International Journal of Nonlinear Analysis and Applications
A mathematical model for scheduling of transportation, routing, and cross-docking in the reverse logistics network of the green supply chain
Document Type : Research Paper
Authors
1 Faculty of Economics and Management, Semnan University, Semnan, Iran
2 Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
Abstract
Cross-docking refers to the practices of unloading materials from inbound vehicles and then loading them directly into outbound ones. Removing or minimizing warehousing costs, space requirements, as well as inventory utilization, cross-docking simplifies supply chains and makes them deliver goods to markets in a faster and more efficient manner. Accordingly, a mixed-integer linear programming ($MILP $) model is developed in the present study to schedule transportation routing and cross-docking in a reverse logistics network ($RLN$). Furthermore, different traffic modes are also considered to reduce fuel consumption, which reduces emissions and pollution. The proposed model is a multi-product, multi-stage, and non-deterministic polynomial-time that is an NP-hard problem. We use the non-dominated sorting genetic algorithm II ($NSGA-II$) to solve the model. A numerical example has been solved to illustrate the efficiency of the method.
Keywords
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address green supply chain network with simultaneous pick-up and split delivery, J. Cleaner Prod. 250 (2020)
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the design and plan of supply chain networks considering new product development, J. Indust. Engin. Int. 14(1)
(2018) 95–109.
[4] A.A. Ardakani and J. Fei, A systematic literature review on uncertainties in cross-docking operations, Mod. Supp.
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[5] A. Baniamerian, M. Bashiri and R. Tavakkoli-Moghaddam, Modified variable neighborhood search and genetic
algorithm for profitable heterogeneous vehicle routing problem with cross-docking, Appl. Soft Comput. 75 (2019)
441–460.
[6] G. Coca, O.D. Castrill´on, S. Ruiz, J.M. Mateo-Sanz and L. Jim´enez, Sustainable evaluation of environmental and
occupational risks scheduling flexible job shop manufacturing systems, J. Cleaner Prod. 209 (2019) 146–168.
[7] K. Deb, S. Agrawal, A. Pratap and T. Meyarivan, A fast elitist non-dominated sorting genetic algorithm for multiobjective optimization: NSGA-II, Int. Conf. Parallel Problem Solving From Nature, Springer, Berlin, Heidelberg,
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[8] B.B. Gardas, R.D. Raut and B. Narkhede, Reducing the exploration and production of oil: Reverse logistics in
the automobile service sector, Sust. Prod. Consump. 16 (2018) 141–153.
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for a cross-dock door assignment problem, Omega. 91 (2020) 102015.
[10] P. He and J. Li, The two-echelon multi-trip vehicle routing problem with dynamic satellites for crop harvesting
and transportation, Appl. Soft Comput. 77 (2019) 387–398.
[11] A. Hendalianpour, Mathematical Modeling for Integrating Production-Routing-Inventory Perishable Goods: A
Case Study of Blood Products in Iranian Hospitals. In International Conference on Dynamics in Logistics,
Springer, Cham, 2018, February, pp. 125-136.
[12] A. Hendalianpour, J. Razmi, M. Fakhrabadi, K. Kokkinos and E.I. Papageorgiou, A linguistic multi-objective
mixed integer programming model for multi-echelon supply chain network at bio-refinery, EuroMed J. Manag.
2(4) (2018) 329–355.
[13] A. Hendalianpour, M. Fakhrabadi, M.S. Sangari and J. Razmi, A combined benders decomposition and Lagrangian
relaxation algorithm for optimizing a multi-product, multi-level omni-channel distribution system, Scientia Iranica,
In press.
[14] A. Hendalianpour, M. Fakhrabadi, X. Zhang, M.R. Feylizadeh, M. Gheisari, P. Liu and N. Ashktorab, Hybrid
model of ivfrn-bwm and robust goal programming in agile and flexible supply chain, a case study: automobile
industry, IEEE Access. 7 (2019) 71481–71492.
