Cost Bounds for Pickup and Delivery Problems with Application to Large-Scale Transportation Systems

Demand-responsive transport (DRT) systems, where users generate requests for transportation from a pickup point to a delivery point, are expected to increase in usage dramatically as the inconvenience of privately-owned cars in metropolitan areas becomes excessive. However, despite the increasing role of DRT systems, there are very few rigorous results characterizing achievable performance (in terms, e.g., of stability conditions). In this paper, our aim is to bridge this gap for a rather general model of DRT systems, which takes the form of a generalized Dynamic Pickup and Delivery Problem. The key strategy is to develop analytical bounds for the optimal cost of the Euclidean Stacker Crane Problem (ESCP), which represents a general static model for DRT systems. By leveraging such bounds, we characterize a necessary and sufficient condition for the stability of DRT systems; the condition depends only on the workspace geometry, the stochastic distributions of pickup and delivery points, customers' arrival rate, and the number of vehicles. Our results exhibit some surprising features that are absent in traditional spatially-distributed queueing systems.Singapore-MIT Alliance for Research and Technology (Future Urban Mobility project)Singapore. National Research Foundatio

Semi-Preemptive Routing on Trees

We study a variant of the pickup-and-delivery problem (PDP) in which the objects that have to be transported can be reloaded at most d times, for a given integer d. This problem is known to be polynomially solvable on paths or cycles and NP-complete on trees. We present a (4/3+epsilon)-approximation algorithm if the underlying graph is a tree. By using a result of Charikar et al. (1998), this can be extended to a O(log n log log n)-approximation for general graphs

Semi-Preemptive Routing on Trees

We study a variant of the pickup-and-delivery problem (PDP) in which the objects that have to be transported can be reloaded at most d times, for a given integer d. This problem is known to be polynomially solvable on paths or cycles and NP-complete on trees. We present a (4/3+epsilon)-approximation algorithm if the underlying graph is a tree. By using a result of Charikar et al. (1998), this can be extended to a O(log n log log n)-approximation for general graphs

Multi-Goal Multi-Agent Pickup and Delivery

In this work, we consider the Multi-Agent Pickup-and-Delivery (MAPD) problem, where agents constantly engage with new tasks and need to plan collision-free paths to execute them. To execute a task, an agent needs to visit a pair of goal locations, consisting of a pickup location and a delivery location. We propose two variants of an algorithm that assigns a sequence of tasks to each agent using the anytime algorithm Large Neighborhood Search (LNS) and plans paths using the Multi-Agent Path Finding (MAPF) algorithm Priority-Based Search (PBS). LNS-PBS is complete for well-formed MAPD instances, a realistic subclass of MAPD instances, and empirically more effective than the existing complete MAPD algorithm CENTRAL. LNS-wPBS provides no completeness guarantee but is empirically more efficient and stable than LNS-PBS. It scales to thousands of agents and thousands of tasks in a large warehouse and is empirically more effective than the existing scalable MAPD algorithm HBH+MLA*. LNS-PBS and LNS-wPBS also apply to a more general variant of MAPD, namely the Multi-Goal MAPD (MG-MAPD) problem, where tasks can have different numbers of goal locations.Comment: IROS 202

Investigating heuristic and meta-heuristic algorithms for solving pickup and delivery problems

The development of effective decision support tools that can be adopted in the transportation industry is vital in the world we live in today, since it can lead to substantial cost reduction and efficient resource consumption. Solving the Vehicle Routing Problem (VRP) and its related variants is at the heart of scientific research for optimizing logistic planning. One important variant of the VRP is the Pickup and Delivery Problem (PDP). In the PDP, it is generally required to find one or more minimum cost routes to serve a number of customers, where two types of services may be performed at a customer location, a pickup or a delivery. Applications of the PDP are frequently encountered in every day transportation and logistic services, and the problem is likely to assume even greater prominence in the future, due to the increase in e-commerce and Internet shopping. In this research we considered two particular variants of the PDP, the Pickup and Delivery Problem with Time Windows (PDPTW), and the One-commodity Pickup and Delivery Problem (1-PDP). In both problems, the total transportation cost should be minimized, without violating a number of pre-specified problem constraints. In our research, we investigate heuristic and meta-heuristic approaches for solving the selected PDP variants. Unlike previous research in this area, though, we try to focus on handling the difficult problem constraints in a simple and effective way, without complicating the overall solution methodology. Two main aspects of the solution algorithm are directed to achieve this goal, the solution representation and the neighbourhood moves. Based on this perception, we tailored a number of heuristic and meta-heuristic algorithms for solving our problems. Among these algorithms are: Genetic Algorithms, Simulated Annealing, Hill Climbing and Variable Neighbourhood Search. In general, the findings of the research indicate the success of our approach in handling the difficult problem constraints and devising simple and robust solution mechanisms that can be integrated with vehicle routing optimization tools and used in a variety of real world applicationsEThOS - Electronic Theses Online ServiceGBUnited Kingdo

Investigating heuristic and meta-heuristic algorithms for solving pickup and delivery problems

