Combating Excessive Overtime in Global Supply Chains: The Workforce Perspective

1. Introduction

Global supply chains of multinational enterprises (MNEs) have faced heightened scrutiny from organizations such as the International Labour Organization (ILO) and various labor-focused nongovernment organizations (NGOs). These organizations have shed light on the widespread issue of excessive working hours in developing economies, especially prevalent within the electronics and fast fashion industries (SACOM 2016, Errighi and Bodwell 2017). According to Messenger (2018), a striking 47.2% of workers in the Asia-Pacific region labor for more than 48 hours per week. In October 2015, a staggering 71.1% of Pegatron’s workforce exceeded Apple’s 60-hour workweek limit, with 64% of them pushed beyond 90 hours of overtime in a single month (China Labor Watch 2016). In Malaysia, workers of suppliers for Samsung and Panasonic reported being compelled to endure 14-hour workdays with limited breaks (Pattisson 2016). SACOM, a labor-focused NGO, conducted investigations in 2015 and 2016, exposing the harsh working conditions at four suppliers of Zara, H&M, and GAP. The report revealed that some workers were forced to toil for up to 14 or even 17 hours per day (SACOM 2016).

Such excessive and prolonged working hours exact a heavy toll on the physical and mental well-being of employees. In a joint report by the World Health Organization (WHO) and the ILO in May 2021, compelling evidence emerged that indicated a heightened risk of ischemic heart disease and stroke among individuals working extended hours, defined as more than 55 hours per week, in comparison with those adhering to standard working hours, which typically range from 35 to 40 hours per week. Shockingly, it was estimated that long work hours contributed to 745,000 deaths worldwide in 2016 (Pega et al. 2021). The consequences of extended working hours are not solely confined to physical health. In a harrowing incident in 2010, 14 employees of Foxconn, a prominent supplier for tech giants such as Apple and Microsoft, tragically took their own lives. These suicides were attributed to the intense emotional pressures stemming from excessively long work hours and inadequate compensation (Berg 2018).

With the growing attention from consumers, NGOs, and government agencies, the exposure of excessively long working hours within the global supply chains of the MNEs can have a significant detrimental impact on their brand image (Summers 2010, Plambeck and Taylor 2016, Kalkanci et al. 2019, Zhang et al. 2025). Consequently, the working hours at the upstream suppliers’ factories have become a pivotal element of MNEs’ corporate social responsibility (CSR) performance. Major MNEs such as Apple, Nike, and Samsung have responded to these concerns by incorporating a 60-hour-per-week limit into their codes of conduct for suppliers (Nike 2021, Samsung 2021, Apple 2022b). When the working hours exceed the standards outlined in these codes of conduct, such as the 60-hour-per-week limit, it is considered as excessive overtime. We provide a more detailed discussion on the definition of excessive overtime in Remark B.1 in Appendix B.

There are several driving forces leading to the persistent phenomenon of excessive overtime in suppliers’ factories despite the codes of conduct. The ILO provides a case study to analyze the root causes of the overtime issue (ILO 2019b). The study lists five categories of drivers: workforce, management, measurement, machinery, and method. The workforce category is further refined to identify root causes such as high turnover, incomplete headcount, recruitment challenges, and low degree of skills. These root causes are inherent to the workforce itself, which suffers directly from the excessive overtime. The management category is classified into causes such as last-minute orders, low production efficiency, and late delivery of raw materials, which are related to the buyer-supplier interaction in a supply chain. The other three categories, measurement, machinery, and method, encompass other factors such as poor sales forecasts, machine breakdowns, and lack of integration in production plants. In this paper, as a first attempt to analytically investigate the issue of excessive overtime in a global supply chain, we primarily focus on the root causes within the workforce and management categories, including high employee turnover and incomplete headcount, low degree of skills, as well as last-minute orders. We next elaborate on these factors.

First, we observe that the turnover rate of workers in labor-intensive industries is high for reasons such as low salaries, unsafe workplaces, and the repetitive and boring nature of work (ILO 2020), resulting in significant randomness of suppliers’ workforce and compromising workflow productivity (DMC 2023, Moon et al. 2023). For example, the average quarterly labor turnover rate in the apparel sector of Myanmar is about 21%, with some factories witnessing rates as high as 36% (Bernhardt et al. 2017, ILO 2019a). For another example, according to Moon et al. (2023), who study manufacturing productivity with worker turnover in a representative supplier in the electronics industry, the quarterly turnover rate of workers can be as high as 76%. The high turnover rate and the incomplete headcount issues are further exacerbated because in practice, although the supplier’s initial nominal workforce may be observable to the MNE through due diligence processes, the realized workforce often remains hidden (Wilshaw et al. 2013). Therefore, MNEs are not aware of whether suppliers’ realized workforce is inadequate or not. To meet delivery deadlines, suppliers often resort to requiring the workforce to work excessive overtime (Wilshaw et al. 2013, ILO 2017b).

Second, a low degree of skills among suppliers’ workforce makes it difficult for suppliers to meet MNEs’ high-volume demands for a wide variety of product offerings, which is often the case in industries such as electronics and apparel. There are two main implications of this low skill level. First, it may indicate low productivity among workers, making it challenging to meet high demand volumes. Second, it may suggest a limited skill set among workers. Nowadays, different products often require workers with specialized skills (Goyal and Netessine 2007, Boyabatlı and Toktay 2011, Dong et al. 2022b). In this context, a low degree of skills implies that workers with expertise in producing one product may be incapable of producing other products.

Third, MNEs often place orders in the last minute when they have a better sense of their fluctuating demands. In a global survey conducted by the ILO,¹ 59% of suppliers who responded identified additional overtime as a direct consequence of insufficient lead times (ILO 2017b). Suppliers’ uncertain and unobservable workforce and MNEs’ unpredictable last-minute orders for a high variety of product offerings make it difficult for the suppliers to forecast the workforce for each product in need and preemptively prepare for it. Therefore, suppliers often lack sufficient incentives to expand their base workforce and, instead, rely on excessive overtime of existing workers to fulfill the orders (Wilshaw et al. 2013, ILO 2017b).²

Coercing labor into working excessive overtime is a type of process violation that cannot be detected by inspecting the final product (Chen and Lee 2017). It is also difficult for the MNEs to observe such violations because the suppliers’ realized workforce is their private information. To address this issue, many MNEs, as well as third-party entities such as NGOs and government agencies, adopt on-site audits, which are usually costly and resource intensive, offering investigators a potential avenue to uncover such violations (Caro et al. 2018, 2021; Cho et al. 2019). During the audits, investigators engage in various activities, including reviews of production schedules, direct observations of production practices, and conducting anonymous interviews with a substantial number of workers (Verité 2004, Fair Labor Association 2012, SACOM 2016). If the violation of a supplier is identified in an internal audit of the MNEs, the supplier usually incurs a penalty and is given an opportunity to rectify and conduct normal production. If the violation of the supplier is identified in an external audit by the NGOs or government agencies and exposed to the public, both the supplier and the MNEs will suffer from significant goodwill loss (Zhang et al. 2022).

In addition to the practice of conducting audits, MNEs also employ supplier development strategies to combat excessive overtime by improving the supplier’s capability to fulfill orders with normal production. There are two major supplier development strategies. The first one is a workforce retention subsidy strategy under which the manufacturer provides direct subsidies for the supplier’s workforce retention initiatives in order to reduce the labor turnover rate. For instance, Apple has taken measures such as offering direct financial bonuses to workers at Foxconn and collaborating with a Chinese supplier to enhance workers’ satisfaction and retention rates by expanding food offerings and providing additional bonuses (Foremski 2010, Apple 2022a). The other one is a cross-training strategy under which the manufacturer provides learning and upskilling opportunities for the supplier’s workers to increase the versatility of the workforce to reduce the mismatch between workforce and demands in the presence of multiple products.³ For example, Apple also offers educational and upskilling opportunities to its suppliers’ workers to make the workforce versatile (Apple 2022a). Nike has implemented a supplier capability-building program, which includes increased investment in worker training, as workers are expected to perform multiple production tasks (Distelhorst et al. 2017, ILO 2017a). SHEIN has announced a $70 million investment over the next five years to empower its ecosystem of third-party manufacturing suppliers and the workers within. One objective of SHEIN’s investment is to provide training and upskilling opportunities for the workers (SHEIN 2023).

Motivated by these observations, we attempt to study operational strategies to combat the phenomenon of excessive overtime in global supply chains from an analytical perspective. Specifically, we investigate the following research questions. When do suppliers have incentives to violate their codes of conduct and force their workers to work excessive overtime? How should the MNEs employ the stick strategy of auditing and/or the carrot strategy of supplier development to combat such violations by their suppliers? How will these strategies interact with each other if employed jointly?

To investigate these research questions, we build a game-theoretic model of a dyadic supply chain in which one manufacturer sources two products from one supplier and then sells them in a downstream market motivated by the high variety of products of the MNEs. The manufacturer’s demands for the two products are random. The supplier’s workforce for each product is random and is determined by the normal work hours of a group of dedicated workers. The manufacturer orders according to the realized demands, reflecting the last-minute orders of the MNEs in practice. The supplier then determines production quantities based on the received orders and the realized (normal) workforce, which is observable to the supplier only.

On the one hand, if the supplier fulfills the orders using normal workforce only, the manufacturer will pay the wholesale price and sell the products in the market. In this case, if the supplier delivers a lower quantity than the order, an underdelivery penalty will be incurred by the supplier. On the other hand, if the supplier decides to produce more than its normal workforce, the supplier can do so by coercing the workers to work excessive overtime. Such a violation may be detected by the manufacturer’s costly and imperfect audit (the probability of detecting a violation corresponds to the audit accuracy) or a third party’s (an NGO or a government agency) exogenous audit. If the violation is detected by the manufacturer, the supplier will be charged a penalty and required to rectify and conduct normal production. However, if such a violation is not detected by the manufacturer (either because the manufacturer does not conduct an audit or the manufacturer conducts an audit but does not detect it), but it is detected and exposed to the public by the third party, both the manufacturer and the supplier incur goodwill losses, respectively. If neither the manufacturer nor the third party detects the violation, the outcome is the same as if the supplier had fulfilled orders with normal workforce. That is, the manufacturer will pay the wholesale price and sell the products in the market without incurring any damages. We refer to the base model as the model with auditing only.