[15] A. Hiassat, A. Diabat and I. Rahwan, A genetic algorithm approach for location-inventory-routing problem with
perishable products, J. Manufac. Syst. 42 (2017) 93–103.
[16] W. Jansen, Efficient Routing and Planning within the Complex Logistical Network: Based on the Integration of a
New Warehouse, AGV Transports and Increased Transportation Rates, (Master’s thesis, University of Twente),
2019.
[17] S. Khodaparasti, M.E. Bruni, P. Beraldi, H.R. Maleki and S. Jahedi, A multi-period location-allocation model for
nursing home network planning under uncertainty, Oper. Res. Health Care. 18 (2018) 4–15.
[18] A.O. Ku¸sakcı, B. Ayvaz, E. Cin and N. Aydın, Optimization of reverse logistics network of End of Life Vehicles
under fuzzy supply: A case study for Istanbul Metropolitan Area, J. Cleaner Prod. 215 (2019) 1036–1051.
[19] I. K¨u¸c¨ukoˇglu and N. Ozt¨urk, ¨ A hybrid meta-heuristic algorithm for vehicle routing and packing problem with
cross-docking, J. Intel. Manufact. 30(8) (2019) 2927–2943.[20] L.K. Lee, P.C.Y. Chen, K.K. Lee and J. Kaur, Menstruation among adolescent girls in Malaysia: a cross-sectional
school survey, Singapore Med. J. 47(10) (2006) 869.
[21] T.Y. Liao, Reverse logistics network design for product recovery and remanufacturing, Appl. Math. Model. 60
(2018) 145–163.
[22] H. Liu and C.Y. Lin, Optimization for multi-objective location-routing problem of cross-docking with fuzzy time
windows, J. Univ. Elect. Sci. Tech. China (Social Sciences Edition). (2019) 05.
[23] S. Mancini, The hybrid vehicle routing problem, Transport. Res. Part C: Emerging Tech. 78 (2017) 1–12.
[24] M.M. Nasiri, A. Rahbari, F. Werner and R. Karimi, Incorporating supplier selection and order allocation into the
vehicle routing and multi-cross-dock scheduling problem, Int. J. Product. Res. 56(19) (2018) 6527–6552.
[25] A.I. Nikolopoulou, P.P. Repoussis, C.D. Tarantilis and E.E. Zachariadis, Adaptive memory programming for the
many-to-many vehicle routing problem with cross-docking, Oper. Res. 19(1) (2019) 1–38.
[26] A. Rahbari, M.M. Nasiri, F. Werner, M. Musavi and F. Jolai, The vehicle routing and scheduling problem with
cross-docking for perishable products under uncertainty: Two robust bi-objective models, Appl. Math. Model. 70
(2019) 605–625.
[27] M. Rahimi and V. Ghezavati, Sustainable multi-period reverse logistics network design and planning under uncertainty utilizing conditional value at risk (CVaR) for recycling construction and demolition waste, J. Cleaner
Prod. 172 (2018) 1567–1581.
[28] Y. Shuang, A. Diabat and Y. Liao, A stochastic reverse logistics production routing model with emissions control
policy selection, Int. J. Prod. Econ. 213 (2019) 201–216.
[29] N. Srinivas and K. Deb, Muiltiobjective optimization using nondominated sorting in genetic algorithms, Evol.
Comput. 2(3) (1994) 221–248.
[30] J. Trochu, A. Chaabane and M. Ouhimmou, Reverse logistics network redesign under uncertainty for wood waste
in the CRD industry, Res. Cons. Recyc. 128 (2018) 32–47.
[31] H. Yu and W.D. Solvang, Incorporating flexible capacity in the planning of a multi-product multi-echelon sustainable reverse logistics network under uncertainty, J. Cleaner Prod. 198 (2018) 285–303.
