On fundamental principles of the optimal number and location of loading bays in urban areas

    Tomislav Letnik Affiliation
    ; Iztok Peruš Affiliation
    ; Stane Božičnik Affiliation
    ; Matej Mencinger Affiliation


The paper is dealing with the problem of finding the optimal number and location of Loading Bays (LBs) for efficient urban last mile deliveries. To solve the problem a multi-parametric model of the idealized urban area is introduced and applied to various instances of a rectangular urban grid structured zones. Multi-parametric approach is used to assess statistically the most relevant number and location of LBs. Computational and graphical results of the idealized model exhibit geometric patterns showing that the optimal Number of LBs (#LB) naturally tends to perfect squares. Moreover, even in case of generalized instances, at a selected number of LBs their distribution is not random but follows specific laws. The optimality is closely related to the prefixed (maximal) walking distance dmax, from the LB to the customer. Based on various simulations the existence and robustness of a descending convex dependence dmax = (#LB) is proven. The results might serve as a decision-making tool to determine the optimal number and location of LBs for any real-life city centre.

Keyword : freight transportation, last mile delivery, facility location, fuzzy clustering, decision-making, loading bay

How to Cite
Letnik, T., Peruš, I., Božičnik, S., & Mencinger, M. (2019). On fundamental principles of the optimal number and location of loading bays in urban areas. Transport, 34(6), 722-740.
Published in Issue
Dec 23, 2019
Abstract Views
PDF Downloads
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.


Aiura, N.; Taniguchi, E. 2005. Planning on-street loading-unloading spaces considering the behaviour of pickup-delivery vehicles, Journal of the Eastern Asia Society for Transportation Studies 6: 2963–2974.

Alho, A. R.; De Abreu e Silva, J. 2014. Analyzing the relation between land-use/urban freight operations and the need for dedicated infrastructure/enforcement – application to the city of Lisbon, Research in Transportation Business & Management 11: 85–97.

Alho, A.; De Abreu e Silva, J.; De Sousa, J. P. 2014. A State-of the-art modeling framework to improve congestion by changing the configuration/enforcement of urban logistics loading/unloading bays, Procedia – Social and Behavioral Sciences 111: 360–369.

Berman, O.; Kalcsics, J.; Krass, D. 2016. On covering location problems on networks with edge demand, Computers & Operations Research 74: 214–227.

Bezdek, J. C. 1981. Pattern Recognition with Fuzzy Objective Function Algorithms. Springer. 256 p.

Blanquero, R.; Carrizosa, E.; G.-Tóth, B. 2016. Maximal covering location problems on networks with regional demand, Omega 64: 77–85.

Boeing, G. 2017. OSMnx: new methods for acquiring, constructing, analyzing, and visualizing complex street networks, Computers, Environment and Urban Systems 65: 126–139.

Buldeo Rai, H.; Van Lier, T.; Meers, D.; Macharis, C. 2017. Improving urban freight transport sustainability: Policy assessment framework and case study, Research in Transportation Economics 64: 26–35.

Callaghan, B.; Salhi, S.; Nagy, G. 2017. Speeding up the optimal method of Drezner for the p-centre problem in the plane, European Journal of Operational Research 257(3): 722–734.

Colmenar, J. M.; Martí, R.; Duarte, A. 2018. Multi-objective memetic optimization for the bi-objective obnoxious p-median problem, Knowledge-Based Systems 144: 88–101.

Comi, A.; Buttarazzi, B.; Schiraldi, M. M.; Innarella, R.; Varisco, M.; Rosati, L. 2017. DynaLOAD: a simulation framework for planning, managing and controlling urban delivery bays, Transportation Research Procedia 22: 335–344. Elsevier.

Cooper, L. 1963. Location-allocation problems, Operations Research 11(3): 331–343.

Crainic, T. G.; Errico, F.; Rei, W.; Ricciardi, N. 2016. Modeling demand uncertainty in two-tier city logistics tactical planning, Transportation Science 50(2): 559–578.

