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Abstract
Apiculture has gained worldwide interest because of its contributions to economic incomes and environmental conservation. In view of these, migratory beekeeping, as a high-yielding technique, is extensively adopted. However, because of the lack of an overall routing plan, beekeepers who follow the experiential migratory routes frequently encounter unexpected detours and suffer losses when faced with problems such as those related to nectar source capacities and the production of bee products. The migratory beekeeping routing problem (MBRP) is proposed based on the practical background of the commercial apiculture industry to optimize the global revenue for beekeepers by comprehensively considering nectar source allocation, migration, production and sales of bee products, and corresponding time decisions. The MBRP is a new variant of the vehicle routing problem but with significantly different production time decisions at the vertices (i.e., nectar sources). That is, only the overlaps between residence durations and flowering periods generate production benefits. Different sales visits cause different gains from the same products; in turn, these lead to different production time decisions at previously visited nectar source locations and even change the visits for production. To overcome the difficulty resulting from the complicated time decisions, we utilize the Dantzig–Wolfe decomposition method and propose a revised labeling algorithm for the pricing subproblems. The tests, performed on instances and a real-world case, demonstrate that the column generation method with the revised labeling algorithm is efficient for solving the MBRP. Compared with traditional routes, a more efficient overall routing schedule for migratory beekeepers is proposed.
Summary of Contribution. Based on the practical background of commercial apiculture industry, this paper proposes a new type of routing problem named the migratory beekeeping routing problem (MBRP), which incorporates the selection of productive nodes and sales nodes as well as the production time decision at the productive nodes on a migratory beekeeping network. To overcome the difficulty resulting from the complicated time decisions, we utilize the Dantzig–Wolfe decomposition method and propose a revised labeling algorithm for the pricing subproblems. The tests, performed on instances and a real-world case, demonstrate that the column generation method with the revised labeling algorithm is efficient for solving the MBRP. Compared with traditional routes, a more efficient overall routing schedule for migratory beekeepers is proposed. Therefore, this paper is congruent with, and contributes to, the scope and mission of INFORMS Journal on Computing, especially the area of Network Optimization: Algorithms & Applications.
... Generating a lead in this direction, recently, Ma et al. (2020) recognized the disadvantage of arbitrary routing based on experience or intuition. These scholars emphasized the fact that dynamic variables can lead to frequent changes in route plans which may increase transportation costs as well as opportunity losses. ...
... MBRP cannot fit perfectly into traditional models of vehicle routing problem (VRP) (Ma et al., 2020). First of all, each flowering region has its unique flower species to result in a unique flowering period, which resembles a "time window" in VRP modelling. ...
... As we know, VRP and its variants are NPhard problems (Lenstra, 1981) for which heuristics and metaheuristics are more effective in solving large instances than exact algorithms (Braekers et al., 2016). When contrasting this logic with that of Ma et al. (2020), these scholars generate a vital initiating solution framework of MBRP based on exact algorithms. Thus, in this paper, we intend to complement their leads by formulating a metaheuristic driven MBRP. ...
Commercial beekeeping is an emerging business segment which not only generates income, but also contributes to the conservation of biodiversity. In practice, complex decision optimization issues prevailing in beekeeping requires attention to help this business flourish and improve its profitability. Migratory beekeeping is an important initiative in this regard for the continued movement of bee colonies to different locations for beekeeping production. In this article, a migratory beekeeping routing problem (MBRP) which is considered as a variant of the VRP, and considers mainly homogeneous beekeepers, restricted flowering periods at flowering regions, environment maximum capacity of flowering regions, multiple home region and flexible terminal region, as well as selection of best markets for honey produced in different floral regions is studied. We propose a variable neighborhood search (VNS) algorithm to solve the MBRP and apply thirty computational instances to test it. The results indicate the feasibility and efficiency of the VNS algorithm to achieve acceptably good near-optimal solutions while reducing computation time when compared to the exact algorithms in the existing paper. The performance of the proposed VNS is also compared with the ant colony system (ACS) based metaheuristics. We also provide cost–benefit analyses on maintaining the biological balance and extending the flowering period to get extensive information on the issue. Practically, the outcome of this paper can help commercial apiculture organizations to change outdated beekeeping production and operation methods, thus enhancing the production efficiency and reducing costs.
