Document Type : Research Paper


1 Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Faculty of Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran.


In this paper, a two-stage model is designed for arranging and locating vehicle routes with simultaneous pickup and delivery. The model developed in the first stage optimizes the arrangement of products in packages and thus optimizes packages' length, width, and height for delivery to customers. In the second stage, the goal is to provide customers with vehicle in simultaneous pickup and delivery. In this part of the model, the location of distribution centers is potentially considered, and the demand and cost parameters are considered uncertain. To solve the problem, precise methods and meta-heuristic algorithms of PSO for the first stage and multi-objective meta-heuristic algorithms NSGA II and MOALO for the set have been used. The results of examining the efficiency of the algorithms in the second stage show the high efficiency of the MOALO algorithm with a valuable weight of 0.8388. Therefore, to implement the model in the real problem (Golrang Broadcasting Company), the MOLAO algorithm has been used, the management results include obtaining 15 efficient answers.


Main Subjects

  1. Ahmadizar, F., Zeynivand, M., & Arkat, J. (2015). Two-level vehicle routing with cross-docking in a three-echelon supply chain: a genetic algorithm approach. Applied mathematical modelling39(22), 7065-7081.
  2. Arnold, F., & Sörensen, K. (2019). Knowledge-guided local search for the vehicle routing problem. Computers & operations research105, 32-46.
  3. Anuar, W. K., Lee, L. S., Seow, H. V., & Pickl, S. (2021). A multi-depot vehicle routing problem with stochastic road capacity and reduced two-stage stochastic integer linear programming models for rollout algorithm. Mathematics9(13), 1572.
  4. Avci, M., & Topaloglu, S. (2016). A hybrid metaheuristic algorithm for heterogeneous vehicle routing problem with simultaneous pickup and delivery. Expert systems with applications53, 160-171.
  5. Belgin, O., Karaoglan, I., & Altiparmak, F. (2018). Two-echelon vehicle routing problem with simultaneous pickup and delivery: mathematical model and heuristic approach. Computers & industrial engineering115, 1-16.
  6. Brandão, J. (2018). Iterated local search algorithm with ejection chains for the open vehicle routing problem with time windows. Computers & industrial engineering120, 146-159.
  7. Curtois, T., Landa-Silva, D., Qu, Y., & Laesanklang, W. (2018). Large neighbourhood search with adaptive guided ejection search for the pickup and delivery problem with time windows. EURO journal on transportation and logistics7(2), 151-192.
  8. Dambakk, C. (2019). The maritime pickup and delivery problem with cost and time window constraints: system modeling and A* based solution(Master of thesis, University of Agder).
  9. Dell’Amico, M., Furini, F., & Iori, M. (2020). A branch-and-price algorithm for the temporal bin packing problem. Computers & operations research114, 104825.
  10. Du, J., Li, X., Yu, L., Dan, R., & Zhou, J. (2017). Multi-depot vehicle routing problem for hazardous materials transportation: a fuzzy bilevel programming. Information sciences399, 201-218.
  11. Erdoğan, S., & Miller-Hooks, E. (2012). A green vehicle routing problem. Transportation research part E: logistics and transportation review48(1), 100-114.
  12. Engin, O., & İşler, M. (2022). An efficient parallel greedy algorithm for fuzzy hybrid flow shop scheduling with setup time and lot size: a case study in apparel process. Journal of fuzzy extension and applications3(3), 249-262.
  13. Hoseini Tabatabaei, S. A., Naami, A., & Rousta, A. (2021). Identifying and ranking the factors affecting the transportation of products from a marketing perspective using the fuzzy analytic hierarchy process approach. International journal of research in industrial engineering10(3), 187-205.
  14. Fakhrzad, M. B., Hoseini Shorshani, S. M., Hosseininasab, H., & Mostafaeipour, A. (In Prees). Developing a green vehicle routing problem model with time windows and simultaneous pickup and delivery under demand uncertainty: Minimizing fuel consumption. International journal of nonlinear analysis and applications. DOI: 22075/ijnaa.2021.23209.2493
  15. Fu, Y., & Banerjee, A. (2020). Heuristic/meta-heuristic methods for restricted bin packing problem. Journal of heuristics26(5), 637-662.
