Global Sourcing for Supply Resilience in the Presence of Emergency Contract Renegotiation

1. Introduction

Traditionally, global brands like Apple and Mattel have prioritized sourcing products worldwide to achieve superior quality and access advanced production technologies (EC Sourcing Group, 2024; Tang, 2008). However, the increasing frequency of global emergencies in recent years has led these companies to reevaluate their global sourcing strategies. One notable example is the COVID-19 pandemic, which significantly disrupted global supply chains across various industries. Such emergencies can have several potential consequences. Firstly, they often result in global delivery delays, as complete disruptions are relatively rare in the post-pandemic era, with most emergencies causing delays instead. Accenture reported that since the pandemic, the majority of suppliers in the manufacturing sector have experienced production and logistics delays (Accenture, 2024). For instance, Toyota, a leading Japanese automaker, had to postpone vehicle production due to pandemic-related disruptions in Vietnam and Malaysia (The Financial Times, 2021). Additionally, another critical consequence is the increased post-recovery costs incurred by affected suppliers, such as elevated production and logistics expenses compared to pre-emergency conditions (International Monetary Fund, 2022; S&P Global, 2021).

To mitigate these potential damages, dual sourcing has become a prevalent strategy. Global brands can incorporate a local supplier, typically situated nearby, into their supply networks, even though this local supplier may be of lower quality as compared to the globally selected high-quality counterpart (KPMG, 2024: 11; Tomlin and Wang, 2011). A notable example is Ford’s recent partnership with GlobalFoundries, a US semiconductor chip supplier, aimed at reducing its reliance on Taiwanese chips to enhance supply chain resilience (The New York Times, 2021). This global dual-sourcing approach, involving both overseas and local suppliers, intuitively helps balance supply resilience with high-quality products. However, it also introduces challenges, such as increased supply maintenance costs (Art of Procurement, 2020; Tang and Kouvelis, 2011), elevated procurement prices due to exposure to supply risks (Forbes, 2022; Niu et al., 2021), and quality inconsistency between suppliers (Li et al., 2020; Niu et al., 2019). These challenges may contribute to the findings of the KPMG survey, which states, “Just 32% of procurement leaders taking part in our global survey say their company is planning, or likely to initiate, onshoring or nearshoring of supply sources” (KPMG, 2024: 11).

Although the effectiveness of dual sourcing as a resilience strategy and the associated trade-offs have been well-documented in both literature and business practice, we note that a growing number of corporations have recognized the importance of renegotiating contracts during emergencies, particularly following the disruptions caused by the pandemic (Katok and Tan, 2025). Andrew Butt, co-founder and CEO of Enable, emphasizes that “contracts shouldn’t be viewed as fixed agreements that companies have to observe no matter what” (Forbes, 2021). The KPMG survey echoes this sentiment, highlighting the necessity for the ability to renegotiate contracts (KPMG, 2024: 18).

In practice, when pre-signed contracts lack explicit renegotiation clauses, emergencies typically result in two possible and widely observed contractual outcomes. The first is contract termination, akin to a complete disruption, a scenario widely adopted in the literature to capture the consequences of such events (Shan et al., 2022; Tang et al., 2014). The second is contract continuation, grounded in the legal principle that a signed supply contract is binding and cannot be altered arbitrarily, as per the legal doctrine of pacta sunt servanda. Consequently, even if emergencies cause delays and increased costs for the supplier, it remains obligated to fulfill the original contract terms. This scenario is analogous to the concept of “forced compliance” discussed by Cachon and Lariviere (2001). In contrast to these two extreme scenarios, the inclusion of contract renegotiation provides contractual parties with a new, more desired option for responding to emergencies.

To facilitate contract renegotiation during emergencies beyond a party’s reasonable control, parties can include a renegotiation clause in their initial contract. This clause essentially allows for the modification of certain terms, adhering to the principle of good faith (Trans-lex, 2024). It ensures a rational allocation of risk and damage, preventing the burden from falling solely on the affected party and aiding in the stabilization of supply chains. The scope of circumstantial changes that can trigger renegotiation—such as delivery delays and cost escalations resulting from emergencies—as well as the specific aspects subject to adjustment, are typically outlined in the initial contract, serving as an ex-ante commitment between the contractual parties. For instance, hardship is one of the conditions that triggers renegotiation, and the hardship clause can be considered a subset of renegotiation clauses. Articles 6.2.2 and 6.2.3 of the UNIDROIT Principles of International Commercial Contracts (PICC), a private law framework for international contracts ratified by 65 member states, state that “There is hardship where the occurrence of events fundamentally alters the equilibrium of the contract either because the cost of a party’s performance has increased … In case of hardship, the disadvantaged party is entitled to request renegotiations” (UNIDROIT, 2016: 19). Many jurisdictions also mandate the duty to renegotiate under unavoidable emergencies or hardships in their Civil Codes, such as Article 533 of the Civil Code of China (The State Council of the People’s Republic of China, 2020). Additionally, the 2016 reform of French contract law formally recognized the concept of hardship and the right to renegotiation in Article 1195 of the Civil Code (Clifford Chance, 2016: 3; Legifrance, 2024). A summary by Freshfields (2021), one of the world’s largest multinational law firms serving clients in over 150 countries, indicates that many jurisdictions allow parties to invoke changes of circumstances to modify their contracts in good faith, provided the contract contains a renegotiation clause.

The evolving business cognitions and legal frameworks underscore the growing recognition of renegotiation as a critical mechanism for maintaining contractual relationships and sustaining contractual performance during emergencies. The proactive incorporation of renegotiation clauses reflects a shift towards more adaptable contracting, especially in the context of recurrent emergencies that do not result in complete disruption (hereafter referred to as “delivery delay” for clarity). In this study, we treat emergency renegotiation as a default business phenomenon and investigate the novel insights it introduces into the existing literature on supply diversification. Specifically, we aim to analyze how this anticipatory renegotiation influences the operational decisions and interactions among supply chain parties. This analysis is particularly relevant for global brands that are wavering on global sourcing configurations, a topic that is underrepresented in the current literature of single- and dual-sourcing strategies.

To these purposes, we develop a game-theoretical model comprising a global brand, a local rival, a local supplier, and an overseas supplier. The two suppliers differ in terms of delivery delay risk and production quality: the overseas supplier is chosen for its superior production quality but is susceptible to potential overseas delivery delays and incurs additional post-recovery costs. By contrast, the local supplier is reliable in terms of delivery but faces issues with quality yield. The brand, which traditionally relies on high-quality global sourcing (referred to as Strategy S), has the option to transition to a dual-sourcing configuration (referred to as Strategy D) at the additional cost of maintaining dual suppliers. Meanwhile, the local rival sources exclusively from the local supplier. In the main model, which includes emergency renegotiation, the overseas supplier and the brand renegotiate and execute a new contract, including revised wholesale price and order quantity, in response to delivery delays and additional post-recovery costs as stipulated by the renegotiation clause. This setup can be considered a blended mechanism of “ex ante commitment” and “ex post negotiation” as defined by Li (2013), where a price or contract committed ex-ante is subject to renegotiation ex-post.

We begin by analyzing two widely observed benchmark scenarios in the absence of overseas emergency renegotiation: contract termination and contract continuation at recovery cost. In the first benchmark, we assume that an overseas delivery delay results in contract termination, meaning the brand receives nothing from the overseas supplier, akin to a complete overseas disruption. In the second benchmark, the overseas supplier is obligated to fulfill the original contract despite the delivery delay, which incurs an additional post-recovery unit cost. Subsequently, we compare these benchmarks with our main model to identify which outcomes from the benchmarks remain consistent and which are uniquely induced by the presence of emergency renegotiation. Among others, we highlight the following key insights.

In the contract termination benchmark, the brand’s wholesale prices under both strategies increase with the delay probability. However, when overseas emergency renegotiation is introduced, the overseas supplier may instead reduce the wholesale price charged to the brand as the delay probability increases. This suggests that the presence of emergency renegotiation would allow overseas suppliers to mitigate potential losses from increased delay probabilities by focusing on increasing sales volume, rather than maintaining a high margin. This price-cutting behavior encourages the brand to order more from the overseas supplier than from the local supplier even when the overseas delay probability is high, a result absent in the benchmark.

