Inverzná optimalizácia v obehových rozvrhoch autobusov

In this paper we study nontraditional model which can occur for the bus scheduling problems. It is motivated by answer to the question: At what minimum shortening of the driving time in some sections of the transport network will happen that an existing bus schedule is optimum? The possibility of using linear programming approach is presented. First, a new model for calculating the distance matrix in the transport network is formulated. Following is a known model for the bus scheduling problem with the minimum fleet size which is formulated as an assignment problem. In the conclusion, original model is derived to the one that connects this two formulations using shadow prices from the dual formulation of the assignment problem. Our nontraditional approach to the bus scheduling problem could affect to the economics of companies, which provide public bus services

Optimalizačné modely tvorby grafikonu vlakovej dopravy

V příspěvku se seznámíte s poznatky řešitelů grafikonu vlakové dopravy GVD pro komerční systém SENA v letech 1988-2000. Analyzuje tři základní optimalizační modely tvorby GVD. Formuluje nové otevřené problémy související s kvalitou aplikovaných metod

Inverse optimization for bus scheduling problems

In this paper we study nontraditional model which can occur for the bus scheduling problems. It is motivated by answer to the question: At what minimum shortening of the driving time in some sections of the transport network will happen that an existing bus schedule is optimum? The possibility of using linear programming approach is presented. First, a new model for calculating the distance matrix in the transport network is formulated. Following is a known model for the bus scheduling problem with the minimum fleet size which is formulated as an assignment problem. In the conclusion, original model is derived to the one that connects this two formulations using shadow prices from the dual formulation of the assignment problem. Our nontraditional approach to the bus scheduling problem could affect to the economics of companies, which provide public bus services

Alternate Criteria in LP Solutions of Public Transport Line Planning

In the paper, the public transportation line planning means planning of routes and frequencies of vehicles on them. In the world literature, different criteria are used in this context; mainly the variable costs of lines, the fixed costs of lines, the fixed plus variable costs of lines, the number of direct travellers, the total or average riding time and the total or average travelling time. The current paper adds two more: the total number of used vehicles (to be minimized when all passengers are transported) and relative excess of supply over demand (to be maximized without exceeding the number of available vehicles). Basic mathematical models for both cases are presented and the motivation of such approach is described including a brief excursion into the history of the Czech and Slovak research of line planning where the use of these objectives has arisen. Further, the basic models were modified for the cases of fourteen special practical requirements, e.g. heterogeneous vehicle fleet (= rolling stock), limitation of transfers, elastic demand, limited total number of lines, etc. The brief outline of the experience with practical use is added as well.</p

Robust p-median problem in changing networks

The robust p-median problem in changing networks is a version of known discrete p-median problem in network with uncertain edge lengths where uncertainty is characterised by given interval. The uncertainty in edge lengths may appear in travel time along the edges in any network location problem. Several possible future scenarios with respect to the lengths of edges are presented. The planner will want a strategy of positioning p medians that will be working “as well as possible" over the future scenarios. We present MILP formulation of the problem and the solution method based on exchange MILP heuristic. The cluster of each median is presented by rooted tree with the median as root. The performance of the proposed heuristic is compared to the optimal solution found via Gurobi solver for MILP models through some illustrative instances of Slovak road network in Žilina

Vehicle scheduling with heterogeneous bus fleet

The paper studies vehicle scheduling problem formulated as to minimize the number of vehicles with several types of buses. A general mathematical model is presented using graph coloring and bivalent linear programming formulation. A suboptimal algorithm is designed and the way is proposed how to exploit its result to reduce the corresponding bivalent linear programming model