Pickup Tours Research Articles

LPPCM: A Low-Cost Package Pickup Covering Mechanism for Cooperative Express Services

With the swift development of express delivery industry, the increasingly attention has been shifted to express delivery mechanism design. Generally, the revenue of the courier is the difference between the users' express fee and the courier's pickup cost. In order to improve the revenue of courier without increasing the user's express fee, this paper presents a low-cost package pickup covering system to find an optimal Hamiltonian pickup tour for the courier over a subset of packages, where packages who are not on the tour should be covered exactly by one package on the tour. A billing rule discounting the express fee to incentivize users to deliver their packages is also proposed. We formulate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Low-cost Package Pickup Covering (LPPC)</i> problem to maximize the revenue of the courier. Considering the complexity of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LPPC</i> , we propose a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Low-cost Package Pickup Covering Mechanism (LPPCM)</i> to solve the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LPPC</i> problem including problem transformation, hardness analyzing, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Attention Model based on Encoder-Decoder Architecture (AMEDA)</i> model design and model training. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AMEDA</i> is trained by a deep reinforcement learning algorithm in an unsupervised manner and it can directly output the solution based on the given instances. Through extensive simulations, we demonstrate that the average revenue of courier for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AMEDA</i> is at least 10.1% higher than the traditional heuristic local search and is 18.5% lower than the optimal solution on average. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AMEDA</i> provides a desired trade-off between the execution time and solution quality, which is well suited for the large-scale tasks which require quick decisions.

The consistent electric-Vehicle routing problem with backhauls and charging management

We consider a consistent vehicle routing problem for the delivery of parcels with electric vehicles. Stemming from a real-world problem, we assume that vehicles can only be charged with electricity between their delivery tours in the morning and their pickup tours in the afternoon. For this purpose, a charging station with a limited amount of charging slots is available at the depot. We aim at generating a set of vehicle routes that are driver- and time-consistent and efficiently use limited charging resources, while optimizing the sum of vehicle fixed cost, vehicle/driver operating time, arrival time consistency and driver consistency. We present a mathematical model to describe the problem in detail. For solving the real-world problem, a template-based Adaptive Large Neighborhood Search is developed, complemented with constraint programming for charging management and quadratic programming for delivery and pickup trip scheduling. Computational experiments for different settings and scenarios, based on data from an Austrian parcel delivery company, are presented and analysed.

Approximation of the Double Traveling Salesman Problem with Multiple Stacks

The Double Traveling Salesman Problem with Multiple Stacks, DTSPMS, deals with the collect and delivery of n commodities in two distinct cities, where the pickup and the delivery tours are related by LIFO constraints. During the pickup tour, commodities are loaded into a container of k rows, or stacks, with capacity c. This paper focuses on computational aspects of the DTSPMS, which is NP-hard. We first review the complexity of two critical subproblems: deciding whether a given pair of pickup and delivery tours is feasible and, given a loading plan, finding an optimal pair of pickup and delivery tours, are both polynomial under some conditions on k and c. We then prove a (3k)/2 standard approximation for the Min Metric k DTSPMS, where k is a universal constant, and other approximation results for various versions of the problem. We finally present a matching-based heuristic for the 2 DTSPMS, which is a special case with k=2 rows, when the distances are symmetric. This yields a 1/2−o(1), 3/4−o(1) and 3/2+o(1) standard approximation for respectively Max 2 DTSPMS, its restriction Max 2 DTSPMS(1,2) with distances 1 and 2, and Min 2 DTSPMS(1,2), and a 1/2−o(1) differential approximation for Min 2 DTSPMS and Max 2 DTSPMS.

A Dynamic Strategy for Home Pick-Up Service with Uncertain Customer Requests and Its Implementation

In this paper, a home service problem is studied, where a capacitated vehicle collects customers’ parcels in one pick-up tour. We consider a situation where customers, who have scheduled their services in advance, may call to cancel their appointments, and customers, who do not have appointments, also need to be visited if they request for services as long as the capacity is allowed. To handle those changes that occurred over the tour, a dynamic strategy will be needed to guide the vehicle to visit customers in an efficient way. Aimed at minimizing the vehicle’s total expected travel distance, we model this problem as a multi-dimensional Markov Decision Process (MDP) with finite exponential scale state space. We exactly solve this MDP via dynamic programming, where the computing complexity is exponential. In order to avoid complexity continually increasing, we aim to develop a fast looking-up method for one already-examined state’s record. Although generally this will result in a huge waste of memory, by exploiting critical structural properties of the state space, we obtain an O ( 1 ) looking-up method without any waste of memory. Computational experiments demonstrate the effectiveness of our model and the developed solution method. For larger instances, two well-performed heuristics are proposed.

