The Multi Trip Vehicle Routing Problem with Time Windows and Release Dates

International audienceIn this paper the Multi Trip Vehicle Routing Problem with Time Windows and Release Dates is introduced. The problem is particularly interesting in the City Logistics context, where trucks deliver merchandise to depots located in the outskirts of the city. Goods continuously arrive during the day becoming available for final distribution after the working day has started. This introduces the concept of release dates associated with merchandise. In this paper, a set of instances is introduced and a hybrid genetic algorithm is proposed to solve the problem

The Multi Trip Vehicle Routing Problem with Time Windows and Release Dates

The Multi-Trip Vehicle Routing Problem with Time Windows and Release Dates is a variant of the Multi-Trip Vehicle Routing Problem where a time windows is associated with each customer and a release date is associated with each merchandise to be delivered at a certain client. The release date represents the moment the merchandise becomes available at the depot for final delivery. The problem is relevant in city logistics context, where delivery systems based on city distribution centers (CDC) are studied. Trucks arrive at the CDC during the whole working day to deliver goods that are transferred to eco-friendly vehicles in charge of accomplish final deliveries to customers. We propose a population-based algorithm for the problem based on giant tour representation of the chromosomes as well as a split procedure to obtain solutions from individuals

An exact solution framework for multitrip vehicle-routing problems with time windows

Multitrip vehicle-routing problems (MTVRPs) generalize the well-known VRP by allowing vehicles to perform multiple trips per day. MTVRPs have received a lot of attention lately because of their relevance in real-life applications - for example, in city logistics and last-mile delivery. Several variants of the MTVRP have been investigated in the literature, and a number of exact methods have been proposed. Nevertheless, the computational results currently available suggest that MTVRPs with different side constraints require ad hoc formulations and solution methods to be solved. Moreover, solving instances with just 25 customers can be out of reach for such solution methods. In this paper, we proposed an exact solution framework to address four different MTVRPs proposed in the literature. The exact solution framework is based on a novel formulation that has an exponential number of variables and constraints. It relies on column generation, column enumeration, and cutting plane. We show that this solution framework can solve instances with up to 50 customers of four MTVRP variants and outperforms the state-of-the-art methods from the literature

Solving the Traveling Salesman Problem with release dates via branch and cut

In this paper we study the Traveling Salesman Problem with release dates (TSP-rd) and completion time minimization. The TSP-rd considers a single vehicle and a set of customers that must be served exactly once with goods that arrive to the depot over time, during the planning horizon. The time at which each requested good arrives is called release date and it is known in advance. The vehicle can perform multiple routes, however, it cannot depart to serve a customer before the associated release date. Thus, the release date of the customers in each route must not be greater than the starting time of the route. The objective is to determine a set of routes for the vehicle, starting and ending at the depot, where the completion time needed to serve all customers is minimized. We propose a new Integer Linear Programming model and develop a branch and cut algorithm with tailored enhancements to improve its performance. The algorithm proved to be able to significantly reduce the computation times when compared to a compact formulation tackled using a commercial mathematical programming solver, obtaining 24 new optimal solutions on benchmark instances with up to 30 customers within one hour. We further extend the benchmark to instances with up to 50 customers where the algorithm proved to be efficient. Building upon these results, the proposed model is adapted to new TSP-rd variants (Capacitated and Prize-Collecting TSP), with different objectives: completion time minimization and traveling distance minimization. To the best of our knowledge, our work is the first in-depth study to report extensive results for the TSP-rd through a branch and cut, establishing a baseline and providing insights for future approaches. Overall, the approach proved to be very effective and gives a flexible framework for several variants, opening the discussion about formulations, algorithms and new benchmark instances

Reinforcement Learning Approaches for the Orienteering Problem with Stochastic and Dynamic Release Dates

In this paper, we study a sequential decision making problem faced by e-commerce carriers related to when to send out a vehicle from the central depot to serve customer requests, and in which order to provide the service, under the assumption that the time at which parcels arrive at the depot is stochastic and dynamic. The objective is to maximize the number of parcels that can be delivered during the service hours. We propose two reinforcement learning approaches for solving this problem, one based on a policy function approximation (PFA) and the second on a value function approximation (VFA). Both methods are combined with a look-ahead strategy, in which future release dates are sampled in a Monte-Carlo fashion and a tailored batch approach is used to approximate the value of future states. Our PFA and VFA make a good use of branch-and-cut-based exact methods to improve the quality of decisions. We also establish sufficient conditions for partial characterization of optimal policy and integrate them into PFA/VFA. In an empirical study based on 720 benchmark instances, we conduct a competitive analysis using upper bounds with perfect information and we show that PFA and VFA greatly outperform two alternative myopic approaches. Overall, PFA provides best solutions, while VFA (which benefits from a two-stage stochastic optimization model) achieves a better tradeoff between solution quality and computing time

