Locomotive Assignment Problem with Heterogeneous Vehicle Fleet and Hiring External Locomotives

Karel Golc,Michal Dorda,Dušan Teichmann,Helena Bínová

doi:10.1155/2015/583909

Abstract

This paper focuses on solving the problem of how to assign locomotives to assembled trains optimally. To solve the problem, linear programming is applied. The situation we model in the paper occurs in the conditions of a transport operator that provides rail transport in the Czech Republic. In the paper, an extended locomotive assignment problem is modeled; the transport operator can use different classes of the locomotives to serve individual connections, some connections must be served by a predefined locomotive class, and the locomotives can be allocated to several depots at the beginning. The proposed model also takes into consideration the fact that some connections can be served by the locomotives of external transport companies or operators. The presented model is applied to a real example in order to test its functionality.

Highlights

Vjsk: The variable that models the locomotive of the class k ∈ K deadheading to the destination depot s ∈ S (Vjsk = 1) after serving the connection j ∈ L; if not Vjsk = 0
The paper focuses on a special type of locomotive scheduling mathematical model
The request for the presented mathematical model was made by the actual transport operator

Summary

Introduction

Optimization methods are of vital importance for transport processes. The optimization methods can be employed especially to control the transport processes. In the paper we present one of the special applications— the problem of the optimal assignment of locomotives to assembled trains. In the literature this problem is denoted most frequently by the locomotive assignment problem, locomotive scheduling problem, or locomotive routing problem. (ii) The transport operator has enough locomotives but the operator is not willing to use all of them because the operator is awaiting some more lucrative jobs In such situations some connections can be served by the locomotives that the transport operator hires from other transport operators or companies, external locomotives. Our paper extends the spectrum of existing mathematical models used for solving the locomotive assignment problem by a model devoted to the specific scheduling application. The authors have not met with such application in studied literature but the situations often exist in practice (a case study presented in Section 6 confirms the statement)

State of the Art

Basic Terminology Used in the Paper

The Problem Formulation

The Linear Mathematical Model

Case Study

Findings

Conclusions