... Local beekeeping and migratory beekeeping are two main modes of the apiculture industry globally. This work primarily focuses on migratory beekeeping since it can improve beekeepers' benefits by moving the bee colonies to appropriate places with ample floral resources at the right time to harvest throughout the production year, compared to local beekeeping (Kumsa et al., 2020;Ma et al., 2021). The migratory beekeeping practice has proven that its profitability in the annual production depends on the migratory routes. ...
... As the recommendation system matures, it has been frequently applied in the transportation and tourism industries to recommend cruising routes and travel itineraries for vacant taxis and tourists. As for the previously studied migratory beekeeping routing problem (MBRP), the beekeepers gain profits by migrating bee colonies to the selected locations with abundant floral resources for effective production, where both the migratory route and production time are crucial elements (Ma et al., 2021). Nevertheless, it is still challenging for an individual beekeeper to optimize the migratory route and the corresponding production time on nectar sources based on the massive spatio-temporal information (e.g., nectar resource location, flowering period, honey yield, etc.) and the fluctuating market prices of bee products. ...
... The migratory beekeeping routing problem (MBRP) was first proposed by Ma et al. (2021), which optimizes the productive migration route and time decisions for multiple groups of beekeepers, including nectar sources assignment, migratory routes planning, production time arrangement, and sales markets selection. An exact algorithm involving Dantzig-Wolfe decomposition, column generation, and a revised labeling algorithm was presented to solve the MBRP efficiently. ...
Due to the lack of scientific guidance, most migratory beekeepers currently arrange their migratory beekeeping routes by experience. The production mode is extensive, and the quality and efficiency need to be improved. Therefore, this study investigates a dynamic migratory route recommendation problem considering the stochastic yield of nectar sources and uncertain disastrous weather events, by which the beekeeper can dynamically follow the practical and effective recommended route to cope with production risk to reach a better revenue. To this end, the problem is first formulated as a Markov decision process considering various flowering durations of nectar sources, migration costs and time, the prices of bee products, and, most importantly, uncertain yields. Then, an approximate dynamic programming algorithm incorporated with offline and online learning procedures is proposed to deal with the curse of dimensionality. Several acceleration methods are also provided to solve the problem more efficiently. The conducted numerical study shows that the proposed model and algorithm perform well in approximation precise and computational efficiency. Finally, the computational results show that the proposed migratory beekeeping route recommendation method effectively deals with yield uncertainty and significantly improves the migratory beekeeping revenue.
... In many countries, for example, in the USA (Rucker and Thurman, 2019), Indonesia (Gratzer et al., 2019), Ethiopia (Kumsa et al., 2020), Turkey (Özkirim, 2018), migratory beekeeping is very common, and beekeepers are forced to change the apiary location often to provide food sources for their bees to increase the production rate. Apiculture has gained worldwide interest because of its contribution to economic incomes (Popescu and Popescu, 2019), sustainable environmental conservation (Kass Degu and Regasa Megerssa, 2020;Mudzengi et al., 2020) and, in view of this, migratory beekeeping, as a high-yielding technique, is applied extensively (Ma et al., 2021). Therefore, to make modern beekeeping more profitable and sustainable, migratory apiary management is an important option, not only to enhance overall honey yield, but also to reduce supplementary feeding costs of the colony during food resources scarcity periods. ...
To perform transition to circular economy, firms must engage in application of new efficient ways to improve the product life cycle. Our study focuses on identifying bibliometric and thematic trends to bring inferential clarity about “Product life cycle in Circular Economy.” We have used literature of 266 studies from Scopus database and performed Descriptive Analysis to identify themes. Our results show bibliometric networks based on Country, Keywords, Citations, & Impact Factors. It gives inference about research trends in extensive literature of 15 years. Implications of study show research gaps in literature and gives future direction based on identified trends.
This paper discusses the biological features of growing bee and drone broods of the Far Eastern honey bee. The development of bee individuals has two peak values, the first before the main honey harvest from linden - 230.1 squares and the second at the end of August during the period of building up the winter generation - 236.4 squares. The drone brood is reared simultaneously with the bee brood and reaches a maximum of 24.1 squares in mid-June and 20.5 squares in early August. During the July honey harvest, the minimum amount of brood is raised - 54.2 squares of bees and 1.3 squares of drones. This is due to the fact that the bees begin to limit the egg production of the queen bee by filling free cells with honey, thereby freeing the nurse bees from brood feeding and switching them to the preparation of nectar.
