87 (2017), 258-269. https://doi.org/10.1016/j.cor.2016.07.001 doi: 10.1016/j.cor.2016.07.001
[18]	H. Liu, The optimization of worker's quantity based on cross-utilization in two departments, Intell. Decis. Technol., 11 (2017), 3–13. https://doi.org/10.3233/IDT-160273 doi: 10.3233/IDT-160273
[19]	D. Simchi-Levi, Y. Wei, Understanding the performance of the long chain and sparse designs in process flexibility, Oper. Res., 60 (2012), 1125–1141. https://doi.org/10.1287/opre.1120.1081 doi: 10.1287/opre.1120.1081
[20]	O. Fontalvo Echavez, L. Fuentes Quintero, C. A. Henao, V. I. González, Two-stage stochastic optimization model for personnel days–off scheduling using closed-chained multiskilling structures, in Production Research: ICPR-Americas 2020, Communications in Computer and Information Science (eds. D. A. Rossit, F. Tohmé and G. Mejía Delgadillo), Springer, Cham, 1407 (2021), 19–32. https://doi.org/10.1007/978-3-030-76307-7_2
[21]	A. F. Porto, C. A. Henao, A. Lusa, O. Polo Mejía, R. Porto Solano, Solving a staffing problem with annualized hours, multiskilling with 2-chaining, and overtime: a retail industry case, Comput. Ind. Eng., 167 (2022), 107999. https://doi.org/10.1016/j.cie.2022.107999 doi: 10.1016/j.cie.2022.107999
[22]	J. Birge, F. Louveaux F, Introduction to stochastic programming, (2011), Springer, New York. https://doi.org/10.1007/978-1-4614-0237-4
[23]	D. Bertsimas, M. Sim, Robust discrete optimization and network flows, Math. Program., 98 (2003), 49–71. https://doi.org/10.1007/s10107-003-0396-4 doi: 10.1007/s10107-003-0396-4
[24]	D. Bertsimas, M. Sim, The price of robustness, Oper. Res., 52 (2004), 35–53. https://doi.org/10.1287/opre.1030.0065 doi: 10.1287/opre.1030.0065
[25]	W. Wiesemann, D. Kuhn, M. Sim, Distributionally robust convex optimization, Oper. Res., 62 (2014), 1358–1376. https://doi.org/10.1287/opre.2014.1314 doi: 10.1287/opre.2014.1314
[26]	A. Ernst, H. Jiang, M. Krishnamoorthy, B. Owens, D. Sier, An annotated bibliography of personnel scheduling and rostering, Ann. Oper. Res., 127 (2004), 21–144. https://doi.org/10.1023/B:ANOR.0000019087.46656.e2 doi: 10.1023/B:ANOR.0000019087.46656.e2
[27]	P. Brucker, R. Qu, E. Burke, Personnel scheduling: Models and complexity, Eur. J. Oper. Res., 210 (2011), 467–473. https://doi.org/10.1016/j.ejor.2010.11.017 doi: 10.1016/j.ejor.2010.11.017
[28]	J. Van den Bergh, J. Belien, P. De Bruecker, E. Demeulemeester, L. De Boeck, Personnel scheduling: A literature review, Eur. J. Oper. Res., 226 (2013), 367–385. https://doi.org/10.1016/j.ejor.2012.11.029 doi: 10.1016/j.ejor.2012.11.029
[29]	E. H. Özder, E. Özcan, T. Eren, A systematic literature review for personnel scheduling problems, Int. J. Inform. Technol. Decision Making, 19 (2020), 1695–1735. https://doi.org/10.1142/S0219622020300050 doi: 10.1142/S0219622020300050
[30]	J. F. Bard, D. P. Morton, Y. M. Wang, Workforce planning at USPS mail processing and distribution centers using stochastic optimization, Ann. Oper. Res., 155 (2007), 51–78. https://doi.org/10.1007/s10479-007-0213-1 doi: 10.1007/s10479-007-0213-1
[31]	X. Zhu, H. D. Sherali, Two-stage workforce planning under demand fluctuations and uncertainty, J. Oper. Res. Soc., 60 (2009), 94–103. https://doi.org/10.1057/palgrave.jors.2602522 doi: 10.1057/palgrave.jors.2602522
[32]	T. R. Robbins, T. P. Harrison, A stochastic programming model for scheduling call centers with global service level agreements, Eur. J. Oper. Res., 207 (2010), 1608–1619. https://doi.org/10.1016/j.ejor.2010.06.013 doi: 10.1016/j.ejor.2010.06.013
[33]	G.M. Campbell, A two-stage stochastic program for scheduling and allocating cross-trained workers, J. Oper. Res. Soc., 62 (2011), 1038–1047. https://doi.org/10.1057/jors.2010.16 doi: 10.1057/jors.2010.16
[34]	S. Liao, G. Koole, C. Van Delft, O. Jouini, Staffing a call center with uncertain non-stationary arrival rate and flexibility, OR Spectrum, 34 (2012), 691–721. https://doi.org/10.1007/s00291-011-0257-0 doi: 10.1007/s00291-011-0257-0
[35]	S. Liao, C. Van Delft, J. P. Vial, Distributionally robust workforce scheduling in call centres with uncertain arrival rates, Optim. Methods Software, 28 (2013), 501–522. https://doi.org/10.1080/10556788.2012.694166 doi: 10.1080/10556788.2012.694166
