A note on exact algorithms for the identical parallel machine scheduling problem

A recently published paper by Mokotoff presents an exact algorithm for the classical P//Cmax scheduling problem, evaluating its average performance through computational experiments on a series of randomly generated test problems. It is shown that, on the same types of instances, an exact algorithm proposed 10 years ago by the authors of the present note outperforms the new algorithm by some orders of magnitud

Heuristic algorithms and scatter search for the cardinality constrained P//Cmax problem

We consider the generalization of the classical P//Cmax problem (assign n jobs to m identical parallel processors by minimizing the makespan) arising when the number of jobs that can be assigned to each processor cannot exceed a given integer k. The problem is strongly NP-hard for any fixed k > 2. We briefly survey lower and upper bounds from the literature. We introduce greedy heuristics, local search and a scatter search approach. The effectiveness of these approaches is evaluated through extensive computational comparison with a depth-first branch-and-bound algorithm that includes new lower bounds and dominance criteri

A descriptive study on public transport user behaviour from Live Bus Arrivals

In order to offer public transport that meet citizens’ needs for transport and further increase the use of bus services, Public Authorities need to analyse and understand travellers behaviour. Automatic Vehicle Location (AVL) data provide information on the observed time of arrival and departure of a bus at each stop. These data are fed into an algorithm to provide information to users on the expected time of arrival at the bus stop by an on-line service. In the city of London this service is called Live Bus Arrivals. This work describes the general behaviour of Live Bus Arrivals users by analysing the type of requests, localising them and compare them in different days of the week and time ranges. The objective is to identify some of the main passengers’ origin, destination and interchanges behaviour that could be of value to decision-makers and planners

Lower bounds and heuristic algorithms for the ki-partitioning problem

We consider the problem of partitioning a set of positive integers values into a given number of subsets, each having an associated cardinality limit, so that the maximum sum of values in a subset is minimized, and the number of values in each subset does not exceed the corresponding limit. The problem is related to scheduling and bin packing problems. We give combinatorial lower bounds, reduction criteria, constructive heuristics, a scatter search approach, and a lower bound based on column generation. The outcome of extensive computational experiments is presente

Assessing the consistency between observed and modelled route choices through GPS data

In traffic engineering, different assumptions on user behaviour are adopted in order to model the traffic flow propagation on the transport network. This paper deals with the classical hypothesis that drivers use the shortest possible path for their trip, pointing out the error related to using such approximation in practice, in particular in the context of dynamic origin-destination (OD) matrix estimation. If this problem is already well known in the literature, only few works are available, which provide quantitative and empirical analysis of the discrepancy between observed and modelled route sets and choices. This is mainly related to the complexity of collecting suitable data: to analyse route choice in a systematic way, it is necessary to have observations for a large period of time, since observing trajectories for the single user on a specific day could not be enough. Information is required for several days in order to analyse the repetitiveness and understand which elements influence this choice. In this work the use of the real shortest path for a congested network is evaluated, showing the differences between what we model and what users do. Results show that there is a systematic difference between the best possible choice and the actual choice, and that users clearly consider route travel time reliability in their choice process.In traffic engineering, different assumptions on user behaviour are adopted in order to model the traffic flow propagation on the transport network. This paper deals with the classical hypothesis that drivers use the shortest possible path for their trip, pointing out the error related to using such approximation in practice, in particular in the context of dynamic origin-destination (OD) matrix estimation. If this problem is already well known in the literature, only few works are available, which provide quantitative and empirical analysis of the discrepancy between observed and modelled route sets and choices. This is mainly related to the complexity of collecting suitable data: to analyse route choice in a systematic way, it is necessary to have observations for a large period of time, since observing trajectories for the single user on a specific day could not be enough. Information is required for several days in order to analyse the repetitiveness and understand which elements influence this choice. In this work the use of the real shortest path for a congested network is evaluated, showing the differences between what we model and what users do. Results show that there is a systematic difference between the best possible choice and the actual choice, and that users clearly consider route travel time reliability in their choice process

An Enhanced Path Planner for Electric Vehicles Considering User-Defined Time Windows and Preferences

A number of decision support tools facilitating the use of Electric Vehicles (EVs) have been recently developed. Due to the EVs’ limited autonomy, routing and path planning are the main challenges treated in such tools. Specifically, determining at which Charging Stations (CSs) to stop, and how much the EV should charge at them is complex. This complexity is further compounded by the fact that charging times depend on the CS technology, the EV characteristics, and follow a nonlinear function. Considering these factors, we propose a path-planning methodology for EVs with user preferences, where charging is performed at public CSs. To achieve this, we introduce the Electric Vehicle Shortest Path Problem with time windows and user preferences (EVSPPWP) and propose an efficient heuristic algorithm for it. Given an origin and a destination, the algorithm prioritizes CSs close to Points of Interest (POIs) that match user inputted preferences, and user-defined time windows are considered for activities such as lunch and spending the night at hotels. The algorithm produces flexible solutions by considering clusters of charging points (CPs) as separate CSs. Furthermore, the algorithm yields resilient paths by ensuring that recommended paths have a minimum number of CSs in their vicinity. The main contributions of our methodology are the following: modeling user-defined time windows, including user-defined weights for different POI categories, creating CSs based on clusters of CPs with sufficient proximity, using resilient paths, and proposing an efficient algorithm for solving the EVSPPWP. To facilitate the use of our methodology, the algorithm was integrated into a web interface. We demonstrate the use of the web interface, giving usage examples and comparing different settings

Locating and Sizing Electric Vehicle Chargers Considering Multiple Technologies

In order to foster electric vehicle (EV) adoption rates, the availability of a pervasive and efficient charging network is a crucial requirement. In this paper, we provide a decision support tool for helping policymakers to locate and size EV charging stations. We consider a multi-year planning horizon, taking into account different charging technologies and different time periods (day and night). Accounting for these features, we propose an optimization model that minimizes total investment costs while ensuring a predetermined adequate level of demand coverage. In particular, the setup of charging stations is optimized every year, allowing for an increase in the number of chargers installed at charging stations set up in previous years. We have developed a tailored heuristic algorithm for the resulting problem. We validated our algorithm using case study instances based on the village of Gardone Val Trompia (Italy), the city of Barcelona (Spain), and the country of Luxembourg. Despite the variability in the sizes of the considered instances, our algorithm consistently provided high-quality results in short computational times, when compared to a commercial MILP solver. Produced solutions achieved optimality gaps within 7.5% in less than 90 s, often achieving computational times of less than 5 s