A Column Generation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem

[EN] This paper addressed the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), in which the vehicles are not required to return to the depot after completing a service. In this new problem, the demands of customers are fulfilled by a heterogeneous fixed fleet of vehicles having various capacities, fixed costs and variable costs. This problem is an important variant of the open vehicle routing problem (OVRP) and can cover more practical situations in transportation and logistics. Since this problem belongs to NP-hard Problems, An approach based on column generation (CG) is applied to solve the HFFOVRP. A tight integer programming model is presented and the linear programming relaxation of which is solved by the CG technique. Since there have been no existing benchmarks, this study generated 19 test problems and the results of the proposed CG algorithm is compared to the results of exact algorithm. Computational experience confirms that the proposed algorithm can provide better solutions within a comparatively shorter period of time.Yousefikhoshbakht, M.; Dolatnejad, A. (2017). A Column Generation for the Heterogeneous Fixed Fleet Open Vehicle Routing Problem. International Journal of Production Management and Engineering. 5(2):55-71. doi:10.4995/ijpme.2017.5916SWORD557152Aleman, R. E., & Hill, R. R. (2010). A tabu search with vocabulary building approach for the vehicle routing problem with split demands. International Journal of Metaheuristics, 1(1), 55. doi:10.1504/ijmheur.2010.033123Anbuudayasankar, S. P., Ganesh, K., Lenny Koh, S. C., & Ducq, Y. (2012). Modified savings heuristics and genetic algorithm for bi-objective vehicle routing problem with forced backhauls. Expert Systems with Applications, 39(3), 2296-2305. doi:10.1016/j.eswa.2011.08.009Brandão, J. (2009). A deterministic tabu search algorithm for the fleet size and mix vehicle routing problem. 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The capacitated vehicle routing problem with stochastic demands and time windows. Computers & Operations Research, 38(12), 1775-1783. doi:10.1016/j.cor.2011.02.007Li, X., Leung, S. C. H., & Tian, P. (2012). A multistart adaptive memory-based tabu search algorithm for the heterogeneous fixed fleet open vehicle routing problem. Expert Systems with Applications, 39(1), 365-374. doi:10.1016/j.eswa.2011.07.025Li, X., Tian, P., & Aneja, Y. P. (2010). An adaptive memory programming metaheuristic for the heterogeneous fixed fleet vehicle routing problem. Transportation Research Part E: Logistics and Transportation Review, 46(6), 1111-1127. doi:10.1016/j.tre.2010.02.004Penna, P. H. V., Subramanian, A., & Ochi, L. S. (2011). An Iterated Local Search heuristic for the Heterogeneous Fleet Vehicle Routing Problem. Journal of Heuristics, 19(2), 201-232. doi:10.1007/s10732-011-9186-ySaadati Eskandari, Z., YousefiKhoshbakht, M. (2012). Solving the Vehicle Routing Problem by an Effective Reactive Bone Route Algorithm, Transportation Research Journal, 1(2), 51-69.Subramanian, A., Drummond, L. M. A., Bentes, C., Ochi, L. S., & Farias, R. (2010). A parallel heuristic for the Vehicle Routing Problem with Simultaneous Pickup and Delivery. Computers & Operations Research, 37(11), 1899-1911. doi:10.1016/j.cor.2009.10.011Syslo, M., Deo, N., Kowalik, J. (1983). Discrete Optimization Algorithms with Pascal Programs, Prentice Hall.Taillard, E. D. (1999). A heuristic column generation method for the heterogeneous fleet VRP, RAIRO Operations Research, 33, 1-14. https://doi.org/10.1051/ro:1999101Tarantilis, C. D., & Kiranoudis, C. T. (2007). A flexible adaptive memory-based algorithm for real-life transportation operations: Two case studies from dairy and construction sector. European Journal of Operational Research, 179(3), 806-822. doi:10.1016/j.ejor.2005.03.059Wang, H.-F., & Chen, Y.-Y. (2012). A genetic algorithm for the simultaneous delivery and pickup problems with time window. Computers & Industrial Engineering, 62(1), 84-95. doi:10.1016/j.cie.2011.08.018Yousefikhoshbakht, M., Didehvar, F., & Rahmati, F. (2013). Solving the heterogeneous fixed fleet open vehicle routing problem by a combined metaheuristic algorithm. International Journal of Production Research, 52(9), 2565-2575. doi:10.1080/00207543.2013.855337Yousefikhoshbakht, M., & Khorram, E. (2012). Solving the vehicle routing problem by a hybrid meta-heuristic algorithm. Journal of Industrial Engineering International, 8(1). doi:10.1186/2251-712x-8-1