Analyzing the model with auditing only, we find that the supplier forces excessive overtime if the realized workforce is lower than the order and the audit accuracy of the manufacturer is low. In this case, the supplier’s expected cost to commit the violation is small relative to the benefit from increased order fulfillment with overtime production. As the manufacturer’s audit accuracy increases, the supplier’s violation is more likely to be detected, and therefore, the supplier is likely to incur a higher violation cost and is less likely to commit a violation. We also find that the manufacturer decides to audit if its audit cost is smaller than an audit cost threshold.

To better investigate the impact of the manufacturer’s auditing strategy on excessive overtime and social welfare, we introduce two benchmarks—a no-audit benchmark and a centralized supply chain benchmark. In the no-audit benchmark, the auditing strategy is not viable to the manufacturer, and the supplier forces overtime under workforce shortages and always produces according to the orders in equilibrium. In the centralized supply chain benchmark, the supplier and the manufacturer act as an integrated firm that does not force overtime and always conducts normal production. We find that auditing can partially mitigate excessive overtime and improve social welfare relative to the no-audit benchmark, but it may not completely eliminate excessive overtime or improve social welfare to the level under the centralized supply chain benchmark.

Motivated by the practices of Apple, Nike, and SHEIN, we next analyze how the MNE should employ the “stick” (i.e., auditing) together with the “carrot” (i.e., a supplier development strategy) to combat the use of excessive overtime by the supplier. In particular, we consider two supplier development strategies—a workforce retention subsidy strategy and a cross-training strategy, respectively. With the workforce retention subsidy strategy, the manufacturer can directly subsidize the supplier’s workforce retention initiative so as to decrease the workers’ turnover rate and increase the probability of the supplier’s workforce being high. We refer to this model as the model with both workforce retention subsidy and auditing. With the cross-training strategy, the MNE can invest in educating a proportion of the supplier’s single-skilled workers to be multiskilled to improve the flexibility of the workforce. We refer to this model as the model with both cross-training and auditing.

Comparing the model with both workforce retention subsidy and auditing to the model with auditing only, contrary to the naive intuition that workforce retention subsidy and auditing should always be substitutes, that is, the manufacturer should have a lower willingness to audit after workforce retention subsidy, we find that workforce retention subsidy and auditing can be complements, that is, the manufacturer may have a higher willingness to audit after workforce retention subsidy. The main intuition is that as the workforce retention subsidy improves the supplier’s workforce, whereas the overall probability of the supplier meeting demands with normal workforce is improved, there could be a higher chance that the supplier is in a scenario where only one product experiences workforce shortage relative to the setting with auditing only. In such a case, if the supplier’s violation behavior is identified, the opportunity cost of the manufacturer from auditing (i.e., the reduced supply quantity because the supplier needs to rectify such behavior and not use overtime labor) is lower compared with the scenario where both products experience workforce shortage. Therefore, the manufacturer may have a higher willingness to audit.

In addition, we characterize conditions under which the manufacturer can achieve a win-win outcome by both subsidizing and auditing the supplier. We find that the supplier development strategies have two effects: a direct order-fulfillment-improvement effect because the supplier’s subsidy directly increases the available workforce to produce for the order and an indirect audit-willingness-adjustment effect because the subsidy and auditing can be substitutes or complements. When subsidizing the supplier does not reduce the manufacturer’s willingness to audit the supplier or when the audit accuracy is low such that even if the manufacturer audits less of the supplier, the negative effect is dominated by the positive order-fulfillment-improvement effect, the manufacturer can earn a higher profit and reduce the supplier’s overtime at the same time. Compared with the no-audit and centralized supply chain benchmarks, we also find that the combination of workforce retention subsidy and auditing may not only mitigate overtime but also improve social welfare, sometimes, to a level that is even higher than that in the centralized supply chain benchmark (without workforce retention subsidy) as a consequence of supplier development.

However, when these conditions are not satisfied, the workforce retention subsidy may backfire and result in a higher level of excessive overtime by the supplier. Specifically, when the workforce retention subsidy and auditing are substitutes, the manufacturer has a lower willingness to audit after the workforce retention subsidy, which leads to a lower cost for the supplier to force overtime.

Comparing the model with both cross-training and auditing to the model with auditing only, we also find that cross-training and auditing can be complements. This counterintuitive result is driven by the fact that the improved flexibility of the supplier’s workforce reduces the manufacturer’s opportunity cost because of the identification of the supplier’s violation. Therefore, the manufacturer could have a higher willingness to audit the supplier. Similar to the workforce retention subsidy above, we also identify conditions under which cross-training could lead to a win-win outcome where the manufacturer earns a higher profit and the supplier uses less of overtime, and conditions under which cross-training may backfire and result in a higher level of excessive overtime by the supplier. In addition, cross-training and auditing could lead to a higher social welfare level than that under the centralized supply chain benchmark (without cross-training).

Our analysis yields the following managerial insights for practitioners. First of all, supplier development activities such as workforce retention subsidy or cross-training can be either a substitute or complement for auditing in mitigating the supplier’s excessive overtime issue. Therefore, the MNEs should be careful when simultaneously adopting the carrot-and-stick strategies because they might not have synergies. That is, these strategies may not always be substitutes, and reducing audit under the mistaken belief that carrots can replace the stick may not only fail to curb excessive overtime but could also diminish the MNE’s overall profitability when the two strategies are, in fact, complements. Second, supplier development activities may increase the manufacturer’s profit and reduce excessive overtime, leading to a win-win outcome, but they may also backfire and lead to increased excessive overtime. As a result, the MNEs who intrinsically care about excessive overtime issues should not have a slack mind on the violation behaviors even after providing resources to develop the suppliers’ capability.

2. Literature Review

Our work relates to the literature on socially responsible operations, capacity management, and supply risk management. Below, we review the literature in each of the three streams and explain the contributions of our work.

Within socially responsible operations (Kalkanci et al. 2019, Sunar and Swaminathan 2022), our work relates to the literature that analyzes how manufacturers can use audit/inspection as a strategy for monitoring their suppliers’ compliance with codes of conduct (Dawande and Qi 2021). Plambeck and Taylor (2016) study the effectiveness of audits in a dyadic supply chain under the possibility that the supplier can hide its unsafe practices from the buyer’s audit. Cho et al. (2019) examine a firm’s auditing policy and wholesale price decisions to combat a supplier’s use of child labor. Kraft et al. (2020) study a firm’s investment in a supplier’s SR capabilities. Kalkanci and Plambeck (2020) study CSR problems involving a supplier’s potentially inadequate capacity. Ha et al. (2023) examine the incentive for competing manufacturers to share supplier audit information, based on which the manufacturers determine their sourcing strategies. Several other papers also examine the auditing strategy in a one-buyer/regulator-one-supplier setting, focusing on issues including product adulteration (Rui and Lai 2015, Lee and Li 2018, Mu et al. 2019, Levi et al. 2020, Dong et al. 2022a), contracting (Chen and Lee 2017), voluntary disclosure of self-noncompliance (Lu and Tomlin 2022), and supplier-auditor collusion (Chen et al. 2020b). Other papers study the impact of the auditing strategy in supply networks, including Caro et al. (2018), Chen et al. (2020a), Fang and Cho (2020), Feng et al. (2022), Huang et al. (2022), and Zhang et al. (2022). Our paper complements the works above in several respects. We model the unique feature of the excessive overtime problem reflected by the uncertain base workforce and the mismatch between demands and workforce for multiple products. We also consider supplier development strategies, including workforce retention subsidy and cross-training, to improve the supplier’s capability to match supply with demand.

Our work also relates to the literature on capacity management with volume or product flexibility and supply risk management with uncertain demand because workforce is an important component of the supplier’s capacity. Previous work on capacity management has focused on issues such as the choice of flexible or dedicated technology (Goyal and Netessine 2007, Boyabatlı et al. 2016) and capacity reservation (Qi et al. 2019). For supply risk management, prior works have analyzed the value of mix-flexibility and dual sourcing (Tomlin and Wang 2005), optimal design of flexibility under dynamic disruption risks (Saghafian and Van Oyen 2016), diversification under correlated random yields (Dong et al. 2022c), optimal multiple-sourcing strategies when facing reliable and unreliable suppliers (Hu and Kostamis 2015), and optimal flexibility configuration of a supply network (Wang and Webster 2022), among others. Our work complements these streams of literature by incorporating endogenous risk because of excessive overtime in capacity and supply risk management problems.

3. Model Framework

Consider a dyadic supply chain with one manufacturer and one supplier. The manufacturer sources two products (labeled by 1 and 2) from the supplier and then sells them in the downstream market. Following Plambeck and Taylor (2016) and Chen et al. (2020a), we consider the wholesale price and the retail price for each product to be w and p, respectively.

The demand of products 1 and 2 is $\mathit{D}=(D_1,D_2)$, where $D_1$ and $D_2$ are correlated discrete random variables. The marginal distribution of $D_i$, $i=1,2$, is a “boom-bust” distribution (Taylor and Plambeck 2007), where the realized value is H with probability (w.p.) $\alpha$ and L w.p. $1-\alpha$, where $L<H$. Let $\beta$ denote the conditional probability of product i’s demand being H given that product $3-i$’s demand is also H. Fixing the probability of the marginal distribution $\alpha$, the correlation between $D_1$ and $D_2$ changes linearly in $\beta$. We consider $\alpha ,\beta \in (0,1)$ to avoid trivial cases. The joint distribution of $\mathit{D}$ is as follows: $\mathrm{Pr}(\mathit{D}=(H,H))=\beta \alpha$, $\mathrm{Pr}(\mathit{D}=(H,L))=\mathrm{Pr}(\mathit{D}=(L,H))=(1-\beta )\alpha$, and $\mathrm{Pr}(\mathit{D}=(L,L))=1-2\alpha +\beta \alpha$. The correlation between the two demands is $\rho =(\beta -\alpha )/(1-\alpha )$. This distribution has been used in the literature, for example, Qi et al. (2019), to characterize correlated random demands for analytical tractability. After observing the realized demands $\mathit{d}=(d_1,d_2)$, the manufacturer orders $\mathit{d}$ from the supplier.

