Document Type : Article

**Authors**

Faculty of Engineering, University of Kurdistan, Sanandaj, Iran

**Abstract**

Due to the importance of routing order pickers, there has been extensive research in the area of routing in warehouses. Still, there are some prominent factors that should receive more attention, as they may provide unsatisfactory services and incur considerable operational costs if ignored. In real-world applications, warehouse configuration, width of aisles, and controlling the vehicle congestion in the aisles greatly influence the efficiency of the routing process. Therefore, this paper proposes a mixed-integer programming model. The model aims to minimize maximum delivery time by finding the shortest pickup and delivery routes of all goods for all vehicles. Since the problem is NP-hard, a Simulated Annealing metaheuristic approach is designed to solve the model in large-size problems. This research contributes to picker routing literature by considering dynamic congestion, narrow and wide aisles, and pickup times and proposing a metaheuristic algorithm. The validation and efficiency of our proposed model are proved by solving some various generated benchmark problems. In summary, the developed route planning mathematical model works effectively for any two-dimensional rectangular layout, and the collision prevention constraints are incorporated in the mathematical model.

**Keywords**

References:

1. Tompkins, J.A., White, J.A., Bozer, Y.A., et al., Facilities Planning, John Wiley & Sons: NJ (2003).

2. Ten Hompel, M. and Schmidt, T., Warehouse Management- Automation and Organisation of Warehouse and Order Picking System, Springer-Verlag: Berlin Heidelberg (2007).

3. Petersen, C.G. and Aase, G. "A comparison of picking, storage, and routing policies in manual order picking", International Journal of Production Economics, 92(1), pp. 11-19 (2004).

4. De Koster, R., Le-Duc, T. Roodbergen K.J., et al. "Design and control of warehouse order picking", European Journal of Operational Research, 182(2), pp. 481-501 (2007).

5. Petersen, C.G. "An evaluation of order picking routing policies", International Journal of Operations & Production Management, 17(11), pp. 1098-1111 (1997).

6. Goetschalckx, M. and Ashayeri, J. "Classification and design of order picking systems", Logistics World (June), 2(2), pp. 99-106 (1989).

7. De Koster, R. "How to assess a warehouse operation in a single tour", Report, RSM Erasmus University, the Netherlands (2004).

8. Gu, J., Goetschalckx, M., and McGinnis, L.F. "Research on warehouse operation: A comprehensive review", European Journal of Operational Research, 177, pp. 1-21 (2007).

9. Gademann, N. and Van de Velde, S. "Batching to minimize total travel time in a parallel-aisle warehouse", IIE Transactions, 37(1), pp. 63-75 (2005).

10. Chen, M.C. and Wu, H.P. "An association-based clustering approach to order batching considering customer demand patterns", Omega International Journal of Management Science, 33(4), pp. 333-343 (2005).

11. Le-Duc, T. and De Koster, R. "An approximation for determining the optimal picking batch size for order picker in single aisle warehouses", In R., Meller, M.K., Ogle, B.A., Peters, G.D., Taylor, J., Usher (Eds.), Progress in Material Handling Research, pp. 267-286 (2003).

12. Parikh Pratik, J. "Designing order picking systems for distribution centers", Ph.D. Thesis, Department of Industrial and Systems Engineering Virginia Tech (2006).

13. Petersen, C.G. "Considerations in order picking zone configuration", International Journal of Operations and Production Management, 27(7), pp. 793-805 (2002).

14. Jane, C.C. "Storage location assignment in a distribution center", International Journal of Physical and Logistics Management, 30(1), pp. 55-71 (2000).

15. Jewkes, E., Lee, C., and Vickson, R. "Product location, allocation and server home base location for an order picking line with multiple servers", Computers and Operations Research, 31, pp. 623-626 (2004).

16. Roodbergen, K.J. "Layout and routing methods for warehouses", Ph.D. Thesis, RSM Erasmus University, the Netherlands (2001).

17. Roodbergen, K.J. and De Koster, R. "Routing methods for warehouses with multiple cross aisles", International Journal of Production Research, 39(9), pp. 1865-1883 (2001).

18. Zhang, M., Batta, R., and Nagi, R. "Modeling of workflow congestion and optimization of flow routing in a manufacturing/warehouse facility", Management Science, 55(2), pp. 267-280 (2009).

19. Smith, J. and Li, W. "Quadratic assignment problems and M/G/C/C state dependent network flow", J. Combined Optimization, 5(4), pp. 421-443 (2001).

