Capacitated Vehicle Research Articles

Demand robust counterpart open capacitated vehicle routing problem time windows and deadline model of garbage transportation with LINGO 13.0

Demand robust counterpart-open capacitated vehicle routing problem with time windows and deadline (DRC-OCVRPtw,d) model formed and explained in this paper, is the model used to find the minimum distance and the time needed for vehicles to transport garbage in Sukarami Sub-District, Palembang that consists of the time it takes for the vehicle to pass through the route. Time needed to transport garbage to the vehicle is called time windows. Combination of the thoses times is called deadline. The farther 
 the distance passed by vehicle and the more garbage transported, the longer the deadline is needed. This DRC-OCVRPtw,d model is completed by LINGO 13.0 to obtain the optimal route and time deadline for Sukarami Sub-District. The model shows that the improved model of open vehicle routing problem involving the robustness, time windows and deadline can achieve the optimal routes that enable driver to save operational time in picking up the garbage compared to similar problem not involving no-time windows and deadline stated in previous research.

A multi-commodity two-Echelon capacitated vehicle routing problem with time windows: Model formulations and solution approach

This paper studies the multi-commodity two-echelon capacitated vehicle routing problem with time windows. Specifically, we take customer-specific origin to destination, non-substitutable demands into account. The main components are: (i) first echelon tours, (ii) second echelon tours and (iii) movement of commodities from first echelon to second echelon, considering route connection and synchronization. Exploiting the structure of the problem, we propose a decomposition scheme which decouples the first and second echelon routing problems, by deleting the third component, and re-couples them by using constraints ensuring movement of commodities between the two echelons. Based on this decomposition, we present (i) a number of model formulations for the MC-2E-VRPTW, and (ii) develop an exact solution approach for this real-life problem. A computational study on a comprehensive set of instances shows the effectiveness in terms of computational effort and solution quality.

The single-vehicle two-echelon one-commodity pickup and delivery problem

We present in this paper a generalization of the one-commodity pickup and delivery traveling salesman problem where each customer supplies or demands a given amount of a certain product. The objective is to design a minimum cost two-echelon transportation network. The first echelon is the route of a capacitated vehicle that visits some customers, and the second echelon consists in the allocation of the non-visited customers to visited ones. The customers that must be visited by the vehicle and the ones that must be allocated to others are not predefined. We present three mathematical models for the problem, design an exact branch-and-cut algorithm to solve it, and show extensive computational results on benchmark instances.

USULAN RUTE DISTRIBUSI MENGGUNAKAN ALGORITMA SWEEP DAN LOCAL SEARCH (STUDI KASUS DI PERUSAHAAN X)

A company has to deliver its product to thirty-five points/customers. In delivering process, there are limitations such as the number of vehicles, vehicle capacity, and driver's working hours. The company wants to find a better/shorter route in distributing its product to customer in order to minimize the transportation cost. The problem can considered as the Capacited Vehicle Routing Problem. In this paper, the Sweep algorithm are first used to find the initial solution. The local search procedures are used to the solution obtained by the Sweep algorithm. Four local searches are applied, 1-insertion intra-route, 1- insertion inter-route, 1-1 intra –route and 1-1 inter-route. The solutions produced by each local search are then compared, and the best one is selected. The best solution is given by the 1-Insertion intra-route procedure. It is 27,923 km shorter (15% better) than the current routes.

A dynamic decision support model for the seasonal transportation of raw milk

This paper presents a seasonal transportation of raw milk (SToRM) model. Irish raw milk collection is estimated to annually cost in excess of €80 million. Employing a capacitated vehicle routing problem (CVRP) methodology and incorporating geographic information system (GIS) data, SToRM simulates a two‐day collection schedule using the Irish road network. Differences of over 60% in total route distance required between January (trough) and May (peak) were observed. However, varied seasonal patterns did not dramatically affect overall transport needs. Results highlight the need for dynamic scheduling. SToRM provides practitioners access to a powerful model for use in milk collection scheduling.

