April  2016, 12(2): 431-447. doi: 10.3934/jimo.2016.12.431

A mixed integer programming model for solving real-time truck-to-door assignment and scheduling problem at cross docking warehouse

1. 

Department of Computer and Mathematical Sciences, Universiti Teknologi MARA, 72000, Kuala Pilah, Negeri Sembilan, Malaysia

2. 

Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450, Shah Alam, Selangor, Malaysia, Malaysia

Received  April 2014 Revised  February 2015 Published  June 2015

This paper address the problem at the inbound phase at the cross docking warehouse. The fundamental issues in cross docking facility is to assign the incoming truck to the door and to coordinate the sequences of the trucks in order to minimize the completion time at the inbound phase. Using the theories and methodologies of assignment and scheduling, paper on hand proposed a mixed integer programming model for solving the truck-to-door assignment and scheduling problem with the objective to minimize the total service time of trucks. Meanwhile, reduce the waiting time of trucks before being served at the designated door. A preliminary computation is conducted to verify the logic of the mathematical model proposed.
Citation: Wan Nor Ashikin Wan Ahmad Fatthi, Adibah Shuib, Rosma Mohd Dom. A mixed integer programming model for solving real-time truck-to-door assignment and scheduling problem at cross docking warehouse. Journal of Industrial & Management Optimization, 2016, 12 (2) : 431-447. doi: 10.3934/jimo.2016.12.431
References:
[1]

D. Agustina, C. Lee and R. Piplani, A review: Mathematical modles for cross docking planning,, International Journal of Engineering Business Management, 2 (2010), 47. doi: 10.5772/9717. Google Scholar

[2]

U. Aickelin and A. Adewunmi, Simulation optimization of the crossdock door assignmnet problem,, Proceedings of the Operational Research Society Simulation Workshop 2006 (SW 2006), (2006). Google Scholar

[3]

A. Amini, R. Tavakkoli-Moghaddam and A. Omidvar, Cross-docking truck scheduling with the arrival times for inbound trucks and the learning effect for unloading/loading processes,, Production & Manufacturing Research, 2 (2014), 784. Google Scholar

[4]

U. M. Apte and S. Viswanathan, Effective cross docking for improving distribution efficiencies,, International Journal of Logistics, 3 (2000), 291. doi: 10.1080/713682769. Google Scholar

[5]

A. B. Arabani, M. Zandieh and S. F. Ghomi, A cross-docking scheduling problem with sub-population multi-objective algorithms,, The International Journal of Advanced Manufacturing Technology, 58 (2012), 741. Google Scholar

[6]

M. Bachlaus, M. K. Pandey, C. Mahajan, R. Shankar and M. K. Tiwari, Designing an integrated multi-echelon agile supply chain network: A hybrid taguchi-particle swarm optimization approach,, Journal of Intelligent Manufacturing, 19 (2008), 747. doi: 10.1007/s10845-008-0125-1. Google Scholar

[7]

J. J. Bartholdi and K. R. Gue, The best shape for a crossdock,, Transportation Science, 38 (2004), 235. doi: 10.1287/trsc.1030.0077. Google Scholar

[8]

L. Berghman, R. Leus and F. C. Spieksma, Optimal solutions for a dock assignment problem with trailer transportation,, Annals of Operations Research, 213 (2014), 3. doi: 10.1007/s10479-011-0971-7. Google Scholar

[9]

N. Boysen, Truck scheduling at zero-inventory cross docking terminals,, Computers & Operations Research, 37 (2010), 32. doi: 10.1016/j.cor.2009.03.010. Google Scholar

[10]

N. Boysen, D. Briskorn and M. Tschöke, Truck scheduling in cross-docking terminals with fixed outbound departures,, OR spectrum, 35 (2013), 479. doi: 10.1007/s00291-012-0311-6. Google Scholar

[11]

F. Chen and C.-Y. Lee, Minimizing the makespan in a two-machine cross-docking flow shop problem,, European Journal of Operational Research, 193 (2009), 59. doi: 10.1016/j.ejor.2007.10.051. Google Scholar