20. Chiang, W., Kouvelis, P., and Urban, T. "Incorporating work flow interference in facility layout design: The quartic assignment problem", Management Science, 48(4), pp. 584-590 (2002).

21. Chiang, W., Kouvelis, P., and Urban, T. "Single and multi-objective facility layout with work flow interference considerations", Eur. J. Oper. Res., 174(3), pp. 1414-1426 (2006).

22. Herrmann, J., Ioannou, G., Minis, I., et al. "Design of material flow networks in manufacturing facilities", J. Manufacturing Systems, 14(4), pp. 277-288 (1995).

23. Bakkalbasi, O. "Flow path network and layout configuration for material delivery systems", Ph.D. Thesis, Georgia Institute of Technology, Atlanta (1990).

24. Vosniakos, G. and Davies, B. "On the path layout and operation of an AGV system serving an FMS", Internat. J. Advanced Manufacturing Tech, 4, pp. 243- 262 (1989).

25. Kim, C. and Tanchoco, J. "Operational control of a bi-directional automated guided vehicle system", Internat. J. Production Res, 31(9), pp. 2123-2138 (1993).

26. Beamon, B. "System reliability and congestion in a material handling system", Comput. Indust. Engrg, 36(3), pp. 673-684 (1999).

27. Pan, J.C-H. and Wu, M-H. "Throughput analysis for order picking system with multiple pickers and aisle congestion considerations", Computers and Operations Research, 39, pp. 1661-1672 (2012).

28. Hong, S., Johnson, A.L., and Peters, B.A. "Batch picking in narrow-aisle order picking systems with consideration for picker blocking", European Journal of Operational Research, 221(4), pp. 557-570 (2012).

29. Kim, B. and Lee, W. "A multi-product dynamic inbound ordering and shipment scheduling problem at a third-party warehouse", International Journal of Industrial Engineering: Theory, Applications and Practice, 20(1-2), pp. 36-46 (2013).

30. Gokhan Ozden, S. "A computational system to solve the warehouse aisle design problem", Ph.D. thesis, Auburn University (2017).

31. Scholz, A. andWascher, G. "Order batching and picker routing in manual order picking systems: the benefits of integrated routing", Central European Journal of Operations Research, 25, pp. 491-520 (2017).

32. Chen, F., Xu, G., and Wei, Y. "An integrated metaheuristic routing method for multiple-block warehouse with ultranarrow aisles and access restriction", Complexity, 2019, pp. 1-14, ID 1280285 (2019).

33. Hojaghania, L., Nematian, J., Shojaiea, A., et al. "Metaheuristics for a new MINLP model with reduced response time for on-line order batching", Scientia Iranica, 28(5), pp. 2789-2811 (2021).

34. Tajima, E., Suzuki, M., Ishighki, A., et al. "Effect of picker congestion on travel time in an order picking operation", Journal of Advanced Mechanical Design, Systems, and Manufacturing, 14(5), pp. 1-16 (2020).

35. Zuniga, J., Martinez, J., Fierro, T., et al. "Optimization of the storage location assignment and the picker-routing problem by using mathematical programming", Appl. Sci., 10(2), pp. 1-15 (2020).

36. Cano, J., Correa-Espinal, A., and Gomez-Montoya, R. "Mathematical programming modeling for joint order batching, sequencing and picker routing problems in manual order picking systems", Journal of King Saud University- Engineering Sciences, 32(3), pp. 219-228 (2020).

37. Pai, A.S. "Development of deterministic collisionavoidance algorithms for routing automated guided vehicles", MSc Thesis, Department of Industrial and Systems Engineering, Kate Gleason College of Engineering (2008).

38. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., et al. "Equation of state calculation by fast computing machines", J. of Chem. Phys., 21, pp. 1087-1092(1953).

39. Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P. Optimization by simulated annealing", Science, 220, pp. 671-680 (1983).

40. Cerny, V. "A thermo dynamical approach to the traveling salesman problem: An efficient simulation algorithm", Journal of Optimization Theory and Applications, 4, pp. 41-45 (1985).

41. Aarts, E. and Lenstra, J.K., Local Search in Combinatorial Optimization. New Jersey: Princeton University Press (2003).

42. Modiri-Delshad, M., Aghay Kaboli, S.Hr., Taslimi, E., et al. "An iterated-based optimization method for economic dispatch in power system", IEEE Conference on Clean Energy and Technology (CEAT) (2013).

43. Modiri-Delshad, M., Aghay Kaboli, S.Hr., Taslimi-Renani, E., et al. "Backtracking search algorithm for solving economic dispatch problems with valve-point effects and multiple fuel options", Energy, 116, pp. 637-649 (2016).