Dablanc, L.; Giuliano, G.; Holliday, K.; O’Brien, T. 2013. Best practices in urban freight management: lessons from an international survey, Transportation Research Record: Journal of the Transportation Research Board 2379: 29–38.

De Abreu e Silva, J.; Alho, A. R. 2017. Using structural equations modeling to explore perceived urban freight deliveries parking issues, Transportation Research Part A: Policy and Practice 102: 18–32.

Delaître, L.; Routhier, J.-L. 2010. Mixing two French tools for delivery areas scheme decision making, Procedia – Social and Behavioral Sciences 2(3): 6274–6285.

Dezi, G.; Dondi, G.; Sangiorgi, C. 2010. Urban freight transport in Bologna: planning commercial vehicle loading/unloading zones, Procedia – Social and Behavioral Sciences 2(3): 5990–6001.

Dijkstra, L.; Poelman, H. 2014. A Harmonised Definition of Cities and Rural Areas: the New Degree of Urbanisation. Working Paper WP 01/2014. European Commmission. 28 p. Available from Internet:

Farahani, R. Z.; Asgari, N.; Heidari, N.; Hosseininia, M.; Goh, M. 2012. Covering problems in facility location: a review, Computers & Industrial Engineering 62(1): 368–407.

Farahani, R. Z.; SteadieSeifi, M.; Asgari, N. 2010. Multiple criteria facility location problems: a survey, Applied Mathematical Modelling 34(7): 1689–1709.

Fu, J.; Jenelius, E. 2018. Transport efficiency of off-peak urban goods deliveries: a Stockholm pilot study, Case Studies on Transport Policy 6(1): 156–166.

Guastaroba, G.; Speranza, M. G.; Vigo, D. 2016. Intermediate facilities in freight transportation planning: a survey, Trans-portation Science 50(3): 763–789.

Hajipour, V.; Fattahi, P.; Tavana, M.; Di Caprio, D. 2016. Multi-objective multi-layer congested facility location-allocation problem optimization with Pareto-based meta-heuristics, Applied Mathematical Modelling 40(7–8): 4948–4969.

Holguín-Veras, J.; Sánchez-Díaz, I. 2016. Freight demand management and the potential of receiver-led consolidation programs, Transportation Research Part A: Policy and Practice 84: 109–130.

Husslage, B. G. M.; Rennen, G.; Van Dam, E. R.; Den Hertog, D. 2011. Space-filling Latin hypercube designs for computer experiments, Optimization and Engineering 12(4): 611–630.

Iyigun, C.; Ben-Israel, A. 2010. A generalized Weiszfeld method for the multi-facility location problem, Operations Research Letters 38(3): 207–214.

Jánošíková, L.; Herda, M.; Haviar, M. 2017. Hybrid genetic algorithms with selective crossover for the capacitated p-median problem, Central European Journal of Operations Research 25(3): 651–664.

Janssen, H. 2013. Monte-Carlo based uncertainty analysis: sampling efficiency and sampling convergence, Reliability Engineering & System Safety 109: 123–132.

Karatas, M.; Yakıcı, E. 2018. An iterative solution approach to a multi-objective facility location problem, Applied Soft Computing 62: 272–287.

Kikuno, T.; Yoshida, N.; Kakuda, Y. 1980. NP-completeness of some type of p-center problem, Discrete Applied Mathematics 2(4): 361–363.

Letnik, T.; Farina, A.; Mencinger, M.; Lupi, M.; Božičnik, S. 2018. Dynamic management of loading bays for energy efficient urban freight deliveries, Energy 159: 916–928.

Lin, J.; Ban, Y. 2017. Comparative analysis on topological structures of urban street networks, ISPRS International Journal of Geo-Information 6(10): 295.

Lindholm, M. 2013. Urban freight transport from a local authority perspective – a literature review, European Transport / Trasporti Europei (54): 3.

Lopez, C.; Gonzalez-Feliu, J.; Chiabaut, N.; Leclercq, L. 2016. Assessing the impacts of goods deliveries’ double line parking on the overall traffic under realistic conditions, in 6th International Conference on Information Systems, Logistics and Supply Chain: ILS Conference 2016, 1–4 June 2016, Bordeaux, France, 1–7.

