One-commodity Pickup Research Articles

A branch-and-cut algorithm for the one-commodity pickup and delivery location routing problem

This paper introduces a new problem that combines characteristics of the Location and Routing Problem and the One-commodity Pickup and Delivery Traveling Salesman Problem. We are given a set of customers that provide or demand given amounts of a product, and a set of potential facility locations that can be opened or not in order to give service to the customers. Each facility has an opening cost and is the depot of a vehicle with capacity Q. The problem consists in deciding which facilities to open, assigning customers to open facilities, and designing the routes that connect each facility with its customers. The objective is to minimize the sum of the cost of the routes and the facilities. This NP-hard problem has not been previously studied. We propose for it two mathematical formulations, compare them, and present a branch-and-cut algorithm able to solve instances with up to 100 nodes.

Factors affecting the final solution of the bike-sharing rebalancing problem under heuristic algorithms

The bike-sharing rebalancing problem (BRP) belongs to a class of one-commodity pickup and delivery vehicle route problems (1-PDVRPs) which often must be solved using heuristic algorithms due to the large problem size. However, an open question is which factors affect the quality of the final solutions for the BRP with heuristic algorithms, and how they affect the solution quality. This study proposed six initial solution construction methods and two heuristic algorithms, and applied 32 instances to explore this question in greater depth. The results showed that problem size and the algorithms' searching capacity are the most important factors affecting the quality of final solutions. Furthermore, the influence of the quality and diversity of initial solutions cannot be ignored. The quality of final solutions is negatively correlated with problem size, and positively correlated with the algorithms' searching capacity, and the quality and diversity of initial solutions. The influence of the quality and diversity of initial solutions on the quality of final solutions is positively correlated with problem size. For algorithms with insufficient (powerful) searching capacity, the influence of the quality (diversity) of initial solutions is more significant than that of their diversity (quality). High-quality and rich-diversity initial solutions are very helpful for algorithms to find high-quality final solutions. In addition, the CPU time of heuristic algorithms is generally positively correlated with their searching capacity. These findings have certain universal applicability and reference value for solving the 1-PDVRPs with similar solution structures using heuristic algorithms.

A simheuristic algorithm for the stochastic one-commodity pickup and delivery travelling salesman problem

ABSTRACT The one-commodity pickup and delivery traveling salesman problem (1-PDTSP) concerns the transportation of single-type goods that are picked up from supply locations to be delivered to the demand points while minimizing transportation costs. 1-PDTSP finds several applications in practice including the food redistribution operations, where excess edible foods from restaurants and food vendors are collected and delivered to food banks or meal centers, which are then made available to those in need. This paper addresses the realistic case where the pickup and delivery quantities are rarely known in advance and studies the 1-PDTSP with stochastic demand and supply values. We propose a novel simheuristic algorithm, which combines VND metaheuristic with Monte Carlo simulation (SimVND) to solve the stochastic 1-PDTSP. The resulting algorithm takes into account both the transportation cost and the penalty cost, which is incurred due to the inability to satisfy the entire demand. The experimental results indicate that the SimVND solution performs well on deterministic data sets when compared with the existing solutions in the literature. On the stochastic problems, this algorithm leads to a significant decrease in the penalty costs compared to those observed under deterministic solutions. When the penalty costs of not being able to meet demand are high, simheuristic techniques provide a more reliable solution than deterministic heuristic solutions or limited scenario-based solutions.

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.

A multi-start evolutionary local search for the one-commodity pickup and delivery traveling salesman problem

This article addresses the one-commodity pickup and delivery traveling salesman problem (1-PDTSP), which is a generalization of the well-known traveling salesman problem. The 1-PDTSP aims to find a Hamiltonian tour in which a set of supply points (pickup locations), demand points (delivery locations) are visited and, the total traveled distance is minimized. We propose a hybrid metaheuristic based on multi-start evolutionary local search and variable neighborhood descent to solve the 1-PDTSP. To test the performance of our algorithm, we solve instances with up to 500 nodes available in the literature and we demonstrate that our approach is able to provide competitive results when comparing to other existing strategies. Since a direct application of the 1-PDTSP arises as the bicycle repositioning problem, we also use our metaheuristic algorithm to solve a set of real-case instances based on EnCicla, the bicycle sharing system in the Aburra Valley (Antioquia, Colombia).

Continuous approximation for demand balancing in solving large-scale one-commodity pickup and delivery problems

The one-commodity pickup and delivery problem (1-PDP) has a wide range of applications in the real world, e.g., for repositioning bikes in large cities to guarantee the sustainable operations of bike-sharing systems. It remains a challenge, however, to solve the problem for large-scale instances. This paper proposes a hybrid modeling framework for 1-PDP, where a continuum approximation (CA) approach is used to model internal pickup and delivery routing within each of multiple subregions, while matching of net surplus or deficit of the commodity out of these subregions is addressed in a discrete model with a reduced problem size. The interdependent local routing and system-level matching decisions are made simultaneously, and a Lagrangian relaxation based algorithm is developed to solve the hybrid model. A series of numerical experiments are conducted to show that the hybrid model is able to produce a good solution for large-scale instances in a short computation time.