Following the discussions about the uncertain workforce in the introduction, the supplier’s workforce $\mathit{K}=(K_1,K_2)$, determined by the normal work hours of dedicated workers for each product, are correlated discrete random variables. Similar to the demands, the marginal distribution of workforce $K_i$, $i=1,2$ is also a “boom-bust” distribution, with $\mathrm{Pr}(K_i=H)={\gamma }_0$ and $\mathrm{Pr}(K_i=L)=1-{\gamma }_0$. Let ${\beta }_K$ denote the conditional probability of product i’s workforce being H given that product $3-i$’s workforce is also H. We consider ${\gamma }_0,{\beta }_K\in (0,1)$ to avoid trivial cases. It follows that the probabilities of the joint distribution of the supplier’s workforce are $\mathrm{Pr}(\mathit{K}=(H,H))={\beta }_K{\gamma }_0$, $\mathrm{Pr}(\mathit{K}=(H,L))=\mathrm{Pr}(\mathit{K}=(L,H))=(1-{\beta }_K){\gamma }_0$, and $\mathrm{Pr}(\mathit{K}=(L,L))=1-2{\gamma }_0+{\beta }_K{\gamma }_0$. The correlation between the two groups within the supplier’s workforce is ${\rho }_K=({\beta }_K-{\gamma }_0)/(1-{\gamma }_0)$. Given the linear relationship between ${\beta }_K$ and ${\rho }_K$, for expositional convenience, we utilize ${\beta }_K$ as a proxy for correlation in subsequent analyses, referring to it as the (proxy) workforce correlation. In our analysis, we consider the range of parameters such that the probabilities are well defined. The uncertainty is resolved when the supplier receives the order quantities from the manufacturer. In addition, the realized workforce $\mathit{k}=(k_1,k_2)$ are observable to the supplier only. Therefore, the manufacturer cannot simply infer whether excessive overtime has been forced from the production quantity.

Given the manufacturer’s order quantities $\mathit{d}$ and the realized workforce $\mathit{k}$, the supplier determines the production quantities $\mathit{q}=(q_1,q_2)$, which may be different from the manufacturer’s order. Specifically, for product i, the supplier can produce and deliver $q_i=d_i$ without using excessive overtime if the order $d_i\le k_i$, which is referred to as the normal production. However, if the order $d_i>k_i$, the supplier may conduct a normal production and deliver a quantity equal to $k_i$ only and incur an underdelivery cost, or force excessive overtime to stretch its workforce and deliver the quantity $d_i$. Let $b_i$ denote the degree of excessive overtime for product i, the ratio of the nonnegative difference between the supplier’s production quantity and the realized normal workforce to the workforce; that is, $b_i={(q_i-k_i)}^{+}/k_i$, where $x^{+}\triangleq \max \{x,0\}$. The degree of excessive overtime is bounded from above by $\overline{b}$ reflecting the physical constraint of human workers; that is, $b_i\le \overline{b}$. The unit underdelivery cost is u for both products and is transferred to the manufacturer as a part of the manufacturer’s profit. The unit production cost is c for both products, regardless of whether they are produced in normal production or with excessive overtime. Our results continue to hold qualitatively if we consider the setting in which firms pay a wage premium for overtime. The unit production cost c also denotes the unit salary paid to workers, and other costs are normalized to zero.

If the supplier conducts normal production only, the supplier is considered to be in a safe state. In the safe state, the manufacturer pays the total amount ${\sum }_{i=1}^2(w{q}_i-u(d_i-q_i{)}^{+})$ to the supplier and earns $p{\sum }_{i=1}^2{q}_i$ from the downstream market, and no damages because of the violation of social responsibility should incur to either the manufacturer or the supplier.

However, if the supplier forces excessive overtime, that is, ${\sum }_{i=1}^2{b}_i>0$, the supplier is considered to be in an unsafe state. Let $h(b_1,b_2)={\mathbf{1}}_{\{{\sum }_{i=1}^2{b}_i>0\}}$, where ${\mathbf{1}}_{\{C\}}$ is an indicator function that equals one if condition C is true, and zero otherwise. The supplier is in the unsafe state when $h(b_1,b_2)=1$ and in the safe state when $h(b_1,b_2)=0$. The binary state of the supplier being unsafe is a common assumption in socially responsible operations literature (e.g., Babich and Tang 2012, Cho et al. 2019) for analytical tractability. The manufacturer may incur a cost to audit the supplier to detect the supplier’s violation behavior with an audit decision e, which corresponds to the probability of the manufacturer detecting the violation behavior of the supplier conditional on the supplier being unsafe.

Following Cho et al. (2019), we consider a binary audit decision $e\in \{e_H,e_L\}$, where $e_H$ and $e_L$ denote the high and low audit accuracy, respectively; $e_H\in (0,1]$; and $e_L$ is normalized to zero. The corresponding auditing costs are $R(e_H)=R\ge 0$ and $R(e_L)=0$. We consider the setting in which the manufacturer makes its audit decision e before the realization of demands. That is, the manufacturer’s audit decision is public information that can be observed by the supplier, corresponding to the practice where measures to combat excessive overtime were disclosed by companies such as Apple and Nike in their annual social responsibility reports (Nike 2021, Apple 2022a), and large retailers and manufacturers in California are required by the government to publicly disclose their efforts on combating forced labor, including excessive overtime (Aiken et al. 2017, Cho et al. 2019). In Appendix D, we examine a setting in which the manufacturer makes its audit decision after observing the realized demands and show that our main insights continue to hold qualitatively. Throughout this paper, we define $X\wedge Y\triangleq \min \{X,Y\}$ and $X\vee Y\triangleq \max \{X,Y\}$ for ease of exposition.

If the supplier’s violation behavior is detected by the manufacturer, the supplier is charged a penalty $m_1>0$, which is transferred to the manufacturer as a part of the manufacturer’s profit, and is required to rectify the violation behavior.⁴ In this case, the supplier produces $k_i\wedge d_i$ for each product, the manufacturer pays the total payment ${\sum }_{i=1}^2(w(k_i\wedge d_i)-u{(d_i-k_i)}^{+})$ to the supplier and earns $p{\sum }_{i=1}^2(k_i\wedge d_i)$ from the downstream market, and no damages because of the violation of social responsibility should incur to either the manufacturer or the supplier.

The supplier’s violation behavior, if not detected by the manufacturer’s audit, may be detected and exposed to the public through external audits conducted by third parties (such as NGOs). The external audit accuracy is exogenous and denoted by $\tau \in (0,1)$. That is, conditional on the supplier’s violation behavior, if any, not being detected by the manufacturer’s audit, it can be detected and exposed by NGOs with probability $\tau$. In this case, the manufacturer and the supplier incur a goodwill loss l and $m_2$, respectively. If the supplier is unsafe but the violation behaviors were detected by neither the manufacturer nor the NGOs, the outcome is the same as when the supplier is safe.

The sequence of events is summarized in Figure 1. We use backward induction to derive the equilibrium decisions. The subscripts S and M indicate the supplier and the manufacturer, respectively. First, given the manufacturer’s audit decision e and the realized demands $\mathit{d}$ and workforce $\mathit{k}$, the supplier decides its production quantities $\mathit{q}=(q_1,q_2)$ to maximize its profit as follows, where the degree of excessive overtime $b_i={(q_i-k_i)}^{+}/k_i$:

Let ${\widehat{q}}_i(e)$ denote the supplier’s best-response production quantity. When the supplier is indifferent between forcing overtime production and conducting normal production, we assume that the supplier conducts normal production as a tie-breaking rule. Anticipating the supplier’s best response $({\widehat{q}}_1(e),{\widehat{q}}_2(e))$, the manufacturer decides the audit decision $e\in \{e_H,0\}$ to maximize the manufacturer’s expected profit ${\mathbb{E}}_{\mathit{D},\mathit{K}}[{\pi }_M(e)]$, where ${\pi }_M(e)$ is the manufacturer’s realized profit:

Assumptions.

To avoid trivial and less relevant cases, we assume that $0<u<(p-w)$, $0<u\le (w-c)L/(H-L)$, and $0<\tau l<(p-w)(H+L)$. The first assumption indicates that the manufacturer’s margin from selling the product is larger than the unit underdelivery cost paid by the supplier. The second assumption guarantees that the supplier’s profit is positive when conducting normal production, and the third assumption ensures that the manufacturer’s profit is positive when the manufacturer does not audit the supplier. We also assume that $H\le (1+\overline{b})L$, which means the supplier may satisfy an order of size H with excessive overtime; otherwise, the manufacturer can trivially infer from a delivered quantity between L and H that excessive overtime is used. In addition, we assume that $\tau m_2<(w+u-c)(H-L)$ so that the supplier may have incentives to use excessive overtime when its realized normal workforce is inadequate; relaxing the assumption will necessitate discussions for more cases without generating new insights, as the supplier will have weaker incentives to commit violations under certain demand and workforce scenarios when this assumption does not hold. Finally, we assume that $\tau (l+m_2)>2(p-c)(H-L)$, indicating that from the supply chain perspective, the total expected goodwill loss is larger than the maximum gain from overtime production.

4. Base Model: Auditing Only

In this section, we examine a setting in which auditing is the sole viable tool for the manufacturer to combat excessive overtime. In what follows, we first analyze the supplier’s production decision for a given audit decision, order quantities, and realized workforce in Section 4.1 and then characterize the manufacturer’s equilibrium audit decision in Section 4.2. In Section 4.3, we first introduce two benchmarks—a no-audit benchmark and a centralized supply chain benchmark— and then examine the impact of audit on excessive overtime and social welfare.