44. Pourdaryaei, A., Mokhlis, H., Azil Illias, H., et al. "Hybrid ANN and artificial cooperative search algorithm to forecast short-term electricity price in deregulated electricity market", IEEE Access, 7, pp. 125369-125386 (2019).

45. Hlal, M.I., Ramachanaramurthya, V., Padmanaban, S., et al. "NSGA-II and MOPSO based optimization for sizing of hybrid PV/wind/battery energy storage system", Int. J. Power Electron and Drive Syst, 10(1), pp. 463-478 (2019).

2. Ten Hompel, M. and Schmidt, T., Warehouse Management- Automation and Organisation of Warehouse and Order Picking System, Springer-Verlag: Berlin Heidelberg (2007).

3. Petersen, C.G. and Aase, G. "A comparison of picking, storage, and routing policies in manual order picking", International Journal of Production Economics, 92(1), pp. 11-19 (2004).

4. De Koster, R., Le-Duc, T. Roodbergen K.J., et al. "Design and control of warehouse order picking", European Journal of Operational Research, 182(2), pp. 481-501 (2007).

5. Petersen, C.G. "An evaluation of order picking routing policies", International Journal of Operations & Production Management, 17(11), pp. 1098-1111 (1997).

6. Goetschalckx, M. and Ashayeri, J. "Classification and design of order picking systems", Logistics World (June), 2(2), pp. 99-106 (1989).

7. De Koster, R. "How to assess a warehouse operation in a single tour", Report, RSM Erasmus University, the Netherlands (2004).

8. Gu, J., Goetschalckx, M., and McGinnis, L.F. "Research on warehouse operation: A comprehensive review", European Journal of Operational Research, 177, pp. 1-21 (2007).

9. Gademann, N. and Van de Velde, S. "Batching to minimize total travel time in a parallel-aisle warehouse", IIE Transactions, 37(1), pp. 63-75 (2005).

10. Chen, M.C. and Wu, H.P. "An association-based clustering approach to order batching considering customer demand patterns", Omega International Journal of Management Science, 33(4), pp. 333-343 (2005).

11. Le-Duc, T. and De Koster, R. "An approximation for determining the optimal picking batch size for order picker in single aisle warehouses", In R., Meller, M.K., Ogle, B.A., Peters, G.D., Taylor, J., Usher (Eds.), Progress in Material Handling Research, pp. 267-286 (2003).

12. Parikh Pratik, J. "Designing order picking systems for distribution centers", Ph.D. Thesis, Department of Industrial and Systems Engineering Virginia Tech (2006).

13. Petersen, C.G. "Considerations in order picking zone configuration", International Journal of Operations and Production Management, 27(7), pp. 793-805 (2002).

14. Jane, C.C. "Storage location assignment in a distribution center", International Journal of Physical and Logistics Management, 30(1), pp. 55-71 (2000).

15. Jewkes, E., Lee, C., and Vickson, R. "Product location, allocation and server home base location for an order picking line with multiple servers", Computers and Operations Research, 31, pp. 623-626 (2004).

16. Roodbergen, K.J. "Layout and routing methods for warehouses", Ph.D. Thesis, RSM Erasmus University, the Netherlands (2001).

17. Roodbergen, K.J. and De Koster, R. "Routing methods for warehouses with multiple cross aisles", International Journal of Production Research, 39(9), pp. 1865-1883 (2001).

18. Zhang, M., Batta, R., and Nagi, R. "Modeling of workflow congestion and optimization of flow routing in a manufacturing/warehouse facility", Management Science, 55(2), pp. 267-280 (2009).

19. Smith, J. and Li, W. "Quadratic assignment problems and M/G/C/C state dependent network flow", J. Combined Optimization, 5(4), pp. 421-443 (2001).

20. Chiang, W., Kouvelis, P., and Urban, T. "Incorporating work flow interference in facility layout design: The quartic assignment problem", Management Science, 48(4), pp. 584-590 (2002).

21. Chiang, W., Kouvelis, P., and Urban, T. "Single and multi-objective facility layout with work flow interference considerations", Eur. J. Oper. Res., 174(3), pp. 1414-1426 (2006).

22. Herrmann, J., Ioannou, G., Minis, I., et al. "Design of material flow networks in manufacturing facilities", J. Manufacturing Systems, 14(4), pp. 277-288 (1995).

23. Bakkalbasi, O. "Flow path network and layout configuration for material delivery systems", Ph.D. Thesis, Georgia Institute of Technology, Atlanta (1990).