Furthermore, we show that the emergency renegotiation in the main model introduces a new incentive for the brand to prefer Strategy D. Specifically, compared to Strategy S, the local supplier under Strategy D may suppress its local rival channel by setting a higher wholesale price, particularly when the overseas supplier’s post-recovery unit cost is high. This suppression is not achievable in the contract continuation benchmark, where the wholesale price charged by the local supplier to the local rival is consistently lower under Strategy D than that under Strategy S. Consequently, the brand is inclined to adopt Strategy D if the overseas supplier’s post-recovery cost is either low or high.

The remainder of this article is organized as follows. We review the relevant literature in Section 2. In Section 3, we describe the model by illustrating the notations, assumptions, supply chain structures, and game sequences. Two benchmarks without overseas emergency renegotiation (contract termination and contract continuation) are examined in Section 4. Then we analyze the main model with overseas emergency renegotiation in Section 5. We provide several extensions in Section 6. Concluding remarks are given in Section 7. All the proofs and additional results are relegated to the Appendices.

2. Literature Review

Our work is closely related to the literature on managing supply chain resilience, particularly the stream on dual sourcing (Dong et al., 2023; Liu et al., 2016; Li et al., 2023; Tomlin, 2006; Tomlin and Wang, 2011), which is widely recognized as an effective approach to enhancing supply chain resilience by allowing firms to adjust order allocations across suppliers with varying levels of supply uncertainty. Prior studies have extensively investigated operational decisions (e.g., price, order quantity, and quality level) under supply risk and explored the conditions under which firms are incentivized to adopt a dual-sourcing strategy. For instance, Burke et al. (2007) find that only when the supply capacity significantly exceeds demand can single-sourcing be the optimal strategy; otherwise, dual sourcing tends to dominate. Xiao et al. (2015) consider a dual-sourcing strategy where the buyer can source from a responsive spot market or sign a forward-buying contract with postponed delivery, and analyze how procurement cost fluctuations influence the buyer’s optimal price and sourcing decisions.

Aligned with the aforementioned stream, we focus on the bright and dark sides of dual sourcing under supply uncertainty. The delivery delay serves as a supply risk for the affected supplier, rendering it at a disadvantage in competing for downstream orders compared to the supplier at low/no risk, which is similar to Hu and Kostamis (2015). However, our work differs by incorporating suppliers’ endogenous pricing decisions, enabling us to capture their competitive interactions more explicitly. Specifically, as the overseas delay probability increases, the unaffected local supplier will be endowed with more pricing power so that a higher wholesale price is charged. In this sense, introducing a local supplier may not entail supplier competition that leads to lower wholesale prices than the single-sourcing structure, but instead result in a higher wholesale price. However, the brand may still prefer dual sourcing even if the wholesale price from the local supplier exceeds that under the single-sourcing structure. This contrasts with the result by Tang et al. (2014) that dual sourcing is favored primarily when supplier competition drives prices down. This is because in our model, the local supplier may suppress the local rival, indirectly benefiting the brand. Furthermore, under endogenous wholesale prices, a higher post-recovery cost of the overseas supplier does not necessarily encourage the brand to adopt dual sourcing, which complements the results of Hu and Kostamis (2015) and Dong et al. (2022) that a new supplier will be included if the existing suppliers are of high cost. We also differ in model setup: while their studies focus on the impact of the ex-ante cost difference on supply diversification strategy, we consider cost increases that occur ex-post.

The optimal order allocation under dual sourcing has also been extensively explored. Our model is similar to the scenario of “one sole sources, the other dual sources” by Tang and Kouvelis (2011), which solely highlights the difference in supply chain structures and shows that under symmetric suppliers and exogenous wholesale prices, the dual-sourcing buyer always allocates a larger (or smaller) order to the exclusive (or common) supplier. In our model where suppliers are asymmetric in supply risk and wholesale prices are endogenous, however, the brand may place a larger order with the common local supplier if the overseas delay probability is moderate. This result highlights the impact of the delay probability on suppliers’ pricing power. Moreover, some studies, such as Dada et al. (2007), Hu and Kostamis (2015), Li et al. (2013), and Shan et al. (2022), reveal the cost-first-reliability-second principle when there exist both reliable and unreliable suppliers. We echo this finding by showing that the risky overseas supplier may still obtain more orders from the brand if the local supplier charges a high wholesale price (under a high overseas delay probability), which further underscores the role of pricing power and how it is shaped by some important parameters.

Second, we contribute to the broad literature on supply random yield. Some studies take suppliers’ yield rate as the measure of supply uncertainty (Dong et al., 2022; Kouvelis et al., 2021; Tang and Kouvelis, 2011), whereas others interpret yield uncertainty as the production/service quality level. For example, Federgruen and Yang (2009) build a quality competition model where suppliers compete by setting their yield rates, yield deviations, or both. Wang et al. (2014) model yield uncertainty as a reflection of production quality and examine why the manufacturer may benefit from supporting supplier quality improvement. Niu et al. (2019) study a brand’s incentive to introduce a non-competitive supplier with low production quality to manage the competitive supplier that develops a self-brand. Consistent with the above papers, we also interpret yield uncertainty as an indicator of production quality and model it using a proportional yield formulation (Yano and Lee, 1995). Differently, we study the overseas delivery delay which follows a binomial distribution (Hu and Kostamis, 2015; Tang et al., 2014), while the local supplier’s quality follows a continuous distribution of yield uncertainty. This joint consideration of both the overseas supplier’s delivery delay and the local supplier’s poor quality contributes to capturing the competitiveness asymmetry between the two suppliers in a global supply chain with possible emergencies.

The third stream of literature relevant to our work is global operations. The first sub-stream is on tax-effective operations, where three common taxes are extensively studied—corporate income taxes (Lai et al., 2021; Shunko et al., 2014), tariffs (Wu et al., 2024), and export-oriented taxes (Hsu and Zhu, 2011; Xu et al., 2018). Another sub-stream is on global supply chain networks involving activities such as sourcing, production, and distribution, among which global sourcing is the most relevant. Wu and Zhang (2014) delve into two single-sourcing strategies (local or overseas sourcing) under local competition and highlight the tradeoff of local sourcing between high production cost and accurate demand information. Shao et al. (2020) study a sourcing game in which competing firms choose between a factory with a transparent cost and one with uncertain but potentially lower cost. Chen et al. (2022) investigate how tariffs, global sourcing costs, and local consumer price premiums affect a global brand’s choice between local and overseas sourcing. Compared with the aforementioned studies, we investigate a global supply chain where the high-quality supplier is located overseas and subject to emergency-induced delivery delay and additional post-recovery cost. Within this setting, we explore how the presence of overseas emergency renegotiation influences supplier interactions and, consequently, the brand’s global sourcing strategy. We find that under emergency renegotiation, the brand may prefer dual sourcing when the overseas supplier’s post-recovery unit cost is either low or high.

Finally, our work is also related to the literature on contract renegotiation. While some of them focus on capacity re-allocation or optimal contract design under renegotiation, such as Kemahlıoğlu-Ziya (2015), Li (2013), Plambeck and Taylor (2007a), and Plambeck and Taylor (2007b), we shift the focus to the brand’s global sourcing strategy and examine what differences will be engendered when considering renegotiation. Our analysis is similar in spirit to Kemahlıoğlu-Ziya (2015), which first studies the case without renegotiation and then the case with renegotiation, with a comparison to derive distinctions. Katok and Tan (2025) design a behavioral experiment to investigate the renegotiation effect in mitigating disruption-related losses. In their setting, the supplier bears an additional cost when responding to a disruption and renegotiating with the buyer, which conceptually aligns with the post-recovery cost in our model. Moreover, in our context, the ability of renegotiation is not grounded in information asymmetry, but rather the growing practice in which more and more firms pre-commit to renegotiation clauses in their ex-ante contracts. These clauses are triggered by stipulated circumstances, such as hardship or some other predefined emergencies. We treat emergency renegotiation as a model context and examine how its presence influences global sourcing strategy preference and supplier decision-making. One key implication is that emergency renegotiation may transform a simultaneous game into a sequential one. The resulting benefit is the overseas supplier’s ex-ante wholesale price potentially decreasing with its delay probability on the ground that the overseas supplier and the brand are in consensus to strive for a high sales volume at the ex-ante stage.

