The driver scheduling problem (DSP) is type of problem in operations research and theoretical computer science.
The DSP consists of selecting a set of duties (assignments) for the drivers or pilots of vehicles (e.g., buses, trains, boats, or planes) involved in the transportation of passengers or goods, [1] [2] within the constraints of various legislative and logistical criteria.
This very complex problem involves several constraints related to labour and company rules and also different evaluation criteria and objectives. Being able to solve this problem efficiently can have a great impact on costs and quality of service for public transportation companies. [3] There is a large number of different rules that a feasible duty might be required to satisfy, such as
Operations research has provided optimization models and algorithms that lead to efficient solutions for this problem. Among the most common models proposed to solve the DSP are the Set Covering and Set Partitioning Models (SPP/SCP). [4] [5] In the SPP model, each work piece (task) is covered by only one duty. In the SCP model, it is possible to have more than one duty covering a given work piece. In both models, the set of work pieces that needs to be covered is laid out in rows, and the set of previously defined feasible duties available for covering specific work pieces is arranged in columns. The DSP resolution, based on either of these models, is the selection of the set of feasible duties that guarantees that there is one (SPP) or more (SCP) duties covering each work piece while minimizing the total cost of the final schedule.
Management science (MS) is the broad interdisciplinary study of problem solving and decision making in human organizations, with strong links to management, economics, business, engineering, management consulting, and other fields. It uses various scientific research-based principles, strategies, and analytical methods including mathematical modeling, statistics and numerical algorithms to improve an organization's ability to enact rational and accurate management decisions by arriving at optimal or near optimal solutions to complex decision problems. Management science helps businesses to achieve goals using various scientific methods.
Linear programming is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming.
Mathematical optimization or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
A digital signal processor (DSP) is a specialized microprocessor chip, with its architecture optimized for the operational needs of digital signal processing. DSPs are fabricated on MOS integrated circuit chips. They are widely used in audio signal processing, telecommunications, digital image processing, radar, sonar and speech recognition systems, and in common consumer electronic devices such as mobile phones, disk drives and high-definition television (HDTV) products.
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints are linear.
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead.
Branch and bound is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm.
In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a set of vertices such that for every two vertices in , there is no edge connecting the two. Equivalently, each edge in the graph has at most one endpoint in . A set is independent if and only if it is a clique in the graph's complement. The size of an independent set is the number of vertices it contains. Independent sets have also been called "internally stable sets", of which "stable set" is a shortening.
Multiple-criteria decision-making (MCDM) or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly evaluates multiple conflicting criteria in decision making. Conflicting criteria are typical in evaluating options: cost or price is usually one of the main criteria, and some measure of quality is typically another criterion, easily in conflict with the cost. In purchasing a car, cost, comfort, safety, and fuel economy may be some of the main criteria we consider – it is unusual that the cheapest car is the most comfortable and the safest one. In portfolio management, managers are interested in getting high returns while simultaneously reducing risks; however, the stocks that have the potential of bringing high returns typically carry high risk of losing money. In a service industry, customer satisfaction and the cost of providing service are fundamental conflicting criteria.
Scheduling is the process of arranging, controlling and optimizing work and workloads in a production process or manufacturing process. Scheduling is used to allocate plant and machinery resources, plan human resources, plan production processes and purchase materials.
A schedule or a timetable, as a basic time-management tool, consists of a list of times at which possible tasks, events, or actions are intended to take place, or of a sequence of events in the chronological order in which such things are intended to take place. The process of creating a schedule — deciding how to order these tasks and how to commit resources between the variety of possible tasks — is called scheduling, and a person responsible for making a particular schedule may be called a scheduler. Making and following schedules is an ancient human activity.
Retiming is the technique of moving the structural location of latches or registers in a digital circuit to improve its performance, area, and/or power characteristics in such a way that preserves its functional behavior at its outputs. Retiming was first described by Charles E. Leiserson and James B. Saxe in 1983.
The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers?". It generalises the well-known travelling salesman problem (TSP). It first appeared in a paper by George Dantzig and John Ramser in 1959, in which the first algorithmic approach was written and was applied to petrol deliveries. Often, the context is that of delivering goods located at a central depot to customers who have placed orders for such goods. The objective of the VRP is to minimize the total route cost. In 1964, Clarke and Wright improved on Dantzig and Ramser's approach using an effective greedy algorithm called the savings algorithm.
Drivers' working hours is the commonly used term for regulations that govern the activities of the drivers of commercial goods vehicles and passenger carrying vehicles. In the United States, they are known as hours of service.
The Not-To-Exceed (NTE) standard promulgated by the United States Environmental Protection Agency (EPA) ensures that heavy-duty truck engine emissions are controlled over the full range of speed and load combinations commonly experienced in use. NTE establishes an area under the torque curve of an engine where emissions must not exceed a specified value for any of the regulated pollutants. The NTE test procedure does not involve a specific driving cycle of any specific length. Rather it involves driving of any type that could occur within the bounds of the NTE control area, including operation under steady-state or transient conditions and under varying ambient conditions. Emissions are averaged over a minimum time of thirty seconds and then compared to the applicable NTE emission limits.
The smallest-circle problem is a mathematical problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane. The corresponding problem in n-dimensional space, the smallest bounding sphere problem, is to compute the smallest n-sphere that contains all of a given set of points. The smallest-circle problem was initially proposed by the English mathematician James Joseph Sylvester in 1857.
An intercity bus driver is a bus driver whose duties involve driving a bus between cities. It is one of four common positions available to those capable of driving buses. Intercity bus drivers may be employed for public or private companies. It varies by country which is more common. But many countries have regulations on the training and certification requirements and the hours of intercity drivers.
Iterated Local Search (ILS) is a term in applied mathematics and computer science defining a modification of local search or hill climbing methods for solving discrete optimization problems.
Variable neighborhood search (VNS), proposed by Mladenović & Hansen in 1997, is a metaheuristic method for solving a set of combinatorial optimization and global optimization problems. It explores distant neighborhoods of the current incumbent solution, and moves from there to a new one if and only if an improvement was made. The local search method is applied repeatedly to get from solutions in the neighborhood to local optima. VNS was designed for approximating solutions of discrete and continuous optimization problems and according to these, it is aimed for solving linear program problems, integer program problems, mixed integer program problems, nonlinear program problems, etc.
The Public Utility Vehicle Modernization Program (PUVMP) was launched by the Department of Transportation of the Philippines in 2017, with the goal of making the country's public transportation system efficient and environmentally friendly by 2020. The program calls for the phasing-out jeepneys, buses and other Public Utility Vehicles (PUVs) that are at least 15 years old and replacing them with safer, more comfortable and more environmentally-friendly alternatives over the next three years. Currently, there are 220,000 jeepney units operating throughout the country.