Joint optimization of price, warranty and service investment for capital-intensive equipment considering maintenance capacity limits

Highlights

• Maintenance capacity investment is integrated with the design of price and warranty.

• The influence of limited maintenance capacity on sales is captured by dynamic WOM effect.

• Dynamic maintenance demand is predicted by combing dynamic sales process and failure rate.

• Warranty options with and without PM actions are investigated and compared.

• The proposed model helps determine the most profitable strategy in a static/dynamic market.

Abstract

The insufficient maintenance capacity has recently brought challenges to original equipment manufacturers (OEMs) for capital-intensive equipment in the service for new products. Different from the existing studies of the price and warranty strategy on the premise of unlimited maintenance capacity, this paper considers the influence of limited maintenance capacity and investigates the joint optimization of capacity investment and marketing strategy. For a static/dynamic market, the profit models capturing the interaction among price, warranty length and improved maintenance capacity are developed under two warranty options (with and without preventive maintenance). The proposed models characterize the dynamic negative word-of-mouth effect, the penalty for unmet maintenance demand and the maintenance capacity investment. By maximizing the profit models, OEMs can determine the most profitable strategy to deal with maintenance capacity limits. Furthermore, a case study is conducted verifying the methodology effectiveness and providing managerial insights. The results reveal the differences in strategy design between the scenarios with and without capacity limits. Meanwhile, the conditions determining whether to adopt preventive maintenance actions in the warranty are given. Finally, the sensitivity analysis demonstrates the influence of price/warranty sensitivity, providing practical guidelines for the design of the most profitable strategy responding to different environments.

Introduction

Nowadays, with the increased competition in the capital-intensive equipment industry, original equipment manufacturers (OEMs) are motivated to develop new strategies integrating the competitive advantages in both products and services (Adrodegari et al., 2018, Lin, 2004). Especially, as capital-intensive equipment requires high reliability in use, a suitable warranty service plays an important role in promoting the sales and reputation of the product (Murthy and Djamaludin, 2002, Liu et al., 2021). In addition to the price, the warranty has become a powerful marketing weapon for OEMs of capital-intensive equipment to gain competitive advantages (Cheong et al., 2021). For example, the warranty period of the aircraft has been extended to 60–120 months or 5000–10000 h of flight, much longer than the warranty period (30 months or 2500 h of flight) in the early 1990s (Shafiee and Chukova, 2013). Besides, far beyond the warranty covering 36,000 miles or three years in the past, nowadays, most automobile warranties last for 10 years or 100,000 miles in the intensive service competition (Jones, 2021). Hence, it is critical for OEMs to consider the joint optimization of the pricing and warranty strategy to win profits in today’s competitive market.

Since capital-intensive equipment needs frequent maintenance over a long-life cycle, the increasing in-service equipment from the global market brings rapid growth in maintenance demand. Meanwhile, the technical complexity of capital-intensive equipment increases the difficulty in obtaining sufficient maintenance resources such as facilities, high-tech labor and special spare parts. Hence, the OEMs of capital-intensive equipment are inevitably faced with the challenge of inadequate maintenance capacity. For instance, as new engines continue to roll off the assembly line at an unprecedented rate, the capacity-straining convergence of maintenance demand for older and newer engines is booming, especially in OEM maintenance shops (Adams, 2019). Additionally, a shortage of aviation mechanics within the next decade brings more pressure to aviation maintenance (Satair, 2019). Hence, the lack of sufficient maintenance capacity has become a bottleneck for aircraft engine OEMs.

It is known that maintenance activities in the warranty that are not completed within the required time result in delay time that generates financial losses such as penalty costs (Iskandar and Husniah, 2017, Huang et al., 2021). Not only that, negative word-of-mouth (WOM) caused by untimely maintenance services will cause damages to the reputation of OEMs (Dinis et al., 2019a). It has a negative influence on the subsequent sales of the products, resulting in a loss of the OEM’s revenue. Thus, on the one hand, it is important for OEMs to design an attractive marketing strategy (price and warranty) to promote product sales. On the other hand, faced with limited maintenance capacity, the OEM has to adjust the warranty coverage according to the maintenance capacity to control the financial and reputational damages in an affordable range. Therefore, the constraint of maintenance capacity is a key issue that must be considered in the design of the product price and warranty service package for OEMs.

Limited by inadequate maintenance capacity, many OEMs of capital-intensive equipment are investing in labor, facilities and other maintenance resources to expand maintenance capacity (Adam, 2019). For example, aircraft engine manufacturers such as General Electric and MTU Aero Engines are expanding the internal and external capacity at all locations. Pratt & Whitney has invested about $450 million since June 2016 at its Columbus facility to expand its geared turbofan engine (GTF) maintenance capacity. It is noticed that the notable improvement of the maintenance capacity brings high investment costs, but an inadequate improved maintenance capacity leads to high financial penalties and damages to the reputation. Therefore, it is also critical for OEMs to make the optimal balance between the available maintenance capacity and required maintenance capacity (Dinis et al., 2019a). For a type of product, the price and warranty strategy determine the maintenance demand. Meanwhile, the maintenance capacity investment decides the available maintenance capacity. Hence, from both the demand and the supply views, incorporating the maintenance capacity investment strategy with the price and warranty decisions for OEMs of capital-intensive equipment is urgently needed.