3. Model Setup

We consider a global supply chain consisting of an overseas supplier facing possible overseas delivery delay, a local supplier, a brand originally sourcing from the overseas supplier, and a local rival sourcing locally. The overseas supplier has advanced manufacturing techniques superior to the local supplier but is exposed to the delivery delay risk and additional post-recovery cost. The brand can choose either to engage both the overseas and local suppliers (dual-sourcing strategy, abbreviated as Strategy D) or to continue sourcing solely from the overseas supplier (single-sourcing strategy, abbreviated as Strategy S). In Section 6.5, we extend the model to allow for the possibility that the local supplier is also subject to emergencies and may face local delivery delays. The supply chain structures are illustrated in Figure 1.

OPEN IN VIEWER

Figure 1.

Supply chain structures.

In this article, we focus on the manufacturing industry in which overseas delivery delays caused by emergencies are common (e.g., the automotive and smartphone industries), and production is one-shot with a long lead time. Accordingly, the two downstream buyers (i.e., the brand and the local rival) typically determine their order quantities in advance, anticipating future delivery delay. The market is characterized by an inverse demand function p = a − b Q , wherein p is the market price, a denotes the market potential, b represents the quantity sensitivity (normalized to one without loss of generality), and Q denotes the total supply in the market.

The local supplier faces a production quality issue due to inferior manufacturing processes. Specifically, if the local supplier receives an order quantity q i from the downstream buyer i , only e q i units meet the buyer’s quality standards, where e is a random variable on the interval ( 0 , 1 ) with mean μ and variance σ 2 (Yano and Lee, 1995). Buyers pay only for the units that satisfy the quality requirement, that is, e q i (Tang and Kouvelis, 2011). An increase in μ or a decrease in σ reflects an improvement in the local supplier’s production quality (Federgruen and Yang, 2009). For ease of interpretation, we define a parameter t = μ 2 / σ 2 to capture the production quality of the local supplier. To be consistent with the practical reality, we assume a qualified rate of more than 50% (Jung, 2020), that is, μ > 1 / 2 ⇒ t > 1 . ¹ We remark that our main results remain robust even if the local supplier’s quality matches that of the overseas supplier.

We use subscripts “ l s ,” “ o s ,” “ b ,” and “ r ” to label the local supplier, the overseas supplier, the brand, and the local rival, respectively. “ S ” and “ D ” are mnemonics for two sourcing strategies. The subscripts “ b o ” and “ b l ” are used to distinguish the different suppliers of the brand. Under Strategy D, the brand determines two production quantities (i.e., q b o D and q b l D ) to the suppliers, while it sources exclusively from the overseas supplier (i.e., q b o S ) under Strategy S. The inverse demand functions under two sourcing strategies are: p S = a − e q r S − q b o S for Strategy S and p D = a − e q r D − ( q b o D + e q b l D ) for Strategy D, respectively.

As previously discussed, with overseas emergency renegotiation, a new contract will be re-signed once the overseas supplier suffers from delivery delay and incurs an extra post-recovery cost. To maintain consistency between ex-ante and ex-post decision-making and avoid additional tradeoffs blurring our analysis, we assume that the power of the parties remains unchanged during renegotiation (Li, 2013). That is, it remains the case that the overseas supplier quotes a new wholesale price at which the brand determines a new order quantity. Such a new re-signed contract will differ from the original one because the brand and the overseas supplier act as second movers after observing the rival’s decisions, which can be viewed as an indirect cost of delivery delay while the post-recovery cost is the direct one. We further consider other possible damage/constraint associated with overseas delivery delay in Section 6, where the overseas supplier has a capacity constraint (Section 6.3) or quality deterioration (Section 6.4) upon delay. The subscripts including “ _ R ” denote new variables when the overseas delivery delay occurs. If the overseas supplier incurs delivery delay, the inverse demand functions under two strategies are revised as: p _ R S = a − e q r S − q b o _ R S for Strategy S and p _ R D = a − e q r D − ( q b o _ R D + e q b l D ) for Strategy D, respectively. We also incorporate two additional considerations: the brand’s ability to reorder from the local supplier ex-post if the overseas delivery delay occurs (in Section 6.1), and the consumer loss experienced by the brand due to the delivery delay (cf. Proposition EC.1 in Appendix A).

We use the parameter α ∈ ( 0 , 1 ) to represent the probability of overseas delivery delay (referred to as the delay probability from hereon). We normalize the unit production cost to zero and focus on an extra post-recovery cost incurred by the overseas supplier in the event of a delivery delay. Specifically, we exclude any post-recovery fixed costs, as they do not alter the equilibria, and consider only the post-recovery unit cost, denoted by c ( > 0 ) . All the supply chain members are profit-maximizing and risk-neutral. Their respective profit functions are defined as follows.

Strategy S:

π r S = ( 1 − α ) ( p S − w r S ) e q r S + α ( p _ R S − w r S ) e q r S ; π b S = ( 1 − α ) ( p S − w b o S ) q b o S + α ( p _ R S − w b o _ R S ) q b o _ R S ; π l s S = w r S e q r S ; π o s S = ( 1 − α ) w b o S q b o S + α ( w b o _ R S − c ) q b o _ R S .

Strategy D:

π r D = ( 1 − α ) ( p D − w r D ) e q r D + α ( p _ R D − w r D ) e q r D ; π b D = ( 1 − α ) [ ( p D − w b o D ) q b o D + ( p D − w b l D ) e q b l D ] + α [ ( p _ R D − w b o _ R D ) q b o _ R D + ( p _ R D − w b l D ) e q b l D ] − F ; π l s D = w r D e q r D + w b l D e q b l D ; π o s D = ( 1 − α ) w b o D q b o D + α ( w b o _ R D − c ) q b o _ R D .

The sequence of events is illustrated in Figure 2. In Stage 1, the brand decides its sourcing strategy, single-sourcing or dual-sourcing. In Stage 2 (ex-ante), the original wholesale price contracts are signed. The local supplier and the overseas supplier determine their wholesale prices w r j and w b o j , respectively, and then the brand and the local rival determine their order quantities q b o j and q r j , respectively, ( j ∈ { S , D } ) . Under Strategy D, the local supplier additionally quotes a wholesale price w b l D to the brand, whereby the brand determines its order quantity q b l D . In Stage 3 (ex-post), if the overseas delivery delay occurs, the overseas supplier and the brand under both strategies will re-sign a new contract with a new wholesale price w b o _ R j and a new order quantity q b o _ R j ( j ∈ { S , D } ) . Otherwise (no delivery delay occurs), all supply chain members adhere to the original contract formulated in Stage 2. To ensure that all equilibrium outcomes are positive, we impose an upper bound on the post-recovery unit cost c , denoted by c ¯ , with the expression relegated to Appendix B.3 of the E-Companion. All the derivations, equilibrium outcomes, and expressions of thresholds throughout this work are presented in the appendices, for the sake of expositional brevity.

OPEN IN VIEWER

Figure 2.

Sequence of events.

In this section, we examine the scenario without overseas emergency renegotiation, focusing on two extreme benchmarks concerning procurement contracts affected by overseas delays: (1) contract termination and (2) contract continuation at an additional post-recovery unit cost. These two benchmarks represent two widely observed and practically relevant contractual outcomes of delay when no explicit renegotiation clause is included. The contract termination benchmark captures situations where delays lead to a complete breakdown of the contractual relationship, a scenario often assumed in the literature to model all-or-nothing disruption. By contrast, in the contract continuation benchmarks, the affected overseas supplier is compelled to fulfill the original contract despite increased costs, in line with real-world practices governed by legal doctrines such as pacta sunt servanda. We focus on the impact of the overseas delay probability in the first benchmark and the impact of the overseas supplier’s post-recovery cost in the second one. This analysis aids in understanding the role of emergency renegotiation, which not only inherits certain attributes from these benchmarks but also introduces new characteristics. It is important to note that all the subsequent discussions are conducted with respect to the final equilibrium outcomes, with all the sub-game derivations relegated to the Appendices.