The Electric Vehicle Routing Problem with Time Windows (EVRPTW) is an extension to the well-known Vehicle Routing Problem with Time Windows (VRPTW) where the fleet consists of electric vehicles (EVs). Since EVs have limited driving range due to their battery capacities they may need to visit recharging stations while servicing the customers along their route. The recharging may take place at any battery level and after the recharging the battery is assumed to be full. In this paper, we relax the full recharge restriction and allow partial recharging (EVRPTW-PR), which is more practical in the real world due to shorter recharging duration. We formulate this problem as a 0–1 mixed integer linear program and develop an Adaptive Large Neighborhood Search (ALNS) algorithm to solve it efficiently. We apply several removal and insertion mechanisms by selecting them dynamically and adaptively based on their past performances, including new mechanisms specifically designed for EVRPTW and EVRPTW-PR. These new mechanisms include the removal of the stations independently or along with the preceding or succeeding customers and the insertion of the stations with determining the charge amount based on the recharging decisions. We test the performance of ALNS by using benchmark instances from the recent literature. The computational results show that the proposed method is effective in finding high quality solutions and the partial recharging option may significantly improve the routing decisions.
Abstract The aim of this paper is to propose an algorithm based on the philosophy of the Variable Neighborhood Search (VNS) to solve Multi Depot Vehicle Routing Problems with Time Windows. The paper has two main contributions. First, from a technical point of view, it presents the first application of a VNS for this problem and several design issues of VNS algorithms are discussed. Second, from a problem oriented point of view the computational results show that the approach is competitive with an existing Tabu Search algorithm with respect to both solution quality and computation times. Ke yW ords: Metaheuristic, Variable Neighborhood Search, VNS, Multi Depot Vehicle Routing Problem with
Abstract This paper addresses the split delivery vehicle routing problem with time windows (sdvrptw) that consists of determining least-cost vehicle routes to service a set of cus- tomer demands,while respecting vehicle capacity and customer time windows. The de- mand of each customer can be fulfilled by several vehicles. For solving this problem, we propose a new exact branch-and-price-and-cut method, where the column generation subproblem is a resource-constrained elementary shortest path problem combined with the linear relaxation of a bounded,knapsack problem. Each generated column is asso- ciated with a feasible route and a compatible delivery pattern. As opposed to existing branch-and-price methods for the sdvrptw or its variant without time windows, integral- ity requirements in the integer master problem are not imposed on the variables generated dynamically, but rather on additional variables. An ad hoc label-setting algorithm is de-
We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branchand -bound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. We then discuss computational issues and implementation of column generation, branch-andbound algorithms, including special branching rules and efficient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality. February 1994 Revised May 1995 Revised January 1996 01 Currently at MIT 02 Currently at Auburn University 0 This research has been supported by the following This research has been supported by the following grants and contracts: NSF SES-91-22674, NSF and AFORS DDM-9115768, NSF DDM-9058074, NSF DMI-9410102, and IBM MHV2379. 0y An abbreviat...
While the joint optimization of production and outbound distribution decisions in a manufacturing context have been intensively studied in the past decade, the integration of production, inventory, and inbound transportation from suppliers have received much less attention despite its practical relevance. This paper aims to fill the gap by introducing a general model for the assembly routing problem (ARP), which consists of simultaneously planning the assembly of a finished product at a plant and the routing of vehicles collecting materials from suppliers to meet the inventory requirements imposed by the production. We formulate the problem as a mixed-integer linear program and we propose a three-phase decomposition matheuristic that relies on the iterative solution of different subproblems. The first phase determines a setup schedule while the second phase optimizes production quantities, supplier visit schedules and shipment quantities. The third phase solves a vehicle routing problem for each period in the planning horizon. The algorithm is flexible, and we show how it can also be used to solve two well-known outbound distribution problems related to the ARP: the production routing problem and the inventory routing problem. Using the same parameter setting for all problems and instances, we obtain 781 new best-known solutions out of 2,628 standard IRP and PRP test instances. In particular, on large-scale multivehicle instances, the new algorithm outperforms specialized state-of-the-art heuristics for these two problems.
The online appendix is available at https://doi.org/10.1287/ijoc.2018.0817 .
