Exact and Approximation Algorithms for the Multi-Depot Capacitated Arc Routing Problems

In this work,we investigate a generalization of the classical capacitated arc routing problem,called the Multi-depot Capacitated Arc Routing Problem(MCARP).We give exact and approximation algorithms for different variants of the MCARP.First,we obtain the first constant-ratio approximation algorithms for the MCARP and its nonfixed destination version.Second,for the multi-depot rural postman problem,i.e.,a special case of the MCARP where the vehicles have infinite capacity,we develop a(2-1/2k+1)-approximation algorithm(k denotes the number of depots).Third,we show the polynomial solvability of the equal-demand MCARP on a line and devise a 2-approximation algorithm for the multi-depot capacitated vehicle routing problem on a line.Lastly,we conduct extensive numerical experiments on the algorithms for the multi-depot rural postman problem to show their effectiveness.

A multi-agent deep reinforcement learning approach for solving the multi-depot vehicle routing problem

The multi-depot vehicle routing problem(MDVRP)is one of the most essential and useful variants of the traditional vehicle routing problem(VRP)in supply chain management(SCM)and logistics studies.Many supply chains(SC)choose the joint distribution of multiple depots to cut transportation costs and delivery times.However,the ability to deliver quality and fast solutions for MDVRP remains a challenging task.Traditional optimization approaches in operation research(OR)may not be practical to solve MDVRP in real-time.With the latest developments in artificial intelligence(AI),it becomes feasible to apply deep reinforcement learning(DRL)for solving combinatorial routing problems.This paper proposes a new multi-agent deep reinforcement learning(MADRL)model to solve MDVRP.Extensive experiments are conducted to evaluate the performance of the proposed approach.Results show that the developed MADRL model can rapidly capture relative information embedded in graphs and effectively produce quality solutions in real-time.

A Branch and Cut Algorithm for Two-Echelon Inventory Routing Problem with End-of-Tour Replenishment Policy

This study presents a two-echelon inventory routing problem (2E-IRP) with an end-of-tour replenishment (ETR) policy whose distribution network consists of a supplier, several distribution centers (DCs) and several retailers on a multi-period planning horizon. A formulation of the problem based on vehicle indices is proposed in the form of a mixed integer linear program (MILP). The mathematical model of the problem is solved using a branch and cut (B&C) algorithm. The results of the tests are compared to the results of a branch and price (B&P) algorithm from the literature on 2E-IRP with a classical distribution policy. The results of the tests show that the B&C algorithm solves 197 out of 200 instances (98.5%). The comparison of the B&C and B&P results shows that 185 best solutions are obtained with the B&C algorithm on 197 instances (93.9%). Overall, the B&C algorithm achieves cost reductions ranging from 0.26% to 41.44% compared to the classic 2E-IRP results solved with the B&P algorithm, with an overall average reduction of 18.08%.