4.1. Supplier’s Production Decision

In our setting, there are four scenarios in which the supplier may stretch its workforce using excessive overtime. In each of the scenarios, the normal workforce is not enough to meet the demand for at least one of the two products. We denote such a scenario by notation ${\mathbb{S}}_{d_i{d}_{3-i}}^{k_i{k}_{3-i}}$, where the subscript and the superscript indicate the realized demands $(d_i,d_{3-i})$ and the realized workforce $(k_i,k_{3-i})$, respectively, and the four scenarios are denoted by ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, ${\mathbb{S}}_{HL}^{LL}$, and ${\mathbb{S}}_{HH}^{LL}$. For example, ${\mathbb{S}}_{HL}^{LH}$ indicates the demand for one product is less than the corresponding workforce, whereas the demand for the other product is more than the corresponding workforce. Note that scenario ${\mathbb{S}}_{HL}^{LH}$ is a cross-mismatching scenario in the sense that there is redundant workforce for one product and insufficient workforce for the other. In the other three scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LL}$, and ${\mathbb{S}}_{HH}^{LL}$, there is no redundant workforce for either product, and only insufficient workforce is observed for at least one product.

After observing the audit decision e, the realized workforce $\mathit{k}$, and demands $\mathit{d}$, the supplier decides on the production quantities as shown in the following proposition. All proofs of results in Section 4 are relegated to Online Appendix B.

Proposition 1

(Supplier’s Production Quantities). Given the manufacturer’s audit decision e, realized workforce $\mathit{k}$, and demands $\mathit{d}$, the supplier’s production quantities in scenario ${\mathbb{S}}_{d_i{d}_{3-i}}^{k_i{k}_{3-i}}$ are as follows.

1. When there is enough workforce for both products, that is, $k_i\ge d_i$ for $i=1\hspace{0.17em}\text{and}\hspace{0.17em}2$, the supplier conducts normal production with quantities $({\widehat{q}}_1(e),{\widehat{q}}_2(e))=(d_1,d_2)$ and accrues the profit ${\pi }_S({\widehat{q}}_1(e),{\widehat{q}}_2(e)|e)={\sum }_{i=1}^2(w-c)d_i.$

2. When there is not enough workforce for at least one of the two products, that is, $k_i<d_i$ for $i=1$ and/or 2, there exists a scenario-dependent audit threshold

   $$\tilde{e}(\mathit{d},\mathit{k})=\frac{\sum _{i=1}^2(w+u-c){(d_i-k_i)}^{+}-\tau m_2}{m_1+\sum _{i=1}^2(w+u-c){(d_i-k_i)}^{+}-\tau m_2}$$(2)

   such that the supplier forces excessive overtime with production quantities $({\widehat{q}}_1(e),{\widehat{q}}_2(e))=(d_1,d_2)$ and accrues the profit ${\pi }_S({\widehat{q}}_1(e),{\widehat{q}}_2(e)|e)={\sum }_{i=1}^2((w-c)d_i-e(w+u-c){(d_i-k_i)}^{+})-e{m}_1-(1-e)\tau m_2$ if the manufacturer’s audit decision $e<\tilde{e}(\mathit{d},\mathit{k})$. Otherwise, the supplier conducts normal production with quantities $({\widehat{q}}_1(e),{\widehat{q}}_2(e))=(k_1\wedge d_1,k_2\wedge d_2)$ and accrues the profit ${\pi }_S({\widehat{q}}_1(e),{\widehat{q}}_2(e)|e)={\sum }_{i=1}^2((w-c)(k_i\wedge d_i)-u{(d_i-k_i)}^{+}).$

The proposition shows that when the workforce is sufficient to satisfy the demands, the supplier fulfills the orders with normal production. However, when the workforce for at least one product is insufficient to satisfy the demand, the supplier may force overtime production to fulfill the order if the manufacturer’s audit decision e is small. That is, the chance to discover the supplier’s violation behavior is low. If the supplier uses excessive overtime for product i, it will produce the ordered quantity $d_i$. Otherwise, the manufacturer may infer that overtime production is used if the delivered quantity is strictly between L and $d_i$. It follows that $2(H-L)$ units of products will be produced with the overtime workforce in scenario ${\mathbb{S}}_{HH}^{LL}$, and $H-L$ units of products will be produced with the overtime workforce in scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, or ${\mathbb{S}}_{HL}^{LL}$.

The condition to force excessive overtime, that is, $e<\tilde{e}(\mathit{d},\mathit{k})$, is derived from comparing the supplier’s profit of forcing excessive overtime, ${\pi }_S(d_1,d_2|e)$, with its profit of conducting normal production only, ${\pi }_S(k_1\wedge d_1,k_2\wedge d_2|e)$, in part 2 of Proposition 1. Note that the condition $e<\tilde{e}(\mathit{d},\mathit{k})$ is equivalent to

In (3), the left-hand and right-hand sides are the benefit and cost of using overtime, respectively. Specifically, compared with when the supplier does not force overtime, if the supplier forces overtime and its violation behavior is not detected by the manufacturer, then the supplier can obtain the margin $w-c$ and also save the unit underdelivery cost u for each additional unit of product fulfilled with overtime production. It follows that the benefit from using overtime is $(1-e){\sum }_{i=1}^2(w+u-c){(d_i-k_i)}^{+}$. On the other hand, if the supplier forces overtime and its violation behavior is detected by either the manufacturer or external NGOs, then the supplier incurs penalty $m_1$ or goodwill loss $m_2$, respectively. It follows that the cost of using overtime is $e{m}_1+(1-e)\tau m_2$.

We next show in Corollary 1 that the manufacturer’s audit becomes more effective in combating the supplier’s overtime violation as the audit becomes more efficient (that is, the chance to discover the violation, if any, increases). For ease of exposition, we label the scenario-dependent audit threshold as $\underset{¯}{e}$ for ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$ and ${\mathbb{S}}_{HL}^{LL}$, and $\overline{e}$ for ${\mathbb{S}}_{HH}^{LL}$ in the sequel. For example, $\underset{¯}{e}\triangleq \tilde{e}(H,H,H,L)=\tilde{e}(H,H,L,H)$ for scenario ${\mathbb{S}}_{HH}^{HL}$ by (2).

Corollary 1

(Impact of Manufacturer’s Audit on Supplier’s Violation Behavior). The relationship among the scenario-dependent audit thresholds is $0<\underset{¯}{e}<\overline{e}<1$. The number of scenarios in which the supplier forces overtime production decreases with the manufacturer’s audit decision e. Specifically,

1. if $0\le e<\underset{¯}{e}$, the supplier forces overtime in scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, ${\mathbb{S}}_{HL}^{LL}$, and ${\mathbb{S}}_{HH}^{LL}$;

2. if $\underset{¯}{e}\le e<\overline{e}$, the supplier forces overtime in scenario ${\mathbb{S}}_{HH}^{LL}$;

3. if $\overline{e}\le e\le 1$, the supplier does not force overtime in any of the four scenarios.

The relationship $0<\underset{¯}{e}<\overline{e}<1$ characterized in Corollary 1 implies that the supplier has a smaller and equal incentive to force overtime in scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, and ${\mathbb{S}}_{HL}^{LL}$ and a larger incentive in scenario ${\mathbb{S}}_{HH}^{LL}$. To understand the driving forces, let us consider the supplier’s benefit and cost from using overtime production specified in (3). On the one hand, the costs of using overtime production in all of these four scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, ${\mathbb{S}}_{HL}^{LL}$, and ${\mathbb{S}}_{HH}^{LL}$ are the same. On the other hand, the benefits from forcing overtime in scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, and ${\mathbb{S}}_{HL}^{LL}$ are smaller than that in ${\mathbb{S}}_{HH}^{LL}$ because the supplier benefits from increased production quantity for both products in the latter case. Therefore, the supplier has a smaller and equal overtime incentive in ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, and ${\mathbb{S}}_{HL}^{LL}$ and a larger one in ${\mathbb{S}}_{HH}^{LL}$.

4.2. Manufacturer’s Audit Decision

Anticipating the supplier’s best-response production decision, the manufacturer makes its audit decision before the realization of demands and workforce as follows. We use the superscript $\mathcal{A}$ to denote the model with auditing only.

Proposition 2

(Equilibrium Audit). There exists an audit cost threshold ${\overline{R}}^{\mathcal{A}}(e_H)$ such that the manufacturer’s equilibrium audit decision is

$$e^{\mathcal{A}}=\{\begin{array}{ll}{e}_H,& \text{if}\hspace{0.17em}R\le {\overline{R}}^{\mathcal{A}}(e_H);\\ 0,& \text{otherwise}.\end{array}$$

Furthermore, ${\overline{R}}^{\mathcal{A}}(e_H)$ increases in $e_H$ with ${\lim }_{e_H\to 0^{+}}{\overline{R}}^{\mathcal{A}}(e_H)=0.$

Proposition 2 shows that the manufacturer audits the supplier only when the audit cost R is not too large (Figure 2). Moreover, the manufacturer’s willingness to audit increases in the audit accuracy $e_H$; that is, the audit cost threshold ${\overline{R}}^{\mathcal{A}}(e_H)$ increases in $e_H$. To understand the result, recall from Corollary 1 that $\underset{¯}{e}$ is the threshold above which the supplier does not force overtime in scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, and ${\mathbb{S}}_{HL}^{LL}$, and $\overline{e}$ is the threshold above which the supplier does not force overtime in scenario ${\mathbb{S}}_{HH}^{LL}$. Because the manufacturer prefers the supplier not to force overtime, the manufacturer’s willingness to audit discontinuously increases at the two thresholds $\underset{¯}{e}$ and $\overline{e}$, as shown in Figure 2. We next explain the reason why the manufacturer’s willingness to audit increases when $0<e_H<\underset{¯}{e}$, $\underset{¯}{e}\le e_H<\overline{e}$, and $\overline{e}\le e_H\le 1$, respectively.