[36]	A. Gnanlet, W. Gilland, Impact of productivity on cross-training configurations and optimal staffing decisions in hospitals, Eur. J. Oper. Res., 238 (2014), 254–269. https://doi.org/10.1016/j.ejor.2014.03.033 doi: 10.1016/j.ejor.2014.03.033
[37]	J. Paul, L. MacDonald, Modeling the benefits of cross-training to address the nursing shortage, Int. J. Prod. Econ., 150 (2014), 83–95. https://doi.org/10.1016/j.ijpe.2013.11.025 doi: 10.1016/j.ijpe.2013.11.025
[38]	K. Kim, S. Mehrotra, A two-stage stochastic integer programming approach to integrated staffing and scheduling with application to nurse management, Oper. Res., 63 (2015), 1431–1451. https://doi.org/10.1287/opre.2015.1421 doi: 10.1287/opre.2015.1421
[39]	A. Parisio, C. N. Jones, A two-stage stochastic programming approach to employee scheduling in retail outlets with uncertain demand, Omega, 53 (2015), 97–103. https://doi.org/10.1016/j.omega.2015.01.003 doi: 10.1016/j.omega.2015.01.003
[40]	M. Bodur, J. R. Luedtke, Mixed-integer rounding enhanced benders decomposition for multiclass service-system staffing and scheduling with arrival rate uncertainty, Manag. Sci., 63 (2017), 2073–2091. https://doi.org/10.1287/mnsc.2016.2455 doi: 10.1287/mnsc.2016.2455
[41]	S. Mattia, F. Rossi, M. Servilio, S. Smriglio, Staffing and scheduling flexible call centers by two-stage robust optimization, Omega, 72 (2017), 25–37. https://doi.org/10.1016/j.omega.2016.11.001 doi: 10.1016/j.omega.2016.11.001
[42]	M. I. Restrepo, B. Gendron, L. M. Rousseau, A two-stage stochastic programming approach for multi-activity tour scheduling, Eur. J. Oper. Res., 262 (2017), 620–635. https://doi.org/10.1016/j.ejor.2017.04.055 doi: 10.1016/j.ejor.2017.04.055
[43]	D. S. Altner, A. C. Rojas, L. D. Servi, A two-stage stochastic program for multi-shift, multi-analyst, workforce optimization with multiple on-call options, J. Schedul., 21 (2018), 517–531. https://doi.org/10.1007/s10951-017-0554-9 doi: 10.1007/s10951-017-0554-9
[44]	D. S. Altner, E. K. Mason, L. D. Servi, Two–stage stochastic days–off scheduling of multi–skilled analysts with training options, J. Comb. Optim., 38 (2019), 111–129. https://doi.org/10.1007/s10878-018-0368-5 doi: 10.1007/s10878-018-0368-5
[45]	H.G. Beyer, B. Sendhoff, Robust optimization - A comprehensive survey, Computer Methods Appl. Mech. Eng., 196 (2007), 3190–3218. https://doi.org/10.1016/j.cma.2007.03.003 doi: 10.1016/j.cma.2007.03.003
[46]	P. Kouvelis, G. Yu, Robust discrete optimization and its applications, Springer, Boston, 2013. https://doi.org/10.1007/978-1-4757-2620-6
[47]	V. Gabrel, C. Murat, A. Thiele, Recent advances in robust optimization: An overview, Eur. J. Oper. Res., 235 (2014), 471–483. https://doi.org/10.1016/j.ejor.2013.09.036 doi: 10.1016/j.ejor.2013.09.036
[48]	D. Bertsimas, A. Thiele, A robust optimization approach to inventory theory, Oper. Res., 54 (2006), 150–168. https://doi.org/10.1287/opre.1050.0238 doi: 10.1287/opre.1050.0238
[49]	C. Bohle, S. Maturana, J. Vera, A robust optimization approach to wine grape harvesting scheduling, Eur. J. Oper. Res., 200 (2010), 245–252. https://doi.org/10.1016/j.ejor.2008.12.003 doi: 10.1016/j.ejor.2008.12.003
[50]	F. Robuste, C. F. Daganzo, R. R. Souleyrette Ⅱ, Implementing vehicle routing models, Transport. Res. Part B Methodol., 24 (1990), 263–286. https://doi.org/10.1016/0191-2615(90)90002-G doi: 10.1016/0191-2615(90)90002-G
[51]	J. M. Del Castillo, A heuristic for the traveling salesman problem based on a continuous approximation, Transport. Res. Part B Methodol., 33 (1990), 123–152. https://doi.org/10.1016/S0191-2615(98)00034-4 doi: 10.1016/S0191-2615(98)00034-4
[52]	C. F. Daganzo, Logistics Systems Analysis (4th edition), Springer, Berlin, 2005.
[53]	C. A. Henao, A. Batista, A. F. Porto, V. I. González, A benchmark dataset for the retail multiskilled personnel planning under uncertain demand, Data Brief, Forthcoming 2022.
[54]	A. F. Porto, C. A. Henao, H. López-Ospina, E. R. González, V. I. González, Dataset for solving a hybrid flexibility strategy on personnel scheduling problem in the retail industry, Data Brief, 32 (2020), 106066. https://doi.org/10.1016/j.dib.2020.106066 doi: 10.1016/j.dib.2020.106066

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