In recent years, as important marketing strategies, the joint optimization of price and warranty policy has received intensive attention. Lin and Shue, 2005, Zhou et al., 2009 investigated optimal policies for price and warranty length in a static/dynamic demand market respectively. Hosseini-Motlagh et al. (2022) studied this issue in a competitive dual-channel retailing system. Besides, Xie, 2017, Taleizadeh and Mokhtarzadeh, 2020, Cheong et al., 2021 studied the optimal price and two-dimensional warranty policy. Zhang et al. (2022) proposed a systematic warranty-reliability-price decision model for two-dimensional warranted products. Su and Yang (2021) and Wang et al. (2021) further considered a two-stage renewing warranty policy and a performance-based warranty policy respectively. Furthermore, Huang et al., 2007, Wu et al., 2009, Chen et al., 2017 incorporated the design of reliability, production rate and production run length into the optimization of price and warranty policy respectively. In addition to basic replacement and corrective maintenance policy, as an effective tool to recover the degradation of equipment in industry, preventive maintenance (PM) has been widely applied (Ayed et al., 2017; Xia, Sun et al., 2021; Xia, Zhang et al., 2021; Xia, Dong et al., 2021; Zhu et al., 2022). Correspondingly, several studies have investigated the joint decision issue on price and warranty strategy performing PM actions (Yeh and Fang, 2015, Darghouth et al., 2017, He et al., 2020, Ruan et al., 2022).

The above literature mainly investigates the optimization of price and warranty strategies on the premise of unlimited maintenance capacity. Among these works, the challenges brought by the inadequate capacity for OEMs of capital-intensive equipment involved in the product and service competition in today’s market have not been considered. Since the limitation of maintenance capacity is a key factor influencing the maintenance planning in industrial practice, several studies have taken this factor into consideration. Incorporating the capacity of workforces, facilities and spare parts into the constraints, the optimal maintenance schedules have been studied under the limited maintenance capacity to maximize the system availability (de Smidt-Destombes et al., 2009, Seif and Yu, 2018, Chen et al., 2021) or minimize the total cost (Safaei and Jardine, 2018, Ertogral and Öztürk, 2019, Deng et al., 2020, Witteman et al., 2021). These studies take maintenance capacity as a fixed constraint. Different from that, several studies integrate the decision on maintenance capacity with the maintenance planning (Zhou et al., 2016, Erkoc and Ertogral, 2016, Turan et al., 2020). Meanwhile, some studies focus on the optimization of maintenance capacity scheduling for aircraft maintenance providers (Kurz, 2016, Dinis et al., 2019a, Dinis et al., 2019b). However, these studies focus more on the limitation of maintenance capacity in the maintenance schedule for a single specific object at an operational level. From the perspective of OEMs challenged by inadequate maintenance capacity, the interaction between the marketing strategy (price and warranty policy) and the maintenance capacity investment has not been jointly studied at a strategic level.

To overcome these gaps, considering the influence of limited maintenance capacity on the marketing strategy design, this paper aims to investigate the joint optimization of price, warranty and maintenance capacity investment for OEMs to address the new challenges caused by maintenance capacity shortage. In practice, for an OEM in charge of the warranty cost, it is worthwhile to perform PM actions only if the reduction in the corrective maintenance (CM) cost exceeds the cost of PM actions. In order to figure out the more profitable warranty option, the warranty policies with and without PM actions are investigated and compared in this study. Moreover, a static market (with constant price and warranty length) and a dynamic market (with changing price and warranty length) are both considered. For each warranty option, aiming at maximizing the expected profit of the OEM over the planning horizon, we study the optimal combination of price, warranty length and improved maintenance capacity in a static market and a dynamic market respectively.

The main contributions of this study are given as follows. First, we extend the warranty-price optimization model by considering the new challenges brought by the limited maintenance capacity for OEMs. Especially, rather than regarding the limited maintenance capacity as a fixed constraint as related studies, the decision maintenance capacity investment strategy is unprecedentedly incorporated into the warranty-price optimization model. Second, the influence of limited maintenance capacity is captured by considering the dynamic negative WOM effect and the penalty caused by unmet maintenance demand. For this purpose, a new sales function integrating the influence of dynamic negative WOM is proposed. Meanwhile, in order to obtain the dynamic gap between capacity and demand, different from calculating the total maintenance demand as the existing studies, we predict the dynamic maintenance demand incorporating the sales process and failure distribution. Lastly, in addition to the CM action, the PM action is considered in the warranty. Two warranty options with and without PM actions are investigated and compared in two types of the market (a static demand market and a dynamic demand market). The new findings obtained from the model application provide OEMs with managerial insights into determining the more profitable warranty option and corresponding joint optimization strategy to reach maximum profit in practice.

The remainder of this paper is organized as follows. Section 2 describes the optimization problem investigated in this paper. The sales volume, maintenance demand and expected profit model are formulated in Section 3. In Section 4, case studies are performed, and several managerial insights are given through sensitivity analysis and comparative study. Finally, Section 5 gives the conclusions and future work.