[12]

R. Chen, B. Fan and G. Tang, Scheduling problems in cross docking,, in Combinatorial Optimization and Applications, (2009), 421. doi: 10.1007/978-3-642-02026-1_40. Google Scholar

[13]

H. Davoudpour, P. Hooshangi-Tabrizi and P. Hoseinpour, A genetic algorithm for truck scheduling in cross docking systems,, Journal of American Science, 8 (2012), 96. Google Scholar

[14]

W. N. A. W. A. Fatthi, A. Shuib and R. M. Dom, Estimating unloading time at cross docking centre by using fuzzy logic,, Research Journal of Business Management, 7 (2013), 1. Google Scholar

[15]

M. Golias, S. Ivey, K. Ji and M. Lipinski, A bi-objective model to minimize service and storage time at a cross dock facility,, in 51st Annual Transportation Research Forum, (2010). Google Scholar

[16]

S. S. Heragu, J. C. Huang, R. J. Mantel and P. C. Schuur, An efficient model for allocating products and designing a warehouse,, Progress in Material Handling Research, (2004), 143. Google Scholar

[17]

C. M. Joo and B. S. Kim, Scheduling compound trucks in multi-door cross-docking terminals,, The International Journal of Advanced Manufacturing Technology, 64 (2013), 977. doi: 10.1007/s00170-012-4035-1. Google Scholar

[18]

J. Karlof, Integer Programming: Theory and Practice, chapter 4: Decomposition in Integer Linear Programming,, Florida, (). Google Scholar

[19]

S. Kreipl and M. Pinedo, Planning and scheduling in supply chains: an overview of issues in practice,, Production and Operations management, 13 (2004), 77. doi: 10.1111/j.1937-5956.2004.tb00146.x. Google Scholar

[20]

V. B. Kreng and F.-T. Chen, The benefits of a cross-docking delivery strategy: a supply chain collaboration approach,, Production Planning and Control, 19 (2008), 229. Google Scholar

[21]

Y. Kuo, Optimizing truck sequencing and truck dock assignment in a cross docking system,, Expert Systems with Applications, 40 (2013), 5532. doi: 10.1016/j.eswa.2013.04.019. Google Scholar

[22]

R. Larbi, G. Alpan, P. Baptiste and B. Penz, Scheduling of transhipment operations in a single strip and stack doors crossdock,, in 19th International Conference on Production Research, (2007). Google Scholar

[23]

R. Larbi, G. Alpan and B. Penz, Scheduling transshipment operations in a multiple inbound and outbound door crossdock,, in International Conference on Computers & Industrial Engineering, (2009), 227. doi: 10.1109/ICCIE.2009.5223927. Google Scholar

[24]

K. Lee, B. S. Kim and C. M. Joo, Genetic algorithms for door-assigning and sequencing of trucks at distribution centers for the improvement of operational performance,, Expert Systems with Applications, 39 (2012), 12975. doi: 10.1016/j.eswa.2012.05.057. Google Scholar

[25]

Z. Li, M. Low, M. Shakeri and Y. Lim, Crossdocking planning and scheduling: Problems and algorithms,, SIMTech Technical Reports, 10 (2009), 159. Google Scholar

[26]

L. A. Li, Y and B. Rodrigues, Crossdocking-jit scheduling with time windows,, Journal of the Operational Research Society, 55 (2004), 1342. doi: 10.1057/palgrave.jors.2601812. Google Scholar

[27]

T. Liao, P. Egbelu and P.-C. Chang, Simultaneous dock assignment and sequencing of inbound trucks under a fixed outbound truck schedule in multi-door cross docking operations,, International Journal of Production Economics, 141 (2013), 212. doi: 10.1016/j.ijpe.2012.03.037. Google Scholar

[28]

J. T. Mentzer, W. DeWitt, J. S. Keebler, S. Min, N. W. Nix, C. D. Smith and Z. G. Zacharia, Defining supply chain management,, Journal of Business logistics, 22 (2001), 1. doi: 10.1002/j.2158-1592.2001.tb00001.x. Google Scholar

