On Fundamental Principles of the Optimal Number and Location of Loading Bays in Urban Areas

Abstract

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.

Flexible Assignment of Loading Bays for Efficient Vehicle Routing in Urban Last Mile Delivery

“…Before finally confirming this results on some real life cases, further research could also investigate the impact of different densities of the road network (including variants with an uneven distribution of roads that are closer to some specific real-life situations), different densities of customers, and different numbers and location of access gates. Nevertheless, on the results presented in this article and the research experience gained in determining the optimal number and locations of loading bays [42], we assume that the results will not be significantly different from those shown. Another proposal is to run the optimization also for the walking part of delivery, which would additionally save some walking distances.…”

“…In Letnik et al [42] a multi-parametric model of the idealized urban area was introduced and applied to different instances of rectangular urban grid structured zones to determine statistically the most relevant number and location of loading bays. The main criterion for the evaluation of the results was the predefined maximum allowed walking distance from the loading bay to the customer.…”

“…For this purpose, Latin hypercube sampling (LHS) algorithm is used [43]. The positions of loading bays are determined by the fuzzy C-means (FCM) procedure [42], access gates are located randomly on each side of the urban area perimeter also using LHS algorithm. Note that the model allows to create different instances of orthogonal urban area with different density of network, customers, and loading bays.…”

“…Potential location of loading bays in the model is therefore determined by using fuzzy C-means (FCM) clustering procedure. FCM was chosen to get some flexibility to the model with the possibility to simulate different membership degrees of customers to cluster centers, in our case loading bays [42].…”