Genetic scatter search algorithm to solve the one-commodity pickup and delivery vehicle routing problem

PurposeIn this paper, the author introduces a new variant of the pickup and delivery transportation problem, where one commodity is collected from many pickup locations to be delivered to many delivery locations within pre-specified time windows (one–to many–to many). The author denotes to this new variant as the 1-commodity pickup-and-delivery vehicle routing problem with soft time windows (1-PDVRPTW).Design/methodology/approachThe author proposes a hybrid genetic algorithm and a scatter search to solve the 1-PDVRPTW. It proposes a new constructive heuristic to generate the initial population solution and a scatter search (SS) after the crossover and mutation operators as a local search. The hybrid genetic scatter search replaces two steps in SS with crossover and mutation, respectively.FindingsSo, the author proposes a greedy local search algorithm as a metaheuristic to solve the 1-PDVRPTW. Then, the author proposes to hybridize the metaheuristic to solve this variant and to make a good comparison with solutions presented in the literature.Originality/valueThe author considers that this is the first application in one commodity. The solution methodology based on scatter search method combines a set of diverse and high-quality candidate solutions by considering the weights and constraints of each solution.

A heuristic algorithm for a single vehicle static bike sharing rebalancing problem

The static bike rebalancing problem (SBRP) concerns the task of repositioning bikes among stations in self-service bike-sharing systems. This problem can be seen as a variant of the one-commodity pickup and delivery vehicle routing problem, where multiple visits are allowed to be performed at each station, i.e., the demand of a station is allowed to be split. Moreover, a vehicle may temporarily drop its load at a station, leaving it in excess or, alternatively, collect more bikes from a station (even all of them), thus leaving it in default. Both cases require further visits in order to meet the actual demands of such station. This paper deals with a particular case of the SBRP, in which only a single vehicle is available and the objective is to find a least-cost route that meets the demand of all stations and does not violate the minimum (zero) and maximum (vehicle capacity) load limits along the tour. Therefore, the number of bikes to be collected or delivered at each station must be appropriately determined in order to respect such constraints. We propose an iterated local search (ILS) based heuristic to solve the problem. The ILS algorithm was tested on 980 benchmark instances from the literature and the results obtained are competitive when compared to other existing methods. Moreover, our heuristic was capable of finding most of the known optimal solutions and also of improving the results on a number of open instances.

A destroy and repair algorithm for the Bike sharing Rebalancing Problem

In this paper, we deal with the Bike sharing Rebalancing Problem (BRP), which is the problem of driving a fleet of capacitated vehicles to redistribute bicycles among the stations of a bike sharing system. We tackle the BRP with a destroy and repair metaheuristic algorithm, which makes use of a new effective constructive heuristic and of several local search procedures. The computational effort required for the neighborhood explorations is reduced by means of a set of techniques based on the properties of feasible BRP solutions. In addition, the algorithm is adapted to solve the one-commodity Pickup and Delivery Vehicle Routing Problem with maximum Duration (1-PDVRPD), which is the variant of the BRP in which a maximum duration is imposed on each route.Extensive computational results on instances from the literature and on newly-collected large-size real-world instances are provided. Our destroy and repair algorithm compares very well with respect to an exact branch-and-cut algorithm and a previous metaheuristic algorithm in the literature. It improves several best-known solutions, providing high quality results on both problem variants.

Notes on the single route lateral transhipment problem

Previous research has analyzed deterministic and stochastic models of lateral transhipments between different retailers in a supply chain. In these models the analysis assumes given fixed transhipment costs and determines under which situations (magnitudes of excess supply and demand at various retailers) the transhipment is profitable. However, in reality, these depend on aspects like the distance between retailers or the transportation mode chosen. In many situations, combining the transhipments may save transportation costs. For instance, one or more vehicle routes may be used to redistribute the inventory of the potential pickup and delivery stations. This can be done in any sequence as long as the vehicle capacity is not violated and there is enough load on the vehicle to satisfy demand. The corresponding problem is an extension of the one-commodity pickup and delivery traveling salesman and the pickup and delivery vehicle routing problem. When ignoring the routing aspect and assuming given fixed costs, transhipment is only profitable if the quantities are higher than a certain threshold. In contrast to that, the selection of visited retailers is dependent on the transportation costs of the tour and therefore the selected retailers are interrelated. Hence the problem also has aspects of a (team) orienteering problem. The main contribution is the discussion of the tour planning aspects for lateral transhipments which may be valuable for in-house planning but also for price negotiations with external contractors. A mixed integer linear program for the single route and single commodity version is presented and an improved LNS framework to heuristically solve the problem is introduced. Furthermore, the effect of very small load capacity on the structure of optimal solutions is discussed.

Load-dependent and precedence-based models for pickup and delivery problems

We address the one-to-one multi-commodity pickup and delivery traveling salesman problem (m-PDTSP) which is a generalization of the TSP and arises in several transportation and logistics applications. The objective is to find a minimum-cost directed Hamiltonian path which starts and ends at given depot nodes and such that the demand of each given commodity is transported from the associated source to its destination and the vehicle capacity is never exceeded. In contrast, the many-to-many one-commodity pickup and delivery traveling salesman problem (1-PDTSP) just considers a single commodity and each node can be a source or target for units of this commodity. We show that the m-PDTSP is equivalent to the 1-PDTSP with additional precedence constraints defined by the source–destination pairs for each commodity and explore several models based on this equivalence. In particular, we consider layered graph models for the capacity constraints and introduce new valid inequalities for the precedence relations. Especially for tightly capacitated instances with a large number of commodities our branch-and-cut algorithms outperform the existing approaches. For the uncapacitated m-PDTSP (which is known as the sequential ordering problem) we are able to solve to optimality several open instances from the TSPLIB and SOPLIB.