Exact approaches for routing capacitated electric vehicles

We investigate a variant of the standard Capacitated Vehicle Routing Problem (CVRP), where each vehicle is powered exclusively by electricity stored in its rechargeable battery. Consequently, each vehicle should visit not only customer nodes but also (possibly) some charging stations before the battery got depleted. The importance of this problem stems from the fact that logistics companies are increasingly relying on electric vehicles in urban distribution. We propose three exact approaches. The first one requires solving a compact polynomial-sized formulation. The second approach is a branch-and-cut algorithm. An original feature of this algorithm is that it embeds the first exact separation of the well-known rounded capacity constraints. Finally, the third approach is a hybrid algorithm that requires solving an augmented variant of the compact formulation. We report the results of a computational study that was carried out on a set of 125 instances, providing evidence that the polynomial-sized formulation can consistently solve instances having up to 30 customer nodes and 21 charging stations, and that the hybrid algorithm solves some instances having up to 100 customer nodes and 21 charging stations while requiring moderate CPU times. Furthermore, the proposed approach was shown to exhibit limitations in solving some large-scale tightly-constrained instances.

Preemptive stacker crane problem: Extending tree-based properties and construction heuristics

The stacker crane problem (SCP) considers the cost-minimal routing of a single unit-capacity vehicle that needs to satisfy a given set of one-to-one pickup and delivery requests. In the preemptive stacker crane problem (PSCP), the vehicle is additionally allowed to temporarily drop its payload at arbitrary intermediate locations. While a payload is stored at an intermediate location, other requests may be performed. Prior work in the literature has shown that a specific tree structure is sufficient to represent optimal solutions for the PSCP. Building on this tree structure, this work establishes bounds on the benefits of preemption and additional drop locations that are neither associated with a pickup nor a delivery location, proposes reduced solution representations and describes algorithms for subproblems solvable in polynomial time. Furthermore, heuristic construction methods adapted for the PSCP from well-known heuristics for the asymmetric traveling salesman problem (ATSP) and capacitated vehicle routing problem (CVRP) are presented. The previously described and newly proposed adapted heuristics are evaluated and compared in a large scale computational study with respect to computation time, solution quality and other solution characteristics.

Solving Capacitated Vehicle Routing Problem Using Chicken Swarm Optimization with Genetic Algorithm

Solving Capacitated Vehicle Routing Problem Using Chicken Swarm Optimization with Genetic Algorithm

Tactical waste collection: column generation and mixed integer programming based heuristics

Environmental considerations and corresponding legislation cause a shift from waste management to materials management, requiring efficient collection of these flows. This paper develops a model for building tactical waste collection schemes in which a set of capacitated vehicles visits a set of customers during a given time period. Each vehicle must visit the disposal facility to discharge the waste after each customer visit. This is motivated by the fact that the waste of each customer has to be weighed at the disposal facility. The goal is to find a set of routes for each vehicle that satisfy both the demand and the frequency constraints and minimize the total cost. Since a state-of-the-art solver could not find a solution with a reasonable gap within an acceptable time limit, a column generation and a mixed integer programming-based heuristic are proposed. While the mixed integer programming-based heuristic outperforms the column generation heuristic in terms of solution quality, the lower bound provided by column generation allows to prove the small optimality gaps of the solutions obtained. Moreover, by applying both heuristics on instances derived from real-life data, they proved to be capable of finding good quality solutions in small computation times.

A Large Neighborhood Search for the Pickup and Delivery Problem with Time Windows, Split Loads and Transshipments

In the pickup and delivery problem (PDP) a fleet of capacitated vehicles must be routed in order to satisfy a set of customer requests. In this article, we address a variant of the one-to-one PDP where each customer location can be visited several times and load may be transshipped from one vehicle to another at specific locations. The goal is to minimize the sum of travel costs and transshipment costs. The corresponding problem is called the PDP with time windows, split loads and transshipments. We present an arc-based mixed-integer formulation for the problem and propose a large neighbourhood search metaheuristic for solving it. Extensive computational experiments using both benchmark instances from the literature and instances based on real-world data illustrate the performance of the solution method and give insights regarding the benefits of combining split loads and transshipments.