24. Vosniakos, G. and Davies, B. "On the path layout and operation of an AGV system serving an FMS", Internat. J. Advanced Manufacturing Tech, 4, pp. 243- 262 (1989).

25. Kim, C. and Tanchoco, J. "Operational control of a bi-directional automated guided vehicle system", Internat. J. Production Res, 31(9), pp. 2123-2138 (1993).

26. Beamon, B. "System reliability and congestion in a material handling system", Comput. Indust. Engrg, 36(3), pp. 673-684 (1999).

27. Pan, J.C-H. and Wu, M-H. "Throughput analysis for order picking system with multiple pickers and aisle congestion considerations", Computers and Operations Research, 39, pp. 1661-1672 (2012).

28. Hong, S., Johnson, A.L., and Peters, B.A. "Batch picking in narrow-aisle order picking systems with consideration for picker blocking", European Journal of Operational Research, 221(4), pp. 557-570 (2012).

29. Kim, B. and Lee, W. "A multi-product dynamic inbound ordering and shipment scheduling problem at a third-party warehouse", International Journal of Industrial Engineering: Theory, Applications and Practice, 20(1-2), pp. 36-46 (2013).

30. Gokhan Ozden, S. "A computational system to solve the warehouse aisle design problem", Ph.D. thesis, Auburn University (2017).

31. Scholz, A. andWascher, G. "Order batching and picker routing in manual order picking systems: the benefits of integrated routing", Central European Journal of Operations Research, 25, pp. 491-520 (2017).

32. Chen, F., Xu, G., and Wei, Y. "An integrated metaheuristic routing method for multiple-block warehouse with ultranarrow aisles and access restriction", Complexity, 2019, pp. 1-14, ID 1280285 (2019).

33. Hojaghania, L., Nematian, J., Shojaiea, A., et al. "Metaheuristics for a new MINLP model with reduced response time for on-line order batching", Scientia Iranica, 28(5), pp. 2789-2811 (2021).

34. Tajima, E., Suzuki, M., Ishighki, A., et al. "Effect of picker congestion on travel time in an order picking operation", Journal of Advanced Mechanical Design, Systems, and Manufacturing, 14(5), pp. 1-16 (2020).

35. Zuniga, J., Martinez, J., Fierro, T., et al. "Optimization of the storage location assignment and the picker-routing problem by using mathematical programming", Appl. Sci., 10(2), pp. 1-15 (2020).

36. Cano, J., Correa-Espinal, A., and Gomez-Montoya, R. "Mathematical programming modeling for joint order batching, sequencing and picker routing problems in manual order picking systems", Journal of King Saud University- Engineering Sciences, 32(3), pp. 219-228 (2020).

37. Pai, A.S. "Development of deterministic collisionavoidance algorithms for routing automated guided vehicles", MSc Thesis, Department of Industrial and Systems Engineering, Kate Gleason College of Engineering (2008).

38. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., et al. "Equation of state calculation by fast computing machines", J. of Chem. Phys., 21, pp. 1087-1092(1953).

39. Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P. Optimization by simulated annealing", Science, 220, pp. 671-680 (1983).

40. Cerny, V. "A thermo dynamical approach to the traveling salesman problem: An efficient simulation algorithm", Journal of Optimization Theory and Applications, 4, pp. 41-45 (1985).

41. Aarts, E. and Lenstra, J.K., Local Search in Combinatorial Optimization. New Jersey: Princeton University Press (2003).

42. Modiri-Delshad, M., Aghay Kaboli, S.Hr., Taslimi, E., et al. "An iterated-based optimization method for economic dispatch in power system", IEEE Conference on Clean Energy and Technology (CEAT) (2013).

43. Modiri-Delshad, M., Aghay Kaboli, S.Hr., Taslimi-Renani, E., et al. "Backtracking search algorithm for solving economic dispatch problems with valve-point effects and multiple fuel options", Energy, 116, pp. 637-649 (2016).

44. Pourdaryaei, A., Mokhlis, H., Azil Illias, H., et al. "Hybrid ANN and artificial cooperative search algorithm to forecast short-term electricity price in deregulated electricity market", IEEE Access, 7, pp. 125369-125386 (2019).

45. Hlal, M.I., Ramachanaramurthya, V., Padmanaban, S., et al. "NSGA-II and MOPSO based optimization for sizing of hybrid PV/wind/battery energy storage system", Int. J. Power Electron and Drive Syst, 10(1), pp. 463-478 (2019).

Transactions on Industrial Engineering (E)

November and December 2022Pages 3455-3469