Resilient and Sustainable Restaurant Supply Chain Operations Considering Multi-Brand Strategies

Abstract

This study analyzes the performance and strategic implications of multi-brand kitchen restaurants from a supply chain perspective. Multi-brand kitchens are increasingly adopted in franchise systems as they enhance resilience by pooling demand risks and enabling substitution across brands. They also promote environmental sustainability by integrating operations and reducing land use. However, limited research has examined how such models perform under different supply chain structures and contract types. To address this gap, we develop analytical models comparing five configurations that vary by brand scope (single- vs. multi-brand) and integration level (centralized vs. decentralized). We examine how optimal pricing, brand portfolio, and royalty structures influence profits across franchisors, franchisees, and the overall chain under diverse market environments. Our findings reveal that multi-brand strategies improve profitability, particularly under high demand and favorable market potential. However, decentralized systems show greater profit fluctuations, highlighting the need for alignment between contracts and operations. Theoretically, this study contributes to the restaurant supply chain literature by modeling coordination across organizational boundaries. Practically, it offers actionable insights for franchisors and restaurant operators on when and how to implement multi-brand kitchen strategies for resilient and sustainable supply chain operations.

1. Introduction

The food service industry has undergone significant transformation over the past decade due to shifting consumer preferences, technological advancements, and global disruptions such as the COVID-19 pandemic [1]. The most notable innovation is the emergence of multi-brand kitchen restaurants—a model in which multiple food brands are operated within a shared kitchen infrastructure [2].

In this paper, we use the term ‘multi-brand franchise system’ to refer to a multi-brand kitchen that operates under a franchising structure in which the franchisor develops, governs, and supports multiple brand concepts within a shared kitchen. This organizational form integrates the operational flexibility of cloud kitchens with the governance mechanisms of franchising—such as brand development, standardization, training, menu engineering, and marketing support—allowing a single restaurant unit to manage several brands simultaneously in a scalable and consistent manner.

In practice, multi-brand kitchen operations supported by franchising have been adopted by several well-known companies. Examples include Rebel Foods, Kitchen United, Taster, Nolboo, and DNY Hospitality, all of which operate multiple branded concepts within a shared kitchen infrastructure while relying on centralized brand development, operational standards, and marketing support. These firms illustrate how the multi-brand franchise system functions as an integrated organizational form that combines the flexibility of cloud kitchens with the governance advantages of franchising.

The shift from single-brand to multi-brand cloud kitchens can be seen as a strategic response to increasing market pressure and the risks of relying on a single brand. While single-brand cloud kitchen models provide operational advantages by eliminating physical dine-in spaces and lowering fixed costs [1,3], their reliance on the performance of a single brand makes them increasingly vulnerable in a competitive environment. In a contemporary environment increasingly dominated by third-party aggregators such as Uber Eats and DoorDash, the risks of operating under a single brand have grown more acute. These platforms control key aspects of customer access—visibility, digital placement, and delivery costs—leaving single-brand operators vulnerable to unfavorable fee structures, limited exposure, and high customer acquisition costs [4,5]. In response, firms like Rebel Foods (India), Kitchen United (USA), and Taster (Europe) have pioneered the multi-brand cloud kitchen model as a form of strategic adaptation [6,7,8]. By offering multiple virtual restaurant brands from a single kitchen infrastructure, this model enhances customer value—allowing mixed-brand orders under one delivery fee—and boosts sustainable operational efficiency by sharing kitchen space, staff, and procurement systems [4,9,10].

These multi-brand operations, compared with traditional single-brand restaurants, enable enhanced market expansion and operational flexibility [6]. Moreover, multi-brand strategies help enhance sustainable restaurant operations by reducing redundant use of space, labor, and supply chain resources [11,12,13].

Franchising naturally complements multi-brand kitchen operations and provides the structural support necessary for managing multiple brands within a single facility. They can take advantage of franchisors’ reputation, operational support, and expertise [14]. Well-known brands can alleviate customers’ doubt about the taste and quality of the food itself and delivery which is especially crucial to online-based restaurants [2]. The franchisor’s capabilities in standardized training, operational design, and centralized marketing can also help streamline workflows and reduce complexity in managing multiple brands [15]. Moreover, in practice, the development and sustainable operations of multiple distinct brands is actually beyond the capacity of a single independent restaurant; such a model is feasible only within the structural and operational support of a franchise system.

A multi-brand franchise system also enhances supply chain resilience by pooling demand risks and enabling substitution across brands within a shared operational platform [16]. Centralizing capacity or inventory across multiple demand streams reduces expected shortage and holding costs through risk pooling [17]. Shared resources allow firms to dynamically reallocate inventory or production among products to buffer stochastic demand shocks [18]. In the restaurant context, consumer substitution models indicate that diversified menus and brand portfolios sustain sales by redirecting customers toward available alternatives during disruptions [19]. The multi-branding strategies of firms such as KFC–Taco Bell illustrate how cross-brand flexibility can stabilize revenues and maintain service continuity under fluctuating demand, although excessive operational complexity may limit these benefits [20]. Collectively, these mechanisms explain how multi-brand franchise structures achieve revenue stability and adaptive recovery, key dimensions of supply chain resilience. In our context, supply chain resilience refers to the system’s ability to maintain revenue performance under unfavorable market shifts by exploiting cross-brand substitution, pooling demand risks, and reallocating shared resources within the multi-brand kitchen.

Accordingly, this study examines the resilience and sustainability of a new organizational form in the restaurant industry: the multi-brand franchise restaurant supply chain. While recent trends underscore the growing significance of multi-brand franchise strategies in the restaurant industry, academic research on this topic remains limited and fragmented. To address this gap, our study focuses on the structural and operational design of franchise supply chains that adopt multi-brand kitchens.

In doing so, we highlight how multi-brand franchising differs from both single-brand and cloud-kitchen models by introducing a decision regarding the number of brands operated—a strategic dimension absent in prior research. To this end, we introduce and compare various franchise-based restaurant supply chain models along key structural dimensions, including integration level (integrated vs. decentralized) and brand scope (single-brand vs. multi-brand). Specifically, we investigate the optimal pricing strategies, brand portfolio configurations, and royalty structures under each model.

Our objective is to derive managerial insights and strategic implications for franchise chains and restaurant operators considering the adoption and sustainable operations of multi-brand kitchen systems. We evaluate market performance and profit outcomes across different franchise structures and analyze how these outcomes change under various business environments.