The vehicle routing problem with time windows (VRPTW) consists of finding least-cost vehicle routes to satisfy the demands of customers that can be visited within specific time windows.We introduce two enhancements for the exact solution of the VRPTW by branch-price-and-cut (BPC). First, we develop a sharper form of the limited-memory subset-row inequalities by representing the memory as an arc subset rather than a node subset. Second, from the elementary inequalities introduced by Balas in 1977, we derive a family of inequalities that dominate them. These enhancements are embedded into an exact BPC algorithm that includes state-of-the-art features such as bidirectional labeling, decremental state-space relaxation, completion bounds, variable fixing, and route enumeration. Computational results show that these enhancements are particularly effective for the most difficult instances and that our BPC algorithm can solve all 56 Solomon instances with 100 customers and 51 of 60 Gehring and Homberger instances with 200 customers.
This paper develops a framework and solution methodology for optimizing the integration of production, inventory, and distribution for supplying retail demand locations from a production facility. Two mathematical programming-based heuristics are developed which use a relaxed mixed integer model to determine an initial solution. One approach uses set partitioning and another approach employs the concept of seed routes to determine an approximate solution and a vehicle routing metaheuristic is used to sequence routes for each time period in the planning horizon. A multi-iteration improvement procedure determines the final solution. The proposed multi-phase approach achieves many new best known solutions to test problems for this challenging supply chain optimization problem. Additionally, experiments are conducted to assess the inclusion of fixed vehicle costs and the impact on fleet size and solution quality.
We study the vehicle routing problem with roaming delivery locations in which the goal is to find a least-cost set of delivery routes for a fleet of capacitated vehicles and in which a customer order has to be delivered to the trunk of the customer’s car during the time that the car is parked at one of the locations in the (known) customer’s travel itinerary. We formulate the problem as a set-covering problem and develop a branch-and-price algorithm for its solution. The algorithm can also be used for solving a more general variant in which a hybrid delivery strategy is considered that allows a delivery to either a customer’s home or to the trunk of the customer’s car. We evaluate the effectiveness of the many algorithmic features incorporated in the algorithm in an extensive computational study and analyze the benefits of these innovative delivery strategies. The computational results show that employing the hybrid delivery strategy results in average cost savings of nearly 20% for the instances in our test set.
Diversity of geographical features particularly in the tropics and subtropics plays a key role in determining the topography, climate, and plant species of the region. Such regions provide abundant opportunities for both migratory and non migratory beekeeping. Current agricultural transformation, once linked to apicultural operations, offers much scope for income generation from beekeeping. Till now only 10 % of the existing potential has been utilized. For instance, India has a potential to keep about 120 million bee colonies that can provide self-employment to over 6 million rural and tribal families. In terms of production, these bee colonies can produce over 1.2 million tonnes of honey and about 15,000 tonnes of beeswax. Organized collection of forest honey and beeswax using improved methods can result in an additional production of at least 120,000 tonnes and 10,000 tonnes of honey and beeswax, respectively. Thus, it is expected to generate income of worth satisfying needs of five million tribal families. The present global status as well as future strategies for conservation of beekeeping is discussed in detail.
Effective route planning for battery electric commercial vehicle (ECV) fleets has to take into account their limited autonomy and the possibility of visiting recharging stations during the course of a route. In this paper, we consider four variants of the electric vehicle-routing problem with time windows: (i) at most a single recharge per route is allowed, and batteries are fully recharged on visit of a recharging station; (ii) multiple recharges per route, full recharges only; (iii) at most a single recharge per route, and partial battery recharges are possible; and (iv) multiple, partial recharges. For each variant, we present exact branch-price-and-cut algorithms that rely on customized monodirectional and bidirectional labeling algorithms for generating feasible vehicle routes. In computational studies, we find that all four variants are solvable for instances with up to 100 customers and 21 recharging stations. This success can be attributed to the tailored resource extension functions (REFs) that enable efficient labeling with constant time feasibility checking and strong dominance rules, even if these REFs are intricate and rather elaborate to derive. The studies also highlight the superiority of the bidirectional labeling algorithms compared to the monodirectional ones. Finally, we find that allowing multiple as well as partial recharges both help to reduce routing costs and the number of employed vehicles in comparison to the variants with single and with full recharges.
