A heuristic algorithm for optimal fleet composition with vehicle routing considerations

This paper proposes a fast heuristic algorithm for solving a combined optimal fleet composition and multi-period vehicle routing problem. The aim of the problem is to determine an optimal fleet mix, together with the corresponding vehicle routes, to minimize total cost subject to various customer delivery requirements and vehicle capacity constraints. The total cost includes not only the fixed, variable, and transportation costs associated with operating the fleet, but also the hiring costs incurred whenever vehicle requirements exceed fleet capacity. Although the problem under consideration can be formulated as a mixed-integer linear program (MILP), the MILP formulation for realistic problem instances is too large to solve using standard commercial solvers such as the IBM ILOG CPLEX optimization tool. Our proposed heuristic decomposes the problem into two tractable stages: in the first (outer) stage, the vehicle routes are optimized using cross entropy; in the second (inner) stage, the optimal fleet mix corresponding to a fixed set of routes is determined using dynamic programming and golden section search. Numerical results show that this heuristic approach generates high-quality solutions and significantly outperforms CPLEX in terms of computational speed

Variable-depth adaptive large meighbourhood search algorithm for Open Periodic Vehicle Routing Problem with time windows

The Open Periodic Vehicle Routing Problem with Time Windows (OPVRPTW) is a practical transportation routing and scheduling problem arising from real-world scenarios. It shares some common features with some classic VRP variants. The problem has a tightly constrained large-scale solution space and requires well balanced diversification and intensification in search. In Variable Depth Neighbourhood Search, large neighbourhood depth prevents the search from trapping into local optima prematurely, while small depth provides thorough exploitation in local areas. Considering the multi-dimensional solution structure and tight constraints in OPVRPTW, a Variable-Depth Adaptive Large Neighbourhood Search (VD-ALNS) algorithm is proposed in this paper. Contributions of four tailored destroy operators and three repair operators at variable depths are investigated. Comparing to existing methods, VD-ALNS makes a good trade-off between exploration and exploitation, and produces promising results on both small and large size benchmark instances

Workload Equity in Vehicle Routing Problems: A Survey and Analysis

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature. However, there has been only limited discussion about how workload equity should be modeled in VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences. This article addresses this gap with an analysis of classical and alternative equity functions for biobjective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs. In the analysis, we identify a set of axiomatic properties that an ideal equity measure should satisfy, collect six common measures, and point out important connections between their properties and those of the resulting Pareto-optimal solutions. To gauge the extent of these implications, we also conduct a numerical study on small biobjective VRP instances solvable to optimality. Our study reveals two undesirable consequences when optimizing equity with nonmonotonic functions: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent, i.e. composed of tours whose workloads are all equal to or longer than those of other Pareto-optimal solutions. We show that the extent of these phenomena should not be underestimated. The results of our biobjective analysis are valid also for weighted sum, constraint-based, or single-objective models. Based on this analysis, we conclude that monotonic equity functions are more appropriate for certain types of VRP models, and suggest promising avenues for further research.Comment: Accepted Manuscrip

Integrating partner objectives in horizontal logistics optimisation models

In this paper a general solution framework is presented for optimising decisions in a horizontal logistics cooperation. The framework distinguishes between the objective of the group and the objectives of the individual partners in the coalition. Although the importance of the individual partner interests is often acknowledged in the literature, the proposed solution framework is the first to include these objectives directly into the objective function of the optimisation model. The solution framework is applied to a collaborative variant of the clustered vehicle routing problem, for which we also create a set of benchmark instances. We find that by only considering a global coalition objective, the obtained solution is often suboptimal for some partners in the coalition. Providing a set of high quality alternative solutions that are Pareto efficient with respect to the partner objectives, gives additional insight in the sensitivity of a solution, which can support the decision making process. Our computational results therefore acknowledge the importance of including the individual partner objectives into the optimisation procedure

Using Simulation to Assess the Opportunities of Dynamic Waste Collection

In this paper, we illustrate the use of discrete event simulation to evaluate how dynamic planning methodologies can be best applied for the collection of waste from underground containers. We present a case study that took place at the waste collection company Twente Milieu, located in The Netherlands. Even though the underground containers are already equipped with motion sensors, the planning of container emptying’s is still based on static cyclic schedules. It is expected that the use of a dynamic planning methodology, that employs sensor information, will result in a more efficient collection process with respect to customer satisfaction, profits, and CO2 emissions. In this research we use simulation to (i) evaluate the current planning methodology, (ii) evaluate various dynamic planning possibilities, (iii) quantify the benefits of switching to a dynamic collection process, and (iv) quantify the benefits of investing in fill‐level sensors. After simulating all scenarios, we conclude that major improvements can be achieved, both with respect to logistical costs as well as customer satisfaction

Column generation based heuristic for tactical planning in multi-period vehicle routing

International audienceThe periodic vehicle routing problem (PVRP) consists in establishing a planning of visits to clients over a given time horizon so as to satisfy some service level while optimizing the routes used in each time period. The tactical planning model considered here restricts its attention to scheduling visits and assigning them to vehicles while leaving sequencing decisions for an underlying operational model. The objective is twofold: to optimize regional compactness of the routes in a desire to specialize routes to restricted geographical area and to balance the workload evenly between vehicles. Approximate solutions are constructed using a truncated column generation procedure followed by a rounding heuristic. This mathematical programming based procedure can deal with problems with 50–80 customers over five working days which is the range of size of most PVRP instances treated in the literature with meta-heuristics. The paper highlights the importance of alternative optimization criteria not accounted for in standard operational models and provides insights on the implementation of a column generation based rounding heuristic

Uma meta-heurística Adaptive Large Neighborhood Search com mecanismos de paralelismo, detecção de estagnação e perturbações para o problema de roteamento de veículos com frota heterogênea, periódico e Multi-Trips

The planning of vehicle routes is a major issue involved in supply chains. In real environment we can find situations involving a very large number of clients or constraints witch indicate that exact methods should be avoided. In this context, this work presents an metaheuristic for solving some variants of the vehicle routing problem (VRP): Heterogeneous VRP, VRP Periodic and VRP with multi-trips. The metaheuristic chosen, called Adaptive Large Neighborhood Search (ALNS), combines the power of successful strategies in the literature as a large neighborhood search and adaptive mechanisms with new features such as parallelism, detection of stagnation and perturbations. Our ALNS was implemented in such a way that all variants of the VRP are solved without changes in the code. The results for several instances proposed in the literature are satisfactory, showing the good performance of the approach.A atribuição e o planejamento de rotas de veículos são problemas importantes envolvidos nas cadeias de suprimentos. Em ambiente real é comum encontrar situações que envolvam uma quantidade muito grande de clientes ou de restrições que consequentemente fogem do alcance de métodos exatos. Neste contexto, este trabalho apresenta uma meta-heurística capaz de resolver algumas variantes do problema de roteamento de veículos (PRV) combinadas: o PRV capacitado com frota heterogênea, o PRV periódico e o PRV com multi-trips. A meta-heurística escolhida, denominada Adaptive Large Neighborhood Search (ALNS), combina a força de estratégias bem-sucedidas na literatura como busca em vizinhança ampla e mecanismos adaptativos e também novos mecanismos como paralelismo, detecção de estagnação e perturbações. O ALNS foi implementado de tal maneira que todas as variantes do PRV citadas pudessem ser resolvidas sem alterações de código. Os resultados obtidos, em diversas instâncias propostas na literatura foram satisfatórios, mostrando o bom desempenho do método proposto