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Thirty years of heterogeneous vehicle routing

It has been around 30 years since the heterogeneous vehicle routing problem was introduced, and significant progress has since been made on this problem and its variants. The aim of this survey paper is to classify and review the literature on heterogeneous vehicle routing problems. The paper also presents a comparative analysis of the metaheuristic algorithms that have been proposed for these problems.

A hybrid evolutionary algorithm for heterogeneous fleet vehicle routing problems with time windows

This paper presents a hybrid evolutionary algorithm (HEA) to solve heterogeneous fleet vehicle routing problems with time windows. There are two main types of such problems, namely the fleet size and mix vehicle routing problem with time windows (F) and the heterogeneous fixed fleet vehicle routing problem with time windows (H), where the latter, in contrast to the former, assumes a limited availability of vehicles. The main objective is to minimize the fixed vehicle cost and the distribution cost, where the latter can be defined with respect to en-route time (T) or distance (D). The proposed unified algorithm is able to solve the four variants of heterogeneous fleet routing problem, called FT, FD, HT and HD, where the last variant is new. The HEA successfully combines several metaheuristics and offers a number of new advanced efficient procedures tailored to handle the heterogeneous fleet dimension. Extensive computational experiments on benchmark instances have shown that the HEA is highly effective on FT, FD and HT. In particular, out of the 360 instances we obtained 75 new best solutions and matched 102 within reasonable computational times. New benchmark results on HD are also presented. HighlightsWe develop a unified algorithm for four heterogeneous routing problems.We introduce a new heterogeneous routing problem.The algorithm combines two state-of-the-art metaheuristic concepts.Out of the 360 instances we obtain 75 strictly new best solutions.

The green vehicle routing problem

We develop a solution approach to solve the green vehicle routing problem.We propose a simulated annealing heuristic to improve the quality of solutions.We present a new formulation having fewer variable and constraints.We evaluate the algorithm in terms of the several performance criterions.Our algorithm is able to optimally solve 22 of 40 benchmark instances. This paper develops a simulated annealing heuristic based exact solution approach to solve the green vehicle routing problem (G-VRP) which extends the classical vehicle routing problem by considering a limited driving range of vehicles in conjunction with limited refueling infrastructure. The problem particularly arises for companies and agencies that employ a fleet of alternative energy powered vehicles on transportation systems for urban areas or for goods distribution. Exact algorithm is based on the branch-and-cut algorithm which combines several valid inequalities derived from the literature to improve lower bounds and introduces a heuristic algorithm based on simulated annealing to obtain upper bounds. Solution approach is evaluated in terms of the number of test instances solved to optimality, bound quality and computation time to reach the best solution of the various test problems. Computational results show that 22 of 40 instances with 20 customers can be solved optimally within reasonable computation time.

The fleet size and mix location-routing problem with time windows: Formulations and a heuristic algorithm

This paper introduces the fleet size and mix location-routing problem with time windows (FSMLRPTW) which extends the location-routing problem by considering a heterogeneous fleet and time windows. The main objective is to minimize the sum of vehicle fixed cost, depot cost and routing cost. We present mixed integer programming formulations, a family of valid inequalities and we develop a powerful hybrid evolutionary search algorithm (HESA) to solve the problem. The HESA successfully combines several metaheuristics and offers a number of new advanced efficient procedures tailored to handle heterogeneous fleet dimensioning and location decisions. We evaluate the strengths of the proposed formulations with respect to their ability to find optimal solutions. We also investigate the performance of the HESA. Extensive computational experiments on new benchmark instances have shown that the HESA is highly effective on the FSMLRPTW.

A Multiperiod Location-Routing Problem Arising in the Collection of Olive Oil Mill Wastewater

The process by which olive oil is produced yields two by-products, one of which is the brown-coloured Olive Oil Mill Wastewater (OMWW) and has no direct use. OMWW is generally disposed of into soil or rivers, potentially contaminating the environment. OMWW can be treated using ultrafiltration facilities, but this requires that OMWW is collected from oil mills and delivered to the treatment facilities using a fleet of vehicles in an economically viable manner. Such considerations give rise to a multiperiod location-routing problem. This paper formally introduces the problem and proposes an adaptive large neighbourhood search metaheuristic for its solution. The algorithm is applied on a case study drawn from one of the major olive oil producing countries. The paper presents computational and managerial results.

An evolutionary algorithm for supply chain network design with assembly line balancing

This paper investigates the combined impact of assembly line balancing decisions within a supply chain network design. The aim of the problem is to design a supply chain network between manufacturers, assemblers, and customers for specific periods, as well as balancing the assembly lines in assemblers. The main objective is to minimize the sum of transportation costs and fixed costs of stations in assemblers. Solving this problem poses several methodological challenges. To this end, the paper developed a powerful evolutionary algorithm (EA) which was successfully applied to a large pool of benchmark instances. The EA solved instances with up to 140 manufacturers and customers, and with up to 130 assemblers. Computational analyses are performed to empirically calculate the effect of various problem parameters, such as total cost, transportation cost and number of stations. The EA is validated on benchmark instances where it provides competitive solutions. Several managerial insights are also presented.

Long-haul vehicle routing and scheduling with idling options

Abstract This paper introduces the vehicle routing and truck driver scheduling problem with idling options, an extension of the long-haul vehicle routing and truck driver scheduling problem with a more comprehensive objective function that accounts for routing cost, driver cost and idling cost, i.e., the cost associated with energy supply used to maintain drivers’ comfort when the vehicle is not moving. For the idling cost, we consider Electrified Parking Space (EPS) and Auxiliary Power Unit (APU) usage costs. The use of EPSs or APUs avoids keeping the engine running while the vehicle is not moving. We develop a multi-start matheuristic algorithm that combines adaptive large neighborhood search and mixed integer linear programming. We present extensive computational results on instances derived from the Solomon test bed.

The Multi-Vehicle Probabilistic Covering Tour Problem

Abstract This paper introduces the Multi-Vehicle Probabilistic Covering Tour Problem (MVPCTP) which extends the Covering Tour Problem (CTP) by incorporating multiple vehicles and probabilistic coverage. As in the CTP, total demand of customers is attracted to the visited facility vertices within the coverage range. The objective function is to maximize the expected customer demand covered. The MVPCTP is first formulated as an integer non-linear programming problem, and then a linearization is proposed, which is strengthened by several sets of valid inequalities. An effective branch-and-cut algorithm is developed in addition to a local search heuristic based on Variable Neighborhood Search to obtain upper bounds. Extensive computational experiments are performed on new benchmark instances adapted from the literature.