Considering an uncertain demand, this study evaluates the potential benefits of using a multiskilled workforce through a k-chaining policy with $k \ge 2$. For the service sector and, particularly for the retail industry, we initially propose a deterministic mixed-integer linear programming model that determines how many employees should be multiskilled, in which and how many departments they should be trained, and how their weekly working hours will be assigned. Then, the deterministic model is reformulated using a two-stage stochastic optimization (TSSO) model to explicitly incorporate the uncertain personnel demand. The methodology is tested for a case study using real and simulated data derived from a Chilean retail store. We also compare the TSSO approach solutions with the myopic approaches' solutions (i.e., zero and total multiskilling). The case study is oriented to answer two key questions: how much multiskilling to add and how to add it. Results show that TSSO approach solutions always report maximum reliability for all levels of demand variability considered. It was also observed that, for high levels of demand variability, a k-chaining policy with $k \ge 2$ is more cost-effective than a 2-chaining policy. Finally, to evaluate the conservatism level in the solutions reported by the TSSO approach, two truncation types in the probability density function (pdf) associated with the personnel demand were considered. Results show that, if the pdf is only truncated at zero (more conservative truncation) the levels of required multiskilling are higher than when the pdf is truncated at 5th and 95th percentiles (less conservative truncation).
Citation: Yessica Andrea Mercado, César Augusto Henao, Virginia I. González. A two-stage stochastic optimization model for the retail multiskilled personnel scheduling problem: a k-chaining policy with $k \ge 2$[J]. Mathematical Biosciences and Engineering, 2022, 19(1): 892-917. doi: 10.3934/mbe.2022041
Considering an uncertain demand, this study evaluates the potential benefits of using a multiskilled workforce through a k-chaining policy with $k \ge 2$. For the service sector and, particularly for the retail industry, we initially propose a deterministic mixed-integer linear programming model that determines how many employees should be multiskilled, in which and how many departments they should be trained, and how their weekly working hours will be assigned. Then, the deterministic model is reformulated using a two-stage stochastic optimization (TSSO) model to explicitly incorporate the uncertain personnel demand. The methodology is tested for a case study using real and simulated data derived from a Chilean retail store. We also compare the TSSO approach solutions with the myopic approaches' solutions (i.e., zero and total multiskilling). The case study is oriented to answer two key questions: how much multiskilling to add and how to add it. Results show that TSSO approach solutions always report maximum reliability for all levels of demand variability considered. It was also observed that, for high levels of demand variability, a k-chaining policy with $k \ge 2$ is more cost-effective than a 2-chaining policy. Finally, to evaluate the conservatism level in the solutions reported by the TSSO approach, two truncation types in the probability density function (pdf) associated with the personnel demand were considered. Results show that, if the pdf is only truncated at zero (more conservative truncation) the levels of required multiskilling are higher than when the pdf is truncated at 5th and 95th percentiles (less conservative truncation).
[1] | 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, Comput. Ind. Eng., Forthcoming. |
[2] | R. Pastor, J. Olivella, Selecting and adapting weekly work schedules with working time accounts: A case of a retail clothing chain, Eur. J. Oper. Res., 184 (2008), 1–12. doi: 10.1016/j.ejor.2006.10.028. doi: 10.1016/j.ejor.2006.10.028 |
[3] | Ö. Kabak, F. Ülengin, E. Aktas, S. Önsel, Y. I. Topcu, Efficient shift scheduling in the retail sector through two-stage optimization, Eur. J. Oper. Res., 184 (2008), 76–90. doi: 10.1016/j.ejor.2006.10.039. doi: 10.1016/j.ejor.2006.10.039 |
[4] | 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. doi: 10.1057/jors.2015.9. doi: 10.1057/jors.2015.9 |