4.1. Benchmark 1: Contract Termination

In the first benchmark, we assume that the overseas delivery delay will entail the contract termination so that the brand receives nothing from the overseas supplier, equivalent to the complete overseas disruption (Hu and Kostamis, 2015; Shan et al., 2022). We add the term “ T ” in the superscript to distinguish it from our main model. The parameter c has no impact here, so we solely focus on the delay probability α .

Proposition 1

In the benchmark of contract termination, the following statements about the brand’s wholesale prices hold. (a)

Under both strategies, the brand’s wholesale prices increase with α , that is, ∂ w i j T / ∂ α > 0 ∀ ( i , j ) ∈ { ( b o , S ) , ( b o , D ) , ( b l , D ) } .

(b)

The comparison between the brand’s wholesale prices under the two sourcing strategies yields: i.

w b o D T < w b o S T .

ii.

There exists a threshold α 1 T such that w b l D T < w b o S T if α < α 1 T and w b l D T ≥ w b o S T otherwise.

In a competitive environment, delivery delays cause indirect harm by allowing the market of the affected party (i.e., the brand) to be captured by a competitor not exposed to the same risk (i.e., the local rival). Once no delivery delay occurs, this ex-ante captured market places the brand at a competitive disadvantage. To counteract this, the brand is incentivized to secure its market share by placing larger orders ex-ante as the delay probability, denoted by α , increases. Proposition 1(a) suggests that the overseas supplier is better off maintaining a higher profit margin to mitigate losses from an increased α , that is, it sets a higher wholesale price as α increases. This result highlights the divergent decision-making between the brand and the overseas supplier. However, in the presence of emergency renegotiation, the overseas supplier may instead lower its wholesale price as α increases, stimulating the brand to place larger orders and thereby helping it resist market capture from the local rival (cf. Lemma 2).

Under Strategy D, the local supplier’s wholesale price to the brand also increases with α , which is tied to two aspects. First, the brand will rely more on the local supplier for product supply than the overseas one, since the ex-ante order placed to the local supplier is not exposed to the risk, and thus more effective in counteracting the damage of overseas delivery delay. This intuitively empowers the local supplier with price-hiking under a larger α . Besides, the increase in α also indicates the local rival is more likely to enjoy the first-mover advantage, so it is more profitable for the local supplier to quote a high wholesale price to the brand and focus more on the local rival channel. Such price hikes by suppliers are not uncommon during emergencies such as the COVID-19 pandemic, as global supply disruptions afford them this leverage (Efficio Consulting, 2024; Forbes, 2022).

Proposition 1(b) aligns with the established consensus in the literature on supply diversification: in the absence of supply risk, dual sourcing can promote supplier competition, resulting in lower wholesale prices under Strategy D compared to Strategy S, which involves an exclusive supplier. However, when accounting for the impact of overseas delay, the strong pricing power granted to the local supplier by a large α can lead to a situation where the local supplier’s wholesale price charged to the brand under Strategy D may exceed the single wholesale price under Strategy S, despite the presence of supplier competition.

Proposition 2

In the benchmark of contract termination, the difference in the brand’s profits under the two sourcing strategies (i.e., E [ π b D T ] − E [ π b S T ] ) decreases with α .

Based on the preceding analysis, the advantage of dual-sourcing, namely supplier competition, diminishes as α increases. Thus, in this benchmark of contract termination, dual sourcing is less appealing for the brand as the delay probability increases.

4.2. Benchmark 2: Contract Continuation at Post-Recovery Cost

In this benchmark scenario, the overseas supplier is obligated to fulfill the pre-existing contract despite the occurrence of an overseas delivery delay, which induces an additional post-recovery unit cost. We refer to this benchmark as contract continuation hereafter. This situation is analogous to the concept of “forced compliance” by Cachon and Lariviere (2001). The term “ C ” in the superscript is to distinguish it from the main model.

Compared to Strategy S, Strategy D presents two intrinsic structural distinctions: (1) the brand sources from two upstream suppliers, and (2) the (common) local supplier serves two downstream buyers. The former distinction involves supplier interactions that are reflected in the wholesale prices charged to the brand, resulting in an increase in the brand’s quantity due to this dual-sourcing structure. Regarding the latter distinction, we focus on the variation in the local supplier’s wholesale price charged to the local rival under the two strategies, which indicates its incentive to coordinate the two channels. Based on these insights, we obtain the following proposition by comparing the two strategies.

Proposition 3

In the benchmark of contract continuation, comparing the two strategies, we have the following statements. (a)

For the brand’s wholesale prices, w i D C < w b o S C ∀ i ∈ { b o , b l } .

(b)

For the brand’s total quantity, define q b D C ≐ q b o D C + E [ e q b l D C ] , then q b D C > q b o S C .

(c)

For the local rival’s wholesale price, w r D C < w r S C .

This benchmark essentially represents a simultaneous game, ² wherein the overseas contract continues to be executed despite the occurrence of a delivery delay. As a monopolistic position becomes unattainable under conditions of overseas delay, the local rival is unlikely to significantly increase its order to capture the market. Consequently, only the direct damage from the delivery delay, namely the post-recovery cost, is present, while the indirect damage identified in the first benchmark is absent. As a result, the brand has a diminished incentive, as compared to the first benchmark, to source from the local supplier ex-ante, thereby reducing the local supplier’s leverage to increase prices. Supplier competition under Strategy D will dominate and result in lower wholesale prices than under Strategy S (cf. Proposition 3(a)). As suggested by Feng and Lu (2013), the equilibrium wholesale prices are higher in the common-supplier structure (i.e., one-to-two) than in an exclusive-supplier structure (i.e., channel-to-channel), since a high wholesale price of the common supplier can alleviate the downstream competition. Our findings diverge from theirs and underscore the unique characteristics of this dual-sourcing and dual-sales-channel structure. Specifically, it highlights the interplay between supplier competition, arising from supplier interaction in the two-to-one structure, and the softened downstream competition incentive, stemming from channel coordination in the one-to-two structure. In this benchmark, the influence of supplier competition predominates over that of the softened downstream competition.

Beyond supplier competition, the dual-sourcing structure offers an additional advantage: a larger total quantity compared to Strategy S. This benefit is driven by two main factors. First, wholesale prices under Strategy D are lower than those under Strategy S. Furthermore, the inclusion of a reliable local supplier reduces supply risk, thereby enhancing the brand’s competitiveness. As a result, this increase in quantity naturally reduces the local rival’s market share. Anticipating this, the local supplier will adjust its dual sales channels by lowering the wholesale price to the less competitive local rival. This outcome can also be interpreted from the perspective of downstream competition: since the brand faces lower wholesale prices under Strategy D, the local rival’s wholesale price should also be lower to remain competitive.

Note that α and c here have equivalent effects, as they both contribute to the overseas supplier’s disadvantage through the expected cost of α c . Consequently, our analysis focuses mainly on the impact of the post-recovery cost c , with the understanding that all the results holds true with respect to α .

Lemma 1

In the benchmark of contract continuation, the following statements about the impact of c hold. (a)

For the brand’s wholesale prices, ∂ w b o D C ∂ c > ∂ w b o S C ∂ c > ∂ w b l D C ∂ c > 0 .

(b)

For the brand’s total quantity, 0 > ∂ q b o S C ∂ c > ∂ q b D C ∂ c .

Lemma 1 shows the impact of c on the brand’s wholesale prices and total quantity, which facilitates our understanding of how the brand strategy preference varies with c . An increase in c contributes directly to a higher wholesale price of the overseas supplier, which indirectly leads the local supplier to raise its wholesale price due to supplier interaction under Strategy D. Thus, under Strategy D, the brand’s wholesale prices increase with c , with that charged by the overseas supplier increasing at a higher rate than that charged by the local one. We further find that the effect of c on the wholesale price charged by the overseas supplier is more significant under Strategy D than under Strategy S. This is because, under Strategy D, the overseas supplier receives a smaller order, making it more sensitive to increases in c . In this context, moderating the wholesale price to secure a larger order from the brand is not an optimal response, leading the overseas supplier to pass on more of the cost increase through price adjustments.