We investigate the exact solution of the vehicle routing problem with time windows, where multiple trips are allowed for the vehicles. In contrast to previous works in the literature, we specifically consider the case in which it is mandatory to visit all customers and there is no limitation on duration. We develop two branch-and-price frameworks based on two set covering formulations: a traditional one where columns (variables) represent routes, that is, a sequence of consecutive trips, and a second one in which columns are single trips. One important difficulty related to the latter is the way mutual temporal exclusion of trips can be handled. It raises the issue of time discretization when solving the pricing problem. Our dynamic programming algorithm is based on concept of groups of labels and representative labels. We provide computational results on modified small-sized instances (25 customers) from Solomon's benchmarks in order to evaluate and compare the two methods. Results show that some difficult instances are out of reach for the first branch-and-price implementation, while they are consistently solved with the second. © 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS).
In this paper, we consider a multi-attribute vehicle routing problem derived from a real-life milk collection system. This problem is characterized by the presence of a heterogeneous fleet of vehicles, multiple depots, and several resource constraints. A branch-and-price methodology is proposed to tackle the problem. In this methodology, different branching strategies, adapted to the special structure of the problem, are implemented and compared. The computational results show that the branch-and-price algorithm performs well in terms of solution quality and computational efficiency.
This paper proposes a column generation algorithm for the multidepot vehicle routing problem with interdepot routes. This problem is an extension of the multidepot vehicle routing problem in which the vehicles are allowed to stop at intermediate depots along their routes to replenish. The problem can be modeled as a set covering problem in which the variables are rotations corresponding to feasible combinations of routes. We consider two pricing subproblems to generate rotations. The first one generates rotations directly by solving an elementary shortest path problem with resource constraints on a modified version of the original customer-depot network. The second one exploits the relationship between the sets of routes and rotations but results in a model with many columns. We discuss some issues related to solving this second pricing subproblem by column generation and we introduce an alternate approach to alleviate these difficulties. We show through computational experiments that the second pricing mechanism performs better than the first to compute the linear programming relaxation lower bound. We then embed it within a branch-and-bound algorithm to compute optimal integer solutions. Moreover, we assess the benefits of allowing interdepot routes in multidepot vehicle routing.
Driven by new laws and regulations concerning the emission of greenhouse gases, carriers are starting to use electric vehicles for last-mile deliveries. The limited battery capacities of these vehicles necessitate visits to recharging stations during delivery tours of industry-typical length, which have to be considered in the route planning to avoid inefficient vehicle routes with long detours. We introduce the electric vehicle-routing problem with time windows and recharging stations (E-VRPTW), which incorporates the possibility of recharging at any of the available stations using an appropriate recharging scheme. Furthermore, we consider limited vehicle freight capacities as well as customer time windows, which are the most important constraints in real-world logistics applications. As a solution method, we present a hybrid heuristic that combines a variable neighborhood search algorithm with a tabu search heuristic. Tests performed on newly designed instances for the E-VRPTW as well as on benchmark
The inventory-routing problem (IRP) dates back 30 years. It can be described as the combination of vehicle-routing and inventory management problems, in which a supplier has to deliver products to a number of geographically dispersed customers, subject to side constraints. It provides integrated logistics solutions by simultaneously optimizing inventory management, vehicle routing, and delivery scheduling. Some exact algorithms and several powerful metaheuristic and matheuristic approaches have been developed for this class of problems, especially in recent years. The purpose of this article is to provide a comprehensive review of this literature, based on a new classification of the problem. We categorize IRPs with respect to their structural variants and the availability of information on customer demand.
The Vehicle Routing Problem with Simultaneous Pickup and Delivery with Time Limit (VRPSPDTL) is a variant of the basic Vehicle Routing Problem where the vehicles serve delivery as well as pick up operations of the clients under time limit restrictions. The VRPSPDTL determines a set of vehicle routes originating and terminating at a central depot such that the total travel distance is minimized. For this problem, we propose a mixed-integer mathematical optimization model and a perturbation based neighborhood search algorithm combined with the classic savings heuristic, variable neighborhood search and a perturbation mechanism. The numerical results show that the proposed method produces superior solutions for a number of well-known benchmark problems compared to those reported in the literature and reasonably good solutions for the remaining test problems.