[5] | N. Chapados, M. Joliveau, L'Ecuyer, L. M. Rousseau, Retail store scheduling for profit, Eur. J. Oper. Res., 239 (2014), 609–624. doi: 10.1016/j.ejor.2014.05.033. doi: 10.1016/j.ejor.2014.05.033 |
[6] | 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. doi: 10.1016/j.ijpe.2016.06.013 doi: 10.1016/j.ijpe.2016.06.013 |
[7] | 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. doi: 10.1016/j.cie.2018.11.061 doi: 10.1016/j.cie.2018.11.061 |
[8] | 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. doi: 10.1016/j.cie.2020.106884 doi: 10.1016/j.cie.2020.106884 |
[9] | 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. doi: 10.1016/j.cie.2017.09.045 doi: 10.1016/j.cie.2017.09.045 |
[10] | R. Cuevas, J. C. Ferrer, M. Klapp, J. C. Muñoz, A mixed integer programming approach to multi–skilled workforce scheduling, J. Scheduling, 19 (2016), 91–106. doi: 10.1007/s10951-015-0450-0. doi: 10.1007/s10951-015-0450-0 |
[11] | 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. doi: 10.1016/j.cie.2019.04.049. doi: 10.1016/j.cie.2019.04.049 |
[12] | R. Wallace, W. Whitt, A staffing algorithm for call centers with skill-based routing, Manufacturing Service Oper. Manag., 7 (2005), 276–294. doi: 10.1287/msom.1050.0086. doi: 10.1287/msom.1050.0086 |
[13] | S. Iravani, M. Van Oyen, K. Sims, Structural flexibility: A new perspective on the design of manufacturing and service operations, Manag. Sci., 50 (2005), 151–166. doi: 10.1287/mnsc.1040.0333 doi: 10.1287/mnsc.1040.0333 |
[14] | D. Simchi-Levi, Y. Wei, Understanding the performance of the long chain and sparse designs in process flexibility, Oper. Res., 60 (2012), 1125–1141. doi: 10.1287/opre.1120.1081 doi: 10.1287/opre.1120.1081 |
[15] | C. A. Henao, Diseño de una fuerza laboral polifuncional para el sector servicios: caso aplicado a la industria del retail, Ph.D thesis, Pontificia Universidad Católica de Chile in Santiago de Chile, 2015. |
[16] | Y. Wang, J. Tang, Optimized skill configuration for the seru production system under an uncertain demand, Ann. Oper. Res., 2020 (2020), 1–21. doi: 10.1007/s10479-020-03805-3. doi: 10.1007/s10479-020-03805-3 |
[17] | 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. doi: 10.1007/978-3-030-76307-7_2. |
[18] | 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. doi: 10.1007/s10479-020-03850-y. doi: 10.1007/s10479-020-03850-y |
[19] | 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. doi: 10.1007/978-3-030-76307-7_12. |
[20] | 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. doi: 10.1007/978-3-030-76310-7_18. |
[21] | C. A. Henao, A. Batista, A. F. Porto, V. I. González, Multiskilled personnel assignment problem under uncertain demand: A benchmarking analysis, Ann. Oper. Res., Forthcoming. |
[22] | W. Hopp, E. Tekin, M. Van Oyen, Benefits of skill chaining in serial production lines with cross-trained workers, Manuf. Serv. Oper. Manage., 50 (2004), 83–98. doi: 10.1287/mnsc.1030.0166. doi: 10.1287/mnsc.1030.0166 |
[23] | 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., Forthcoming. |
[24] | A. Muriel, A. Somasundaram, Y. Zhang, Impact of partial manufacturing flexibility on production variability, J. Manuf. Serv. Oper. Manage., 58 (2006), 192–205. doi: 10.1287/msom.1060.0099. doi: 10.1287/msom.1060.0099 |
[25] | K. K. Yang, A comparison of cross–training policies in different job shops, Int. J. Prod. Res., 45 (2007), 1279–1295. doi: 10.1080/00207540600658039. doi: 10.1080/00207540600658039 |
[26] | H. Parvin, M. Van Oyen, D. Pandelis, D. Williams, J. Lee, Fixed task zone chaining: worker coordination and zone design for inexpensive cross–training in serial CONWIP lines, ⅡE Trans., 44 (2012), 1–21. doi: 10.1080/0740817X.2012.668264. doi: 10.1080/0740817X.2012.668264 |
[27] | T. Deng, Z. Shen, Process flexibility design in unbalanced networks, Manuf. Serv. Oper. Manage., 15 (2013), 24–32. doi: 10.1287/msom.1120.0390. doi: 10.1287/msom.1120.0390 |
[28] | D. Simchi-Levi, Y. Wei, Worst–case analysis of process flexibility designs, J. Oper. Res., 63 (2015), 166–185. doi: 10.1287/opre.2014.1334. doi: 10.1287/opre.2014.1334 |
[29] | X. Wang, J. Zhang, Process flexibility: A distribution-free bound on the performance of k-chain, Oper. Res., 63 (2015), 555–571. doi: 10.1287/opre.2015.1370. doi: 10.1287/opre.2015.1370 |
