Bicycles are becoming an increasingly popular mean of transport. Being healthy and affordable, they provide a sustainable alternative way of movement, for both leisure and work commuting. In both cases demand increases when bike devoted tracks are available. Providing bike trails that connect touristic spots is a cheap way of increasing the appeal and promoting the development of those regions featuring beautiful landscapes, strong cultural traditions, and historical monuments within a small area. This is the case of the Trebon region, South Bohemia, whose local administrators face the problem of optimally investing scarce resources to set up a network of cycle-dedicated tracks, exploiting existing trails or by reconstruction works, turning gravel roads or unsurfaced forest tracks into paved bike trails. As a first step, we address the design of a single route, modeled as a path on a directed graph between two given nodes, maximizing a utility function related to the attractiveness of the path.\ud Attractiveness depends on several features, such as a service facility, a restaurant serving typical food, an historical village, or a scenic landscape to be enjoyed along the way. Two kinds of resource constraints bound the solution. A path maximum duration, which depends on how many times each arc is traversed, and a maximum budget for setting up the infrastructure, which depends on which arcs are selected. Since a cyclist may be willing to traverse an edge more than once - think, for example, of a detour from the main way to be travelled back and forth to reach a point of interest – cycles can be part of the route. The attractiveness function is concave and decreases after reaching its maximum at a few traversals. Such features make the problem new and challenging. We present an integer linear programming model and validate it by an experimental campaign on realistic data for the Trebon region

The paper deals with the situation when a low populated area is in need of public transport service. It is necessary to design a bus route, passing through the area and meeting the accessibility and efficiency requirements. The article presents a mathematical formulation of the problem in terms of the network theory together with two exact and several heuristic methods for finding a solution. The paper describes that the problem is NP-hard, and therefore computing experience is outlined.

The main purpose of the paper is to present theoretical findings suitable as a support of decision-making on economic sustainability and accessibility of public transport. Czech experience with solving this problem is taken into account. The paper focuses on the relationship between two of three pillars of public transport sustainability -social and economic. Accessibility of public transport service for the clients is considered the main feature of the social pillar. Three types of accessibility are taken into account: spatial, time and economic. Indicators of all three types are presented and their role is studied in details. The main factors influencing the indicators are described. It is shown that, usually, strengthening the social pillar is then weakening the economic one. Further, the public transport accessibility issues are discussed in the most complicated case -in the weak demand areas. Demand Responsible Transport (DRT) is presented as an efficient and effective tool in maintaining the public transport sustainable in these areas. Different types of DRT are outlined and evaluated for the purpose of deciding which one to choose.

No abstract

Abstract:The paper introduces a family of subnetwork optimization problems as a part of network management theory. Three optimization problems are formulated and the solution methods are described. Five practical situations, when these solutions may be applied, are presented. Possibilities of future research are outlined as well.