  16. Golsefidi, A. H., & Jokar, M. R. A. (2020). A robust optimization approach for the production-inventory-routing problem with simultaneous pickup and delivery. Computers & industrial engineering143, 106388.
  17. Hadian, H., Golmohammadi, A., Hemmati, A., & Mashkani, O. (2019). A multi-depot location routing problem to reduce the differences between the vehicles’ traveled distances; a comparative study of heuristics. Uncertain supply chain management7(1), 17-32. DOI: 5267/j.uscm.2018.6.001
  18. Kalayci, C. B., & Kaya, C. (2016). An ant colony system empowered variable neighborhood search algorithm for the vehicle routing problem with simultaneous pickup and delivery. Expert systems with applications66, 163-175.
  19. Kara, I., Kara, B. Y., & Yetis, M. K. (2007). Energy minimizing vehicle routing problem. International conference on combinatorial optimization and applications(pp. 62-71). Springer, Berlin, Heidelberg.
  20. Kartal, Z., Hasgul, S., & Ernst, A. T. (2017). Single allocation p-hub median location and routing problem with simultaneous pick-up and delivery. Transportation research part E: logistics and transportation review108, 141-159.
  21. Koç, Ç., Laporte, G., & Tükenmez, İ. (2020). A review of vehicle routing with simultaneous pickup and delivery. Computers & operations research122, 104987.
  22. Kuo, Y. (2010). Using simulated annealing to minimize fuel consumption for the time-dependent vehicle routing problem. Computers & industrial engineering59(1), 157-165.
  23. Kumar-Das, S. (2019). A new method for solving fuzzy linear fractional programming problem with new ranking function. International journal of research in industrial engineering8(4), 384-393.
  24. Lagos, C., Guerrero, G., Cabrera, E., Moltedo, A., Johnson, F., & Paredes, F. (2018). An improved particle swarm optimization algorithm for the VRP with simultaneous pickup and delivery and time windows. IEEE Latin America transactions16(6), 1732-1740. DOI: 1109/TLA.2018.8444393
  25. Lalla-Ruiz, E., Expósito-Izquierdo, C., Taheripour, S., & Voß, S. (2016). An improved formulation for the multi-depot open vehicle routing problem. OR spectrum38(1), 175-187.
  26. Lee, Y. H., Jung, J. W., & Lee, K. M. (2006). Vehicle routing scheduling for cross-docking in the supply chain. Computers & industrial engineering51(2), 247-256.
  27. Li, J., Li, T., Yu, Y., Zhang, Z., Pardalos, P. M., Zhang, Y., & Ma, Y. (2019). Discrete firefly algorithm with compound neighborhoods for asymmetric multi-depot vehicle routing problem in the maintenance of farm machinery. Applied soft computing81, 105460.
  28. Liu, R., Jiang, Z., Fung, R. Y., Chen, F., & Liu, X. (2010). Two-phase heuristic algorithms for full truckloads multi-depot capacitated vehicle routing problem in carrier collaboration. Computers & operations research37(5), 950-959.
  29. Ma, Y., Li, Z., Yan, F., & Feng, C. (2019). A hybrid priority-based genetic algorithm for simultaneous pickup and delivery problems in reverse logistics with time windows and multiple decision-makers. Soft computing23(15), 6697-6714.
  30. Misni, F., Lee, L. S., & Seow, H. V. (2020). Hybrid harmony search-simulated annealing algorithm for location-inventory-routing problem in supply chain network design with defect and non-defect items. Applied sciences10(18), 6625.
  31. Mousavi, S. M., & Tavakkoli-Moghaddam, R. (2013). A hybrid simulated annealing algorithm for location and routing scheduling problems with cross-docking in the supply chain. Journal of manufacturing systems32(2), 335-347.