Both suppliers’ wholesale prices increasing with c under Strategy D renders the brand’s total quantity more sensitive to c under Strategy D than under Strategy S, where only one supplier’s wholesale price functions on the order quantity. The result in Lemma 1(b) provides one driving force for the brand to prefer Strategy S as c increases.

Proposition 4

In the benchmark of contract continuation, the difference in the brand’s profits under the two sourcing strategies (i.e., E [ π b D C ] − E [ π b S C ] ) decreases with c .

Based on the preceding analysis, the advantage derived from a larger quantity, which encourages the brand to opt for Strategy D, diminishes as c increases, thereby making Strategy S more appealing. Note that in the main model, the presence of emergency renegotiation introduces a new key effect that results in a non-monotonic pattern of the brand’s strategy preference regarding c (cf. Section 5).

5. Main Model: With Overseas Emergency Renegotiation

In this section, we analyze the key differences and insights introduced by emergency renegotiation (the main model outlined in Section 3). We highlight two distinct driving forces absent in the two preceding benchmarks: (1) the overseas supplier’s price-cutting, and (2) the local supplier’s suppression of the local rival. These forces contribute to our understanding of how the presence of emergency renegotiation shapes the brand’s order allocation and sourcing strategy preference. A concise summary of the subsequent analysis roadmap is illustrated in Figure 3.

OPEN IN VIEWER

Figure 3.

Logic framework with key results.

Note that, if an overseas delay occurs, the contract will be reformulated based on the ex-post residual market that takes into account ex-ante decisions. To counteract the potential disadvantage of being a second-mover and the cost increase imposed by the overseas supplier, the brand is inclined to place larger orders in the ex-ante stage to effectively compete with the local rival, who acts as the first mover. Consequently, it is intuitive that the brand’s expected profitability is contingent upon its ex-ante decisions, as high profitability for both the original and new contracts can be achieved if the brand demonstrates strong competitiveness ex-ante. Therefore, we focus exclusively on the ex-ante operational decisions, in parallel with the benchmarks, to identify the distinctive implications of emergency renegotiation for supply diversification strategies.

Lemma 2

Assume c = 0 , with overseas emergency renegotiation, the following statements about the impact of α on the brand’s ex-ante wholesale prices hold. (a)

Under Strategy S, ∂ w b o S ∂ α < 0 .

(b)

Under Strategy D, ∂ w b l D ∂ α > 0 , and there exists a threshold α 1 such that ∂ w b o D ∂ α < 0 if α < α 1 and ∂ w b o D ∂ α ≥ 0 otherwise.

In sharp contrast to the contract termination benchmark, Lemma 2(a) shows that the wholesale price set by the overseas supplier w b o j ( ∀ j ∈ { S , D } ) may decrease with α . Particularly when we exclude the impact of c (i.e., c = 0 ), the overseas supplier under Strategy S lowers its wholesale price as α increases, which is diametrically opposed to what it would be without renegotiation (cf. Proposition 1(a)). Put differently, the operational focus of the brand and the overseas supplier to hedge against the possible loss from an increased α becomes consistent. Both of them prefer to strive for a high sales volume, contrary to the overseas supplier striving for a high margin in the contract termination benchmark. The underlying reason is that, under both strategies, the overseas supplier charges a higher new wholesale price in the ex-post contract compared to the original one, that is, w b o _ R j > w b o j ( ∀ j ∈ { S , D } ). It is because of a high ex-post wholesale price that the overseas supplier strategically sacrifices itself in the original contract to assist the brand in competing with the local rival. Such a result elucidates why the overseas supplier cuts its ex-ante wholesale price as α increases (referred to as the overseas supplier’s price-cutting). We further find that when incorporating the role of c , the overseas supplier’s wholesale price under Strategy S decreases first and then increases with α on the ground that the post-recovery cost exerts a similar role as the expected cost of α c , eventually limiting the price-cutting behavior aforementioned.

Under Strategy D, the overseas supplier’s tendency to lower its wholesale price as α rises persists. However, interaction with the local supplier, who raises its wholesale price in response, results in a U-shaped relationship between the overseas supplier’s wholesale price and α . This price-cutting behavior by the overseas supplier has a significant impact on the brand’s order allocation, as shown in the following proposition.

Proposition 5

Assume c = 0 , with overseas emergency renegotiation, there exist two thresholds α 2 and α 3 such that q b o D < E [ e q b l D ] if α ∈ ( α 2 , α 3 ) and q b o D ≥ E [ e q b l D ] otherwise.

Proposition 5 excludes the impact of c and compares the brand’s expected order quantities from its two supply channels. This result extends the insight of Tang and Kouvelis (2011): in a symmetric supplier setting with exogenous wholesale prices, the dual-sourcing buyer always allocates more orders to the exclusive supplier and fewer to the common supplier. Our finding underscores the vital role of asymmetric supplier attributes and their influence on pricing, which in turn shapes the brand’s order decisions. Given a small α , the two suppliers are nearly symmetric, and the rationale by Tang and Kouvelis (2011) continues to apply here. As α increases, the brand prefers to allocate more orders to the local supplier to hedge against the indirect damage of delivery delay (i.e., second-mover disadvantage). Yet, a sufficiently high α reverses this pattern: the overseas supplier receives a larger order as it cuts the wholesale price while the local supplier raises its wholesale price as α increases (cf. Lemma 2(b)), which is unattainable in the contract termination benchmark (cf. Corollary EC.1 in Appendix A).

Although the presence of emergency renegotiation may alter the overseas supplier’s decision-making, the role of α on the brand’s sourcing strategy preference remains fundamentally unchanged (cf. Corollary EC.2 in Appendix A), as compared to the first benchmark.

In what follows, we find another key distinction elicited by overseas emergency renegotiation: the local supplier has the incentive to suppress the local rival channel by setting a higher wholesale price under Strategy D than Strategy S, particularly under a large c . This new driving force will significantly shape the role of c on the brand’s strategy preference. Note that the impact of c on the brand’s wholesale prices and total sales in the main model mirrors that in the contract continuation benchmark (cf. Lemma 1), so we relegate it to Lemma EC.1 in Appendix A.

Proposition 6

With overseas emergency renegotiation, comparing wholesale prices under the two sourcing strategies, the following statements hold. (a)

For the brand’s ex-ante wholesale prices, i.

w b o D < w b o S .

ii.

There exist thresholds α 4 and c 1 such that w b l D < w b o S if α < α 4 and c < c 1 , and w b l D ≥ w b o S otherwise. Further, we have α 4 > α 1 T by comparing the threshold of α in Proposition 1(bii).

(b)

For the local rival’s wholesale price, there exist thresholds α 5 and c 2 such that w r D < w r S if α < α 5 and c < c 2 , and w r D ≥ w r S otherwise. Further, we have α 5 < α 4 by comparing the threshold of α in Proposition 6(aii).

Proposition 6(a) echoes Proposition 1(b), with the rationale recapped as follows. Supply diversification may engender supplier competition as both suppliers compete for the brand’s order, compared with Strategy S with an exclusive overseas supplier. Therefore, the local supplier faces a tradeoff: lowering its wholesale price to compete for the brand’s order versus leveraging the pricing power granted by a large α to raise the price. A comparison of thresholds α 4 and α 1 T (in Proposition 1(bii)) reveals that the parameter condition under which w b l D < w b o S holds is broader when emergency renegotiation is introduced. This is tied to the potential price-cutting of the overseas supplier in the presence of renegotiation, limiting the ability of the local supplier to raise its price as α increases due to supplier interaction.

Regarding the wholesale price of the local rival channel, a key difference from Proposition 3(c) emerges. Although the local rival is less competitive under Strategy D than Strategy S (i.e., q r D < q r S ), the upstream local supplier may not lower its wholesale price to support the local rival, as it could in the contract continuation benchmark ( w r D C < w r S C , cf. Proposition 3(c)). There are two possible reasons. First, the local supplier may suppress the more competitive channel (the local rival) to coordinate its two channels if the brand also becomes an important downstream buyer. Aside from the direct cost increase to the overseas supplier, the overseas delivery delay results in additional indirect damage to the brand, namely the potential second-mover disadvantage, compared to the contract continuation benchmark. These more severe damages under a large α or c will encourage the brand to favor the local supplier more in the ex-ante order allocation stage. The second reason is attributed to the fact that the high wholesale price of the brand channel will be passed on to the local rival channel due to dual-sales-channel interaction. A large α or c induces the local supplier to raise the wholesale price for the brand, which in turn pushes up the price for the local rival.