A vehicle routing model with split delivery and stop nodes

In this work, a new variant of the Capacitated Vehicle Routing Problem (CVRP) is presented where the vehicles cannot perform any route leg longer than a given length L (although the routes can be longer). Thus, once a route leg length is close to L, the vehicle must go to a stop node to end the leg or return to the depot. We introduce this condition in a variation of the CVRP, the Split Delivery Vehicle Routing Problem, where multiple visits to a customer by different vehicles are allowed. We present two formulations for this problem which we call Split Delivery Vehicle Routing Problem with Stop Nodes: a vehicle flow formulation and a commodity flow formulation. Because of the complexity of this problem, a heuristic approach is developed. We compare its performance with and without the stop nodesSplit delivery vehicle routing problem, Stop node, Granular neighborhood, Tabu search

A Guided Neighborhood Search Applied to the Split Delivery Vehicle Routing Problem

The classic vehicle routing problem considers the distribution of goods to geographically scattered customers from a central depot using a homogeneous fleet of vehicles with finite capacity. Each customer has a known demand and can be visited by exactly one vehicle. Each vehicle services the assigned customers in such a way that all customers are fully supplied and the total service does not exceed the vehicle capacity. In the split delivery vehicle routing problem, a customer can be visited by more than one vehicle, i.e., a customer demand can be split between various vehicles. Allowing split deliveries has been proven to potentially reduce the operational costs of the fleet. This study efficiently solves the split delivery vehicle routing problem using three new approaches. In the first approach, the problem is solved in two stages. During the first stage, an initial solution is found by means of a greedy approach that can produce high quality solutions comparable to those obtained with existing sophisticated approaches. The greedy approach is based on a novel concept called the route angle control measure that helps to produce spatially thin routes and avoids crossing routes. In the second stage, this constructive approach is extended to an iterative approach using adaptive memory concepts, and then a variable neighborhood descent process is added to improve the solution obtained. A new solution diversification scheme is presented in the second approach based on concentric rings centered at the depot that partitions the original problem. The resulting sub-problems are then solved using the greedy approach with route angle control measures. Different ring settings produce varied partitions and thus different solutions to the original problem are obtained and improved via a variable neighborhood descent. The third approach is a learning procedure based on a set or population of solutions. Those solutions are used to find attractive attributes and construct new solutions within a tabu search framework. As the search progresses, the existing population evolves, better solutions are included in it whereas bad solutions are removed from it. The initial set is constructed using the greedy approach with the route angle control measure whereas new solutions are created using an adaptation of the well known savings algorithm of Clarke and Wright (1964) and improved by means of an enhanced version of the variable neighborhood descent process. The proposed approaches are tested on benchmark instances and results are compared with existing implementations

A vehicle routing model with split delivery and stop nodes

In this work, a new variant of the Capacitated Vehicle Routing Problem (CVRP) is presented where the vehicles cannot perform any route leg longer than a given length L (although the routes can be longer). Thus, once a route leg length is close to L, the vehicle must go to a stop node to end the leg or return to the depot. We introduce this condition in a variation of the CVRP, the Split Delivery Vehicle Routing Problem, where multiple visits to a customer by different vehicles are allowed. We present two formulations for this problem which we call Split Delivery Vehicle Routing Problem with Stop Nodes: a vehicle flow formulation and a commodity flow formulation. Because of the complexity of this problem, a heuristic approach is developed. We compare its performance with and without the stop node

Декомпозиция задачи маршрутизации по эвристикам метода Кларка-Райта

For the English abstract and full text of the article please see the attached PDF-File (English version follows Russian version).ABSTRACT The article is devoted to decomposition of the task of transport routing based on heuristic estimates with the Clarke-Wright method. A procedure is proposed for designing an automobile transport system based on the criterion of minimizing the total mileage by various formalized decomposition methods, in particular, using the «benefit functions» algorithm and formation of zones (clusters, subsets) of vehicle maintenance. The advantages of the proposed method are clearly shown in comparison with the method of «the shortest distance matrix», at the example of delivery of ten cargo units from a supplier to ten consumers. The effect of reducing the total mileage on the designed routes was 9,45 %. Keywords: transport routing, Clarke-Wright method, «benefit function», cluster, decomposition method, heuristic estimation, the shortest distances matrixТекст аннотации на англ. языке и полный текст статьи на англ. языке находится в прилагаемом файле ПДФ (англ. версия следует после русской версии).Статья посвящена декомпозиции задачи маршрутизации транспорта по эвристическим оценкам метода Кларка-Райта. Предложена процедура проектирования развозочной автотранспортной системы по критерию минимизации суммарного общего пробега различными формализованными методами декомпозиции, в частности, с помощью алгоритма «функций выгоды» и формирования зон (кластеров, подмножеств, «кустов») обслуживания транспортного средства. Наглядно показаны преимущества предлагаемого метода по сравнению с методом «по матрице кратчайших расстояний» на примере доставки десяти единиц груза от поставщика десяти потребителям по одной грузовой единице. Эффект от сокращения суммарного пробега на построенных маршрутах составил 9,45 %

