Analysis of extended warranties for medical equipment: a game theory based approach using priority queues

Abstract

A growing trend in hiring maintenance services has been observed in companies in general in order to enhance competition and reduce costs. This practice becomes even more evident in the context of health institutions, as they strongly employ technology-intensive equipment that must follow tight quality standards that intend to ensure the continuity of the service and the safety of patients. These characteristics contribute in allowing the maintenance to be executed by the Original Equipment Manufacturer (OEM), since several pre-established procedures must be attended during maintenance. Thus, it becomes relevant to analyze the interaction among customers (hospitals) and the equipment manufacturer in this particular maintenance services market. In the developed model the customers are divided into 2 classes, great size hospitals belong to class 1 and small hospitals belong to class 2 and class 1 customers have priority over class 2 customers. Class 1 customers have the option of hiring an Extended Warranty (EW) with priority or of paying for each maintenance intervention on demand, while class 2 customers have the option of hiring an standard EW (with no priority) or of paying for each maintenance intervention on demand. To model such dynamics a 2-class priority queuing system is implemented. The customers select the option that maximize their expected utilities, as they are risk averse, while the manufacturer needs to set the EW and maintenance intervention prices and select the optimal number of customers of each class to service in order to maximize their expected profit. A Stackelberg Game is used to model the interaction among players, in which the OEM is the leader and the customer is the follower. In the numerical example it has been found that the customers of class 1 decide to hire EW with priority, while class 2 customers decide to pay for maintenance services on demand. Also the OEM decides to service 3 customers of class 1 and 100 customers of class 2, which yields an expected profit of $ 3,204,450. A sensitivity analysis is also performed to analyze how the optimal solution changes due to parameters variations.