[32] Y. Zhang, H. Alshraideh and A. Diabat, A stochastic reverse logistics production routing model with environmental
considerations, Ann. Oper. Res. 271(2) (2018) 1023-1044.
address green supply chain network with simultaneous pick-up and split delivery, J. Cleaner Prod. 250 (2020)
119437.
[2] Z.A. Afrouzy, S.H. Nasseri and I. Mahdavi, A genetic algorithm for supply chain configuration with new product
development, Comput. Indust. Engin. 101 (2016) 440–454.
[3] Z.A. Afrouzy, M.M. Paydar, S.H. Nasseri and I. Mahdavi, A meta-heuristic approach supported by NSGA-II for
the design and plan of supply chain networks considering new product development, J. Indust. Engin. Int. 14(1)
(2018) 95–109.
[4] A.A. Ardakani and J. Fei, A systematic literature review on uncertainties in cross-docking operations, Mod. Supp.
Chain Res. Appl. 2(1) (2020) 2–22.
[5] A. Baniamerian, M. Bashiri and R. Tavakkoli-Moghaddam, Modified variable neighborhood search and genetic
algorithm for profitable heterogeneous vehicle routing problem with cross-docking, Appl. Soft Comput. 75 (2019)
441–460.
[6] G. Coca, O.D. Castrill´on, S. Ruiz, J.M. Mateo-Sanz and L. Jim´enez, Sustainable evaluation of environmental and
occupational risks scheduling flexible job shop manufacturing systems, J. Cleaner Prod. 209 (2019) 146–168.
[7] K. Deb, S. Agrawal, A. Pratap and T. Meyarivan, A fast elitist non-dominated sorting genetic algorithm for multiobjective optimization: NSGA-II, Int. Conf. Parallel Problem Solving From Nature, Springer, Berlin, Heidelberg,
2000, September, pp. 849–858.
[8] B.B. Gardas, R.D. Raut and B. Narkhede, Reducing the exploration and production of oil: Reverse logistics in
the automobile service sector, Sust. Prod. Consump. 16 (2018) 141–153.
[9] S. Gelareh, F. Glover, O. Guemri, S. Hanafi, P. Nduwayo and R. Todosijevi´c, A comparative study of formulations
for a cross-dock door assignment problem, Omega. 91 (2020) 102015.
[10] P. He and J. Li, The two-echelon multi-trip vehicle routing problem with dynamic satellites for crop harvesting
and transportation, Appl. Soft Comput. 77 (2019) 387–398.
[11] A. Hendalianpour, Mathematical Modeling for Integrating Production-Routing-Inventory Perishable Goods: A
Case Study of Blood Products in Iranian Hospitals. In International Conference on Dynamics in Logistics,
Springer, Cham, 2018, February, pp. 125-136.
[12] A. Hendalianpour, J. Razmi, M. Fakhrabadi, K. Kokkinos and E.I. Papageorgiou, A linguistic multi-objective
mixed integer programming model for multi-echelon supply chain network at bio-refinery, EuroMed J. Manag.
2(4) (2018) 329–355.
[13] A. Hendalianpour, M. Fakhrabadi, M.S. Sangari and J. Razmi, A combined benders decomposition and Lagrangian
relaxation algorithm for optimizing a multi-product, multi-level omni-channel distribution system, Scientia Iranica,
In press.
[14] A. Hendalianpour, M. Fakhrabadi, X. Zhang, M.R. Feylizadeh, M. Gheisari, P. Liu and N. Ashktorab, Hybrid
model of ivfrn-bwm and robust goal programming in agile and flexible supply chain, a case study: automobile
industry, IEEE Access. 7 (2019) 71481–71492.
[15] A. Hiassat, A. Diabat and I. Rahwan, A genetic algorithm approach for location-inventory-routing problem with
perishable products, J. Manufac. Syst. 42 (2017) 93–103.
