On the generalized bin packing problem

The generalized bin packing problem (GBPP) is a novel packing problem arising in many transportation and logistic settings, characterized by multiple items and bins attributes and the presence of both compulsory and non-compulsory items. In this paper, we study the computational complexity and the approximability of the GBPP. We prove that the GBPP cannot be approximated by any constant, unless P = NP. We also study the particular case of a single bin type and show that when an unlimited number of bins is available, the GBPP can be reduced to the bin packing with rejection (BPR) problem, which is approximable. We also prove that the GBPP satisfies Bellman’s optimality principle and, exploiting this result, we develop a dynamic programming solution approach. Finally, we study the behavior of standard and widespread heuristics such as the first fit, best fit, first fit decreasing, and best fit decreasing.We show that while they successfully approximate previous versions of bin packing problems, they fail to approximate the GBPP

A Real-time Information System for Public Transport in Case of Delays and Service Disruptions

AbstractPromoting the use of public transportation and Intelligent Transport Systems, as well as improving transit accessibility for all citizens, may help in decreasing traffic congestion and air pollution in urban areas. In general, poor information to customers is one of the main issues in public transportation services, which is an important reason for allocating substantial efforts to implement a powerful and easy to use and access information tool. This paper focuses on the design and development of a real time mobility information system for the management of unexpected events, delays and service disruptions concerning public transportation in the city of Milan. Exploiting the information on the status of urban mobility and on the location of citizens, commuters and tourists, the system is able to reschedule in real time their movements. The service proposed stems from the state of the art in the field of travel planners for public transportation, available for Milan. Peculiarly, we built a representation of the city transit based on a time-expanded graph that considers the interconnections among all the stops of the rides offered during the day. The structure distinguishes the physical stations and the get on/get off stops of each ride, representing them with two different types of nodes. Such structure allows, with regard to the main focus of the project, to model a wide range of service disruptions, much more meaningful than those possible with approaches currently proposed by transit agencies. One of the most interesting point lies in the expressive capability in describing the different disruptions: with our model it is possible, for instance, to selectively inhibit getting on and/or off at a particular station, avoid specific rides, and model temporary deviations

The parking warden tour problem

In this work we introduce the parking warden tour problem (PWTP), a new arc routing problem arising in irregular parking detection to model the maximization of the fines collected by a team of parking wardens.The peculiarity of the PWTP is that the arc revenue depends on the time elapsed from the previous inspection of a warden, since the revenue on a road link slumps to zero if a warden has just visited the link. For this new arc routing problem and a variant of it, we propose two mixed integer linear program formulations, a simple but effective matheuristic based on them and a bounding procedure. All the solution approaches have been tested and compared on both real instances generated on a road network area of Milano, through a survey and on real-like random instances

The relocation problem for the one-way electric vehicle sharing

Traditional car sharing services have been based on the two-way scheme, where the user picks up and returns the vehicle at the same parking station. Some innovative services permit also one-way trips, that is, the user is allowed to return the vehicle in another station. The one-way scheme is more attractive for the users, but may lead to an unbalance between the user demand, and the availability of vehicles or free lots at the stations. In such cases, the service provider could reallocate the fleet and restore a better distribution of the vehicles among the stations. In the case of electric car sharing, such a problem is more complex because the travel range depends on the level of the battery charge. This article presents a new approach for the relocation of electric vehicles (EVs), carried out by the staff of the service provider to keep the system balanced. Such an approach generates a challenging Paired Pickup and Delivery Problem with Time Windows with new features that to the best of our knowledge have never been considered in the literature. We call such a problem the EV relocation problem (EVRP). We yield a mixed integer linear programming (MILP) formulation of the EVRP and some techniques to speedup its solution through a state-of-the-art solver (CPLEX). Moreover, we develop a simple but effective heuristic based on such a formulation and four upper bound generation methods. We test the performances of both the MILP formulation and the heuristic on instances built on the Milan road network

Optimal running and planning of a biomass-based energy production process

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