A Branch-and-Price Method for the Vehicle Routing Problem with Cross-Docking and Time Windows

One important factor in supply chain management is to efficiently control the supply chain flows. Due to its importance, many companies are trying to develop efficient methods to increase customer satisfaction and reduce costs. Cross-docking is considered a good method to reduce inventory and improve responsiveness. The Vehicle Routing Problem with Cross-Docking and Time Windows (VRP-CD-TW) consists on designing the minimum-cost set of routes to serve a given set of transportation requests while respecting constraints on vehicles capacity, customer time windows and using transfers on a cross-docking base. Each customer must be visited just once and mixed tours comprising pick-up and delivery stops are not allowed. For a given vehicle, the designed pick-up tour must precede its delivery tour. In this work, we model the VRP-CD-TW assuming that all feasible orders are known in advance. We present a new mixed integer program to model the VRP-CD-TW and reformulate it via Dantzig–Wolfe decomposition to later develop a column generation procedure. The proposed branch-and-price algorithm shows encouraging results on solving some Solomon-based instances.

The traveling purchaser problem, with multiple stacks and deliveries: A branch-and-cut approach

The Double Traveling Salesman Problem with Multiple Stacks is a pickup-and-delivery single-vehicle routing problem which performs all pickup operations before the deliveries. The vehicle has a loading space divided into stacks of a fixed height that follows a Last-In-First-Out policy. It has to collect products following a Hamiltonian tour in a pickup region, and then deliver them following a Hamiltonian tour in a delivery region. The aim is to minimize the total routing cost while satisfying the vehicle loading constraints.A generalization of this problem considers that each product is offered in several pickup locations at different prices, that is, the pickup locations are markets. That means that the pickup tour may not be Hamiltonian, and therefore the set of locations to be visited during the pickup tour is unknown in advance. The delivery locations represent customers, each requiring a product, and all of them must be visited by the vehicle. Thus, this problem has to select a subset of pickup locations to purchase the products, to determine a tour visiting the selected pickup locations, and to design a Hamiltonian tour which visits the delivery locations. The aim is to minimize the purchasing cost plus the total routing cost, subject to the vehicle loading constraints.This paper introduces and formulates this generalization, called the Traveling Purchaser Problem with Multiple Stacks and Deliveries. It proposes valid inequalities, and adapts some constraints defined for the Double Traveling Salesman Problem with Multiple Stacks by other authors. This formulation motivates a Branch-and-Cut algorithm whose performance has been tested on 240 instances from the literature properly adapted. Our computational experience confirms the effectiveness of the valid inequalities here proposed, and shows that instances of up to 24 products and 32 markets can be solved to optimality.

Exact solutions to the double travelling salesman problem with multiple stacks

AbstractIn this article we present mathematical programming formulations and solution approaches for the optimal solution of the Double Travelling Salesman Problem with Multiple Stacks (DTSPMS). A set of orders is given, each one requiring transportation of one item from a customer in a pickup region to a customer in a delivery region. The vehicle available for the transportation in each region carries a container. The container is organized in rows of given length. Each row is handled independently from the others according to a Last In First Out stack policy. The DTSPMS problem consists of determining the pickup tour, the loading plan of the container and the delivery tour in such a way that the total length of the two tours is minimized. The formulations are based on different modeling ideas and each formulation gives rise to a specific solution approach. We present computational results on a set of benchmark instances that compare the different approaches and show that the most successful one is a decomposition approach applied to a new model. © 2010 Wiley Periodicals, Inc. NETWORKS, 2010

Multi-period vehicle routing and crew scheduling with outsourcing options

The planning problems confronting logistics service providers frequently involve complex decisions. Motivated by a real-life case study, this paper considers short-range weekly planning on the part of postal companies that must decide about pickup tours and delivery tours for fluctuating volume (number of shipments), with time windows for the demand points, in consideration of variable vehicle capacities and personnel planning, and including outsourcing decisions for tours and drivers. This problem can be formulated as a model of combined tour and personnel planning. However, because a real formulation of the problem involves hundreds of millions of variables and numerous constraints, in practice only heuristic solutions prove relevant. This paper proposes a hybrid metaheuristic combined with a construction heuristic that—as computer simulations have demonstrated—are suitable for practice.