Service reliability modeling and profit rate optimization for a fleet of self-service systems

Abstract

Self-service systems, such as charging piles and automated kiosks, have witnessed a significant increase in market penetration in recent years, attributed to their advantages such as not requiring on-site personnel for management. To handle service failures, frequent and thorough maintenance can be conducted to ensure a high service level but may also result in significant maintenance costs. Apparently, balancing the service level (and consequently, the revenue) with maintenance costs is essential for operators aiming to maximize their profit. However, achieving this balance is challenging and underexplored due to the inherent and unique characteristics of self-service systems, which calls upon accurately modeling the quality of service and the profitability these systems provide, and developing the decision references for their maintenance.

Particularly, long-run service reliability—defined as the proportion of demands fulfilled out of all arrived demands—is adopted as the indicator of service quality in this dissertation. The service reliability is determined by the systems’ operational reliability and multiple types of demand-and-system interactions. For example, during service, a customer may switch to other unoccupied systems for service when the selected system is found to be failed or fails during operation. The long-run profit rate is employed as the indicator of fleet profitability and is determined by service reliability and maintenance policy. A novel multi-dimensional maintenance policy is developed that the entire fleet is maintained either when the number of failed systems reaches a threshold, or the time elapsed since the last maintenance exceeds another threshold. Further, if the maintenance actions are imperfect, the replacement is performed for each system when a certain number of imperfect maintenance actions have been performed. In this dissertation, the optimal maintenance policy that maximizes the long-run service reliability or profit rate, is explored under three distinct scenarios.

First scenario focuses on the modeling of service reliability under imperfect monitoring and customer reporting mechanisms. A Markovian model is employed to characterize the fleet state transition process. Then the service reliability, and the impact of monitoring imperfection(s) on it are quantitatively derived.

In the second scenario, it is assumed that the maintenance actions are imperfect when compared to replacement. The long-run profit rate is derived based on a triple-layer state transition model, and the optimal three-dimensional maintenance policy is obtained based on a Kriging-based efficient global optimization algorithm.

In the third scenario, each system is subject to deterioration failures and a demand may have multiple stages with arbitrary distributions of their durations, which aligns more closely with real-world scenarios. A fleet state transition model is developed by characterizing two unique demand-and-system interdependencies. On this basis, a Tabu search algorithm with random exploration is employed to solve the optimal maintenance policy.

Numerical studies on fleets of electrical vehicle charging piles in Hong Kong are provided to illustrate the proposed analytical method and the sensitivity analysis is conducted. It is expected that the managerial insights from this dissertation will assist the operators of such self-service systems in designing the maintenance policy to maximize the long-run service reliability or profit rate.