The threshold of α 5 is smaller than α 4 in Proposition 6(aii), indicating that it is possible for w r D > w r S and w b l D < w b o S to hold simultaneously. Further, we show that as c increases, the rate of increase in the local supplier’s wholesale price to the local rival exceeds that to the brand when α is large, a result absent in the contract continuation benchmark (cf. Lemma EC.2 in Appendix A).

The above results highlight a key insight: under Strategy D, the local supplier may set a higher wholesale price for the local rival than under Strategy S (referred to as the local supplier’s suppression of the local rival). This suppression behavior introduces a new incentive for the brand to adopt Strategy D, especially when α is large.

Proposition 7

With overseas emergency renegotiation, there exist two thresholds α 6 and α 7 such that (a)

When α ≤ α 6 , E [ π b D ] − E [ π b S ] decreases with c for c ∈ ( 0 , c ¯ ) , so there exist two thresholds F 1 and F 2 such that i.

if F < F 1 , E [ π b D ] > E [ π b S ] ,

ii.

if F 1 ≤ F < F 2 , there exists a threshold c 3 such that E [ π b D ] > E [ π b S ] for c < c 3 and E [ π b D ] ≤ E [ π b S ] otherwise,

iii.

if F ≥ F 2 , E [ π b D ] < E [ π b S ] .

(b)

When α 6 < α < α 7 , E [ π b D ] − E [ π b S ] decreases first and then increases with c , so there exists a threshold F 3 such that i.

if F < F 3 , E [ π b D ] > E [ π b S ] ,

ii.

if F 3 ≤ F < max { F 1 , F 2 } , there exists a threshold c 4 such that E [ π b D ] > E [ π b S ] for c < c 3 or c > c 4 and E [ π b D ] ≤ E [ π b S ] otherwise,

iii.

if F ≥ max { F 1 , F 2 } , E [ π b D ] < E [ π b S ] .

(c)

When α ≥ α 7 , E [ π b D ] − E [ π b S ] increases with c for c ∈ ( 0 , c ¯ ) , so i.

if F < F 2 , E [ π b D ] > E [ π b S ] ,

ii.

if F 2 ≤ F < F 1 , E [ π b D ] > E [ π b S ] for c > c 4 and E [ π b D ] ≤ E [ π b S ] otherwise,

iii.

if F ≥ F 1 , E [ π b D ] < E [ π b S ] .

Proposition 7 fully characterizes the brand’s optimal sourcing strategy through the lens of three key parameters. A higher supplier maintenance cost F intuitively discourages the brand from adopting dual sourcing. If the delay probability α is low, the brand’s strategy preference aligns with the contract continuation benchmark (cf. Proposition 4). This is primarily because, as c increases, the brand faces a steeper rise in wholesale prices and a sharper decline in total sales under Strategy D than under Strategy S (cf. Lemma EC.1 in Appendix A), reinforcing its preference for Strategy S.

This result can also be explained from the perspective of supplier competition. Under a small α and c , the brand’s wholesale prices from the two suppliers are lower under Strategy D than Strategy S, leading it to prefer Strategy D. This finding is consistent with Tang et al. (2014), which shows that in a supply chain with two suppliers and one buyer, dual sourcing is favored if supplier competition drives down the wholesale price. However, Proposition 7(bii) reveals a different outcome: dual sourcing becomes the brand’s preferred strategy when the post-recovery unit cost c is either low or high. That is, the brand may prefer Strategy D even if the brand’s wholesale price charged by the local supplier is higher under Strategy D than Strategy S. This is driven by the local supplier’s strategic suppression of the local rival (cf. Proposition 6(b)), which becomes more pronounced as c increases. When α is overly large, this suppression effect outweighs the forces favoring Strategy S, leading the profit difference to widen as c increases (cf. Proposition 7(c)).

The literature on supply diversification, such as Dong et al. (2022) and Hu and Kostamis (2015), shows that given exogenous supply prices, a new supplier will be introduced when the costs of the existing suppliers are high. In the contract continuation benchmark, an increase in the cost disadvantage of overseas suppliers discourages the brand from including the local supplier in its portfolio (cf. Proposition 4). This finding suggests that the classical results in the literature may not hold when wholesale prices are endogenous and emergency renegotiation is absent. By contrast, our main model offers a new perspective to support the results in the literature: in the context of endogenous wholesale pricing and emergency renegotiation, an overly high expected cost of the overseas supplier (i.e., α c ) may encourage the brand to choose dual sourcing, due to the local supplier’s incentive to suppress the local rival channel. This underscores the distinct role of supplier pricing power and strategic behavior under emergency renegotiation. Our result also provides a reasonable explanation for the phenomenon that some brands balk at dual sourcing (Forbes, 2020).

Proposition 8

With overseas emergency renegotiation, the following statements about other parties’ profits hold. (a)

For the overseas supplier, E [ π o s D ] < E [ π o s S ] .

(b)

For the local rival, E [ π r D ] < E [ π r S ] .

(c)

For the local supplier, there exist thresholds α 8 and c 5 such that E [ π l s D ] < E [ π l s S ] if α < α 8 and c < c 5 , and E [ π l s D ] ≥ E [ π l s S ] otherwise.

The brand’s adoption of dual sourcing intuitively harms both the local rival and the overseas supplier, compared to Strategy S. For the local supplier, the intuition is that Strategy D would be beneficial due to the presence of two buyers, namely the brand and the local rival. However, Proposition 8(c) reveals a counterintuitive outcome, indicating that the local supplier may not necessarily benefit from Strategy D. This phenomenon is referred to as the local supplier’s dual-sales-channel dilemma. Dual sourcing can enhance the brand’s competitiveness, thereby negatively impacting the local rival. Consequently, the local supplier can earn more under Strategy D than Strategy S only if it can impose a high wholesale price on the brand. This high margin in the brand channel must compensate for the losses incurred in the local rival channel, a scenario that requires a large α or c .

6. Model Extensions

In this section, we conduct additional analysis and model extensions to both confirm the robustness of our main results and derive new managerial insights. Specifically, we discuss (1) ex-post reorder from the local supplier in Section 6.1; (2) consumer surplus and social welfare in Section 6.2; (3) the impact of capacity constraint of overseas post-recovery production in Section 6.3; (4) the impact of quality deterioration of overseas post-recovery production in Section 6.4; and (5) the impact of local delivery delay in Section 6.5, respectively. In addition, we further discuss the impact of consumer loss from delivery delay in Proposition EC.1 in Appendix A.

6.1. Ex-Post Reorder From Local Supplier

In practice, a brand with dual supply sources may opt to reorder from the reliable local supplier if there is a delay in overseas delivery. This situation, along with the one analyzed in the main text where the brand commits to renegotiating with the overseas supplier in the event of an overseas delay, is integrated into three distinct scenarios under Strategy D. Specifically, under Strategy D, the brand can pre-commit to the following actions if an overseas delay occurs: (1) exclusively renegotiating a new contract with the overseas supplier (Strategy D as outlined in the main model); (2) exclusively entering into a reorder contract with the local supplier (referred to as Strategy DL); or (3) both renegotiating with the overseas supplier and entering into a reorder contract with the local supplier (referred to as Strategy DB). Under Strategy S, it is assumed that the brand, having an exclusive supply channel, lacks the capability to reorder from the local supplier, thereby maintaining the setup and results of Strategy S as presented in the main model. For tractability, we assume that there is no additional cost associated with the local supplier’s ex-post production, as it never suffers from disruption. The subscript “ b l _ R ” represents the decision variables in the ex-post reorder contract between the brand and the local supplier.

