Production disruption, emerging as one of the most important problems in real-world supply chain management, is increasingly arousing the interests of both researchers and practitioners [1,2]. A production disruption not only directly affects the operational performance of manufacturers, but also breaks the balance of the supply chain system and then affects the long-term sustainability of the supply chain. In 2020, for example, the supply disruption due to the COVID-19 pandemic in Europe drove Volkswagen to stop production, which caused significant loss to his partners. Similarly, in Japan, three giant automakers–Toyota, Honda, and Nissan–all suffered from significant operational performance impacts owed to production disruption [3]. Hendricks, Singhal, and Powell summarized the serious damage caused by production disruptions on the operational performance of manufacturers, which may lead to losses in the wealth and the reputation of shareholders [4,5,6]. Obviously, production disruption has a direct impact on the sustainability of the supply chain. Production disruption may also cause an increase in cost and in resource waste, which runs counter to the goal of global sustainable development. As a result, more and more firms have begun to place serious concerns on production disruption management. While they are beginning to appreciate the importance of supply chain disruptions, managing these disruptions remains a major challenge.

Generally, there are two broad categories of risks influencing production disruptions. The first category of risks originates from natural disasters (e.g., earthquake and epidemic) or social/economic events (e.g., strikes, financial crises, terroristic attacks), which are exogenous and uncontrollable. Previous studies on these risks mainly focused on five important strategies, including multiple sourcing, backup supply, inventory, emergency purchases, and demand management. These strategies have been extensively studied, aiming to mitigate the negative consequences of production disruptions [7,8,9]. The second category of risks arises from unqualified raw materials, design deficiency, and a lower technology level, which are more probable to happen but endogenous and controllable. As stated by Tunca and Zhu [10], it is common in the retail industry that a percentage of products offered by a manufacturer have some problems due to process or design issues. This will make the products unsellable, leading to a supply disruption. To deal with this kind of risk, one effective way is to offer incentives to manufacturers to improve their production process reliability. For example, Tang et al. proposed an approach by which retailers invest in improving suppliers’ processes to reduce the likelihood of production disruptions [11].

Among the existing incentives, cost-sharing is an effective approach in improving production process reliability [11]. However, there is an underlying assumption for this strategy, that is, retailers have to be abundant in capital because cost-sharing will bring about additional cost. For those retailers who have insufficient capital at hand, this incentive may not be a good choice, possibly not even a feasible option. This motivates us to consider another type of incentive: to impose a penalty on the manufacturer for his default due to disruption, which is quite common and practical as an ex-ante strategy in supply chain disruption management [12]. Obviously, one of the main advantages of a penalty strategy is that the retailer need not prepare additional funds for the incentive. In fact, it is not unusual that a penalty is imposed for unfulfilling products in the reality. However, they also showed that a higher penalty from the retailer might bankrupt the supplier, which will in turn hurt her own benefit and even the whole supply chain from the viewpoint of long-term sustainability [12]. To this end, the retailer must determine a proper penalty level. In this paper, we will try to answer the question of what strategy should be adopted, cost-sharing or penalty, when incentives are required to stimulate the manufacturer improving his production process reliability to avoid a possible disruption. In addition, what is the most appropriate level of the penalty if a penalty strategy is preferred?

To address these issues, we consider a two-stage supply chain, where the manufacturer and the retailer are directly connected, and discuss their optimal strategies based on a Stackelberg game. First, we start with a basic model consisting of a retailer and a manufacturer, where the retailer faces a deterministic demand and the manufacturer’s production process is subject to uncertain disruptions. Disruption probability is expressed as a function of a manufacturer’s investment in process improvement. The retailer can influence the manufacturer’s investment strategy by providing different incentives. However, demand is not always determined in practice, and actual demand will change with the quality of products, logistics, environment, and other factors, especially for seasonal products, such as electrical appliances. Hence, we extend the basic model to a more general and practical model, where the demand is stochastic. In order to obtain a more robust strategy for the uncertain setting, we also develop a loss-averse model, which shows the retailer’s tradeoff between gain and loss. For all the models, we investigate the interactions between the retailer and the manufacturer with a Stackelberg game framework. The retailer, as a leader, determines the quantity ordered from her upstream firm, the proportion of cost-sharing or the penalty level for non-delivery. The manufacturer, as the follower, decides the investment level, in terms of the level of production process reliability. Based on this framework, we compare the performance of a penalty strategy with that of cost-sharing, and we analyze the efficacy of each strategy in improving production process reliability.

2. Production Disruption