This paper presents several heuristics for a variation of the vehicle routing problem in which the transportation fleet is composed of electric vehicles with limited autonomy in need for recharge during their duties. In addition to the routing plan, the amount of energy recharged and the technology used must also be determined. Constructive and local search heuristics are proposed, which are exploited within a non deterministic Simulated Annealing framework. Extensive computational results on varying instances are reported, evaluating the performance of the proposed algorithms and analyzing the distinctive elements of the problem (size, geographical configuration, recharge stations, autonomy, technologies, etc.).
A technique is presented for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs representing its several parts and a coordinating program that is obtained from the parts by linear transformations. The coordinating program generates at each cycle new objective forms for each part, and each part generates in turn (from its optimal basic feasible solutions) new activities (columns) for the interconnecting program. Viewed as an instance of a “generalized programming problem” whose columns are drawn freely from given convex sets, such a problem can be studied by an appropriate generalization of the duality theorem for linear programming, which permits a sharp distinction to be made between those constraints that pertain only to a part of the problem and those that connect its parts. This leads to a generalization of the Simplex Algorithm, for which the decomposition procedure becomes a special case. Besides holding promise for the efficient computation of large-scale systems, the principle yields a certain rationale for the “decentralized decision process” in the theory of the firm. Formally the prices generated by the coordinating program cause the manager of each part to look for a “pure” sub-program analogue of pure strategy in game theory, which he proposes to the coordinator as best he can do. The coordinator finds the optimum “mix” of pure sub-programs (using new proposals and earlier ones) consistent with over-all demands and supply, and thereby generates new prices that again generates new proposals by each of the parts, etc. The iterative process is finite.
This paper presents a unified tabu search heuristic for the vehicle routing problem with time windows and for two important generalizations: the periodic and the multi-depot vehicle routing problems with time windows. The major benefits of the approach are its speed, simplicity and flexibility. The performance of the heuristic is assessed by comparing it to alternative methods on benchmark instances of the vehicle routing problem with time windows. Computational experiments are also reported on new randomly generated instances for each of the two generalizations.
This paper is concerned with the development of an algorithm for general bilinear programming problems. Such problems find numerous applications in economics and game theory, location theory, nonlinear multi-commodity network flows, dynamic assignment and production, and various risk management problems. The proposed approach develops a new Reformulation-Linearization Technique (RLT) for this problem, and imbeds it within a provably convergent branch-and-bound algorithm. The method first reformulates the problem by constructing a set of nonnegative variable factors using the problem constraints, and suitably multiplies combinations of these factors with the original problem constraints to generate additional valid nonlinear constraints. The resulting nonlinear program is subsequently linearized by defining a new set of variables, one for each nonlinear term. This RLT process yields a linear programming problem whose optimal value provides a tight lower bound on the optimal value to the bilinear programming problem. Various implementation schemes and constraint generation procedures are investigated for the purpose of further tightening the resulting linearization. The lower bound thus produced theoretically dominates, and practically is far tighter, than that obtained by using convex envelopes over hyper-rectangles. In fact, for some special cases, this process is shown to yield an exact linear programming representation. For the associated branch-and-bound algorithm, various admissible branching schemes are discussed, including one in which branching is performed by partitioning the intervals for only one set of variables x or y, whichever are fewer in number. Computational experience is provided to demonstrate the viability of the algorithm. For a large number of test problems from the literature, the initial bounding linear program itself solves the underlying bilinear programming problem.
A personalised electronic tourist guide assists tourists in planning and enjoying their trip. The planning problem that needs to be solved, in real-time, can be modelled as a team orienteering problem with time windows (TOPTW). In the TOPTW, a set of locations is given, each with a score, a service time and a time window. The goal is to maximise the sum of the collected scores by a fixed number of routes. The routes allow to visit locations at the right time and they are limited in length. The main contribution of this paper is a simple, fast and effective iterated local search meta-heuristic to solve the TOPTW. An insert step is combined with a shake step to escape from local optima. The specific shake step implementation and the fast evaluation of possible improvements, produces a heuristic that performs very well on a large and diverse set of instances. The average gap between the obtained results and the best-known solutions is only 1.8% and the average computation time is decreased with a factor of several hundreds. For 31 instances, new best solutions are computed.
In the team orienteering problem, start and end points are specified along with other locations which have associated scores. Given a fixed amount of time for each of the M members of the team, the goal is to determine M paths from the start point to the end point through a subset of locations in order to maximize the total score. In this paper, a fast and effective heuristic is presented and tested on 353 problems ranging in size from 21 to 102 points. The computational results are presented in detail.