Under Strategy DL, the inverse demand functions are p D L = a − e q r D L − ( q b o D L + e q b l D L ) ; p _ R D L = a − e q r D L − ( e q b l _ R D L + e q b l D L ) . Under Strategy DB, the inverse demand functions are p D B = a − e q r D B − ( q b o D B + e q b l D B ) ; p _ R D B = a − e q r D B − ( q b o _ R D B + e q b l _ R D B + e q b l D B ) . The local rival’s profit function is the same as the main model, while the profit functions of the other three parties should be rewritten as follows.

Strategy DL:

π b D L = ( 1 − α ) [ ( p D L − w b o D L ) q b o D L + ( p D L − w b l D L ) e q b l D L ] + α [ ( p _ R D L − w b l _ R D L ) e q b l _ R D L + ( p _ R D L − w b l D L ) e q b l D L ] − F ; π l s D L = w r D L e q r D L + w b l D L e q b l D L + α w b l _ R D L e q b l _ R D L ; π o s D L = ( 1 − α ) w b o D L q b o D L .

Strategy DB:

π b D B = ( 1 − α ) [ ( p D B − w b o D B ) q b o D B + ( p D B − w b l D B ) e q b l D B ] + α [ ( p _ R D B − w b o _ R D B ) q b o _ R D B + ( p _ R D B − w b l _ R D B ) e q b l _ R D B + ( p _ R D B − w b l D B ) e q b l D B ] − F ; π l s D B = w r D B e q r D B + w b l D B e q b l D B + α w b l _ R D B e q b l _ R D B ; π o s D B = ( 1 − α ) w b o D B q b o D B + α ( w b o _ R D B − c ) q b o _ R D B .

Similarly, the above formulas represent a two-stage game, where ex-post decisions (labeled with “ _ R ”) are conducted with the aim to optimize the ex-post profit after the realization of overseas delay. All the derivations, equilibrium outcomes, and feasible regions are relegated to Appendix C.1 of the E-Companion. Similar to the main body, we focus on the brand’s sourcing strategy preference by comparing the two new cases of Strategy D with Strategy S (in the main model). This extension aims to explore how incorporating the ex-post reorder from the local supplier will affect the brand’s strategy preference.

Proposition 9

Considering the case with ex-post reorder from the local supplier, we have the following statements about the brand’s preferred sourcing strategy. (a)

There exists thresholds F l 1 and c l 1 such that E [ π b D L ] > E [ π b S ] if F < F l 1 and c > c l 1 , and E [ π b D L ] ≤ E [ π b S ] otherwise.

(b)

There exists thresholds F b 1 and c b 1 such that E [ π b D B ] > E [ π b S ] if F < F b 1 and c < c b 1 , and E [ π b D B ] ≤ E [ π b S ] otherwise.

Proposition 9(a) shows that when the post-recovery cost of the overseas supplier is high, the brand will prefer Strategy DL under which it can ex-post reorder from the local supplier, rather than sourcing from the high-cost overseas supplier under Strategy S. Instead, a small c will induce the brand to choose Strategy S. Note that, the brand may earn more under Strategy S than Strategy DL even if F = 0 , underscoring that the brand’s benefits from the local reorder under dual-sourcing structure and from overseas emergency renegotiation under single-sourcing structure are comparable. Further, by comparing the brand’s expected profits under Strategy DL and Strategy D (in the main model), we find that the brand may achieve higher profitability under Strategy D, provided a large α or a small c parameter-wise. The key reason lies in how the anticipation of renegotiation alters the overseas supplier’s decision-making focus—shifting from seeking a high margin to prioritizing sales volume. This shift weakens the local supplier’s pricing power and thus benefits the brand, particularly when α is large (cf. Lemma 2). This observation highlights the role and the difference of the supplier’s decision-making dynamics across the two ex-post sourcing cases. It also reveals that under the dual-sourcing structure, renegotiating with the affected overseas supplier may be superior to reordering from the unaffected local supplier even if the latter does not incur an additional ex-post cost.

In Proposition 9(b), the brand will earn more under Strategy DB only if c is small. It is important to note that Strategy DB is similar to Strategy D in the main model, with the key difference being that the brand can source from both suppliers once the overseas delay occurs. Some forces influencing the brand’s optimal sourcing strategy would hence apply here as well, but we show that the situation, where the brand may prefer dual sourcing under a large c in our main model (cf. Proposition 7(bii)), is unattainable if replacing Strategy D with Strategy DB. The underlying reason is detailed as follows. We find that w r D B < w r S , which is the same as the results of the contract continuation benchmark (cf. Proposition 3(c)). Consequently, the key force in the main model, that is, that the suppression of the local rival channel by the local supplier becomes more pronounced as c rises (cf. Proposition 6(b)), will disappear. As such, the profit disparity of the brand under Strategy DB and Strategy S diminishes with c , aligning with the pattern as highlighted in Proposition 4 (in the contract continuation benchmark).

While deriving analytical results comparing the brand’s profits under Strategy DB and Strategy D proves challenging, numerical examples suggest that the brand tends to be more profitable under Strategy DB. This observation is intuitive: introducing an additional supplier can intensify competition at the ex-post stage, thereby benefiting the brand. However, it is important to acknowledge that committing to sourcing from both suppliers ex-post may, in practice, incur additional costs compared to sourcing from a single supplier. Such costs could include start-up expenses for production, which are not accounted for in this extension.

6.2. Consumer Surplus and Social Welfare

Uncertain supply leads to a deficiency in product availability on a societal level, raising the important question of whether the sourcing strategy adopted by a profit-oriented brand can enhance consumer surplus and social welfare. We will dedicate to this issue with the following analysis.

Under Strategy S, the total supply in the market are: Q S = q b o S + e q r S (no delay); Q _ R S = q b o _ R S + e q r S (delay). Under Strategy D, the total supply are: Q D = q b o D + e q b l D + e q r D (no delay); Q _ R D = q b o _ R D + e q b l D + e q r D (delay). The consumer surplus can be computed as the area between the market price and the inverse demand curve (Cohen et al., 2022). For instance, given the market price p ( Q ) under total supply Q , and the inverse demand curve d − 1 ( q ) = a − q , the consumer surplus C S = ∫ 0 Q ( d − 1 ( q ) − p ( Q ) ) d q = a Q − Q 2 / 2 − p ( Q ) Q . The social welfare consists of the profits of all the parties and the consumer surplus. Therefore, the consumer surplus ( C S j ) and social welfare ( S W j ) under the two strategies can be expressed as follows:

C S j = E [ α ( a Q _ R j − ( Q _ R j ) 2 / 2 − p _ R j Q _ R j ) + ( 1 − α ) × ( a Q j − ( Q j ) 2 / 2 − p j Q j ) ] = α 2 E [ ( Q _ R j ) 2 ] + 1 − α 2 E [ ( Q j ) 2 ] ; S W j = C S j + ∑ i = l s , o s , r , b E [ π i j ] , ∀ j ∈ { S , D } .

Proposition 10

The following statements regarding consumer surplus and social welfare hold. (a)

The consumer surplus under Strategy D is higher than that under Strategy S (i.e., C S D > C S S ).

(b)

The comparison result of social welfare under the two strategies is the same as that of the brand’s profit in Proposition 7, with the exception that the expressions for all thresholds differ. Detailed results are provided in Proposition EC.2 in Appendix C.

Strategy D contributes to improving product availability, resulting in a larger total market supply compared to Strategy S, and consequently, a higher consumer surplus.

In Proposition 10(b), the comparison of social welfare, encompassing both consumer surplus and the sum of profits, under the two strategies exhibits a pattern similar to the brand’s strategic preference (cf. Proposition 7). We analyze how c affects the profit difference of each party under the two strategies (i.e., E [ π i D ] − E [ π i S ] ). As c increases, the profit differences of both the local and overseas suppliers increase, while that of the local rival decreases. The result that the local supplier is more profitable under Strategy D than under Strategy S is explained in Proposition 8(c). Compared with Strategy D, the rising c will benefit the local rival more under Strategy S because its wholesale price (resp. quantity) under Strategy S is less (resp. more) sensitive to c (cf. Lemma 2(c)). For the overseas supplier, the negative effect of rising cost is less significant under Strategy D than under Strategy S (cf. Lemma EC.1(a) in Appendix A), resulting in its profit difference increasing with c .