Solving capacitated vehicle routing problem using of Clarke and Wright algorithm and LINGO in LPG distribution

Capacitated vehicle routing problem is a vehicle routing problem that has constraints in the form of vehicle capacity. It is a matter of optimization to find the optimal route for some vehicles with a specific capacity and homogeneous vehicles that serve some agents with several known requests before the distribution process takes place. LPG distribution is the application of capacitated vehicle routing problems. This research aims to determine the LPG distribution route based on the Clarke and Wright Algorithm and LINGO. The capacitated vehicle routing problem model will be solved in two phases. The first stage completes the capacitated vehicle routing problem model using the Clarke and Wright algorithm. The second stage is completing the results of the first stage in the form of LINGO-based sub tours to obtain the optimal solution. The solution of the capacitated vehicle routing problem in distribution LPG using the Clarke and Wright algorithm has a total distance of 151.94 km. The solution of the capacitated vehicle routing problem in distribution LPG using LINGO has a total distance of 161.59 km.

The robust counterpart open capacitated vehicle routing problem with time windows on waste transport problems

The optimum route for garbage transport vehicles is restricted by vehicle capacity and time windows that the garbage transport vehicle starts at the origin and does not return to the origin. The problem of transporting waste routes is a robust optimization problem where the amount of waste in an area and travel time is uncertain. In the real world, traffic jams and vehicle engine damage can cause delays. This paper proposes the robust counterpart open capacitated vehicle routing problem (denoted by RCOCVRP) with soft time windows model. The aim of RCOCVRP with soft time windows model is to find schedule and optimum route of transporting waste. This model calculation uses LINGO software and GAMS software. Finally for the evaluation of the RCOCVRP model with soft time windows on the proposed waste transportation problem is conducted so that it hasa feasible solution.

The robust counterpart open capacitated vehicle routing problem with time windows

The problem of transporting waste vehicle routes is one of the problems faced in big cities. Delay becomes a problem in the process of transporting waste. The route of garbage vehicles motivated this research. Thus, the optimization of vehicle routes is needed to minimize the distance and travel time. We investigated two robust optimization models, which are limited by vehicle capacity and time windows. Robust counterpart open capacitated vehicle routing problems with soft time windows is the first model. This model results in the arrival time of the vehicle on each TDS and FDS that may exceed the working hours. The second model is robust counterpart open capacitated vehicle routing problems with hard time windows. This model results in the arrival time of the vehicle on each TDS and FDS not to exceed the working hours. The two robust optimization models are solved using the exact approach and the heuristic approach. Complete the exact approach using the branch and bound method with LINGO software. Completion of the heuristic approach uses the Nearest Neighbour method. The two models that are solved by the branch and bound method and the Nearest Neighbour algorithm produce the optimal solution, obtained different sub tours.

Secure and efficient routing on nodes, edges, and arcs of simple-graphs and of multi-graphs.

Many security companies offer patrolling services, such that guards inspect facilities or streets on a regular basis. Patrolling routes should be cost efficient, but the inspection patterns should not be predictable for offenders. We introduce this setting as a multi‐objective periodic mixed capacitated general routing problem with objectives being cost minimization and route inconsistency maximization. The problem is transformed into an asymmetric capacitated vehicle routing problem, on both a simple‐graph and a multi‐graph; and three multi‐objective frameworks using adaptive large neighborhood search are implemented to solve it. As tests with both artificial and real‐world instances show that some frameworks perform better for some indicators, a hybrid search procedure, combining two of them, is developed and benchmarked against the individual solution methods. Generally, results indicate that considering more than one shortest path between nodes, can significantly increase solution quality for smaller instances, but is quickly becoming a detriment for larger instances.