From the franchisor’s perspective, the multi-brand model further provides resilient and sustainable advantages by enabling broader market coverage and reducing brand-specific demand risks. In traditional franchising, expanding brand presence often requires opening additional outlets under the same brand identity, a strategy that often leads to internal competition and market saturation [21]. In contrast, multi-brand virtual operations allow franchisors to deploy differentiated brand concepts—such as premium, budget, health-conscious, or ethnic cuisines—without requiring separate physical storefronts. This segmentation enables lower demand risks and higher market penetration within a given geographic radius, especially in densely populated delivery zones, and reduces intra-brand cannibalization. Furthermore, by leveraging shared back-end infrastructure—kitchens, logistics, staff, and supply chains—franchisors benefit from economies of scale while maintaining brand differentiation at the front end [8,10]. This model aligns with platform-based scalability and enables franchisors to strengthen supply chain resilience by responding more effectively to volatile consumer trends and delivery platform dynamics. However, managing a diversified brand portfolio requires careful alignment, and franchise contract design plays a central role in coordinating franchisor–franchisee decisions.

Despite these promising characteristics, existing research remains limited. Prior studies have largely focused on comparing traditional and cloud kitchens without considering the franchise dimension [7,8]. Even the few studies that examine contract issues in franchise-based multi-brand settings—such as Kang and Yoo [22]—restrict their analysis to the franchisee’s restaurant operations, omitting the broader implications for the franchise supply chain management [22].

This study addresses critical gaps in the existing literature by examining the resilient and sustainable operations of multi-brand franchise supply chains from the perspectives of the franchisor, franchisee, and overall supply chain. We develop analytical models to determine the optimal pricing strategies, franchise contracts, and brand portfolio configurations under varying market conditions. To obtain new and important implications through a comprehensive comparison, we also analyze single-brand models and present five distinct cases: (1) Case SF: single-brand first-best case; (2) Case SD: single-brand, decentralized franchisor–franchisee supply chain; (3) Case MF: multi-brand first-best case; (4) Case M1: multi-brand, decentralized supply chain with a single franchise fee, regardless of the number of brands operated; (5) Case MN: multi-brand, decentralized supply chain with multiple franchise fees, proportional to the number of brands. We consider two different multi-brand decentralized supply chain cases, Cases M1 and MN, that are different in franchise fees. This is since in practice, we can often observe multi-brand franchise chains offering single franchise fee regardless of the number of brands, such as DNY Hospitality in India and Nolboo in Korea [23,24].

By evaluating and comparing the performance across these five models under various business environments, we provide actionable insights for designing brand portfolios and franchise contracts that enhance the sustainable operations and overall performance of multi-brand franchise supply chains.

The key findings from the results can be summarized as follows. First, multi-brand kitchens tend to lead to higher profits, especially in the supply chain. Second, multi-brand kitchens are likely to experience greater profit fluctuations than single-brand kitchens as the business environment changes. Third, customer demand is crucial for the success of multi-brand kitchens. These findings help us understand how and when we can benefit from adopting multi-brand kitchens, providing managerial guidelines for restaurant operations in addition to contributing to the literature.

Although online delivery platforms play an important role in shaping consumer access and delivery fees, our analytical model does not treat platforms as strategic decision-makers in the supply chain. Instead, following prior analytical studies, we incorporate platform influences indirectly through the delivery cost parameter, allowing us to focus on the contractual and structural interactions between the franchisor and the franchisee.

2. Literature Review

Restaurant supply chains are decentralized systems that require close coordination across multiple entities, including suppliers, franchisees, franchisors, and third-party delivery platforms. Prior studies emphasize the role of contractual mechanisms and supply chain integration in mitigating inefficiencies such as double marginalization [25,26]. However, most existing research focuses on single-brand formats and does not address the complexity of managing pricing and contracts across multiple brands within a franchise structure.

2.1. Cloud Kitchens and Multi-Brand Operations

Cloud kitchens have emerged as delivery-oriented restaurant models characterized by shared kitchen facilities, limited physical footprints, and the absence of dine-in spaces. Prior studies examine their consumer appeal, operational challenges, and strategic implications—highlighting factors such as perceived convenience, food quality, packaging, and digital engagement [27,28,29,30,31,32]. From a managerial perspective, researchers have also explored operational barriers and success factors, including labor issues, risk assessment, and resource allocation under delivery-based environments [33,34,35]. Game-theoretic and financial analyses further investigate decisions such as driver allocation, delivery times, and cost structures, but these studies largely remain centered on single-brand cloud kitchen formats [36,37].

Within this broader cloud-kitchen landscape, academic studies explicitly focused on multi-brand kitchens remain limited. Beniwal and Mathur [2] describe the operational characteristics and advantages of multi-brand kitchens, emphasizing the importance of integrated Point-of-Sale (POS) systems and efficient resource management for enhancing profitability. Tualeka [38], through a case study of a food service company in Indonesia, argues that multi-brand kitchens offer substantial reductions in operational costs and improvements in efficiency compared with traditional restaurant formats. Kang and Yoo [22] analyze the operational sustainability of multi-brand kitchens and propose conditions under which this model can outperform single-brand formats. However, their analysis focuses primarily on the franchisee’s operations and does not incorporate the franchisor’s role in shaping brand portfolios or contract structures.

The performance of cloud and multi-brand kitchen models is further influenced by the growing prominence of delivery platforms. Prior studies demonstrate that while platform-based delivery services may provide short-term revenue gains, continued reliance on aggregators can erode long-term profitability due to platform fees and increased dependence [39]. Comparative analyses of self-operated versus platform-based delivery services also highlight trade-offs between operational control, cost structures, and sustainability [40]. Further, Chen et al. [41] show that delivery platforms can introduce additional costs without necessarily increasing demand. Although these studies offer important insights into delivery-system performance, most do not explicitly incorporate critical cost components such as delivery fees or franchising-related royalties. The present study addresses this gap by integrating these cost elements into the analytical model of multi-brand franchise operations.

Given that many multi-brand kitchen operations rely on franchising mechanisms for brand development, quality control, and incentive alignment, it is essential to examine how franchise-based governance structures support or constrain multi-brand operations. Accordingly, we next review the literature on franchise systems to establish the theoretical foundations for the contract structures and decision rights modeled in this study.