[30] | 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. doi: 10.1007/978-3-030-76307-7_10. |
[31] | W. J. Abernathy, N. Baloff, J. C. Hershey, S. Wandel, A three–stage manpower planning and scheduling model–A service–sector example, Oper. Res., 21 (1973), 693–711. doi: 10.1287/opre.21.3.693. doi: 10.1287/opre.21.3.693 |
[32] | X. Cai, K. Li, A genetic algorithm for scheduling staff of mixed skills under multi-criteria, Eur. J. Oper. Res., 125 (2000), 359–369. doi: 10.1016/S0377-2217(99)00391-4. doi: 10.1016/S0377-2217(99)00391-4 |
[33] | S. Agnihothri, A. Mishra, D. Simmons, Workforce cross-training decisions in field service systems with two job types, J. Oper. Res. Soc., 54 (2003), 410–418. doi: 10.1057/palgrave.jors.2601535. doi: 10.1057/palgrave.jors.2601535 |
[34] | G. Eitzen, D. Panton, Multi-skilled workforce optimisation, J. Ann. Oper. Res., 127 (2004), 359–372. doi: 10.1023/B:ANOR.0000019096.58882.54. doi: 10.1023/B:ANOR.0000019096.58882.54 |
[35] | J. Bokhorst, J. Slomp, G. Gaalman, Assignment flexibility in a cellular manufacturing system-machine pooling versus labor chaining, in Proceeding of Flexible Automation and Intelligent Manufacturing, 2004. |
[36] | S. Sayin, S. Karavati, Assigning cross–trained workers to departments: A two–stage optimization model to maximize utility and skill improvement, Eur. J. Oper. Res., 176 (2007), 1643–1658. doi: 10.1016/j.ejor.2005.10.045. doi: 10.1016/j.ejor.2005.10.045 |
[37] | A. Bassamboo, R. Randhawa, J. Mieghem, Optimal flexibility configurations in newsvendor networks: Going beyond chaining and pairing, J. Manage. Sci., 56 (2010), 1285–1303. doi: 10.1287/mnsc.1100.1184. doi: 10.1287/mnsc.1100.1184 |
[38] | C. Heimerl, R. Kolisch, Scheduling and staffing multiple projects with a multi–skilled workforce, OR Spectrum, 32 (2010), 343–368. doi: 10.1007/s00291-009-0169-4. doi: 10.1007/s00291-009-0169-4 |
[39] | M. Chou, G. Chua, C. Teo, H. Zheng, Design for process flexibility: Efficiency of the long chain and sparse structure, J. Oper. Res., 58 (2010), 43–58. doi: 10.1287/opre.1080.0664. doi: 10.1287/opre.1080.0664 |
[40] | G. M. Campbell, A two-stage stochastic program for scheduling and allocating cross-trained workers, J. Oper. Res. Soc., 62 (2011), 1038–1047. doi: 10.1057/jors.2010.16. doi: 10.1057/jors.2010.16 |
[41] | J. Paul, L. MacDonald, Modeling the benefits of cross–training to address the nursing shortage, Int. J. Prod. Econ., 150 (2014), 83–95. doi: 10.1016/j.ijpe.2013.11.025. doi: 10.1016/j.ijpe.2013.11.025 |
[42] | 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. doi: 10.1016/j.ejor.2014.03.033. doi: 10.1016/j.ejor.2014.03.033 |
[43] | M. Walter, J. Zimmermann, Minimizing average project team size given multi-skilled workers with heterogeneous skill levels, Comput. Oper. Res., 70 (2016), 163–179. doi: 10.1016/j.cor.2015.11.011. doi: 10.1016/j.cor.2015.11.011 |
[44] | H. Liu, The optimization of worker's quantity based on cross–utilization in two departments, Intell. Decis. Technol., 11 (2017), 3–13. doi: 10.3233/IDT-160273. doi: 10.3233/IDT-160273 |
[45] | S. Ağralı, Z. Caner, A. Tamer, Employee scheduling in service industries with flexible employee availability and demand, J. Oper. Res. Soc., 66 (2017), 159–169. doi: 10.1016/j.omega.2016.03.001. doi: 10.1016/j.omega.2016.03.001 |
[46] | G. Taskiran, X. Zhang, Mathematical models and solution approach for cross–training staff scheduling at call centers, Comput. Oper. Res., 87 (2017), 258–269. doi: 10.1016/j.cor.2016.07.001. doi: 10.1016/j.cor.2016.07.001 |
[47] | 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. doi: 10.1007/s10878-018-0368-5. doi: 10.1007/s10878-018-0368-5 |
[48] | G. Dagkakis, A. Rotondo, C. Heavey, Embedding optimization with deterministic discrete event simulation for assignment of cross-trained operators: An assembly line case study, J. Comput. Oper. Res., 111 (2019), 99–115. doi: 10.1016/j.cor.2019.06.008. doi: 10.1016/j.cor.2019.06.008 |
[49] | J. Birge, F. Louveaux, Introduction to stochastic programming, Springer, New York, 2011. doi: 10.1007/978-1-4614-0237-4. |
[50] | 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. doi: 10.1016/j.dib.2020.106066. doi: 10.1016/j.dib.2020.106066 |