MAGAZINE  №5 (94) October 2019


CATEGORY  Optimization and mathematical modelling Transportation in logistics Industrial companies’ corporate logistics



 Due to an increased volume of cargo transportations the development of the mathematical and software for resolving the routing problems is being actual, whereas the objective is costs reduсtion when cargo is delivered to customers. The problem of cargo's homogeneous delivery to various customers is considered in the paper, which is significant component in supply chain.
The mathematical model accounting such restrictions as a vehicle carrying capacity, the time windows, the planning horizon, a bunch of depots, the split delivery, a heterogeneous vehicle fleet, a possibility of backhauls, the quality and cost of roads, the type of roads, speed limits, as well as goods disposition within a vehicle during the construction of the rational delivery routes is represented. For the given NP-hard combinatorial optimization problem, the heuristic method on the basis of the ant colony algorithm based on population that allows to obtain the rational delivery routes for homogeneous goods with account of restrictions listed is developed.
Herewith, the results of the numerical experiments, which verify the efficiency of the proposed approach based on the developed software are presented.



 Electronic version

 Keywords:  vehicle routing problem 3D Packing problem uniform load vehicle loading Ant colony optimization algorithm evolution algorithm


MAGAZINE №4(87) August 2018



YUNEEVA D.R. - School of Logistics, National Research University Higher School of Economics (Moscow, Russia)

CATEGORY E-commerce corporate logistics Optimization and mathematical modelling Transportation in logistics


Growth rates of internet retailing in Russia outperform brick-and-mortar segment, which raises attractiveness of e-commerce for new players. However a growing number of newcomers make e-tailers seek new competitive advantages and pay specific attention to the logistics support of their businesses. Last mile delivery tends to be one of the most important, though also problematic logistics processes in online retailing.  Potential area of improvement for this process involves application of heuristic routing methods.  These methods allow to find a nearly optimal solution with substantially lower cost of resources compared to traditional methods.

The paper focuses on the heuristic method of a travelling salesman problem solution complicated by the specifics of internet retailing (big number of clients and, hence, delivery points). This method is based on the simulation of ants’ behaviour seeking the shortest path between their colony and the source of food. The authors describe a mathematical model of an ant colony optimization algorithm (ACO) and review its basic steps using the numerical example. Steps of the ACO include definition of the number of nodes, distance between them as well as pheromone concentration; location of couriers (delivery vans) in the nodes; identification of the probability of moving from the initial point (node) to all other points; selection of the movement direction; repetition of the preceding steps (apart from the initial one) for a new node and for the following ones up to the end of the cycle; pheromone renewal; accomplishment of the next cycles (iterations); finding the shortest delivery route. Comparative analysis has shown major ACO benefits including fast solution of high-dimensional problems and algorithm applicability for the non-stationary systems with changing parameters (much resembling online retailing). An opportunity to apply ACO for the last mile delivery routing referring to the vast majority of e-tailers will significantly depend on the speed of development and proliferation of the respective software as well as on improving of selection and adaptation of the algorithm fine-tuning parameters.         

 Electronic version



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