Malik, L.; Sánchez-Díaz, I.; Tiwari, G; Woxenius, J. 2017. Urban freight-parking practices: the cases of Gothenburg (Sweden) and Delhi (India), Research in Transportation Business & Management 24: 37–48.

Marcucci, E.; Gatta, V.; Marciani, M.; Cossu, P. 2017. Measuring the effects of an urban freight policy package defined via a collaborative governance model, Research in Transportation Economics 65: 3–9.

Muñuzuri, J.; Cortés, P.; Onieva, L.; Guadix, J. 2012. Estimation of daily vehicle flows for urban freight deliveries, Journal of Urban Planning and Development 138(1): 43–52.

Muñuzuri, J.; Cortés, P.; Onieva, L.; Guadix, J. 2009. Modeling freight delivery flows: missing link of urban transport analysis, Journal of Urban Planning and Development 135(3): 91–99.

OECD. 2012. Redefining “Urban”: a New Way to Measure Metropolitan Areas. Organisation for Economic Cooperation and Development (OECD). 148 p.

Oses, U.; Rojí, E.; Cuadrado, J.; Larrauri, M. 2018. Multiple-criteria decision-making tool for local governments to evaluate the global and local sustainability of transportation systems in urban areas: case study, Journal of Urban Planning and Development 144(1): 04017019.

Peruš, I.; Poljanšek, K.; Fajfar, P. 2006. Flexural deformation capacity of rectangular RC columns determined by the CAE method, Earthquake Engineering and Structural Dynamics 35(12): 1453–1470.

Peruš, I.; Terčelj, M.; Kugler, G. 2012. Determination of scrap/supply probability curves for the mechanical properties of aluminium alloys in hot extrusion using a neural network-like approach, Expert Systems with Applications 39(5): 5634–5640.

Quak, H. J.; De Koster, M. B. M. 2009. Delivering goods in urban areas: how to deal with urban policy restrictions and the environment, Transportation Science 43(2): 211–227.

Ross, T. J. 2010. Fuzzy Logic with Engineering Applications. 3rd edition. John Wiley & Sons, Ltd. 585 p.

Russo, F.; Comi, A. 2012. City characteristics and urban goods movements: a way to environmental transportation system in a sustainable city, Procedia – Social and Behavioral Sciences 39: 61–73.

Russo, F.; Comi, A. 2011. Measures for sustainable freight transportation at urban scale: expected goals and tested results in Europe, Journal of Urban Planning and Development 137(2): 142–152.

Strano, E.; Viana, M.; Costa, L. da F.; Cardillo, A.; Porta, S.; Latora, V. 2013. Urban street networks, a comparative analysis of ten European cities, Environment and Planning B: Urban Analytics and City Science 40(6): 1071–1086.

Tozzi, M.; Corazza, M. V.; Musso, A. 2014. Urban goods movements in a sensitive context: the case of Parma, Research in Transportation Business & Management 11: 134–141.

Tsiotas, D.; Polyzos, S. 2017. The topology of urban road networks and its role to urban mobility, Transportation Research Procedia 24: 482–490.

Tüzün Aksu, D.; Ocak, Z. 2012. Location of municipal centers for new counties within the Istanbul metropolitan municipality, Journal of Urban Planning and Development 138(2): 143–152.

Wang, J.; Su, K.; Wu, Y. 2018. The reliable facility location problem under random disruptions, Wireless Personal Communications 102(4): 2483–2497.

Zhao, X.; Xia, X.; Wang, L.; Cao, J. 2019. A fuzzy multi-objective immune genetic algorithm for the strategic location planning problem, Cluster Computing 22: 3621–3641.

Zou, W.; Wang, X.; Conway, A.; Chen, Q. 2016. Empirical analysis of delivery vehicle on-street parking pattern in Manhattan area, Journal of Urban Planning and Development 142(2): 04015017.