Vehicle routing problems (VRPs) are very popular mainly because of their interesting combinatorial properties and applications to various industries. Informally, the problem is to provide a service to a set of customers using a fleet of vehicles so as to minimize the ‘transportation costs’ without loosing ‘customer satisfaction’. Many variations of the problem have been formulated corresponding...

This paper investigates a routing problem in a public transportation network, more precisely — the problem of finding an optimal journey plan in the Silesian Bus Network, given a timetable. In our previous experiments we analysed the Ant System which was adapted to the Bus Routing Problem (BRP) [1]. Numerical experiments have shown that the evaluation function applied caused many difficulties a...

The Mixed Capacitated General Routing Problem (MCGRP) is defined over a mixed graph, for which some verticesmust be visited and some linksmust be traversed at least once. The problem consists of determining a set of least-cost vehicle routes that satisfy this requirement and respect the vehicle capacity. Few papers have been devoted to the MCGRP, in spite of interesting real-world applications,...

This paper proposes a new formulation for the school bus scheduling problem (SBSP) which optimizes starting times for schools and associated bus routes to minimize transportation cost. Specifically, the problem determines the minimum number of buses required to complete all bus routes under the constraint that routes for the same school must arrive within a set time window before that school st...

We consider the school bus routing and scheduling problem, where transportation demand is known and bus scheduling can be planned in advance. We present a comprehensive methodology designed to support the decision of practitioners. We first propose a modeling framework where the focus is on optimizing the level of service for a given number of buses. Then, we describe an automatic procedure gen...

This paper describes the use of a new algorithm that solves the school bus routing problem with stops selection. The aim is to reduce the travel time of a set of buses that transport students to a school. The fundamental contribution of the authors is the use of a probability model to describe the feasible solution space distribution and thus to get the best solution. An estimation of distribut...

Domination in graphs is an emerging area of research at present and it has applications to several fields such as School bus routing, Computer communication networks, Facility location problems, Locating radar stations problem etc. Recently dominating functions in domination theory have received much attention. The new concepts viz., unidominating functions and total unidominating functions hav...

This paper studies the problems of permutation routing on different mesh models of parallel computation and simulates algorithms for different mesh models using C. Simple algorithms for permutation routing mesh models with and without bus have been considered, analyzed and simulated. In mesh models with bus, models with fixed bus and reconfigurable buses are dealt. For problems in permutation r...