Optimizing nonlinear charging times of electric vehicle routing with genetic algorithm

With the rising share of electric vehicles used in the service industry, the optimization of their specific constraints is gaining importance. Lowering energy consumption, time of charging and the strain on the electric grid are just some of the issues that must be tackled, to ensure a cleaner and more efficient industry. This paper presents a Two-Layer Genetic Algorithm (TLGA) for solving the capacitated Multi-Depot Vehicle Routing Problem with Time Windows (MDVRPTW) and Electric Vehicles (EV) with partial nonlinear recharging times (NL) – E-MDVRPTW-NL. Here, the optimization goal is to minimize driving times, number of stops at electric charging stations and time of recharging while taking the nonlinear recharging times into account. This routing problem closes the gap between electric vehicle routing problem research on the one hand and its applications to several problems with numerous real-world constraints of electric vehicles on the other. Next to the definition and the formulation of the E-MDVRPTW-NL, this paper presents the evolutionary method for solving this problem using the Genetic Algorithm (GA), where a novel two-layer genotype with multiple crossover operators is considered. This allows the GA to not only solve the order of the routes but also the visits to electric charging stations and the electric battery recharging times. Various settings of the proposed method are presented, tested and compared to competing meta-heuristics using well-known benchmarks with the addition of charging stations.

The Biobjective Bike-Sharing Rebalancing Problem with Balance Intervals: A Multistart Multiobjective Particle Swarm Optimization Algorithm

The bike-sharing system (BSS), as a sustainable way to deal with the “last mile” problem of mass transit systems, is increasingly popular in recent years. Despite its success, the BSS tends to suffer from the mismatch of bike supply and user demand. BSS operators have to transfer bikes from surplus stations to deficit stations to redistribute them among stations by means of trucks. In this paper, we deal with the bike-sharing rebalancing problem with balance intervals (BRP-BIs), which is a variant of the static bike-sharing rebalancing problem. In this problem, the equilibrium of station is characterized by a balance interval instead of a balance point in the literature. We formulate the BRP-BI as a biobjective mixed-integer programming model with the aim of determining both the minimum cost route for a single capacitated vehicle and the maximum average rebalance utility, an index for the balanced degree of station. Then, a multistart multiobjective particle swarm optimization (MS-MOPSO) algorithm is proposed to solve the model such that the Pareto optimal solutions can be derived. The proposed algorithm is extended with crossover operator and variable neighbourhood search to enhance its exploratory capability. Compared with Hybrid NSGA-II and MOPSO, the computational experimental results demonstrate that our MS-MOPSO can obtain Pareto optimal solutions with higher quality.

Mathematical models for the periodic vehicle routing problem with time windows and time spread constraints

The periodic vehicle routing problem (PVRP) is an extension of the well-known vehicle routing problem. In this paper, the PVRP with time windows and time spread constraints (PVRP-TWTS) is addressed, which arises in the high-value shipment transportation area. In the PVRP-TWTS, period-specific demands of the customers must be delivered by a fleet of heterogeneous capacitated vehicles over the several planning periods. Additionally, the arrival times to a customer should be irregular within its time window over the planning periods, and the waiting time is not allowed for the vehicles due to the security concerns. This study, proposes novel mixed-integer linear programming (MILP) and constraint programming (CP) models for the PVRP-TWTS. Furthermore, we develop several valid inequalities to strengthen the proposed MILP and CP models as well as a lower bound. Even though CP has successful applications for various optimization problems, it is still not as well-known as MILP in the operations research field. This study aims to utilize the effectiveness of CP in solving the PVRP-TWTS. This study presents a CP model for PVRP-TWTS for the first time in the literature to the best of our knowledge. Having a comparison of the CP and MILP models can help in providing a baseline for the problem. We evaluate the performance of the proposed MILP and CP models by modifying the well-known benchmark set from the literature. The extensive computational results show that the CP model performs much better than the MILP model in terms of the solution quality.