2.2. Multi-Brand Kitchens in Franchise Systems

Given that many multi-brand kitchens are operated under franchise contracts, relevant literature on franchise-based restaurant models is also reviewed. Castrogiovanni et al. [42] assert that franchise-based restaurants are more likely to succeed compared to independent operations. Supporting this view, Ackermann [43] documents a significant revenue increase for Applebee’s after adopting a franchising model, indicating that franchise systems can enhance financial performance. Franchise models in the food industry generally fall into three categories: full franchises where franchisees manage all operations (e.g., Baskin-Robbins); fully corporate-owned chains managed by franchisors (e.g., Starbucks); and hybrid models involving both franchisor-owned and franchised units (e.g., McDonald’s) [44]. In both full and hybrid models, franchise contracts commonly involve an upfront fixed fee and ongoing royalties based on a percentage of revenue [43,45]. Following these previous studies’ investigations, we similarly consider the franchise contract consisting of the fixed fee and royalties for the multi-brand franchise system.

Extensive research has examined the economic benefits of restaurant franchising. Studies consistently find that franchising improves cash flow stability and reduces operational risks, leading to superior financial performance relative to non-franchised operations [46,47,48,49,50]. Risk mitigation is especially emphasized as a key advantage [49,51,52,53], while Bang et al. [54] discuss the unique structural features of restaurant franchising. Beyond profitability, franchising is also shown to influence accounting practices [47,55] and management systems [56,57]. These advantages explain why most multi-brand restaurants adopt a franchising structure in practice. Reflecting this reality, our models focus on investigating the performance of multi-brand operations under franchise systems.

The implementation and optimization of franchise models have also been investigated. Restaurants with smaller size, rapid growth potential, and suitable ownership structures are more likely to pursue franchising [57,58]. Optimal franchising ratios have been discussed in the literature as critical to profit maximization [51,59]. Once established, franchise contracts can improve operational efficiency through well-defined roles between franchisors and franchisees [60]. Kalnins and Mayer [61] find that local experience can enhance franchise survival rates, while Moon et al. [62] emphasize the importance of knowledge transfer mechanisms for successful franchise performance. These previous studies have revealed various important implications for the franchise model operations, but it is difficult to find ones considering multi-brand franchise models like ours.

The implementation of franchise systems in multi-brand kitchen environments creates structural and contractual complexity beyond that of single-brand formats. Franchisors must coordinate multiple brand concepts within a shared operational base while designing contracts that align incentives with franchisees. From a theoretical perspective, this situation reflects a plural-form governance structure, where multiple brand identities and control mechanisms coexist under one system [63]. In addition, contract theory suggests that franchisors must balance fixed franchise fees and sales-based royalties to manage behavior and ensure quality across decentralized units [64]. These frameworks are particularly relevant to multi-brand models, where the allocation of fees and decision rights varies depending on the number and scope of brands involved. This study incorporates such theoretical considerations by modeling alternative contract structures and analyzing their effects on the performance of the supply chain.

2.3. Research Gap and Contribution of This Study

Despite the extensive literature, a few studies adopt a supply chain perspective that models franchisor–franchisee interactions within a multi-brand, delivery-oriented system. Most franchise-related studies are centered on traditional restaurant formats. Kang and Yoo [22] introduce franchising concepts in the context of multi-brand kitchens, but they focus on profit maximization for a single franchisee. The present study is one of the first to comprehensively consider the business environment of multi-brand franchise supply chain systems as a whole. By bridging the gap among research streams, we aim to contribute to the body of research for resilient and sustainable franchise restaurant operations.

To provide a clearer overview of how prior studies relate to the present research,

Table 1. Summary of major literature streams.

Literature Stream	Representative Studies	Focus	Key Gaps	How This Study Addresses Them
Cloud kitchens	[27,28,29,30,31,32,33,34,35,36,37]	Delivery-oriented operations; single-brand models	Limited attention to multi-brand structures; no franchise setting	Models multi-brand kitchens within a franchise supply chain
Multi-brand kitchens	[2,22,38]	Operational benefits; case evidence	Missing franchisor role; no contract or pricing analysis	Incorporates franchisor–franchisee interaction and brand scope
Delivery platforms	[39,40,41]	Platform effects, profitability, sustainability	No modeling of franchise fees, royalties, or multi-brand costs	Integrates delivery fees and franchise costs into analytical models
Franchise systems	[42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64]	Contracts, fees, risk, operational performance	Focus on traditional formats; no multi-brand configuration	Models fees, royalties, and brand decisions across five structures
Supply chain contracts	[25,26]	Coordination, pricing, double marginalization	No multi-brand factors; no shared kitchen cost synergies	Compares five configurations including integrated and decentralized systems

categorizes the existing literature by major streams and highlights the key knowledge gaps that motivate our theoretical development.

As shown in Table 1, although several research streams contribute valuable insights into cloud kitchens, delivery platforms, and franchising, an integrated supply chain perspective on multi-brand franchise operations is still lacking. Our study fills this gap by analytically comparing five structural configurations and explicitly modeling the franchisor–franchisee interaction under different brand scopes.

3. Model

This study discusses the resilient and sustainable operations of a franchise supply chain for a cloud restaurant, consisting of a franchisor and a franchisee restaurant. Their relationship is categorized by the number of brands (single vs. multiple), types of centralization (integrated vs. decentralized), and policy of franchise fee (altogether vs. per brand), providing five possible cases. Specifically, the cases include: (1) Case SF: single-brand first-best case; (2) Case SD: single-brand; decentralized franchisor–franchisee supply chain; (3) Case MF: multi-brand first-best case; (4) Case M1: multi-brand, decentralized supply chain with a single franchise fee, regardless of the number of brands operated; (5) Case MN: multi-brand, decentralized supply chain with multiple franchise fees, proportional to the number of brands. The interaction of franchise supply chain players are illustrated in Figure 1. In this section, we introduce models for the cases and obtain optimal solutions: the optimal number of brands, franchise contract, and food item prices.

3.1. Case SF: Single-Brand First-Best Case

First, we consider the ideal first-best situation as a benchmark case for a single-brand restaurant supply chain (Case SF), in that the franchisor can perfectly control the franchisee’s behavior like a single entity and hence there is no opportunistic behavior of the franchisee restaurant. This case can be considered an ideal integrated supply chain in which the franchisor integrates the franchisee restaurant without any costs. This case provides a benchmark solution by assuming that the franchisor and franchisee (restaurant) aim to maximize global profit so we can identify the effects of multiple brands and decentralized supply chains in comparison. Before presenting the analytical cases, we summarize the notation used throughout the model in

Table 2. Notation summary.