We present a unified heuristic which is able to solve five different variants of the vehicle routing problem: the vehicle routing problem with time windows (VRPTW), the capacitated vehicle routing problem (CVRP), the multi-depot vehicle routing problem (MDVRP), the site-dependent vehicle routing problem (SDVRP) and the open vehicle routing problem (OVRP).All problem variants are transformed into a rich pickup and delivery model and solved using the adaptive large neighborhood search (ALNS) framework presented in Ropke and Pisinger [An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation Science, to appear]. The ALNS framework is an extension of the large neighborhood search framework by Shaw [Using constraint programming and local search methods to solve vehicle routing problems. In: CP-98, Fourth international conference on principles and practice of constraint programming, Lecture notes in computer science, vol. 1520, 1998. p. 417–31] with an adaptive layer. This layer adaptively chooses among a number of insertion and removal heuristics to intensify and diversify the search. The presented approach has a number of advantages: it provides solutions of very high quality, the algorithm is robust, and to some extent self-calibrating. Moreover, the unified model allows the dispatcher to mix various variants of VRP problems for individual customers or vehicles.As we believe that the ALNS framework can be applied to a large number of tightly constrained optimization problems, a general description of the framework is given, and it is discussed how the various components can be designed in a particular setting.The paper is concluded with a computational study, in which the five different variants of the vehicle routing problem are considered on standard benchmark tests from the literature. The outcome of the tests is promising as the algorithm is able to improve 183 best known solutions out of 486 benchmark tests. The heuristic has also shown promising results for a large class of vehicle routing problems with backhauls as demonstrated in Ropke and Pisinger [A unified heuristic for a large class of vehicle routing problems with backhauls. European Journal of Operational Research, 2004, to appear].
This article addresses an extension of the multi-depot vehicle routing problem in which vehicles may be replenished at intermediate depots along their route. It proposes a heuristic combining the adaptative memory principle, a tabu search method for the solution of subproblems, and integer programming. Tests are conducted on randomly generated instances.
This paper is a survey of the literature on applications of evolutionary algorithms for vehicle routing problems. It reports on genetic algorithms, evolution strategies, and particle swarm optimization when applied to the classical capacitated vehicle routing problem and many of its variants. The performance of evolutionary algorithms is also compared with the best alternative problem-solving approaches on benchmark instances.
The multiple tour maximum collection problem (MTMCP) consists of determining the m optimal time constrained tours which visit a subset of weighted nodes in a graph such that the total weight collected from the subset of nodes is maximized. In this paper, a heuristic for the MTMCP is developed. The results of computational testing reveal that the heuristic has three very attractive features. First, the heuristic will always produce a feasible solution if one exists. Second, the heuristic produces very good solutions. In most cases where the exact solution is known, it produces the optimal solution. And finally, the heuristic has the ability to handle large problems in a very short amount of computation time.
In this article, we propose a solution procedure for the Elementary Shortest Path Problem with Resource Constraints (ESPPRC). A relaxed version of this problem in which the path does not have to be elementary has been the backbone of a number of solution procedures based on column generation for several important problems, such as vehicle routing and crew pairing. In many cases relaxing the restriction of an elementary path resulted in optimal solutions in a reasonable computation time. However, for a number of other problems, the elementary path restriction has too much impact on the solution to be relaxed or might even be necessary. We propose an exact solution procedure for the ESPPRC, which extends the classical label correcting algorithm originally developed for the relaxed (nonelementary) path version of this problem. We present computational experiments of this algorithm for our specific problem and embedded in a column generation scheme for the classical Vehicle Routing Problem with Time Windows. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(3), 216–229 2004
The paper is concerned with the optimum routing of a fleet of gasoline delivery trucks between a bulk terminal and a large number of service stations supplied by the terminal. The shortest routes between any two points in the system are given and a demand for one or several products is specified for a number of stations within the distribution system. It is desired to find a way to assign stations to trucks in such a manner that station demands are satisfied and total mileage covered by the fleet is a minimum A procedure based on a linear programming formulation is given for obtaining a near optimal solution. The calculations may be readily performed by hand or by an automatic digital computing machine. No practical applications of the method have been made as yet. A number of trial problems have been calculated, however.