The aforementioned findings, combined with the result from Proposition 7 that the brand’s profit difference displays a non-monotonic (convex) pattern in c , carry important implications for social welfare. Specifically, the brand’s adoption of dual sourcing may adversely affect social welfare if the overseas supplier’s post-recovery unit cost is moderate.

6.3. Capacity Constraint of Overseas Supplier’s Post-Recovery Production

Here, we investigate another direct damage that the overseas supplier may suffer, that is, the capacity constraint of overseas post-recovery production, denoted by K ( > 0 ) . If K = 0 , the results in this extension are the same as those of the contract termination benchmark. The superscripts “ S K ” and “ D K ” are used to distinguish from the main model. Intuitively, this capacity constraint will lead to the brand’s profit loss, no matter under which strategy. We thus focus on the case where the capacity constraint is binding under both strategies and examine how K affects the brand’s sourcing strategy preference.

Proposition 11

There exists thresholds F k 1 and K k 1 such that E [ π b D K ] > E [ π b S K ] if F < F k 1 and K > K k 1 , and E [ π b D K ] ≤ E [ π b S K ] otherwise.

The result of Proposition 11 is somewhat counterintuitive: a small K may incentivize the brand to opt for Strategy S. A limited capacity can result in higher wholesale prices charged to the brand, reflecting the adverse impact of insufficient capacity. The logic is that when the overseas supplier anticipates an inability to fulfill the brand’s ex-post order due to capacity constraints, it has an incentive to charge a higher wholesale price, which also indirectly pushes up the local supplier’s wholesale price. Further, we show that the brand’s average wholesale price under Strategy D is more sensitive to K than the single wholesale price under Strategy S. In this sense, the above negative effect of a smaller K is weaker under Strategy S than Strategy D. This mirrors the effect of a larger c , where wholesale prices rise more steeply under Strategy D than Strategy S (cf. Lemma EC.1(a) in Appendix A). The rationale is that a small order quantity allocated to the overseas supplier under Strategy D renders its pricing more sensitive to potential damages, whether from a large post-recovery unit cost or a limited post-recovery capacity. Consequently, a smaller K induces the brand to opt for Strategy S.

6.4. Quality Deterioration of Overseas Post-Recovery Production

Delivery delays may lead to a quality issue with the overseas supplier’s products when it hastily produces the required order quantity. We tackle this issue by introducing a random variable e o . Specifically, e o has a mean μ o and variance σ o 2 , with the new parameter t o = μ o 2 / σ o 2 ( > 1 ) used to capture the overseas supplier’s production quality when fulfilling the new ex-post contract. To distinguish quality issues between the two suppliers, we add the subscript “ l ” to the quality-related variables of the local supplier in the main model: e l and t l = μ l 2 / σ l 2 ( > 1 ) . For traceability, we assume that the two random variables e l and e o are independent. Consequently, the inverse demand and profit functions should be reformulated by replacing “ e ” and “ q b o _ R j ” in the main model with “ e l ” and “ e o q b o _ R j .”

We conduct extensive numerical studies to show the impact of the quality problem in overseas post-recovery production (cf. Figure 4). The main findings are summarized in the following observations.

OPEN IN VIEWER

Figure 4.

The brand’s strategy preference in terms of t o and t l considering the quality deterioration of overseas post-recovery production ( a = 1 , c = 0.1 ).

Observation 1

Consider the quality deterioration of overseas post-recovery production. (a)

The brand is less incentivized to choose Strategy D as the supply maintenance cost F increases, or the delay probability α increases. The impact of the overseas post-recovery unit cost c on the brand’s strategy preference remains qualitatively unchanged.

(b)

As the quality of overseas post-recovery production improves (i.e., t o increases), the brand becomes more profitable under Strategy D than under Strategy S.

Observation 1(a) suggests an intuitive result that has been well explained in the main model. Similar to the role of t l in the main model, t o does not fundamentally alter the impact of c on the brand’s strategy preference, and the results are the same as the main model if there is no quality issue with the overseas supplier’s post-recovery production (i.e., t o → ∞ ). The brand can benefit from the improvement in ex-post production quality of the overseas supplier under both strategies, but at different incremental rates. Although a larger t i ( ∀ i ∈ { o , l } ) reflects enhanced supplier competitiveness, it can also signify the intensity of competition between two suppliers when the brand sources from both simultaneously. As such, the supplier competition under Strategy D intensifies as either t o or t l increases, which reinforces the brand’s incentive to prefer Strategy D.

6.5. The Impact of Local Delivery Delay

In this subsection, we formulate a general model where both the local and overseas suppliers may suffer from the potential delivery delay. The local delay probability is indexed as β ∈ ( 0 , 1 ) , which is independent of the overseas delay probability α . Similar to the main model, once the local delivery delay occurs, the local supplier also incurs a post-recovery unit cost c and the contract parties (i.e., the local supplier and the brand/local rival) will re-sign a new ex-post contract. Thus, there are four ex-post cases: without delay ( ( 1 − α ) ( 1 − β ) ), only overseas delay ( α ( 1 − β ) ), only local delay ( ( 1 − α ) β ), and both delay ( α β ). The reverse demand functions are collated in Table 1, with quantities labeled “ _ R ” as ex-post ordering decision.

OPEN IN VIEWER

Table 1.

The reverse demand functions considering the local delivery delay.

	Strategy S	Strategy D
Without delay ( 1 − α ) ( 1 − β )	p S = a − e q r S − q b o S	p D = a − e q r D − ( q b o D + e q b l D )
only overseas delay α ( 1 − β )	p _ R S = a − e q r S − q b o _ R S	p _ R D = a − e q r D − ( q b o _ R D + e q b l D )
only local delay ( 1 − α ) β	p _ R S = a − e q r _ R S − q b o S	p _ R D = a − e q r _ R D − ( q b o D + e q b l _ R D )
both delay α β	p _ R S = a − e q r _ R S − q b o _ R S	p _ R D = a − e q r _ R D − ( q b o _ R D + e q b l _ R D )

Observation 2

Consider both overseas and local delivery delays. (a)

The brand is less incentivized to choose Strategy D as the supply maintenance cost F increases, or the post-recovery unit cost c increases (in most cases).

(b)

Strategy D is preferred only when the overseas and local delay probabilities (i.e., α and β ) are close, either both large or both small. If α and β are one small and the other large, the brand will choose Strategy S.

Figure 5 depicts the impacts of the local and overseas delay probabilities. Intuitively, the supply maintenance cost weakens the brand’s incentive to choose Strategy D. In terms of c , we observe that in most cases, the region where Strategy D is preferred shrinks as c rises. The local supplier’s suppression of the local rival by a high wholesale price, which is the key force for the brand to prefer Strategy D under a large c , is tied to the local supplier’s channel coordination incentive by helping the brand compete with the local rival with great competitiveness. However, the possible local delay probability undermines the local rival’s competitiveness such that the local supplier may not opt to suppress the local rival to assist the brand. Therefore, the previous result that an increase in c strengthens the brand’s preference for Strategy D will disappear. This suppression effect, however, remains significant if β is overly small, where the result of Proposition 7 in the main model exists.

OPEN IN VIEWER

Figure 5.

The brand’s strategy preference in terms of α and β considering both overseas and local delivery delays ( a = 1 , t = 10 ).

Observation 2(b) suggests that Strategy D is preferred only when α and β are similar in magnitude, either both large or both small. Note that Strategy S refers to single sourcing from the overseas supplier only. When the overseas and local delay probabilities are comparable, two suppliers are nearly homogeneous so that neither is granted notable pricing power, preventing excessive wholesale prices under Strategy D. As a result, the supply accessibility from a resilient supply network and the cost advantage due to supplier competition make Strategy D more profitable for the brand. Instead, if α ≫ β , the local supplier’s pricing power, granted by a low local delay probability, is strong enough that the brand prefers Strategy S, aligned with the result in the main model (cf. Corollary EC.2 in Appendix A). If β ≫ α , the high local delay probability renders it unnecessary for the brand to include the local supplier.