Paper Title
Optimal Maintenance Service Contract For Repairable Equipment Involving Three Parties – Manufacturer, Agent And Customer

Abstract
Every engineering object (equipment or machine) is unreliable in a sense that it will degrade with age and/or usage, and eventually will fail. Maintenance actions are required to maintain a good condition of the engineering object. The engineering object of interest is heavy equipment used in an open coal mining such as dragline, dump trucks, excavators, etc. We consider that the heavy equipment is repairable and sold with warranty. Preventive maintenance (PM) and corrective maintenance (CM) actions are needed to keep the equipment in a satisfied condition. In some cases, PM is one package with warranty and hence the maintenance actions are borne by the manufacturer during the warranty, but after the warranty ends, they are borne by the customer (the owner of the equipment) and maintenance can be done in house or by outsource. As maintenance is not a core business of the mining company, often it is outsourced to an external agent (or original equipment manufacturer (OEM)). We examine a situation where the OEM offers PM and/or CM only in the warranty period and after the expiry of the warranty several maintenance options are offered by an agent. Hence, during a life cycle of the equipment, several combinations of maintenance service options offered by OEM and Agent are available for the customer to be selected. The decision problem for OEM or Agent is to determine the price of each option offered. In this paper, we construct a mathematical model that integrates the three decision problems using a Stackelberg game theory formulation. The optimal decision of the maintenance service contract for each party is obtained using a bi-level programming optimization with (i) upper-level problem for maximization manufacturer’s profit with related constrains (ii) lower-level problem for maximization agent’s profit with consumer’s utility function as constrains. Some numerical examples and managerial insights are presented to illustrate the decision problems studied in this paper. Keywords: Maintenance Service Contract, Three-parties, Bi-level Optimization, Reliability.