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.

[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).

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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).

[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.

[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.

[18]

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

[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.

[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.

[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.

[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).

[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.

[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.

[25]

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

[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.

[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.

[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.

[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.

[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.

[31]

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

[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.

[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.

[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.

[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.

[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).

[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.

[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.

[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.

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.

[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).

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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).

[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.

[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.

[18]

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

[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.

[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.

[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.

[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).

[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.

[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.

[25]

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

[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.

[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.

[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.

[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.

[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.

[31]

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

[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.

[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.

[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.

[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.

[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).

[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.

[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.

[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.

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