[29]

Z. Miao, F. Yang, K. Fu and D. Xu, Transshipment service through crossdocks with both soft and hard time windows,, Annals of Operations Research, 192 (2012), 21. doi: 10.1007/s10479-010-0780-4. Google Scholar

[30]

B. Naderi, S. Rahmani and S. Rahmani, A multiobjective iterated greedy algorithm for truck scheduling in cross-dock problems,, Journal of Industrial Engineering, 2014 (2014). doi: 10.1155/2014/128542. Google Scholar

[31]

Y. Pochet and L. A.Wolsey, Production planning by mixed integer programming,, US: Springer Science & Business Media, (2006). Google Scholar

[32]

R. Sadykov, Scheduling incoming and outgoing trucks at cross docking terminals to minimize the storage cost,, Annals of Operations Research, 201 (2012), 423. doi: 10.1007/s10479-012-1232-0. Google Scholar

[33]

M. Shakeri, M. Y. H. Low and Z. Li, A generic model for crossdock truck scheduling and truck-to-door assignment problems,, in 6th IEEE International Conference on Industrial Informatics, (2008), 857. doi: 10.1109/INDIN.2008.4618221. Google Scholar

[34]

M. Shakeri, M. Y. H. Low, S. J. Turner and E. W. Lee, A robust two-phase heuristic algorithm for the truck scheduling problem in a resource-constrained crossdock,, Computers & Operations Research, 39 (2012), 2564. doi: 10.1016/j.cor.2012.01.002. Google Scholar

[35]

A. Shuib and W. N. A. W. A. Fatthi, A review on quantitative approaches for dock door assignment in cross-docking,, International Journal on Advanced Science, 2 (2012), 30. Google Scholar

[36]

R. Tavakkoli-Moghaddam, J. Razmi et al., A new model for cross dock scheduling considering product arrangement,, International Proceedings of Economics Development & Research, 35 (2012). Google Scholar

[37]

J. Van Belle, P. Valckenaers, G. V. Berghe and D. Cattrysse, A tabu search approach to the truck scheduling problem with multiple docks and time windows,, Computers & Industrial Engineering, 66 (2013), 818. Google Scholar

[38]

I. F. Vis and K. J. Roodbergen, Positioning of goods in a cross-docking environment,, Computers & Industrial Engineering, 54 (2008), 677. doi: 10.1016/j.cie.2007.10.004. Google Scholar

[39]

W. Yu and P. J. Egbelu, Scheduling of inbound and outbound trucks in cross docking systems with temporary storage,, European Journal of Operational Research, 184 (2008), 377. doi: 10.1016/j.ejor.2006.10.047. Google Scholar

show all references

References:
[1]

D. Agustina, C. Lee and R. Piplani, A review: Mathematical modles for cross docking planning,, International Journal of Engineering Business Management, 2 (2010), 47. doi: 10.5772/9717. Google Scholar

[2]

U. Aickelin and A. Adewunmi, Simulation optimization of the crossdock door assignmnet problem,, Proceedings of the Operational Research Society Simulation Workshop 2006 (SW 2006), (2006). Google Scholar

[3]

A. Amini, R. Tavakkoli-Moghaddam and A. Omidvar, Cross-docking truck scheduling with the arrival times for inbound trucks and the learning effect for unloading/loading processes,, Production & Manufacturing Research, 2 (2014), 784. Google Scholar

[4]

U. M. Apte and S. Viswanathan, Effective cross docking for improving distribution efficiencies,, International Journal of Logistics, 3 (2000), 291. doi: 10.1080/713682769. Google Scholar

[5]

A. B. Arabani, M. Zandieh and S. F. Ghomi, A cross-docking scheduling problem with sub-population multi-objective algorithms,, The International Journal of Advanced Manufacturing Technology, 58 (2012), 741. Google Scholar

[6]