When $0<e_H<\underset{¯}{e}$, the supplier has incentives to force overtime in all four scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, ${\mathbb{S}}_{HL}^{LL}$, and ${\mathbb{S}}_{HH}^{LL}$. (When the manufacturer does not audit (i.e., $e=0$), the supplier also forces overtime in all four scenarios.) In scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, and ${\mathbb{S}}_{HL}^{LL}$, the supplier forces overtime for one product only. Therefore, by auditing the supplier, the manufacturer could avoid the goodwill loss, receive a penalty imposed on the misbehaving supplier, and incur an opportunity cost of lost sales because of underdelivered quantity for the one product. That is, the net benefit from auditing in these scenarios is $e_H(m_1+\tau l-(p-w-u)(H-L))$. In scenario ${\mathbb{S}}_{HH}^{LL}$, the supplier forces overtime for both products. Compared with the previous three scenarios, the opportunity cost to identify the misbehaving supplier is higher because the cost is due to the underdelivered quantity for both products. That is, the net benefit from auditing in this scenario is $e_H(m_1+\tau l-2(p-w-u)(H-L))$. It follows that the expected net benefit from auditing in all four scenarios (from weighting the net benefit in each scenario by the corresponding probability) increases in $e_H$, leading to the manufacturer’s willingness to audit increasing in the audit accuracy $e_H$.

When $\underset{¯}{e}\le e_H<\overline{e}$, the supplier only forces overtime in scenario ${\mathbb{S}}_{HH}^{LL}$. It follows that the manufacturer’s net benefit from auditing in scenario ${\mathbb{S}}_{HH}^{LL}$ is the same as that in the previous case. However, in scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, and ${\mathbb{S}}_{HL}^{LL}$, the supplier will not force overtime if the manufacturer audits, leading to the manufacturer’s net benefit from auditing increasing to a higher value of $\tau l-(p-w-u)(H-L)$. It follows that the expected net benefit from auditing in all four scenarios and the resulting manufacturer’s willingness to audit increase in the audit accuracy $e_H$.

When $\overline{e}\le e_H\le 1$, the supplier does not force overtime in any of the four scenarios. Therefore, the manufacturer’s net benefit from auditing in scenario ${\mathbb{S}}_{HH}^{LL}$ is increased to $\tau l-2(p-w-u)(H-L)$, whereas the net benefit remains as $\tau l-(p-w-u)(H-L)$ in scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, and ${\mathbb{S}}_{HL}^{LL}$. In this case, it is easy to see that the expected net benefit from auditing in all four scenarios and the resulting manufacturer’s willingness to audit remain constant as the audit accuracy $e_H$ increases.

Remark 1

(Comparison of Net Benefits of Auditing Across Scenarios). In each of the three cases above, $0<e_H<\underset{¯}{e}$, $\underset{¯}{e}\le e_H<\overline{e}$, and $\overline{e}\le e_H\le 1$, we observe that the net benefit from auditing in scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, and ${\mathbb{S}}_{HL}^{LL}$ is higher than that in scenario ${\mathbb{S}}_{HH}^{LL}$, either because the opportunity cost associated with the underdelivered quantity is lower in the former case, or the manufacturer prefers the supplier not to force overtime.

4.3. Impact of Auditing

We first respectively analyze two benchmarks in Section 4.3.1: one is a no-audit benchmark in which the manufacturer cannot audit the supplier, and the other is a centralized supply chain benchmark. We then study the impact of auditing on excessive overtime and social welfare in Section 4.3.2. We use the superscripts $\mathcal{N}$ and $\mathcal{C}$ to denote the no-audit benchmark and the centralized supply chain benchmark, respectively.

4.3.1. Two Benchmarks.

• No-audit benchmark: The no-audit benchmark is a special case of the model with auditing only (when $e=0$). From Proposition 1 and Corollary 1, we have that the supplier always fulfills the orders when $e=0$. It follows that the supplier forces overtime whenever it has a workforce shortage. We have the supplier’s production decision in the no-audit benchmark summarized in the following proposition, where $q_i^{\mathcal{N}}$ denotes the supplier’s equilibrium production quantity of product i.

Proposition 3

(Supplier’s Production Quantities). Given the realized workforce $\mathit{k}$ and demands $\mathit{d}$, the supplier’s production quantities in scenario ${\mathbb{S}}_{d_i{d}_{3-i}}^{k_i{k}_{3-i}}$ are $(q_1^{\mathcal{N}},q_2^{\mathcal{N}})=(d_1,d_2)$. That is, the supplier always fulfills the orders (and forces overtime whenever needed) and accrues the profit ${\pi }_S^{\mathcal{N}}(d_1,d_2)={\sum }_{i=1}^2(w-c)d_i-h(b_1,b_2)\tau m_2$.

Although the manufacturer can anticipate the supplier’s best-response production quantity and is aware that the supplier may force overtime, the manufacturer does not know whether there is violation for sure because the realized workforce $\mathit{k}$ is unobservable to the manufacturer.

• Centralized supply chain benchmark: In the centralized supply chain benchmark, the manufacturer and the supplier integrate as one firm that observes both the realized demands and workforce. It follows that the integrated firm is aware of any violation behavior without auditing, and there is no need to consider auditing in the centralized supply chain benchmark. Given the realized workforce $\mathit{k}$ and demands $\mathit{d}$, the integrated firm determines the production quantities $(q_1,q_2)$ to maximize the profit ${\pi }^{\mathcal{C}}(q_1,q_2)$ as follows:

  $$\begin{array}{l}{\pi }^{\mathcal{C}}(q_1,q_2)=-h(b_1,b_2)\tau (l+m_2)+(p-c)(q_1+q_2).\end{array}$$

  The integrated firm’s production decision is characterized in the following proposition, in which $q_i^{\mathcal{C}}$ denotes the firm’s optimal production quantity of product i.

Proposition 4

(Integrated Firm’s Production Quantities). Given the realized workforce $\mathit{k}$ and demands $\mathit{d}$, the integrated firm’s production quantities in scenario ${\mathbb{S}}_{d_i{d}_{3-i}}^{k_i{k}_{3-i}}$ are $(q_1^{\mathcal{C}},q_2^{\mathcal{C}})=(k_1\wedge d_1,k_2\wedge d_2)$. That is, the integrated firm always conducts normal production and accrues the profit ${\pi }^{\mathcal{C}}(k_1\wedge d_1,k_2\wedge d_2)={\sum }_{i=1}^2(p-c)(k_i\wedge d_i).$

Recall that $\tau (l+m_2)>2(p-c)(H-L)$. That is, from the supply chain perspective, the total expected goodwill loss of using overtime production, $\tau (l+m_2)$, is larger than the maximum gain (which is achieved in scenario ${\mathbb{S}}_{HH}^{LL}$) from using overtime production, $2(p-c)(H-L)$. Therefore, the integrated firm will never force overtime.

4.3.2. Impact of Auditing on Excessive Overtime and Social Welfare.

Having analyzed the equilibrium decisions in the two benchmarks, we next characterize the impact of auditing on two performance metrics, (i) the expected degree of excessive overtime, and (ii) social welfare, by comparing the results in the model with auditing only to those in the two benchmarks. We define the expected degree of excessive overtime and social welfare in (4) and (5), respectively:

where $b_i^j={(q_i^j-k_i)}^{+}/k_i$, $j\in \{\mathcal{N},\mathcal{C},\mathcal{A}\}$, $q_i^j$ denotes the supplier’s (or the integrated firm’s) equilibrium production quantity of product i in model j, and $e^j$ denotes the equilibrium audit decision in model j.⁵ In (5), we have that $W_a^j$ denotes the total salary paid to workers (which equals the total production cost incurred by the supplier) in model j. The parameter g denotes workers’ unit disutility from excessive overtime, and $g(1-e^j){\sum }_{i=1}^2{k}_i{b}_i^j=g(1-e^j){\sum }_{i=1}^2{(q_i-k_i)}^{+}$ means workers’ unit disutility from excessive overtime g times the total amount of overtime for both products. We assume $g\ge \overline{g}$ to capture that workers suffer from excessive overtime heavily, where $\overline{g}$ is defined in Online Appendix B. This assumption ensures the social welfare in the model with audit only increases in the manufacturer’s audit accuracy $e_H$. When this assumption is not satisfied, instances where enforcing excessive overtime improves social welfare may occur, which is inconsistent with our primary context.

Theorem 1

(Expected Degree of Excessive Overtime). The expected degree of excessive overtime in the model with auditing only is smaller than that in the no-audit benchmark and larger than that in the centralized supply chain benchmark. That is, $O{T}^{\mathcal{C}}\le O{T}^{\mathcal{A}}\le O{T}^{\mathcal{N}}$.

Recall from Propositions 3 and 4 that the supplier always fulfills the orders and forces overtime whenever there is a workforce shortage in the no-audit benchmark, and the integrated firm will not force overtime in the centralized supply chain benchmark. In contrast to these two benchmarks, Corollary 1 shows that in the model with auditing only, the number of scenarios in which the supplier forces overtime production decreases with the manufacturer’s audit decision e. It follows that the expected degree of excessive overtime is the highest in the no-audit benchmark, intermediate in the model with auditing only, and the lowest (equal to zero) in the centralized supply chain benchmark.

Theorem 2

(Social Welfare). The social welfare in the model with auditing only is larger than that in the no-audit benchmark and smaller than that in the centralized supply chain benchmark. That is, $S{W}^{\mathcal{N}}\le S{W}^{\mathcal{A}}\le S{W}^{\mathcal{C}}$.

On the one hand, Theorem 2 shows that auditing can improve social welfare compared with the no-audit benchmark because auditing reduces the supplier’s violation incentive and the resulting expected degree of excessive overtime ($O{T}^{\mathcal{A}}\le O{T}^{\mathcal{N}}$ in Theorem 1), and the workers suffer less from excessive overtime. On the other hand, auditing alone cannot improve social welfare to a level higher than that in the centralized supply chain benchmark because the integrated firm does not force overtime.

Although auditing is commonly used by manufacturers as a stick strategy to mitigate excessive overtime issues, it cannot help suppliers improve the matching between their workforce and the orders. To better mitigate excessive overtime, manufacturers may need to employ carrot (i.e., supplier development) strategies in addition to auditing. Therefore, it is worth investigating how the manufacturer should use these stick-and-carrot strategies jointly. In what follows, we first examine a setting in which the manufacturer employs auditing together with directly subsidizing the supplier’s workforce retention initiative in Section 5 and then examine another setting in which the manufacturer employs auditing together with cross-training the supplier’s workers to enhance their skillsets in Section 6.