A Matheuristic Approach for the Split Delivery Vehicle Routing Problem: An Efficient Set Covering-Based Model with Guided Route Generation Schemes

The Split Delivery Vehicle Routing Problem (SDVRP) is a relaxed version of the classical VRP where customers can be visited more than once. The SDVRP is also applicable for problems where one or more of the customers require a demand larger than the vehicle capacity. Constructive heuristics adapted from the parallel savings and the sweep methods are first proposed to generate a set of solutions which is then used in the new and more efficient set covering-based formulation which we put forward. An effective repair mechanism to remedy any infeasibility due to the set covering problem is presented. A reduced set of promising routes is used in our model, instead of the original set of routes, proposing and using well defined reduction schemes. This set covering-based approach is tested on large data sets from the literature with encouraging results. In brief, 7 best solutions including ties are found among the 137 SDVRP instances

Задачи построения комбинированных и раздельных маршрутов перевозки мелкопартионных грузов во внутренних зонах иерархической автотранспортной сети

В работе предложены математические формулировки задач построения комбинированных и раздельных маршрутов для перевозки мелкопартионных грузов во внутренних зонах обслуживания магистральных узлов иерархической транспортной сети. Проведен обзор методов и алгоритмов решения подобных задач. Отмечается возможность решения сформулированных задач с помощью известных пакетов смешанного и целочисленного линейного программирования.В роботі запропоновані математичні формулювання задач побудови комбінованих і роздільних маршрутів для перевезення дрібнопартіонних вантажів у внутрішніх зонах обслуговування магістральних вузлів ієрархічної транспортної мережі. Проведено огляд методів і алгоритмів розв’язання подібних задач. Відзначається можливість розв’язання сформульованих задач за допомогою відомих пакетів змішаного і цілочисельного лінійного програмування.The paper presents mathematical formulations of the vehicle routing problems with simultaneous and split delivery and pickup of small-lot cargo in the internal service areas of trunk nodes of hierarchical transport network. A review of methods and algorithms for solving such problems is conducted. It is marked the possibility of solving the formulated problems by known packages of mixed and integer linear programming

CANADA’S GRAIN HANDLING AND TRANSPORTATION SYSTEM: A GIS-BASED EVALUATION OF POLICY CHANGES

Western Canada is in a post Canadian Wheat Board single-desk market, in which grain handlers face policy, allocation, and logistical changes to the transportation of grains. This research looks at the rails transportation problem for allocating wheat from Prairie to port position, offering a new allocation system that fits the evolving environment of Western Canada’s grain market. Optimization and analysis of the transport of wheat by railroads is performed using geographic information system software as well as spatial and historical data. The studied transportation problem searches to minimize the costs of time rather than look purely at locational costs or closest proximity to port. Through optimization three major bottlenecks are found to constrain the transportation problem; 1) an allocation preference towards Thunder Bay and Vancouver ports, 2) small capacity train inefficiency, and 3) a mismatched distribution of supply and demand between the Class 1 railway firms. Through analysis of counterfactual policies and a scaled sensitivity analysis of the transportation problem, the grains transport system of railroads is found to be dynamic and time efficient; specifically when utilizing larger train capacities, offering open access to rail, and under times of increased availability of supplies. Even under the current circumstances of reduced grain movement and inefficiencies, there are policies and logistics that can be implemented to offer grain handlers in Western Canada with the transportation needed to fulfill their export demands

A Combined Adaptive Tabu Search and Set Partitioning Approach for the Crew Scheduling Problem with an Air Tanker Crew Application

This research develops the first metaheuristic approach to the complete air crew scheduling problem. It develops the first dynamic, integrated, set-partitioning based vocabulary scheme for metaheuristic search. Since no benchmark flight schedules exist for the tanker crew scheduling problem, this research defines and develops a Java™ based flight schedule generator. The robustness of the tabu search algorithms is judged by testing them using designed experiments. An integer program is developed to calculate lower bounds for the tanker crew scheduling problem objectives and to measure the overall quality of solutions produced by the developed algorithms

Operations Research for Planning and Managing City Logistics Systems

The chapter presents the Operations Research models and methods to plan and manage City Logistics systems, in particular their supply components. It presents the main planning issues and challenges, and reviews the proposed methodologies. The chapter concludes with a discussion on perspectives for City Logistics and decision-support methodological developments