A branch-price-and-cut algorithm for the capacitated multiple vehicle traveling purchaser problem with unitary demand

The multiple vehicle traveling purchaser problem (MVTPP) consists of simultaneously selecting suppliers and routing a fleet of homogeneous vehicles to purchase different products at the selected suppliers so that all product demands are fulfilled and traveling and purchasing costs are minimized. We consider variants of the MVTPP in which the capacity of the vehicles can become binding and the demand for each product is one unit. Corresponding solution algorithms from the literature are either branch-and-cut or branch-and-price algorithms, where in the latter case the route-generation subproblem is solved on an expanded graph by applying standard dynamic-programming techniques. Our branch-price-and-cut algorithm employs a novel labeling algorithm that works directly on the original network and postpones the purchasing decisions until the route has been completely defined. Moreover, we define a new branching rule generally applicable in case of unitary product demands, introduce a new family of valid inequalities to apply when suppliers can be visited at most once, and show how product incompatibilities can be handled without considering additional resources in the pricing problem. In comprehensive computational experiments with standard benchmark sets we prove that the new branch-price-and-cut approach is highly competitive.

A Simulated Annealing Algorithm for Solving Two-Echelon Vehicle Routing Problem with Locker Facilities

We consider the problem of utilizing the parcel locker network for the logistics solution in the metropolitan area. Two-echelon distribution systems are attractive from an economic standpoint, whereas the product from the depot can be distributed from or to intermediate facilities. In this case, the intermediate facilities are considered as locker facilities present in an accessible location in the vicinity of the final customers. In addition, the utilization of locker facilities can reduce the cost caused by the unattended deliveries. The problem is addressed as an optimization model that formulated into an integer linear programming model denoted as the two-echelon vehicle routing problem with locker facilities (2EVRP-LF). The objective is to minimize the cost of transportation with regards to the vehicle travelling cost, the intermediate facilities renting cost, and the additional cost to compensate the customer that needs to travel to access the intermediate facilities. Because of its complexity, a simulated annealing algorithm is proposed to solve the problem. On the other hand, the modelling approach can be conducted by generating two-phase optimization model approaches, which are the p-median problem and the capacitated vehicle routing problem. The results from both methods are compared in numerical experiments. The results show the effectiveness of 2EVRP-LF compared to the two-phase optimization. Furthermore, the simulated annealing algorithm showed an effective performance in solving 2EVRP-LF.

Approximation Algorithms for the Load-Balanced Capacitated Vehicle Routing Problem

We study the load-balanced capacitated vehicle routing problem (LBCVRP): the problem is to design a collection of tours for a fixed fleet of vehicles with capacity Q to distribute a supply from a single depot between a number of predefined clients, in a way that the total traveling cost is a minimum, and the vehicle loads are balanced. The unbalanced loads cause the decrease of distribution quality especially in business environments and flexibility in the logistics activities. The problem being NP-hard, we propose two approximation algorithms. When the demands are equal, we present a $$((1-\frac{1}{Q})\rho +\frac{3}{2})-$$ approximation algorithm that finds balanced loads. Here, $$\rho $$ is the approximation ratio for the known metric traveling salesman problem (TSP). This result leads to a $$2.5-\frac{1}{Q}$$ approximation ratio for the tree metrics since an optimal solution can be found for the TSP on a tree. We present an improved $$2-$$ approximation algorithm. When the demands are unequal, we focus on obtaining approximate solutions since finding balanced loads is NP-complete. We propose an algorithm that provides a $$4-$$ approximation for the balance of the loads. We assume a second approach to get around the difficulties of the feasibility. In this approach, we redefine and convert the problem into a multi-objective problem. The algorithm we propose has a 4 factor of approximation.