5. Model: Workforce Retention Subsidy and Auditing

In addition to auditing, MNEs often implement supplier development strategies such as subsidizing suppliers to retain workers. For example, Apple offered direct financial bonuses to workers at Foxconn (Foremski 2010). Apple also worked with a supplier located in Dongguan, China, to improve workers’ satisfaction by offering additional bonuses and improved food choices and, consequently, improved workers’ retention rate (Apple 2022a).

Motivated by these observations, we analyze a workforce retention subsidy strategy under which the manufacturer subsidizes the supplier’s workforce retention initiative. Compared with the base model with auditing only, the manufacturer must decide whether to subsidize the supplier at the beginning of the time horizon. Let the decision variable $y\in \{0,1\}$ denote the manufacturer’s workforce retention subsidy decision, where $y=1$ corresponds to the scenario where the manufacturer subsidizes the supplier’s workforce retention initiative at a fixed cost $\psi >0$, and $y=0$ otherwise. Motivated by the direct subsidy example of Apple, we consider the manufacturer’s workforce retention subsidy cost to be directly added to the total payoff of the workers at the supplier; our results continue to hold qualitatively if a part of the workforce retention subsidy cost is considered as efficiency loss in the workforce retention process.

If the manufacturer subsidizes the supplier’s workforce retention initiative (i.e., $y=1$), then the supplier’s workforce is improved in the first-order stochastic dominance sense. In particular, in this section, we consider the marginal probability of the supplier’s workforce being H is improved from $\mathrm{Pr}(k_i=H)={\gamma }_0$ to $\mathrm{Pr}(k_i=H)=\gamma$ with $0<{\gamma }_0<\gamma <1$. It follows that the probabilities of the joint distribution of the supplier’s workforce are $\mathrm{Pr}(\mathit{K}=(H,H))={\beta }_K\gamma$, $\mathrm{Pr}(\mathit{K}=(H,L))=\mathrm{Pr}(\mathit{K}=(L,H))=(1-{\beta }_K)\gamma$, and $\mathrm{Pr}(\mathit{K}=(L,L))=1-2\gamma +{\beta }_K\gamma$. Following a similar analysis, we can also consider an alternate setting where both ${\gamma }_0$ and ${\beta }_K$ increase after the workforce retention subsidy. The details are omitted for brevity.

Except for the workforce retention subsidy decision, the sequence of events remains the same as that under the model with auditing only, and the details are omitted for brevity. We use backward induction to derive the equilibrium decisions of the supplier and the manufacturer. We next focus on analyzing the equilibrium decisions given that the manufacturer subsidizes the supplier; that is, $y=1$. If the manufacturer does not subsidize the supplier’s workforce retention initiative, that is, $y=0$, then all results remain the same as those under the base model with auditing only. Finally, we derive the manufacturer’s optimal workforce retention subsidy decision $y^{*}$ by comparing the subgame perfect equilibrium profits of the manufacturer given $y=1$ with that given $y=0$.

5.1. Subgame Perfect Equilibrium When Manufacturer Subsidizes (y = 1)

Because the supplier decides the production quantity after observing the realized workforce, the workforce retention subsidy does not affect the supplier’s best-response production decision (see Proposition 1). Anticipating the supplier’s best-response production decision, the manufacturer makes its audit decision as follows. We use the superscript $\mathcal{A}\mathcal{S}$ to denote the model with both auditing and workforce retention subsidy. All proofs of results in Section 5 are relegated to Online Appendix C.

Proposition 5

(Manufacturer’s Audit Decision). Given the manufacturer’s subsidizing decision $y=1$, there exists an audit cost threshold ${\overline{R}}^{\mathcal{A}\mathcal{S}}(e_H)$ such that the manufacturer’s equilibrium audit decision is

$$e^{\mathcal{A}\mathcal{S}}=\{\begin{array}{ll}{e}_H,& \text{if}\hspace{0.17em}R\le {\overline{R}}^{\mathcal{A}\mathcal{S}}(e_H);\\ 0,& \text{otherwise}.\end{array}$$

Furthermore, the audit cost threshold ${\overline{R}}^{\mathcal{A}\mathcal{S}}(e_H)$ increases in $e_H$, with ${\lim }_{e_H\to 0^{+}}{\overline{R}}^{\mathcal{A}\mathcal{S}}(e_H)=0$.

Similar to the result when auditing is the sole viable strategy (see Proposition 2), Proposition 5 shows that the manufacturer audits the supplier only when the audit cost R is small enough. In addition, the audit cost threshold ${\overline{R}}^{\mathcal{A}\mathcal{S}}(e_H)$ is increasing in $e_H$, indicating that the manufacturer has more willingness to audit the supplier if the audit becomes more effective.

5.2. Manufacturer’s Workforce Retention Subsidy Decision

Having characterized the supplier’s production and manufacturer’s auditing decisions in Propositions 1 and 2 given the workforce retention subsidy decision of $y=0$, and those in Propositions 1 and 5 given the workforce retention subsidy decision of $y=1$, we would like to examine the interaction between the manufacturer’s auditing and workforce retention subsidy decisions before analyzing the manufacturer’s equilibrium workforce retention subsidy decision. In particular, we first explore whether the manufacturer has more or less willingness to audit in the presence of workforce retention subsidy in the following theorem. We consider workforce retention subsidy and auditing to be substitutes when the manufacturer has (in a weak sense) less willingness to audit in the presence of workforce retention subsidy, and they are complements otherwise.

Theorem 3

(Interaction Between Workforce Retention Subsidy and Auditing). There exists a workforce correlation threshold ${\overline{\beta }}_K(e_H)$ such that

1. when the workforce correlation is large, that is, ${\beta }_K\ge {\overline{\beta }}_K(e_H)$, the audit cost threshold with both workforce retention subsidy and auditing, ${\overline{R}}^{\mathcal{A}\mathcal{S}}(e_H)$, is smaller than the audit cost threshold with auditing only, ${\overline{R}}^{\mathcal{A}}(e_H)$. That is, workforce retention subsidy and auditing are substitutes in combating excessive overtime.

2. when the workforce correlation is small, that is, ${\beta }_K<{\overline{\beta }}_K(e_H)$, the audit cost threshold with both workforce retention subsidy and auditing, ${\overline{R}}^{\mathcal{A}\mathcal{S}}(e_H)$, is strictly larger than the audit cost threshold with auditing only, ${\overline{R}}^{\mathcal{A}}(e_H)$. That is, workforce retention subsidy and auditing are complements in combating excessive overtime.

Contrary to the naive intuition that workforce retention subsidy and auditing should always be substitutes, interestingly, Theorem 3 shows that workforce retention subsidy can be a substitute or complement for auditing, depending on the correlation between the two groups within the supplier’s workforce measured by ${\beta }_K$. We illustrate the result in Figure 3.

To understand the result, recall that there are four scenarios, ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, ${\mathbb{S}}_{HL}^{LL}$, and ${\mathbb{S}}_{HH}^{LL}$, in which the supplier may force overtime. Whereas the manufacturer’s workforce retention subsidy decreases the total probability of these four scenarios, the impact on scenario ${\mathbb{S}}_{HH}^{LL}$ (where the supplier may force overtime for both products) and that on scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, and ${\mathbb{S}}_{HL}^{LL}$ (where the supplier may force overtime on one product only) are different. As the probability of high workforce increases because of subsidy, the probability of scenario ${\mathbb{S}}_{HH}^{LL}$ decreases. Interestingly, when ${\beta }_K$ is small, such reduced probability may be spilled over to the scenarios where the supplier may force overtime on one product only, leading to an increased probability of such scenarios (i.e., ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, and ${\mathbb{S}}_{HL}^{LL}$). Recall from Remark 1 that the manufacturer’s net benefit from auditing in scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, and ${\mathbb{S}}_{HL}^{LL}$ is higher than that in scenario ${\mathbb{S}}_{HH}^{LL}$. It follows that when ${\beta }_K$ is small, the manufacturer has a higher willingness to audit the supplier with workforce retention subsidy; that is, workforce retention subsidy and auditing are complements. When ${\beta }_K$ is large, the manufacturer has a lower willingness to audit the supplier; that is, workforce retention subsidy and auditing are substitutes.⁶

The correlation between the two workforce groups—as captured by the proxy parameter ${\beta }_K$—may arise from common external factors such as macroeconomic shocks (e.g., economic downturns, regulatory changes) and regional labor market conditions (e.g., wage competition, employment opportunities) and/or from common internal factors, such as supplier-wide management policies (e.g., common human resource practices, standardized compensation schemes) and facility-/group-level operations and management approaches (e.g., similar operational environments and management styles that affect turnover risks). In practice, ${\beta }_K$ tends to be larger when both groups share similar external conditions, centralized management, or consistent supervisory practices—such as producing both product lines in the same facility under common policies—resulting in correlated turnover risks and the substitutive relationship between auditing and supplier development strategies. By contrast, ${\beta }_K$ tends to be smaller when the groups face distinct conditions—such as operating in different regions, under varied operational setups, or with divergent management approaches, leading to more independent turnover dynamics and the complement relationship between auditing and supplier development strategies.

We next discuss the manufacturer’s equilibrium workforce retention subsidy decision. Intuitively, the manufacturer has more willingness to subsidize the supplier’s workforce retention initiative when the workforce retention subsidy cost is lower than a subsidy cost threshold.

Proposition 6

(Manufacturer’s Equilibrium Workforce Retention Subsidy Decision). There exists a subsidy cost threshold ${\overline{\psi }}_M^{\mathcal{A}\mathcal{S}}(e_H,R)$ such that the manufacturer’s equilibrium workforce retention subsidy decision is as follows:

$$y^{*}=\{\begin{array}{ll}1,& \text{if}\hspace{0.17em}\psi \le {\overline{\psi }}_M^{\mathcal{A}\mathcal{S}}(e_H,R);\\ 0,& \text{otherwise}.\end{array}$$

Finally, we explore how the manufacturer’s willingness to subsidize the supplier’s workforce varies with the initial turnover rate of the supplier’s workers. Recall that the workforce uncertainty is primarily driven by the turnover rate, and a higher value of the probability $\mathrm{Pr}(K_i=H)={\gamma }_0$ indicates a lower turnover rate. Intuitively, one may expect that the manufacturer should have a lower willingness to subsidize the supplier if the supplier’s initial turnover rate is lower (or equivalently, the initial retention rate is higher). We formally establish this result in the following corollary.