[16] W. Jansen, Efficient Routing and Planning within the Complex Logistical Network: Based on the Integration of a
New Warehouse, AGV Transports and Increased Transportation Rates, (Master’s thesis, University of Twente),
2019.
[17] S. Khodaparasti, M.E. Bruni, P. Beraldi, H.R. Maleki and S. Jahedi, A multi-period location-allocation model for
nursing home network planning under uncertainty, Oper. Res. Health Care. 18 (2018) 4–15.
[18] A.O. Ku¸sakcı, B. Ayvaz, E. Cin and N. Aydın, Optimization of reverse logistics network of End of Life Vehicles
under fuzzy supply: A case study for Istanbul Metropolitan Area, J. Cleaner Prod. 215 (2019) 1036–1051.
[19] I. K¨u¸c¨ukoˇglu and N. Ozt¨urk, ¨ A hybrid meta-heuristic algorithm for vehicle routing and packing problem with
cross-docking, J. Intel. Manufact. 30(8) (2019) 2927–2943.[20] L.K. Lee, P.C.Y. Chen, K.K. Lee and J. Kaur, Menstruation among adolescent girls in Malaysia: a cross-sectional
school survey, Singapore Med. J. 47(10) (2006) 869.
[21] T.Y. Liao, Reverse logistics network design for product recovery and remanufacturing, Appl. Math. Model. 60
(2018) 145–163.
[22] H. Liu and C.Y. Lin, Optimization for multi-objective location-routing problem of cross-docking with fuzzy time
windows, J. Univ. Elect. Sci. Tech. China (Social Sciences Edition). (2019) 05.
[23] S. Mancini, The hybrid vehicle routing problem, Transport. Res. Part C: Emerging Tech. 78 (2017) 1–12.
[24] M.M. Nasiri, A. Rahbari, F. Werner and R. Karimi, Incorporating supplier selection and order allocation into the
vehicle routing and multi-cross-dock scheduling problem, Int. J. Product. Res. 56(19) (2018) 6527–6552.
[25] A.I. Nikolopoulou, P.P. Repoussis, C.D. Tarantilis and E.E. Zachariadis, Adaptive memory programming for the
many-to-many vehicle routing problem with cross-docking, Oper. Res. 19(1) (2019) 1–38.
[26] A. Rahbari, M.M. Nasiri, F. Werner, M. Musavi and F. Jolai, The vehicle routing and scheduling problem with
cross-docking for perishable products under uncertainty: Two robust bi-objective models, Appl. Math. Model. 70
(2019) 605–625.
[27] M. Rahimi and V. Ghezavati, Sustainable multi-period reverse logistics network design and planning under uncertainty utilizing conditional value at risk (CVaR) for recycling construction and demolition waste, J. Cleaner
Prod. 172 (2018) 1567–1581.
[28] Y. Shuang, A. Diabat and Y. Liao, A stochastic reverse logistics production routing model with emissions control
policy selection, Int. J. Prod. Econ. 213 (2019) 201–216.
[29] N. Srinivas and K. Deb, Muiltiobjective optimization using nondominated sorting in genetic algorithms, Evol.
Comput. 2(3) (1994) 221–248.
[30] J. Trochu, A. Chaabane and M. Ouhimmou, Reverse logistics network redesign under uncertainty for wood waste
in the CRD industry, Res. Cons. Recyc. 128 (2018) 32–47.
[31] H. Yu and W.D. Solvang, Incorporating flexible capacity in the planning of a multi-product multi-echelon sustainable reverse logistics network under uncertainty, J. Cleaner Prod. 198 (2018) 285–303.
[32] Y. Zhang, H. Alshraideh and A. Diabat, A stochastic reverse logistics production routing model with environmental
considerations, Ann. Oper. Res. 271(2) (2018) 1023-1044.
)
Volume 12, Issue 2
November 2021Pages 1909-1927
- Receive Date: 09 December 2020
- Revise Date: 02 January 2021
- Accept Date: 29 January 2021