Bi-objective mathematical modeling for a green last-mile transportation network with an automated parcel locker

Subject Areas : Statistics

Amir-Hossein Zahedi-Anaraki ¹ , Reza Tavakkoli-Moghaddam ² , Ramin Sadeghian ³

1 - Department of Industrial Engineering, Payame Noor University, Tehran, Iran
2 - Department of Industrial Engineering, Campus of Technical Schools, University of Tehran, Tehran, Iran
3 - Department of Industrial Engineering, Payame Noor University, Tehran, Iran

Received: 2020-03-29 Accepted : 2021-07-05 Published : 2021-11-22

Keywords: جستجوی همسایگی متغیر, ارسال محصول به آخرین مشتری, مکان یابی-مسیریابی دوسطحی سبز, الگوریتم تجزیه بندرز, صندوق قفل دار خودکار,

Abstract :

The purpose of this paper is to introduce a more integrated and specialized approach to address the challenging issues known as the "Last-Mile Transportation" and to provide a conceptual-mathematical framework for making a synergy and integration between theoretical concepts and classic urban logistics optimization issues. This is a two-echelon routing-location network consisting of an urban distributor (or warehouse), customers and potential locations to install two types of facilities (automated parcel locker and micro-distributor). After ordering based on their desirability, customers are able to receive their product at the door or at 24-hour parcel locker. A modified Bender decomposition algorithm is used to solve the proposed model, which is amplified by the strategy of rounding of master problem’s variables and local search. To prove the efficiency, we compared the properties obtained from the proposed algorithm with the results obtained from the epsilon-constraint method in the Python software environment, the CPLEX library and ILOG CPLEX Optimization Studio and the results confirms the absolute dominance of this method in large-sized instances. The results of the sensitivity analysis of the role of automated parcel lockers on the network’s cost and produced pollution indicate the efficiency and validity of the proposed model.

References:

1. Goodman. Whatever you call it, just don’t think of last-mile logistics, last. Global Logistics & Supply Chain Strategies 9:46–51(2005).

 

1. Habitat, and H.C.WHO. Unmasking and overcoming health inequities in urban settings. WHO, Geneva (2010).

 

 Unknown. Micro distribution in emerging markets– key issues to consider, Available: https://www.inclusivebusiness.net/ ib-voices/ micro-distribution-emerging-markets-key-issues-consider (2018).

 

 M.Li, K. Loscher, A. Banny Nagi, and A. Sheerazi. GOING THE LAST MILE: Best practices of urban freight movement, Columbia University, New York (2017).

 

McKinsey & Company. Global management consulting’, Available: https://www.mckinsey.com (2019).

 

]6[ م. یوسفی خوشبخت. یک روش رقابت استعماری و یک مدل برنامه‌ریزی صحیح-آمیخته برای مسئله مسیریابی وسیله نقلیه ظرفیت‌دار. مجله پژوهش­های نوین در ریاضی، 9(3): 53-70 (1395) .

 

]7[ ع. محمودی‌راد، ص. نیرومند، م، صانعی و ع. ساجدی نژاد. روش آزاد سازی لاگرانژ برای مسئله حمل و نقل با هزینه ثابت مرحله‌ای. پژوهش­های نوین در ریاضی، 10(3): 19-30 (1396) .

 

 M.Dror, M. Ball, and B. Golden. A computational comparison of algorithms for the inventory routing problem. Annals of Operations Research 4:1–23 (1985).

 

1. Absi, C. Archetti, S. Dauzère-Pérès, and D. Feillet. A two-phase iterative heuristic approach for the production routing problem. Transportation Science 49:784–795(2014).

 

1. Breunig, U., V. Schmid, R.F.
   
   

Hartl, and T. Vidal. A large neighborhood based heuristic for two-echelon routing problems. Computers & Operations Research 76:208–225 (2016).

 

 L.Zhou, D. Baldacci, Vigo, and X. Wang. A Multi-Depot Two-Echelon Vehicle Routing Problem with Delivery Options Arising in the Last Mile Distribution. European Journal of Operational Research 265:765–778 (2018).