Symbol	Definition
p	Sales price set by the restaurant
d	Delivery cost incurred by customers (d ≥ 0)
q	Market demand determined by price and delivery cost
α	Demand potential (α ≥ 0)
β	Price and delivery-cost sensitivity parameter (β ≥ 0)
θ	Market share of multi-brand consumers (0 ≤ θ ≤ 1)
n	Number of brands operated in the restaurant (n ≥ 1)
η	Unit inefficiency cost per brand (η ≥ 0)
λ	Brand development and management cost (λ ≥ 0)
c	Unit production cost (c ≥ 0)
r	Royalty rate specified in the franchise contract (0 ≤ r ≤ 1)
f	Fixed franchise fee (f ≥ 0)
π	Profit of the restaurant, the franchisor, or the entire supply chain

.

These definitions apply to all cases analyzed in Section 3, Section 4 and Section 5 and will be used consistently without further redefinition.

Given that sales price could be one of the most influencing factors for demand, we consider the sales price p. The delivery cost d is also included in the demand function because it may impose a burden on consumers, thereby defining the demand $q_{SF}$ as in Equation (1). We utilize the demand and profit functions of [22], but we extend them for the supply chain context. Specifically, Kang and Yoo [22] focus on the restaurant’s multi-brand operations. Therefore, we adopt the demand and restaurant’s profit functions from [22], but they are extended by adding the franchisor’s profit function and franchise contract terms in this study.

$$q_{SF}=\alpha -\beta \left(p+d\right).$$

(1)

where α is the demand potential and β measures the sensitivity to price and delivery cost. In this study, we focus on consumer behavior factors that are directly related to the subject of this study, online restaurant operations. They are the food price and the delivery cost. In general, consumers hesitate to purchase if the price of food or delivery is high [22]. Therefore, p and d are negatively associated with $q_{SF}$, consistent with the economics and operations management literature. The demand function in Equation (1) describes the standard setting for an integrated single-brand system, where higher prices and delivery costs reduce demand. It serves as the benchmark for comparison with decentralized and multi-brand cases. Equations (2) and (3) present profits of the franchisee restaurant, ${\pi }_{SF}^r$ and franchisor, ${\pi }_{SF}^f$, respectively. Summing up ${\pi }_{SF}^r$ and ${\pi }_{SF}^f$, we obtain the single-brand franchise supply chain’s profit ${\pi }_{SF}$ in Equation (4).

$${\pi }_{SF}^r=q_{SF}\left\{p-r-\left(c+\eta \right)\right\}-f=\{\alpha -\beta \left(p+d\right)\}\left(p-r-c-\eta \right)-f,$$

(2)

$${\pi }_{SF}^f=r{q}_{SF}+f-{\displaystyle \frac{\lambda }{2}}=r\{\alpha -\beta \left(p+d\right)\}+f-{\displaystyle \frac{\lambda }{2}},$$

(3)

$${\pi }_{SF}={\pi }_{SF}^r+{\pi }_{SF}^f=\left\{\alpha -\beta \left(p+d\right)\right\}\left(p-c-\eta \right)-{\displaystyle \frac{\lambda }{2}},$$

(4)

where $r$ is the royalty rate, c is unit food cost, η is unit inefficiency cost, and λ is brand developing and managing cost considering inefficiency. Given the restaurant sells a variety of food items with different p in Equation (2) represents the average unit sales price. The restaurant’s profit decreases as r, c, η, and f increase. In addition to the c, the η is considered to affect the restaurant’s profit negatively. When dealing with multiple brands in one restaurant, the resources that a single brand can consume may be smaller than single-brand operations due to the diseconomies of scale. As we discuss multi-brand cases, η gets multiplied by n in Section 3.3, Section 3.4 and Section 3.5.

The franchise contract between the franchisor and franchisee restaurant consists of the r and f. The royalty r implies the amount the restaurant should pay to the franchisor proportional to the number of sold items. The franchise fee f is another payment from the restaurant to the franchisor, but unlike the r, it is independent of q. Since we discuss a single-brand case in this section, f is used alone as shown in Equation (2). However, when discussing multi-brand cases, f can be considered properly with the number of brands in Section 3.5.

Equation (3) shows the franchisor’s profit, receiving the royalty and franchise fee from the restaurant with λ decreasing the profit. The $rq$ and f in Equation (3) are directly from Equation (2), and λ, representing brand development and management cost to the franchisor, is included in the profit function. The more brands the franchisor develops and manages, the more costs are incurred exponentially due to the diseconomies of scale effect induced by the franchisor’s resource limitation. The λ gets multiplied by the squared number of brands and exponentially increases as more brands are involved as discussed in Section 3.3, Section 3.4 and Section 3.5. The current section is about the single-brand case, so the λ is expressed as it is in Equation (3). The profits of the restaurant and franchisor are summed and shown in Equation (4).

Next, we find the optimal price p. To derive the first-order necessary condition (FONC) as shown in Equation (5), we differentiate ${\pi }_{SF}$ in Equation (4) with respect to $p$. Then, we obtain the optimal $p^{*}$ from Equation (5) as shown in Equation (6). The optimal price maximizes total supply chain profit, providing the benchmark for comparisons later.

$${\displaystyle \frac{\partial {\pi }_{SF}}{\partial p}}=-2\beta p+\beta c+\beta \eta +\mathsf{\alpha }-\beta d=0,$$

(5)

$$p_{SF}^{*}={\displaystyle \frac{\alpha +\beta (c+\eta -d)}{2\beta }}.$$

(6)

We derived the second-order sufficient condition (SOSC) by taking the derivative of Equation (5) with respect to $p$.

$${\displaystyle \frac{{\partial }^2{\pi }_{SF}}{\partial p^2}}=-2\beta <0.$$

(7)

Since the SOSC in Equation (7) is negative-definite, the optimal value $p$ in Equation (6) maximizes the profit ${\pi }_{SF}$ in Equation (4). By plugging $p_{SF}^{*}$ from Equation (6) into Equations (1)–(4), we can obtain the optimal values for $q_{SF}^{*}$, ${\pi }_{SF}^{r*},$ ${\pi }_{SF}^{f* }$, and ${\pi }_{SF}^{*}$ as closed forms, respectively. The optimal solutions for the five cases are summarized in

Table 3. Optimal solutions in Cases SF and SD.

