Fuzzy usage pattern in customizing public transport fleet and its maintenance options

Abstract

In this paper we study a two-dimensional maintenance contract for a fleet of public transport, such as buses, shuttle etc. The buses are sold with a two-dimensional warranty. The warranty and the maintenance contract are characterized by two parameters – age and usage – which define a two-dimensional region. However, we use one dimensional approach to model these age and usage of the buses. The under-laying maintenance service contracts is the one which offers policy limit cost to protect a service provider (an agent) from over claim and to pursue the owner to do maintenance under specified cost in house. This in turn gives benefit for both the owner of the buses and the agent of service contract. The decision problem for an agent is to determine the optimal price for each option offered, and for the owner is to select the best contract option. We use a Nash game theory formulation in order to obtain a win-win solution – i.e. the optimal price for the agent and the optimal option for the owner. We further assume that there will be three different usage pattern of the buses, i.e. low, medium, and high pattern of the usage rate. In many situations it is often that we face a blur boundary between the adjacent patterns. In this paper we look for the optimal price for the agent and the optimal option for the owner, which minimizes the expected total cost while considering the fuzziness of the usage rate pattern.