  32. Moghdani, R., Salimifard, K., Demir, E., & Benyettou, A. (2021). The green vehicle routing problem: a systematic literature review. Journal of cleaner production279, 123691.
  33. Nadizadeh, A., & Kafash, B. (2019). Fuzzy capacitated location-routing problem with simultaneous pickup and delivery demands. Transportation letters11(1), 1-19.
  34. Pishvaee, M. S., & Razmi, J. (2012). Environmental supply chain network design using multi-objective fuzzy mathematical programming. Applied mathematical modelling36(8), 3433-3446.
  35. Polyakovskiy, S., & M’Hallah, R. (2018). A hybrid feasibility constraints-guided search to the two-dimensional bin packing problem with due dates. European journal of operational research266(3), 819-839.
  36. Qin, G., Tao, F., Li, L., & Chen, Z. (2019). Optimization of the simultaneous pickup and delivery vehicle routing problem based on carbon tax. Industrial management & data systems119(9), 2055-2071.
  37. Sadati, M. E. H., Aksen, D., & Aras, N. (2020). The r‐interdiction selective multi‐depot vehicle routing problem. International transactions in operational research27(2), 835-866.
  38. Zarrat Dakhely Parast, Z., Haleh, H., Avakh Darestani, S., & Amin-Tahmasbi, H. (2021). Green reverse supply chain network design considering location-routing-inventory decisions with simultaneous pickup and delivery. Environmental science and pollution research, 1-22.
  39. Saffarian, S., Mahmoudi, A., Shafiee, M., Jasemi, M., & Hashemi, L. (2020). Measuring the effectiveness of AHP and fuzzy AHP models in environmental risk assessment of a gas power plant. Human and ecological risk assessment: an international journal27(5), 1227-1241.
  40. Sethanan, K., & Pitakaso, R. (2016). Differential evolution algorithms for scheduling raw milk transportation. Computers and electronics in agriculture121, 245-259.
  41. Spencer, K. Y., Tsvetkov, P. V., & Jarrell, J. J. (2019). A greedy memetic algorithm for a multiobjective dynamic bin packing problem for storing cooling objects. Journal of heuristics25(1), 1-45.
  42. Tayebi Araghi, M. E., Jolai, F., Tavakkoli-Moghaddam, R., & Molana, M. (2021). A multi-facility AGV location-routing problem with uncertain demands and planar facility locations. Journal of applied research on industrial engineering8(4), 341-364.
  43. Ulmer, M. W., Thomas, B. W., Campbell, A. M., & Woyak, N. (2021). The restaurant meal delivery problem: dynamic pickup and delivery with deadlines and random ready times. Transportation science55(1), 75-100.
  44. Vincent, F. Y., Jewpanya, P., & Redi, A. P. (2016). Open vehicle routing problem with cross-docking. Computers & industrial engineering94, 6-17.
  45. Xiao, Y., Zhao, Q., Kaku, I., & Xu, Y. (2012). Development of a fuel consumption optimization model for the capacitated vehicle routing problem. Computers & operations research39(7), 1419-1431.
  46. Zahedi, M., & Nahr, J. (2020). Designing a hub covering location problem under uncertainty conditions. Management science letters9(3), 477-500. DOI: 5267/j.dsl.2020.2.002
  47. Zhao, Y., Leng, L., & Zhang, C. (2021). A novel framework of hyper-heuristic approach and its application in location-routing problem with simultaneous pickup and delivery. Operational research21(2), 1299-1332.
  48. Zhang, S., Zhang, W., Gajpal, Y., & Appadoo, S. S. (2019). Ant colony algorithm for routing alternate fuel vehicles in multi-depot vehicle routing problem. In Decision science in action(pp. 251-260). Springer, Singapore.
  49. Zhang, S., Lee, C. K. M., Choy, K. L., Ho, W., & Ip, W. H. (2014). Design and development of a hybrid artificial bee colony algorithm for the environmental vehicle routing problem. Transportation research part D: transport and environment31, 85-99.