Case	p*	r*	q*
SF	${\displaystyle \frac{\alpha +\beta (c+\eta -d)}{2\beta }}$	N/A	${\displaystyle \frac{\alpha -\beta (c+\eta +d)}{2}}$
SD	${\displaystyle \frac{3\alpha +\beta (c+\eta -3d)}{4\beta }}$	${\displaystyle \frac{\alpha -\beta (c+\eta +d)}{2\beta }}$	${\displaystyle \frac{\alpha -\beta (c+\eta +d)}{4}}$

and

Table 4. Optimal solutions in Cases MF, M1 and MN.

	Case	Solution
p*	MF	${\displaystyle \frac{5\eta (\theta \alpha -\beta d)+\beta \eta c+2\lambda -\sqrt{\eta (\theta \alpha -\beta (c+d\left)\right)\left(\eta \right(\theta \alpha -\beta (c+d))+8\lambda )+4{\lambda }^2}}{6\eta \beta }}$
	M1	${\displaystyle \frac{11\eta (\theta \alpha -\beta d)+\beta \eta c+4\lambda -\sqrt{\eta (\theta \alpha -\beta (c+d\left)\right)(\theta \alpha \eta -\beta \eta \left(c+d\right)+16\lambda )+16{\lambda }^2}}{12\eta \beta }}$
	MN	${\displaystyle \frac{11\eta (\theta \alpha -\beta d)+\beta \eta c+4\lambda -\sqrt{\eta (\theta \alpha -\beta (c+d\left)\right)(\theta \alpha \eta -\beta \eta \left(c+d\right)+16\lambda )+16{\lambda }^2-24{\eta }^{2}f\beta }}{12\eta \beta }}$
n*	MF	${\displaystyle \frac{2\eta (\theta \alpha -\beta (c+d\left)\right)+2\lambda -\sqrt{\eta (\theta \alpha -\beta (c+d\left)\right)\left(\eta \right(\theta \alpha -\beta (c+d))+8\lambda )+4{\lambda }^2}}{3{\eta }^2\beta }}$
	M1	${\displaystyle \frac{2\eta (\theta \alpha -\beta \left(c+d\right))+4\lambda -\sqrt{\eta (\theta \alpha -\beta (c+d\left)\right)(\theta \alpha \eta -\beta \eta \left(c+d\right)+16\lambda )+16{\lambda }^2}}{3{\eta }^2\beta }}$
	MN	${\displaystyle \frac{2\eta (\theta \alpha -\beta \left(c+d\right))+4\lambda -\sqrt{\eta (\theta \alpha -\beta (c+d\left)\right)(\theta \alpha \eta -\beta \eta \left(c+d\right)+16\lambda )+16{\lambda }^2-24{\eta }^{2}f\beta }}{3{\eta }^2\beta }}$
r*	M1	${\displaystyle \frac{\eta (\theta \alpha -\beta (c+d\left)\right)-4\lambda +\sqrt{\eta (\theta \alpha -\beta (c+d\left)\right)(\theta \alpha \eta -\beta \eta \left(c+d\right)+16\lambda )+16{\lambda }^2}}{6\eta \beta }}$
	MN	${\displaystyle \frac{\eta (\theta \alpha -\beta (c+d\left)\right)-4\lambda +\sqrt{\eta (\theta \alpha -\beta (c+d\left)\right)(\theta \alpha \eta -\beta \eta \left(c+d\right)+16\lambda )+16{\lambda }^2-24{\eta }^{2}f\beta }}{6\eta \beta }}$

in Section 4.

3.2. Case SD: A Single-Brand Decentralized Franchisor–Restaurant Supply Chain

Case SD denotes a supply chain consisting of a franchisor and a restaurant aiming for their own profit maximization when they have a single brand. The demand function and profits of the restaurant and franchisor in Case SD are identical to Equation (1) through (3) in Section 3.1. That is, $q_{SD}=q_{SF}$, ${\pi }_{SD}^r={\pi }_{SF}^r$, and ${\pi }_{SD}^f={\pi }_{SF}^f$. However, Case SD is different from Case SF in that the restaurant and franchisor do not cooperate with each other for global profit maximization. They only consider their own profit maximization, and hence the restaurant and franchisor determine p and r, respectively, that maximize their own profits. It is different from Case SF in which p is determined to maximize the entire supply chain’s profit of Equation (4).

Therefore, we differentiate the restaurant’s profit ${\pi }_{SD}^r$ with respect to $p$ as shown in Equation (8) and derived the SOSC as in Equation (9) to see if the optimal price maximizes the profit of the restaurant. Then, we obtain the optimal $p_{SD}^{r*}$ as a function of r from Equation (8) as shown in Equation (10).

$${\displaystyle \frac{\partial {\pi }_{SD}^r}{\partial p}}=-2\beta p+\beta r+\beta c+\beta \eta +\mathsf{\alpha }-\beta d=0,$$

(8)

$${\displaystyle \frac{{\partial }^2{\pi }_{SD}^r}{\partial p^2}}=-2\beta <0,$$

(9)

$$p_{SD}^{r*}\left(r\right)={\displaystyle \frac{\alpha +\beta \left(c+r+\eta -d\right)}{2\beta }}.$$

(10)

Then, we consider the franchisor’s contract decision, and the optimal royalty $r_{SD}^{f*}$ is obtained for the franchisor to maximize its profit. By applying p in Equation (10), a function of r, into the franchisor’s profit ${\pi }_{SD}^f$ in Equation (3) where ${\pi }_{SD}^f={\pi }_{SF}^f$, the franchisor’s profit ${\pi }_{SD}^f$ becomes ${\pi }_{SD}^f={\displaystyle \frac{r(\alpha -\beta \left(r+c+\eta +d\right))}{2}}+f-{\displaystyle \frac{\lambda }{2}}$ as a quadratic function of r. Then, the FONC, SOSC, and $r_{SD}^{f*}$ are obtained from ${\pi }_{SD}^f$ as in Equations (11) through (13).

$${\displaystyle \frac{\partial {\pi }_{SD}^f}{\partial r}}={\displaystyle \frac{\alpha }{2}}-\beta r-{\displaystyle \frac{\beta c}{2}}-{\displaystyle \frac{\beta \eta }{2}}-{\displaystyle \frac{\beta d}{2}}=0$$

(11)

$${\displaystyle \frac{{\partial }^2{\pi }_{SD}^f}{\partial r^2}}=-\beta <0,$$

(12)

$$r_{SD}^{f*}={\displaystyle \frac{\alpha -\beta (c+\eta +d)}{2\beta }}.$$

(13)

By applying $r_{SD}^{f*}$ in Equation (13) into $p_{SD}^{r*}\left(r\right),$ we obtain $p_{SD}^{r*}$ as the closed form. Then, by applying $r_{SD}^{f*}$ and $p_{SD}^{r*}$ into Equations (1)–(4), we can obtain $q_{SD}^{*}$, ${\pi }_{SD}^{r*}$, ${\pi }_{SD}^{f*}$, and ${\pi }_{SD}^{*}$. The optimal solutions are summarized in Table 3 and Table 4 in Section 4.

