Improved Branch-Cut-and-Price algorithm for the Heterogeneous Vehicle Routing Problem

National audienc

Solving Rich Vehicle Routing Problem Using Three Steps Heuristic

Vehicle Routing Problem (VRP) relates to the problem of providing optimum service with a fleet of vehicles to customers. It is a combinatorial optimization problem. The objective is usually to maximize the profit of the operation. However, for public transportation owned and operated by government, accessibility takes priority over profitability. Accessibility usually reduces profit, while increasing profit tends to reduce accessibility. In this research, we look at how accessibility can be increased without penalizing the profitability. This requires the determination of routes with minimum fuel consumption, maximum number of ports of call and maximum load factor satisfying a number of pre-determined constraints: hard and soft constraints. To solve this problem, we propose a heuristic algorithm. The results from this experiment show that the algorithm proposed has better performance compared to the partitioning set

Order picking problems under weight, fragility, and category constraints

Warehouse order picking activities are among the ones that impact the most the bottom lines of warehouses. They are known to often account for more than half of the total warehousing costs. New practices and innovations generate new challenges for managers and open new research avenues. Many practical constraints arising in real-life have often been neglected in the scientific literature. We introduce, model, and solve a rich order picking problem under weight, fragility, and category constraints, motivated by our observation of a real-life application arising in the grocery retail industry. This difficult warehousing problem combines complex picking and routing decisions under the objective of minimizing the distance traveled. We first provide a full description of the warehouse design which enables us to algebraically compute the distances between all pairs of products. We then propose two distinct mathematical models to formulate the problem. We develop five heuristic methods, including extensions of the classical largest gap, mid point, S-shape, and combined heuristics. The fifth one is an implementation of the powerful adaptive large neighborhood search algorithm specifically designed for the problem at hand. We then implement a branch-and-cut algorithm and cutting planes to solve the two formulations. The performance of the proposed solution methods is assessed on a newly generated and realistic test bed containing up to 100 pickups and seven aisles. We compare the bounds provided by the two formulations. Our in-depth analysis shows which formulation tends to perform better. Extensive computational experiments confirm the efficiency of the ALNS matheuristic and derive some important insights for managing order picking in this kind of warehouses

The heterogeneous fleet vehicle routing problem with light loads and overtime: Formulation and population variable neighbourhood search with adaptive memory

In this paper we consider a real life Vehicle Routing Problem inspired by the gas delivery industry in the United Kingdom. The problem is characterized by heterogeneous vehicle fleet, demand-dependent service times, maximum allowable overtime and a special light load requirement. A mathematical formulation of the problem is developed and optimal solutions for small sized instances are found. A new learning-based Population Variable Neighbourhood Search algorithm is designed to address this real life logistic problem. To the best of our knowledge Adaptive Memory has not been hybridized with a classical iterative memoryless method. In this paper we devise and analyse empirically a new and effective hybridization search that considers both memory extraction and exploitation. In terms of practical implications, we show that on a daily basis up to 8% cost savings on average can be achieved when overtime and light load requirements are considered in the decision making process. Moreover, accommodating for allowable overtime has shown to yield 12% better average utilization of the driver's working hours and 12.5% better average utilization of the vehicle load, without a significant increase in running costs. We also further discuss some managerial insights and trade-offs

Layered graph approaches for combinatorial optimization problems

Extending the concept of time-space networks, layered graphs associate information about one or multiple resource state values with nodes and arcs. While integer programming formulations based on them allow to model complex problems comparably easy, their large size makes them hard to solve for non-trivial instances. We detail and classify layered graph modeling techniques that have been used in the (recent) scientific literature and review methods to successfully solve the resulting large-scale, extended formulations. Modeling guidelines and important observations concerning the solution of layered graph formulations by decomposition methods are given together with several future research directions

A Hybrid Heuristic for a Broad Class of Vehicle Routing Problems with Heterogeneous Fleet

We consider a family of Rich Vehicle Routing Problems (RVRP) which have the particularity to combine a heterogeneous fleet with other attributes, such as backhauls, multiple depots, split deliveries, site dependency, open routes, duration limits, and time windows. To efficiently solve these problems, we propose a hybrid metaheuristic which combines an iterated local search with variable neighborhood descent, for solution improvement, and a set partitioning formulation, to exploit the memory of the past search. Moreover, we investigate a class of combined neighborhoods which jointly modify the sequences of visits and perform either heuristic or optimal reassignments of vehicles to routes. To the best of our knowledge, this is the first unified approach for a large class of heterogeneous fleet RVRPs, capable of solving more than 12 problem variants. The efficiency of the algorithm is evaluated on 643 well-known benchmark instances, and 71.70\% of the best known solutions are either retrieved or improved. Moreover, the proposed metaheuristic, which can be considered as a matheuristic, produces high quality solutions with low standard deviation in comparison with previous methods. Finally, we observe that the use of combined neighborhoods does not lead to significant quality gains. Contrary to intuition, the computational effort seems better spent on more intensive route optimization rather than on more intelligent and frequent fleet re-assignments

A branch-cut-and-price approach for the single-trip and multi-trip two-echelon vehicle routing problem with time windows

The paper studies the two-echelon capacitated vehicle routing problem with time windows, in which delivery of freight from depots to customers is performed using intermediate facilities called satellites. We consider the variant of the problem with precedence constraints for unloading and loading freight at satellites. This variant allows for storage and consolidation of freight at satellites. Thus, the total transportation cost may decrease in comparison with the alternative variant with exact freight synchronization at satellites. We suggest a mixed integer programming formulation for the problem with an exponential number of route variables and an exponential number of precedence constraints which link first-echelon and second-echelon routes. Routes at the second echelon connecting satellites and clients may consist of multiple trips and visit several satellites. A branch-cut-and-price algorithm is proposed to solve efficiently the problem. This is the first exact algorithm in the literature for the multi-trip variant of the problem. We also present a post-processing procedure to check whether the solution can be transformed to avoid freight consolidation and storage without increasing its transportation cost. Our algorithm significantly outperforms another recent one for the single-trip variant of the problem. We also show that all single-trip literature instances solved to optimality admit optimal solutions of the same cost for both variants of the problem either with precedence constraints or with exact synchronization constraints