 

1. Anderluh, V.C. Hemmelmayr, and P.C. Nolz. Synchronizing vans and cargo bikes in a city distribution network. Central European Journal of Operations Research 25:345–376 (2017).

 

 C.Chao, T. Zhihui, and Y. Baozhen. Optimization of two-stage location–routing–inventory problem with time-windows in food distribution network. Annals of Operations Research 273:111–134 (2019).

 

 A.G. Dragomir, D. Nicola, A. Soriano, and M. Gansterer. Multi depot pickup and delivery problems in multiple regions: a typology and integrated model. International Transactions in Operational Research 25:569–597 (2018).

 

1. Schneider, M., A. Stenge, and D. Goeke. The electric vehicle-routing problem with time windows and recharging stations. Transportation Science 48:500–520 (2014).

 

1. Jie, J. Yang, M. Zhang, and Y. Huang. The two-echelon capacitated electric vehicle routing problem with battery swapping stations: Formulation and efficient methodology. European Journal of Operational Research 272:879–904 (2019).

 

1. Soysal, M., J.M. Bloemhof-Ruwaard, and T. Bektaş. The time-dependent two-echelon capacitated vehicle routing problem with environmental considerations. International Journal of Production Economics 164:366–378 (2015).

 

1. Pichka, A.H. Bajgiran, M.E. Petering, J. Jang, and X. Yue. The two echelon open location routing problem: Mathematical model and hybrid heuristic. Computers & Industrial Engineering 121:97–112 (2018).

 

1. Sun, L.P. Veelenturf, M. Hewitt, and T. Van Woensel. The time-dependent pickup and delivery problem with time windows. Transportation Research Part B: Methodological 116:1–24 (2018).

 

1. eutsch, and B. Golany. A parcel locker network as a solution to the logistics last mile problem. International Journal of Production Research 56:251–261 (2018).

 

1. Feillet, P. Dejax, and M. Gendreau. Traveling salesman problems with profits. Transportation Science 39:188–205 (2005).

 

1. Tricoire, A. Graf, and W.J. Gutjahr. The bi-objective stochastic covering tour problem. Computers & Operations Research 39:1582–1592 (2012).

 

M.Strehler, S. Merting, and C. Schwan. Energy-efficient shortest routes for electric and hybrid vehicles. Transportation Research Part B: Methodological 103:111–135 (2017).

 

1. Dukkanci, B.Y. Kara, and T. Bektaş. The green location-routing problem. Computers & Operations Research 105: 187–202 (2019).

 

M.Bashiri, M. Rezanezhad, R. Tavakkoli-Moghaddam, and H. Hasanzadeh. Mathematical modeling for a p-mobile hub location problem in a dynamic environment by a genetic algorithm. Applied Mathematical Modelling 54:151–169 (2018).

 

 J.F. Benders. Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4:238–252 (1962).

 

1. McDaniel, and M. Devine. A modified Benders’ partitioning algorithm for mixed integer programming. Management Science 24:312–319 (1977).

 

1. Bansal, A. Gupta, J. Li, J. Mestre, V. Nagarajan, and A. Rudra.When LP is the cure for your matching woes: Improved bounds for stochastic matchings. Algorithmica 63: 733–762 (2012).

 

1. Byrka, A. Srinivasan, and C. Swamy. Fault-tolerant facility location: a randomized dependent LP-rounding algorithm. In: Proceedings of the International Conference on Integer Programming and Combinatorial Optimization, (Springer), 244–257(2010).

 

 P.N. Thanh, N. Bostel, and O. Péton. A DC programming heuristic applied to the logistics network design problem. International Journal of Production Economics 135: 94–105 (2012).

 

1. Mladenović and P. Hansen. Variable neighborhood search. Computers & Operations Research 24: 1097–1100 (1997).

 

1. Mavrotas and K. Florios. An improved version of the augmented ε-constraint method (AUGMECON2) for finding the exact Pareto set in multi-objective integer programming problems. Applied Mathematics and Computation 219:9652–9669 (2013).