M. Bachlaus, M. K. Pandey, C. Mahajan, R. Shankar and M. K. Tiwari, Designing an integrated multi-echelon agile supply chain network: A hybrid taguchi-particle swarm optimization approach,, Journal of Intelligent Manufacturing, 19 (2008), 747. doi: 10.1007/s10845-008-0125-1. Google Scholar

[7]

J. J. Bartholdi and K. R. Gue, The best shape for a crossdock,, Transportation Science, 38 (2004), 235. doi: 10.1287/trsc.1030.0077. Google Scholar

[8]

L. Berghman, R. Leus and F. C. Spieksma, Optimal solutions for a dock assignment problem with trailer transportation,, Annals of Operations Research, 213 (2014), 3. doi: 10.1007/s10479-011-0971-7. Google Scholar

[9]

N. Boysen, Truck scheduling at zero-inventory cross docking terminals,, Computers & Operations Research, 37 (2010), 32. doi: 10.1016/j.cor.2009.03.010. Google Scholar

[10]

N. Boysen, D. Briskorn and M. Tschöke, Truck scheduling in cross-docking terminals with fixed outbound departures,, OR spectrum, 35 (2013), 479. doi: 10.1007/s00291-012-0311-6. Google Scholar

[11]

F. Chen and C.-Y. Lee, Minimizing the makespan in a two-machine cross-docking flow shop problem,, European Journal of Operational Research, 193 (2009), 59. doi: 10.1016/j.ejor.2007.10.051. Google Scholar

[12]

R. Chen, B. Fan and G. Tang, Scheduling problems in cross docking,, in Combinatorial Optimization and Applications, (2009), 421. doi: 10.1007/978-3-642-02026-1_40. Google Scholar

[13]

H. Davoudpour, P. Hooshangi-Tabrizi and P. Hoseinpour, A genetic algorithm for truck scheduling in cross docking systems,, Journal of American Science, 8 (2012), 96. Google Scholar

[14]

W. N. A. W. A. Fatthi, A. Shuib and R. M. Dom, Estimating unloading time at cross docking centre by using fuzzy logic,, Research Journal of Business Management, 7 (2013), 1. Google Scholar

[15]

M. Golias, S. Ivey, K. Ji and M. Lipinski, A bi-objective model to minimize service and storage time at a cross dock facility,, in 51st Annual Transportation Research Forum, (2010). Google Scholar

[16]

S. S. Heragu, J. C. Huang, R. J. Mantel and P. C. Schuur, An efficient model for allocating products and designing a warehouse,, Progress in Material Handling Research, (2004), 143. Google Scholar

[17]

C. M. Joo and B. S. Kim, Scheduling compound trucks in multi-door cross-docking terminals,, The International Journal of Advanced Manufacturing Technology, 64 (2013), 977. doi: 10.1007/s00170-012-4035-1. Google Scholar

[18]

J. Karlof, Integer Programming: Theory and Practice, chapter 4: Decomposition in Integer Linear Programming,, Florida, (). Google Scholar

[19]

S. Kreipl and M. Pinedo, Planning and scheduling in supply chains: an overview of issues in practice,, Production and Operations management, 13 (2004), 77. doi: 10.1111/j.1937-5956.2004.tb00146.x. Google Scholar

[20]

V. B. Kreng and F.-T. Chen, The benefits of a cross-docking delivery strategy: a supply chain collaboration approach,, Production Planning and Control, 19 (2008), 229. Google Scholar

[21]

Y. Kuo, Optimizing truck sequencing and truck dock assignment in a cross docking system,, Expert Systems with Applications, 40 (2013), 5532. doi: 10.1016/j.eswa.2013.04.019. Google Scholar

[22]

R. Larbi, G. Alpan, P. Baptiste and B. Penz, Scheduling of transhipment operations in a single strip and stack doors crossdock,, in 19th International Conference on Production Research, (2007). Google Scholar

[23]

R. Larbi, G. Alpan and B. Penz, Scheduling transshipment operations in a multiple inbound and outbound door crossdock,, in International Conference on Computers & Industrial Engineering, (2009), 227. doi: 10.1109/ICCIE.2009.5223927. Google Scholar