The development of effective decision support tools that can be adopted in the transportation industry is vital in the world we live in today, since it can lead to substantial cost reduction and efficient resource consumption. Solving the Vehicle Routing Problem (VRP) and its related variants is at the heart of scientific research for optimizing logistic planning. One important variant of the VRP is the Pickup and Delivery Problem (PDP). In the PDP, it is generally required to find one or more minimum cost routes to serve a number of customers, where two types of services may be performed at a customer location, a pickup or a delivery. Applications of the PDP are frequently encountered in every day transportation and logistic services, and the problem is likely to assume even greater prominence in the future, due to the increase in e-commerce and Internet shopping. In this research we considered two particular variants of the PDP, the Pickup and Delivery Problem with Time Windows (PDPTW), and the One-commodity Pickup and Delivery Problem (1-PDP). In both problems, the total transportation cost should be minimized, without violating a number of pre-specified problem constraints. In our research, we investigate heuristic and meta-heuristic approaches for solving the selected PDP variants. Unlike previous research in this area, though, we try to focus on handling the difficult problem constraints in a simple and effective way, without complicating the overall solution methodology. Two main aspects of the solution algorithm are directed to achieve this goal, the solution representation and the neighbourhood moves. Based on this perception, we tailored a number of heuristic and meta-heuristic algorithms for solving our problems. Among these algorithms are: Genetic Algorithms, Simulated Annealing, Hill Climbing and Variable Neighbourhood Search. In general, the findings of the research indicate the success of our approach in handling the difficult problem constraints and devising simple and robust solution mechanisms that can be integrated with vehicle routing optimization tools and used in a variety of real world applicationsEThOS - Electronic Theses Online ServiceGBUnited Kingdo

A General Vehicle Routing Problem

In this paper, we study a rich vehicle routing problem incorporating various complexities found in real-life applications. The General Vehicle Routing Problem (GVRP) is a combined load acceptance and generalised vehicle routing problem. Among the real-life requirements are time window restrictions, a heterogeneous vehicle fleet with different travel times, travel costs and capacity, multi-dimensional capacity constraints, order/vehicle compatibility constraints, orders with multiple pickup, delivery and service locations, different start and end locations for vehicles, and route restrictions for vehicles. The GVRP is highly constrained and the search space is likely to contain many solutions such that it is impossible to go from one solution to another using a single neighbourhood structure. Therefore, we propose iterative improvement approaches based on the idea of changing the neighbourhood structure during the search

Industrial and Tramp Ship Routing Problems: Closing the Gap for Real-Scale Instances

Recent studies in maritime logistics have introduced a general ship routing problem and a benchmark suite based on real shipping segments, considering pickups and deliveries, cargo selection, ship-dependent starting locations, travel times and costs, time windows, and incompatibility constraints, among other features. Together, these characteristics pose considerable challenges for exact and heuristic methods, and some cases with as few as 18 cargoes remain unsolved. To face this challenge, we propose an exact branch-and-price (B&P) algorithm and a hybrid metaheuristic. Our exact method generates elementary routes, but exploits decremental state-space relaxation to speed up column generation, heuristic strong branching, as well as advanced preprocessing and route enumeration techniques. Our metaheuristic is a sophisticated extension of the unified hybrid genetic search. It exploits a set-partitioning phase and uses problem-tailored variation operators to efficiently handle all the problem characteristics. As shown in our experimental analyses, the B&P optimally solves 239/240 existing instances within one hour. Scalability experiments on even larger problems demonstrate that it can optimally solve problems with around 60 ships and 200 cargoes (i.e., 400 pickup and delivery services) and find optimality gaps below 1.04% on the largest cases with up to 260 cargoes. The hybrid metaheuristic outperforms all previous heuristics and produces near-optimal solutions within minutes. These results are noteworthy, since these instances are comparable in size with the largest problems routinely solved by shipping companies

Investigating heuristic and meta-heuristic algorithms for solving pickup and delivery problems

The development of effective decision support tools that can be adopted in the transportation industry is vital in the world we live in today, since it can lead to substantial cost reduction and efficient resource consumption. Solving the Vehicle Routing Problem (VRP) and its related variants is at the heart of scientific research for optimizing logistic planning. One important variant of the VRP is the Pickup and Delivery Problem (PDP). In the PDP, it is generally required to find one or more minimum cost routes to serve a number of customers, where two types of services may be performed at a customer location, a pickup or a delivery. Applications of the PDP are frequently encountered in every day transportation and logistic services, and the problem is likely to assume even greater prominence in the future, due to the increase in e-commerce and Internet shopping. In this research we considered two particular variants of the PDP, the Pickup and Delivery Problem with Time Windows (PDPTW), and the One-commodity Pickup and Delivery Problem (1-PDP). In both problems, the total transportation cost should be minimized, without violating a number of pre-specified problem constraints. In our research, we investigate heuristic and meta-heuristic approaches for solving the selected PDP variants. Unlike previous research in this area, though, we try to focus on handling the difficult problem constraints in a simple and effective way, without complicating the overall solution methodology. Two main aspects of the solution algorithm are directed to achieve this goal, the solution representation and the neighbourhood moves. Based on this perception, we tailored a number of heuristic and meta-heuristic algorithms for solving our problems. Among these algorithms are: Genetic Algorithms, Simulated Annealing, Hill Climbing and Variable Neighbourhood Search. In general, the findings of the research indicate the success of our approach in handling the difficult problem constraints and devising simple and robust solution mechanisms that can be integrated with vehicle routing optimization tools and used in a variety of real world application