3.3. Case MF: Multi-Brand First-Best Case

We now consider the first-best multi-brand franchise model providing benchmark solutions to be compared with multi-brand decentralized supply chains with different types of franchise fees. The demand $q_{MF}$ for multi-brand cases is defined as shown in Equation (14).

$$q_{MF}=n\left(\theta \alpha -\beta \left(p+d\right)\right).$$

(14)

The relative market size of multiple brands $\theta$ and the number of brands $n$ are involved in multi-brand cases. Beniwal and Mathur [3] claim that the main reason that restaurants adopt multi-brand franchise models is to improve their profitability when they suffer from the insufficient market size. Accordingly, we add $\theta$ to express the partial amount of $\alpha$. Since we consider multiple brands in this case, the $n$ is multiplied by the existing demand obtained in Case SF. Thus, the $\theta$ and n are also included in the profits of the restaurant and franchisor as shown in Equations (15) and (16). The $\eta$ increases in proportion to the $n$, reducing the restaurant profit as in Equation (15). The franchisor’s brand development and management cost ${\displaystyle \frac{\lambda n^2}{2}}$ increases as the $n$ increases. As such, we obtain the profits of the restaurant, franchisor, and supply chain in the multi-brand restaurant supply chain as shown in Equations (15)–(17).

$${\pi }_{MF}^r=n\{\theta \alpha -\beta \left(p+d\right)\}\left(p-r-c-n\eta \right)-f,$$

(15)

$${\pi }_{MF}^f=rn\{\theta \alpha -\beta \left(p+d\right)\}+f-{\displaystyle \frac{\lambda n^2}{2}},$$

(16)

$${\pi }_{MF}={\pi }_{MF}^r+{\pi }_{MF}^f=n\left\{\theta \alpha -\beta \left(p+d\right)\right\}\left(p-c-n\eta \right)-{\displaystyle \frac{\lambda n^2}{2}}.$$

(17)

Similarly to Case SF, we differentiate the supply chain’s profit ${\pi }_{MF}$ with respect to $p$ as shown in Equation (18) and derive the SOSC as shown in Equation (19) to obtain the optimal $p_{MF}^{*}$ maximizing the supply chain profits as a function of n as shown in Equation (20).

$${\displaystyle \frac{\partial {\pi }_{MF}}{\partial p}}=n(\beta \eta n-2\beta p+\beta c+\theta \alpha -\beta d)=0,$$

(18)

$${\displaystyle \frac{{\partial }^2{\pi }_{MF}}{\partial p^2}}=-2n\beta <0,$$

(19)

$$p_{MF}^{*}(n)={\displaystyle \frac{\theta \alpha +\beta (c+\eta n-d)}{2\beta }}.$$

(20)

Differently from Case SF, we also need to consider the decision of the $n$ that maximize the supply chain’s overall profit in this Case MF. The FONC and SOSC with respect to n are derived as shown in Equations (21) and (22), respectively, and we find the optimal $n$ as shown in Equation (23) maximizing the supply chain profit.

$${\displaystyle \frac{\partial {\pi }_{MF}}{\partial n}}=\begin{array}{c}(-2\theta \alpha \beta d-2\theta \alpha \beta c+4{\beta }^2\eta nd+4{\beta }^2\eta nc-4\lambda n\beta +3{\beta }^2{\eta }^2{n}^2+2{\beta }^{2}cd\\ +{\theta }^2{\alpha }^2+{\beta }^2{c}^2+{\beta }^2{d}^2-4\theta \alpha \beta \eta n)\end{array}/4\beta =0,$$

(21)

$${\displaystyle \frac{{\partial }^2{\pi }_{MF}}{\partial n^2}}=\beta \eta d+\beta \eta c-\lambda +{\displaystyle \frac{3\beta {\eta }^{2}n}{2}}-\eta \alpha \theta <0,$$

(22)

$$n_{MF}^{*}={\displaystyle \frac{2\eta (\theta \alpha -\beta (c+d))+2\lambda -\sqrt{\eta (\theta \alpha -\beta (c+d))(\eta (\theta \alpha -\beta (c+d))+8\lambda )+4{\lambda }^2}}{3{\eta }^2\beta }}.$$

(23)

Applying the optimal $n_{MF}^{*}$ into $p_{MF}^{*}$ in Equation (20), we obtain $p_{MF}^{*}$ as the closed form. Then, applying $n_{MF}^{*}$ and $p_{MF}^{*}$ into Equations (14) and (17), the optimal values for $q_{MF}^{*}$ and ${\pi }_{MF}^{*}$ can be obtained. Equation (22) is the SOSC, which indicates that a concave profit function can be obtained if there is a proper balance between the parameters that have positive and negative impacts on profit.

3.4. Case M1: Multi-Brand Decentralized Franchisor–Restaurant Supply Chain with Single Franchise Fee

In Case M1, we discuss a franchisor and a restaurant who work for their own profit maximization. This case is similar to Case SD, but we consider multiple brands here. Case M1 can also be differentiated from Case MN in Section 3.5 in the way that a single franchise fee is considered regardless of the number of brands. Such a fee structure is typically adopted when the franchisor views the multi-brand kitchen as a single operational unit, choosing not to charge additional fees for each brand because the marginal cost of managing an extra brand is relatively small. Case M1 reflects the multi-brand restaurant supply chains that offer a single franchise fee regardless of the number of brands, such as DNY Hospitality in India and Nolboo in Korea [23,24].