Corollary 2.

The subsidy cost threshold ${\overline{\psi }}_M^{\mathcal{A}\mathcal{S}}(e_H,R)$ decreases as the probability ${\gamma }_0$ increases.

5.3. Impact of Workforce Retention Subsidy on Excessive Overtime and Social Welfare

Having analyzed the equilibrium decisions of the supplier and the manufacturer, we next characterize the impact of mitigation strategies on the degree of excessive overtime and social welfare; these two performance metrics are defined in (4) and (5), respectively. Also, recall that the manufacturer’s workforce retention subsidy cost is directly added to the total payoff of the workers at the supplier motivated by the direct subsidy example of Apple. Note from Proposition 6 that the manufacturer subsidizes the supplier’s workforce retention initiative (i.e., $y=1$) when $\psi \le {\overline{\psi }}_M^{\mathcal{A}\mathcal{S}}(e_H,R)$.

Theorem 4

(Expected Degree of Excessive Overtime). Consider $\psi \le {\overline{\psi }}_M^{\mathcal{A}\mathcal{S}}(e_H,R)$ under which the manufacturer subsidizes the supplier’s workforce retention in equilibrium.

1. The expected degree of excessive overtime in the model with both workforce retention subsidy and auditing is larger than that in the centralized supply chain benchmark and smaller than that in the no-audit benchmark. That is, $O{T}^{\mathcal{C}}\le O{T}^{\mathcal{A}\mathcal{S}}<O{T}^{\mathcal{N}}$.

2. Compared with the model with auditing only, there exists an audit threshold ${\widehat{e}}^{\mathcal{A}\mathcal{S}}\in (0,1)$ such that workforce retention subsidy strategy simultaneously increases the manufacturer’s profit and decreases the expected degree of excess overtime if and only if one of the following four conditions is satisfied: the workforce correlation is relatively small $({\beta }_K<{\overline{\beta }}_K(e_H))$, the audit cost is small $(R\le {\overline{R}}^{\mathcal{A}\mathcal{S}}(e_H))$, the audit cost is large $(R>{\overline{R}}^{\mathcal{A}}(e_H))$, or the audit accuracy is relatively small $(e_H\le {\widehat{e}}^{\mathcal{A}\mathcal{S}})$.

Similar to the results of auditing only (see Theorem 1), part 1 of Theorem 4 shows that workforce retention subsidy and auditing can also reduce excessive overtime compared with the no-audit benchmark, but may not eliminate overtime. Therefore, the expected degree of excessive overtime under both subsidy and auditing is between the no-audit and centralized supply chain benchmarks.

Part 2 of Theorem 4 characterizes conditions under which a win-win outcome is achieved: not only is the manufacturer’s profit improved, but also the expected excessive overtime of the supplier’s workforce is reduced. Recall from Proposition 6 that the manufacturer subsidizes the supplier’s workforce retention initiatives when the workforce retention subsidy cost is small (i.e., $\psi \le {\overline{\psi }}_M^{\mathcal{A}\mathcal{S}}(e_H,R)$), indicating workforce retention subsidy improves the manufacturer’s profit in this case. We next explain why the excessive overtime is also reduced under the conditions specified in the theorem. On a high level, the workforce retention subsidy affects excessive overtime through two effects: (i) an order-fulfillment-improvement effect under which the subsidy improves the supplier’s overall order fulfillment capability with an increased workforce and, therefore, directly reduces the excessive overtime enforced by the supplier, ceteris paribus; and (ii) an audit-willingness-adjustment effect under which offering the subsidy may increase or decrease the manufacturer’s auditing willingness, depending on whether the two levers are complements or substitutes, respectively, and may correspondingly reduce or increase the use of excessive overtime by the supplier, ceteris paribus. Whether workforce retention subsidy reduces excessive overtime depends on the interplay of these two effects.

When the workforce correlation ${\beta }_K$ is small (i.e., ${\beta }_K<{\overline{\beta }}_K(e_H)$), workforce retention subsidy and auditing are complements; that is, workforce retention subsidy increases the manufacturer’s audit willingness, and the audit-willingness-adjustment effect works in the same direction as the order-fulfillment-improvement effect to reduce excessive overtime. When the audit cost is either small or large (i.e., $R\le {\overline{R}}^{\mathcal{A}\mathcal{S}}(e_H)$ or $R>{\overline{R}}^{\mathcal{A}}(e_H)$), the manufacturer either audits the supplier with subsidy ($R\le {\overline{R}}^{\mathcal{A}\mathcal{S}}(e_H)$) or does not audit the supplier without subsidy ($R>{\overline{R}}^{\mathcal{A}}(e_H)$). In either case, offering a workforce retention subsidy does not decrease the manufacturer’s willingness to audit, and the audit-willingness-adjustment effect joins force with the order-fulfillment-improvement effect in reducing excessive overtime. Finally, when the audit accuracy is relatively small (i.e., $e_H\le {\widehat{e}}^{\mathcal{A}\mathcal{S}}$), auditing is not effective in combating excessive overtime. Therefore, although a workforce retention subsidy may decrease the manufacturer’s willingness to audit, the resulting negative impact is dominated by the positive order-fulfillment-improvement effect, and the excessive overtime is reduced.

In the following corollary of Theorem 4, we emphasize that in sharp contrast with the naive intuition that workforce retention subsidy always reduces excessive overtime, when the subsidy and auditing are substitutes and the negative audit-willingness-adjustment effect dominates the positive order-fulfillment-improvement effect, workforce retention subsidy may backfire and increase the expected degree of excessive overtime.

Corollary 3

(Backfire of Subsidy). Consider $\psi \le {\overline{\psi }}_M^{\mathcal{A}\mathcal{S}}(e_H,R)$, under which the manufacturer subsidizes the supplier’s workforce retention in equilibrium. Workforce retention subsidy backfires and increases the expected degree of excessive overtime $(O{T}^{\mathcal{A}\mathcal{S}}>O{T}^{\mathcal{A}})$ if and only if the workforce correlation is relatively large $({\beta }_K\ge {\overline{\beta }}_K(e_H))$, the audit cost is medium $({\overline{R}}^{\mathcal{A}\mathcal{S}}(e_H)<R\le {\overline{R}}^{\mathcal{A}}(e_H))$, and the audit accuracy is relatively high $(e_H>{\widehat{e}}^{\mathcal{A}\mathcal{S}})$.

We then investigate the impact of workforce retention subsidy on social welfare.

Theorem 5

(Social Welfare). Consider $\psi \le {\overline{\psi }}_M^{\mathcal{A}\mathcal{S}}(e_H,R)$, under which the manufacturer subsidizes the supplier’s workforce retention in equilibrium.

1. The social welfare in the model with both workforce retention subsidy and auditing is larger than that in the no-audit benchmark. That is, $S{W}^{\mathcal{A}\mathcal{S}}>S{W}^{\mathcal{N}}$. Moreover, there exists an audit threshold ${\underset{¯}{e}}^{\mathcal{A}\mathcal{S}}\in [0,1]$ such that the social welfare in the model with both workforce retention subsidy and auditing is larger than that in the centralized supply chain benchmark $(S{W}^{\mathcal{A}\mathcal{S}}>S{W}^{\mathcal{C}})$ if and only if the audit accuracy is large $(e_H>{\underset{¯}{e}}^{\mathcal{A}\mathcal{S}})$.

2. Compared with the model with auditing only, there exists an audit threshold ${\overline{e}}^{\mathcal{A}\mathcal{S}}\in [0,1]$ such that workforce retention subsidy increases the social welfare $(S{W}^{\mathcal{A}\mathcal{S}}\ge S{W}^{\mathcal{A}})$ if and only if one of the following four conditions is satisfied: the workforce correlation is relatively small $({\beta }_K<{\overline{\beta }}_K(e_H))$, the audit cost is small $(R\le {\overline{R}}^{\mathcal{A}\mathcal{S}}(e_H)$, the audit cost is large $(R>{\overline{R}}^{\mathcal{A}}(e_H))$, or the audit accuracy is relatively small $(e_H\le {\overline{e}}^{\mathcal{A}\mathcal{S}})$.

Intuitively, part 1 of Theorem 5 shows that workforce retention subsidy and auditing improve social welfare compared with the no-audit benchmark. More importantly, the combined strategies may improve social welfare to a level higher than that in the centralized supply chain benchmark (without workforce retention subsidy). To understand the result, on the one hand, workforce retention subsidy increases the supplier’s overall efficiency of matching workforce with demands, which tends to improve social welfare, compared with the centralized supply chain benchmark. On the other hand, note from Proposition 4 that the supplier does not force overtime in the centralized supply chain benchmark, whereas Corollary 1 shows that the supplier may still force overtime under both workforce retention subsidy and auditing. However, the supplier’s violation incentive and the resulting suffering of workers decrease with the manufacturer’s audit decision e. When the manufacturer’s audit accuracy is large enough (i.e., $e_H>{\underset{¯}{e}}^{\mathcal{A}\mathcal{S}}$), the effect that workforce retention subsidy increases the overall matching efficiency dominates the effect that workers suffer more in the model with both workforce retention subsidy and auditing, and social welfare under both workforce retention subsidy and auditing is larger than that in the centralized supply chain benchmark.

Part 2 of Theorem 5 characterizes the conditions under which the workforce retention subsidy increases social welfare compared with the model with auditing only. The rationale behind the potential of the workforce retention subsidy to enhance social welfare is analogous to its potential to reduce excessive overtime (see part 2 of Theorem 4 and the corresponding discussions). Also, similar to the observation in Corollary 3, workforce retention subsidy may backfire and reduce social welfare when the conditions in part 2 of Theorem 5 are not satisfied. The details are omitted for brevity.