[24]

K. Lee, B. S. Kim and C. M. Joo, Genetic algorithms for door-assigning and sequencing of trucks at distribution centers for the improvement of operational performance,, Expert Systems with Applications, 39 (2012), 12975. doi: 10.1016/j.eswa.2012.05.057. Google Scholar

[25]

Z. Li, M. Low, M. Shakeri and Y. Lim, Crossdocking planning and scheduling: Problems and algorithms,, SIMTech Technical Reports, 10 (2009), 159. Google Scholar

[26]

L. A. Li, Y and B. Rodrigues, Crossdocking-jit scheduling with time windows,, Journal of the Operational Research Society, 55 (2004), 1342. doi: 10.1057/palgrave.jors.2601812. Google Scholar

[27]

T. Liao, P. Egbelu and P.-C. Chang, Simultaneous dock assignment and sequencing of inbound trucks under a fixed outbound truck schedule in multi-door cross docking operations,, International Journal of Production Economics, 141 (2013), 212. doi: 10.1016/j.ijpe.2012.03.037. Google Scholar

[28]

J. T. Mentzer, W. DeWitt, J. S. Keebler, S. Min, N. W. Nix, C. D. Smith and Z. G. Zacharia, Defining supply chain management,, Journal of Business logistics, 22 (2001), 1. doi: 10.1002/j.2158-1592.2001.tb00001.x. Google Scholar

[29]

Z. Miao, F. Yang, K. Fu and D. Xu, Transshipment service through crossdocks with both soft and hard time windows,, Annals of Operations Research, 192 (2012), 21. doi: 10.1007/s10479-010-0780-4. Google Scholar

[30]

B. Naderi, S. Rahmani and S. Rahmani, A multiobjective iterated greedy algorithm for truck scheduling in cross-dock problems,, Journal of Industrial Engineering, 2014 (2014). doi: 10.1155/2014/128542. Google Scholar

[31]

Y. Pochet and L. A.Wolsey, Production planning by mixed integer programming,, US: Springer Science & Business Media, (2006). Google Scholar

[32]

R. Sadykov, Scheduling incoming and outgoing trucks at cross docking terminals to minimize the storage cost,, Annals of Operations Research, 201 (2012), 423. doi: 10.1007/s10479-012-1232-0. Google Scholar

[33]

M. Shakeri, M. Y. H. Low and Z. Li, A generic model for crossdock truck scheduling and truck-to-door assignment problems,, in 6th IEEE International Conference on Industrial Informatics, (2008), 857. doi: 10.1109/INDIN.2008.4618221. Google Scholar

[34]

M. Shakeri, M. Y. H. Low, S. J. Turner and E. W. Lee, A robust two-phase heuristic algorithm for the truck scheduling problem in a resource-constrained crossdock,, Computers & Operations Research, 39 (2012), 2564. doi: 10.1016/j.cor.2012.01.002. Google Scholar

[35]

A. Shuib and W. N. A. W. A. Fatthi, A review on quantitative approaches for dock door assignment in cross-docking,, International Journal on Advanced Science, 2 (2012), 30. Google Scholar

[36]

R. Tavakkoli-Moghaddam, J. Razmi et al., A new model for cross dock scheduling considering product arrangement,, International Proceedings of Economics Development & Research, 35 (2012). Google Scholar

[37]

J. Van Belle, P. Valckenaers, G. V. Berghe and D. Cattrysse, A tabu search approach to the truck scheduling problem with multiple docks and time windows,, Computers & Industrial Engineering, 66 (2013), 818. Google Scholar

[38]

I. F. Vis and K. J. Roodbergen, Positioning of goods in a cross-docking environment,, Computers & Industrial Engineering, 54 (2008), 677. doi: 10.1016/j.cie.2007.10.004. Google Scholar

[39]

W. Yu and P. J. Egbelu, Scheduling of inbound and outbound trucks in cross docking systems with temporary storage,, European Journal of Operational Research, 184 (2008), 377. doi: 10.1016/j.ejor.2006.10.047. Google Scholar

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