The demand for Case M1 is identical to Equation (14) in Case MF, as both are based on multi-brand. Likewise, the profits of the restaurant ${\pi }_{M1}^r$ and franchisor ${\pi }_{M1}^f$ in Case M1 are also the same as Equations (15) and (16) in Case MF. That is, ${q_{M1}=q}_{MF}$, ${\pi }_{M1}^r={\pi }_{MF}^r$, and ${\pi }_{M1}^f={\pi }_{MF}^f$. However, we consider the restaurant and franchisor’s profits separate from each other since they maximize their own profits in this decentralized supply chain case. First, we differentiate ${\pi }_{M1}^r$ with respect to $p$ as shown in Equation (24) and derive the SOSC as in Equation (25) to obtain the optimal price $p_{M1}^{r*}$ in Equation (26) maximizing the restaurant’s profit.

$${\displaystyle \frac{\partial {\pi }_{M1}^r}{\partial p}}=n(\beta \eta n-2\beta p+\beta r+\beta c+\theta \alpha -\beta d)=0,$$

(24)

$${\displaystyle \frac{{\partial }^2{\pi }_{M1}^r}{\partial p^2}}=-2n\beta <0,$$

(25)

$$p_{M1}^{r*}(r,n)={\displaystyle \frac{\theta \alpha +\beta (c+\eta n-d+r)}{2\beta }}.$$

(26)

Then, we consider the franchisor’s royalty decision. By deriving FONC and SOSC as shown in Equations (27) and (28) with respect to $r$, respectively, we obtain the optimal royalty $r_{M1}^{f*}$ as a function of $n$ as in Equation (29).

$${\displaystyle \frac{\partial {\pi }_{M1}^f}{\partial r}}=-{\displaystyle \frac{n(-\theta \alpha +\beta \eta n+\beta d+2\beta r+\beta c)}{2}}=0,$$

(27)

$${\displaystyle \frac{{\partial }^2{\pi }_{M1}^f}{\partial r^2}}=-n\beta <0,$$

(28)

$$r_{M1}^{f*}\left(n\right)={\displaystyle \frac{\theta \alpha -\beta \left(c+\eta n+d\right)}{2\beta }}.$$

(29)

Differently from the single-brand cases, since multiple brands are involved in Case M1, the optimal number of brands $n$ that maximizes the franchisor’s profit should also be considered. Thus, we differentiate ${\pi }_{M1}^f$ with respect to n as shown in Equation (30) and derive the SOSC as in Equation (31) to obtain the optimal number of brands $n_{M1}^{f*}$ in Equation (32) maximizing the franchisor’s profit.

$${\displaystyle \frac{\partial {\pi }_{M1}^f}{\partial n}}=\begin{array}{c}(-4\beta \eta n\theta \alpha +3{\beta }^2{\eta }^2{n}^2+4{\beta }^2\eta nd+4{\beta }^2\eta nc+{\theta }^2{\alpha }^2-2\theta \alpha \beta d\\ -2\theta \alpha \beta c{+\beta }^2{d}^2+2{\beta }^{2}dc+{\beta }^2{c}^2-8\lambda n\beta )\end{array}/8\beta =0,$$

(30)

$${\displaystyle \frac{{\partial }^2{\pi }_{M1}^f}{\partial n^2}}=-{\displaystyle \frac{\alpha \theta \eta }{2}}+{\displaystyle \frac{3{\beta \eta }^{2}n}{4}}+{\displaystyle \frac{\beta \eta d}{2}}+{\displaystyle \frac{\beta \eta c}{2}}-\lambda <0,$$

(31)

$$n_{M1}^{f*}={\displaystyle \frac{2\eta (\theta \alpha -\beta \left(c+d\right))+4\lambda -\sqrt{\eta (\theta \alpha -\beta (c+d\left)\right)(\theta \alpha \eta -\beta \eta \left(c+d\right)+16\lambda )+16{\lambda }^2}}{3{\eta }^2\beta }}.$$

(32)

The SOSC in Equation (31) is necessary to have the concave profit function. By applying $n_{M1}^{f*}$ into $r_{M1}^{f*}$ and $p_{M1}^{f*}$ in Equations (26) and (29), we obtain the closed-form $r_{M1}^{f*} \mathrm{a}\mathrm{n}\mathrm{d} p_{M1}^{f*}.$

3.5. Case MN: Multi-Brand Decentralized Franchisor–Restaurant Supply Chain with Franchise Fees Proportional to the Number of Brands

Differently from Case M1 addressing a single franchise fee, we consider a more practical situation in that the franchise fee varies with the number of brands in Case MN. Although the demand is the same as that in Cases MF and M1 in Equation (14), the franchise fee increases as we consider more brands. Thus, n is multiplied by $f$. Such a fee structure is commonly observed when each brand requires separate development, marketing, or quality-control efforts, leading franchisors to charge a brand-specific fee rather than treating all brands as a single operational unit. Equations (33) and (34) indicate the restaurant’s and franchisor’s profits in Case MN, respectively.

$${\pi }_{MN}^r=n\{\theta \alpha -\beta \left(p+d\right)\}\left(p-r-c-n\eta \right)-nf,$$

(33)

$${\pi }_{MN}^f=rn\left\{\theta \alpha -\beta \left(p+d\right)\right\}+nf-{\displaystyle \frac{\lambda n^2}{2}}.$$

(34)

The approaches to obtain optimal price p, r, and n that maximize the restaurant and franchisor’s profits are the same as those in Case M1. They are as follows.

$$p_{MN}^{r*}(r,n)={\displaystyle \frac{\theta \alpha +\beta (c+\eta n-d+r)}{2\beta }}.$$

(35)

$$r_{MN}^{f*}(n)={\displaystyle \frac{\theta \alpha -\beta (c+\eta n+d)}{2\beta }},$$

(36)

$$n_{MN}^{f*}={\displaystyle \frac{2\eta (\theta \alpha -\beta \left(c+d\right))+4\lambda -\sqrt{\eta (\theta \alpha -\beta (c+d\left)\right)(\theta \alpha \eta -\beta \eta \left(c+d\right)+16\lambda )+16{\lambda }^2-24{\eta }^{2}f\beta }}{3{\eta }^2\beta }} .$$

(37)

The optimal solutions for Cases SF, SD, MF, M1, and MN are summarized in Table 3 and Table 4 in Section 4.

4. Comparison

We summarize the solutions obtained in Section 3 in Table 3 and Table 4.

Comparing the solutions of the five cases, we obtain the following properties.

Proposition 1.

Comparing Cases SF and SD, $p_{SD}^{*}>p_{SF}^{*}$ and $q_{SF}^{*}>q_{SD}^{*}$ always.

Proof. 