5.4. Numerical Analysis

In this section, we first collected data of representative manufacturers and suppliers in the electronics industry from practical open sources such as firms’ financial reports, business news, and academic literature, for example, Kölbel et al. (2017) and Moon et al. (2023), to construct a practical testing bed.⁷ We then numerically analyze the interaction between workforce retention subsidy and audit, as shown in Figure 4. In addition, we numerically decompose social welfare into two components: worker welfare (including the worker wage and damage because of overtime, if any) and firms’ profits (i.e., the sum of the manufacturer’s and the supplier’s profits). We primarily focus on comparing social welfare, worker welfare, and firms’ profits under $\mathcal{A}\mathcal{S}$ to those under $\mathcal{A}$, as shown in Figure 5.

The parameters are listed below Figures 4 and 5. As an example, we include in the footnote a detailed explanation of how the parameters l and $m_2$, representing the MNEs’ and the supplier’s goodwill loss because of the public exposure of the supplier’s violations, respectively, are obtained.⁸ In the interests of space, the detailed choices of the other parameters are relegated to Online Appendix D, in which we include a more detailed explanation regarding how we obtained data supporting the parameter choices and conduct robustness checks for a few parameters that are difficult to obtain.

The main observations from Figure 4 are that workforce retention subsidy may be a complement for audit when the workforce correlation ${\beta }_K$ is small; see the gray regions in Figure 4. Specifically, workforce retention subsidy and audit are complements in combating excessive overtime if the workforce correlation ${\beta }_K$ is smaller than a threshold (around 0.67 in Figure 4(a) and 0.28 in Figure 4(b)), and they are substitutes otherwise. We note that the observation follows from the intuition of part 2 of Theorem 3. The managerial insight is that the manufacturer in the electronics setting should be careful when simultaneously adopting audit and workforce retention subsidy because they may not always have synergy in combating excessive overtime. That is, these strategies may not always be substitutes, and reducing audit under the mistaken belief that carrots can replace the stick may not only fail to curb excessive overtime but could also diminish the MNE’s overall profitability when the two strategies are complements.

Figure 5 reveals that the improvement in social welfare can be driven by both enhanced worker welfare and firm profitability. The numerical results in Figure 5 correspond to a case in which the manufacturer audits the supplier with or without subsidy. That is, subsidy improves the supplier’s overall fulfillment capability without diminishing the manufacturer’s auditing willingness. Consequently, the social welfare, worker welfare, and firms’ total profits in the model with both auditing and subsidy are higher than those in the model with auditing only, respectively.

To understand why social welfare and the changes in social welfare, worker welfare, and firms’ profits decrease with the workforce correlation ${\beta }_K$ when $e_H=0.25$—see Figure 5, (a) and (c)—while remaining unchanged when $e_H=0.75$—see Figure 5, (b) and (d)—we note from Corollary 1 that there exists an audit decision threshold $\underset{¯}{e}$ above which the supplier does not force overtime in scenarios ${\mathbb{S}}_{HH}^{HL}$, ${\mathbb{S}}_{HL}^{LH}$, and ${\mathbb{S}}_{HL}^{LL}$, and a threshold $\overline{e}$ above which the supplier does not force overtime in scenario ${\mathbb{S}}_{HH}^{LL}$. In our testing bed, $\underset{¯}{e}\approx 0.17$, and $\overline{e}\approx 0.60$. It follows that the supplier forces overtime in ${\mathbb{S}}_{HH}^{LL}$ when $e_H=0.25$ and does not force overtime when $e_H=0.75$. Consequently, social welfare and those changes decrease with ${\beta }_K$ when $e_H=0.25$ because a larger ${\beta }_K$ indicates a larger probability of being in scenario ${\mathbb{S}}_{HH}^{LL}$ in which the supplier forces overtime, and they remain unchanged when $e_H=0.75$ because the supplier does not force overtime in these cases.

6. Model: Cross-Training and Auditing

MNEs often provide learning opportunities to upskill the suppliers’ workers as another form of supplier development, which can enhance workforce flexibility and productivity, thereby helping to mitigate the issue of excessive overtime (Distelhorst et al. 2017, ILO 2017a, Apple 2022a, SHEIN 2023). Motivated by these observations, we analyze the cross-training strategy under which the manufacturer makes a decision on training a proportion of the supplier’s single-skilled workers to become multiskilled, enabling them to produce both products. In the interests of space, we relegate the model and analysis to Appendix A.

By analyzing the model, we find that cross-training and auditing can be either complements or substitutes. The counterintuitive result regarding the complements arises from the fact that enhanced workforce flexibility at the supplier level lowers the manufacturer’s opportunity cost associated with identifying the supplier’s violations. As a result, the manufacturer could exhibit a greater willingness to conduct audits. We also identify conditions under which cross-training could lead to a win-win outcome where the manufacturer earns a higher profit and the supplier uses less of overtime, and conditions under which cross-training may backfire and result in a higher level of excessive overtime by the supplier. In addition, cross-training and auditing could lead to a higher social welfare level than that under the centralized supply chain benchmark (without cross-training).

Finally, we also include an extension on the productivity enhancement effect of the upskilling programs. In this case, the workers’ productivity is improved as a result of the training. We relegate this extension to Appendix E.

7. Concluding Remarks

Numerous reports highlight instances where suppliers in developing economies coerce workers into excessive overtime within the global supply chains of MNEs. Such practices not only pose serious threats to the well-being of workers but also contravene the labor-related codes of conduct established by MNEs, potentially tarnishing their brand image. In this paper, by modeling a supplier’s violation behavior that the supplier may force overtime when its realized normal workforce cannot meet a manufacturer’s orders, we explore how the manufacturer can effectively utilize a stick strategy, that is, auditing, and two carrot strategies, that is, workforce retention subsidy and cross-training, to combat such violation behavior on the part of the supplier.

Our research yields several managerial insights for MNEs aiming to address the issue of excessive overtime in their global supply chains. Firstly, in scenarios where auditing is the sole viable strategy, it is imperative for MNEs to deploy this strategy only when the accuracy of auditing is sufficiently high. However, it is essential to recognize that whereas auditing serves as a deterrent, it alone cannot facilitate improvements in suppliers’ normal workforce to meet order requirements. In addition, because auditing is imperfect, suppliers may still resort to enforcing overtime.

Secondly, when MNEs opt for a combined approach involving the stick strategy alongside one of the carrot strategies (i.e., workforce retention subsidy or cross-training), these strategies may act as either complements or substitutes. This finding challenges a naive belief that these strategies are always substitutes. It underscores the need for MNEs to carefully evaluate the simultaneous adoption of stick-and-carrot strategies to combat excessive overtime, as synergies may not always be present. That is, these strategies may not always be substitutes, and reducing audit under the mistaken belief that carrots can replace the stick may not only fail to curb excessive overtime but could also diminish the MNE’s overall profitability when the two strategies are, in fact, complements. For instance, our numerical study, calibrated using data from the electronics industry, reveals that workforce retention subsidy and auditing are complements when workforce correlation is small. This observation suggests that manufacturers should audit more after implementing a workforce retention subsidy.

Third, we characterize conditions under which the manufacturer can achieve a win-win outcome by employing both the supplier development strategies and auditing. In short, employing the supplier development strategies has a direct order-fulfillment-improvement effect and an indirect auditing-willingness-adjustment effect. When developing the supplier does not reduce the MNE’s auditing willingness, or the auditing accuracy is low, the MNE can earn a higher profit and reduce the overtime of the supplier at the same time. On the contrary, when these conditions are not satisfied, the MNEs must exercise caution, as these carrot strategies may inadvertently lead to adverse outcomes by intensifying the problem of excessive overtime and diminishing overall social welfare. This insight arises from the observation that the implementation of a carrot strategy may diminish the manufacturer’s willingness to audit. Consequently, suppliers may be more inclined toward violation behavior, resulting in an escalation of excessive overtime and a subsequent reduction in social welfare. Therefore, MNEs committed to mitigating excessive overtime and enhancing social welfare should remain vigilant, maintaining ongoing scrutiny of their suppliers’ behavior even after investing resources in developing supplier capabilities to fulfill orders.

Which of the supplier development strategies should be prioritized for adoption depends on a careful benefit-cost analysis. For example, consider the supplier maturity, which reflects a supplier’s systemic capability to (i) uphold fundamental labor compliance (e.g., minimum wage adherence, overtime premiums), and (ii) maintain organizational infrastructure for ongoing workforce development (e.g., skill-based wage adjustments and internal promotion pathways to retain a cross-trained/upskilled workforce). Low-maturity suppliers, such as newly engaged factories in underdeveloped regions, often lack coherent labor systems and structured human resource mechanisms, making it difficult and costly for MNEs to implement capability-building programs in the early stages of the partnership. These suppliers tend to be more responsive to workforce retention subsidy, which help address immediate labor shortages or compliance risks. In contrast, high-maturity suppliers, such as established factories in developed regions, possess institutionalized human resource systems and integrated mechanisms for workforce retention after training and upskilling. They are better equipped to absorb workforce training and upskilling. As a result, MNEs’ structural investments in these suppliers are easier and more likely to generate sustainable and lasting impact.

Our study unveils several promising avenues for future research. Firstly, whereas our focus has been on assessing the efficacy of auditing and supplier development strategies in tackling excessive overtime within a dyadic supply chain, it would be both intriguing and important to extend this inquiry to scenarios where competing MNEs share a common supplier. An exploration of such competitive settings could enhance our comprehension of strategies aimed at improving labor welfare, particularly considering potential spillover effects. Another compelling avenue for future research involves delving into a strategic supplier’s decision-making process regarding unauthorized subcontracting and other illicit means to fulfill orders and how MNEs can deploy operational levers to counteract such behaviors. Moreover, because MNEs’ inflated orders often pressure suppliers into enforcing excessive overtime, exploring strategies to address MNEs’ strategic ordering behavior could be a promising direction for future research. Additionally, as some MNEs may want to cultivate long-term relationships with their suppliers, it would be worthwhile to investigate how manufacturers can address the issue of excessive overtime in a multiperiod setting. Exploring the role of trust and trustworthiness in such contexts could provide valuable insights into fostering sustainable and mutually beneficial relationships. We hope that our paper can serve as a stepping stone for future research on labor welfare in global supply chains.