A Hierarchical Grouping Algorithm for the Multi-Vehicle Dial-a-Ride Problem

Ride-sharing is an essential aspect of modern urban mobility. In this paper, we consider a classical problem in ride-sharing - the Multi-Vehicle Dial-a-Ride Problem (Multi-Vehicle DaRP). Given a fleet of vehicles with a fixed capacity stationed at various locations and a set of ride requests specified by origins and destinations, the goal is to serve all requests such that no vehicle is assigned more passengers than its capacity at any point along its trip. We propose an algorithm HRA, which is the first non-trivial approximation algorithm for the Multi-Vehicle DaRP. The main technical contribution is to reduce the Multi-Vehicle DaRP to a certain capacitated partitioning problem, which we solve using a novel hierarchical grouping algorithm. Experimental results show that the vehicle routes produced by our algorithm not only exhibit less total travel distance compared to state-of-the-art baselines, but also enjoy a small in-transit latency, which crucially relates to riders' traveling times. This suggests that HRA enhances rider experience while being energy-efficient

Minimizing the Maximum Flow Time in the Online Food Delivery Problem

We study a common delivery problem encountered in nowadays online food-ordering platforms: Customers order dishes online, and the restaurant delivers the food after receiving the order. Specifically, we study a problem where k vehicles of capacity c are serving a set of requests ordering food from one restaurant. After a request arrives, it can be served by a vehicle moving from the restaurant to its delivery location. We are interested in serving all requests while minimizing the maximum flow-time, i.e., the maximum time length a customer waits to receive his/her food after submitting the order. We show that the problem is hard in both offline and online settings even when k = 1 and c = ?: There is a hardness of approximation of ?(n) for the offline problem, and a lower bound of ?(n) on the competitive ratio of any online algorithm, where n is number of points in the metric. We circumvent the strong negative results in two directions. Our main result is an O(1)-competitive online algorithm for the uncapacitated (i.e, c = ?) food delivery problem on tree metrics; we also have negative result showing that the condition c = ? is needed. Then we explore the speed-augmentation model where our online algorithm is allowed to use vehicles with faster speed. We show that a moderate speeding factor leads to a constant competitive ratio, and we prove a tight trade-off between the speeding factor and the competitive ratio

On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

Workforce scheduling and planning : a combinatorial approach

This thesis investigates solution methodologies for concrete combinatorial problems in scheduling and planning. In all considered problems, it is assumed that the available information does not change over time; hence these problems have a deterministic structure. The problems studied in this thesis are divided into two groups; \workforce scheduling" and \planning". In workforce scheduling, the center problem is to build a schedule of tasks and technicians. It is assumed that the time line is split into workdays. In every workday, tasks must be grouped as sequences, each being performed by a team of technicians. Skill requirements of every task in a sequence must be met by the assigned team. This scheduling problem with some other aspects is di??cult to solve quickly and e??ciently. We developed a Mixed Integer Programming (MIP) based heuristic approach to tackle this complex scheduling problem. Our MIP model is basically a formulation of the matching problem on bipartite graphs and it enabled us to have a global way of assigning technicians to tasks. It is capable of revising technician-task allocations and performs very well, especially in the case of rare skills. A workday schedule of the aforementioned problem includes many-to-one type workforce assignments. As the second problem in workforce scheduling, stability of these workforce assignments is investigated. The stability de??nition of Gale-Shapley on the Marriage model is extended to the setting of multi-skill workforce assignments. It is shown that ??nding stable assignments is NP-hard. In some special cases stable assignments can be constructed in polynomial time. For the general case, we give linear inequalities of binary variables that describe the set of stable assignments. We propose a MIP model including these linear inequalities. To the best of our knowledge, the Gale-Shapley stability is not studied under the multi-skill workforce scheduling framework so far in the literature. The closed form description of stable assignments is also the ??rst embedding of the Gale-Shapley stability concept into an NP-complete problem. In the second problem group, two vehicle related problems are studied; the "dial a ride problem" and the "vehicle refueling problem". In the former, the goal is to check whether a list of pick-up and delivery tasks can be achieved under several timing constraints. It is shown this feasibility testing can be done in linear time using interval graphs. In the vehicle refueling problem, the goal is to make refueling decisions to reach a destination such that the cost of the travel is minimized. A greedy algorithm is presented to ??nd optimal refueling decisions. Moreover, it is shown that the vehicle refueling problem is equivalent to a ow problem on a special network

Design and operational control of an AGV system

In this paper we first deal with the design and operational control of Automated Guided Vehicle (AGV) systems, starting from the literature on these topics. Three main issues emerge: track layout, the number of AGVs required and operational transportation control. An hierarchical queueing network approach to determine the number of AGVs is decribed. Also basic concepts are presented for the transportation control of both a job-shop and a flow-shop. Next we report on the results of a case study, in which track layout and transportation control are the main issues. Finally we suggest some topics for further research

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