Pemecahan Masalah Rute Kendaraan Dengan Trip Majemuk, Jendela Waktu Dan Pengantaran-penjemputan Simultan Menggunakan Algortima Genetika

Vehicle routing problem (VRP) is one of decision problems having an important role in transportation and distribution activity in the logistic management. The VRP deals with determining vehicle routes that minimizes total distance by satisfying the following constraints: (1) each route starts and ends at the depot, (2) each vehicle serves only one route, (3) each costumer is served by one route, (4) all customers must be served, and (5) total load for each route does not exceed the vehicle capacity. In literature, this definition is the definition for the basic or classical VRP. This paper discusses an extension of the basic VRP including the following characteristics: (1)multiple trips (MT), (2) time windows (TW), and (3) simultaneous pickup-delivery (SPD). A solution method based on genetic algorithm (GA) is proposed to solve the VRP discussed in this papaer. The proposed GA is examined using some hypothetical instances

Optimization of a city logistics transportation system with mixed passengers and goods

International audienceIn this paper, we propose a mathematical model and an adaptive large neighborhood search to solve a two{tiered transportation problem arising in the distribution of goods in congested city cores. In the rst tier, goods are transported in city buses from a consolidation and distribution center to a set of bus stops. The main idea is to use the buses spare capacity to drive the goods in the city core. In the second tier, nal customers are distributed by a eet of near{zero emissions city freighters. This system requires transferring the goods from buses to city freighters at the bus stops. We model the corresponding optimization problem as a variant of the pickup and delivery problem with transfers and solve it with an adaptive large neighborhood search. To evaluate its results, lower bounds are calculated with a column generation approach. The algorithm is assessed on data sets derived from a eld study in the medium-sized city of La Rochelle in France

Optimizing multiple truck trips in a cooperative environment through MILP and Game Theory

Today, the challenge of economy regarding freight transport is to generate flows of goods extremely fast, handling information in short times, optimizing decisions, and reducing the percentage of vehicles that circulate empty over the total amount of transportation means, with benefits to roads congestion and the environment, besides economy. Logistic operators need to pose attention on suitable planning methods in order to reduce their costs, fuel consumption and emissions, as well as to gain economy of scale. To ensure the maximum efficacy, planning should be also based on cooperation between the involved subjects. Collaboration in logistics is an effective approach for business to obtain a competitive edge. In a successful collaboration, parties involved from suppliers, customers, and even competitors perform a coordinated effort to realize the potential benefit of collaboration, including reduced costs, decreased lead times, and improved asset utilization and service level. In addition to these benefit, having a broader supply chain perspective enables firms to make better-informed decisions on strategic issues. The first aim of the present Thesis is to propose a planning approach based on mathematical programming techniques to improve the efficiency of road services of a single carrier combining multiple trips in a port environment (specifically, import, export and inland trips). In this way, in the same route, more than two transportation services can be realized with the same vehicle thus significantly reducing the number of total empty movements. Time windows constraints related to companies and terminal opening hours as well as to ship departures are considered in the problem formulation. Moreover, driving hours restrictions and trips deadlines are taken into account, together with goods compatibility for matching different trips. The second goal of the Thesis is to define innovative planning methods and optimization schemes of logistic networks in which several carriers are present and the decisional actors operate in a cooperative scenario in which they share a portion of their demand. The proposed approaches are characterized by the adoption both of Game Theory methods and of new original methods of profits distribution

Two is better than one? Order aggregation in a meal delivery scheduling problem

We address a single-machine scheduling problem motivated by a last-mile-delivery setting for a food company. Customers place orders, each characterized by a delivery point (customer location) and an ideal delivery time. An order is considered on time if it is delivered to the customer within a time window given by the ideal delivery time , where is the same for all orders. A single courier (machine) is in charge of delivery to all customers. Orders are either delivered individually, or two orders can be aggregated in a single courier trip. All trips start and end at the restaurant, so no routing decisions are needed. The problem is to schedule courier trips so that the number of late orders is minimum. We show that the problem with order aggregation is -hard and propose a combinatorial branch and bound algorithm for its solution. The algorithm performance is assessed through a computational study on instances derived by a real-life application and on randomly generated instances. The behavior of the combinatorial algorithm is compared with that of the best ILP formulation known for the problem. Through another set of computational experiments, we also show that an appropriate choice of design parameters allows to apply the algorithm to a dynamic context, with orders arriving over time