From Table 3, we obtain $p_{SD}^{*}-p_{SF}^{*}={\displaystyle \frac{\alpha -\beta \left(c+\eta +d\right)}{4\beta }}$ and $q_{SF}^{*}-q_{SD}^{*}={\displaystyle \frac{\alpha -\beta \left(c+\eta +d\right)}{4}}$. In Equation (1), $q_{SF}=\alpha -\beta (p+d)>0$, and it is reasonable to consider $p>c+\eta$. Therefore, the relationships in Proposition 1 hold. □

Proposition 1 indicates that the decentralized single-brand restaurant supply chain (Case SD) induces a higher sales price p compared to an integrated supply chain (Case SF), and hence it induces a lower demand q. The lowered demand caused by the price increase in the decentralized supply chain system would lead to inefficiency and lower the supply chain’s entire profit. This comparison highlights that the inefficiency arises from the lack of coordination between the franchisor and the restaurant in decentralized decision making. We will see this by applying a numerical example in the next section.

Proposition 2.

Comparing Cases M1 and MN, $p_{MN}^{*}>p_{M1}^{*}$, $n_{MN}^{*}>n_{M1}^{*}$ and $r_{M1}^{*}>r_{MN}^{*}$ always.

Proof. 

In Table 4, we can observe that the solutions of Cases M1 and MN are very similar. Actually, they are the same except for the existence of the term $(-24{\eta }^{2}f\beta )$ in Case MN in the square root terms. Therefore, the direct comparison of the square root terms is possible, and the square root term of Case MN is smaller than that of Case M1. Therefore, we can obtain the relationships of Proposition 2. □

Proposition 2 points out the different decision structures of two decentralized multi-brand restaurant supply chains. Case MN induces a higher franchise fee $nf$ by requesting to pay multiple franchise fees proportional to the number of brands. Therefore, to increase franchise fee revenue, the franchisor would develop a greater number of brands n, which in turn leads to a higher sales price p. While Case MN involves a higher franchise fee, it imposes a lower royalty than Case M1. This difference arises because a proportional fee structure gives the franchisor a direct incentive to expand the number of brands, which cannot be achieved under a single fixed fee.

The result of the number of brands n implies that Case MN can yield better supply chain resilience and environmental performance. By consolidating a greater number of brands, the multi-brand strategy of Case MN can enhance supply chain resilience by pooling demand risks and enabling substitution across brands within a shared operational platform. Case MN can also reduce land use, energy, water consumption, and food waste by streamlining restaurant operations across more brands and optimizing ingredient utilization and order delivery.

Propositions 1 and 2 reveal important differences between the models. However, due to mathematical complexities introduced by the square root terms as shown in Table 4, it is practically difficult to analytically compare all five single-brand and multi-brand models. Accordingly, we employ a numerical example in the next section to derive additional managerial implications.

5. Numerical Experiment

5.1. Basic Numerical Example

To verify the results in the propositions in the previous section and provide practical implications for franchise restaurant supply chains considering multi-brand kitchen operations, we obtain numerical values based on the models developed in Section 3. Because the multi-brand kitchen is a very recent organizational form, it is practically difficult to obtain datasets. Accordingly, this study adopts a numerical analysis using parameter values and demand/operation characteristics grounded in prior research on multi-brand restaurant operations [22]. Moreover, we set the parameters not only to properly satisfy the SOSC but also to comprehensively show the solutions of all five cases. We carefully set parameter values to avoid arbitrary situations where consistently superior results are obtained in certain cases and to ensure the robustness of our analysis results. Therefore, we set the basic parameters as: the demand potential α = 1000, demand sensitivity to price and delivery cost β = 20, unit delivery cost d = 10, unit food item cost c = 10, unit inefficiency cost from brands η = 0.3, franchise fee f = 100, relative market size of multiple brands θ = 0.8, and magnitude of brand development cost λ = 200.

Table 5. Basic numerical example.

	Single-Brand SC		Multi-Brand SC
	Benchmark	Decentralized	Benchmark	Decentralized
	Case SF	SD	MF	M1	MN
Number of brands $n^{*}$	1.00	1.00	6.42	3.89	4.28
Unit royalty $r^{*}$		14.85		9.42	9.36
Unit sales price $p^{*}$	25.15	32.58	20.96	25.29	25.32
Transfer payment $T^{*}$		2305.23		3545.66	4174.62
Demand $q^{*}$	297.00	148.50	1161.01	365.89	400.37
Franchisor profit ${\pi }^{f*}$		2205.23		2036.07	2344.25
Restaurant profit ${\pi }^{r*}$		1002.61		1622.83	1445.57
Supply chain profit ${\pi }^{*}$	4310.45	3207.84	6364.45	3658.91	3789.82

Note. SF: Single-brand First-best; SD: Single-brand Decentralized; MF: Multi-brand First-best; M1: Multi-brand Decentralized (single franchise fee); MN: Multi-brand Decentralized (multiple franchise fees).

shows the results of the basic numerical example.

In Table 5, we first observe that the results in Proposition 1 holds. That is, $p_{SD}^{*}>p_{SF}^{*}$ and $q_{SF}^{*}>q_{SD}^{*}$. Due to the restaurant’s higher sales price decision p in the decentralized single brand system, the demand request in Case SD is much smaller than the fully integrated supply chain in Case SF, and hence we observe that it devastates the decentralized supply chain’s overall profit, ${\pi }_{SF}^{*}>{\pi }_{SD}^{*}.$

The results in Proposition 2 for multi-brand restaurant supply chains are also verified in Table 5. That is, $p_{MN}^{*}>p_{M1}^{*},$ $n_{MN}^{*}>n_{M1}^{*}$ and $r_{M1}^{*}>r_{MN}^{*}.$ Comparing the overall performance of Cases M1 and MN, to the franchisor’s willingness to introduce more brands n in Case MN offers a chance to enjoy the higher sales price, demand, and supply chain’s overall profit, $p_{MN}^{*}>p_{M1}^{*}$, $q_{MN}^{*}>q_{M1}^{*}$ and ${\pi }_{MN}^{*}>{\pi }_{M1}^{*}$. We also need to note that the difference in contract terms, a single franchise fee in Case M1 and multiple franchise fees in Case MN, is a key factor that makes the difference in the transfer payment and hence profit allocation. We can observe in Table 5 that the total transfer payment $T$ is the sum of the royalty ($rq$) and franchise fee (f in Case M1 and nf in Case MN), which is 17.73% higher in Case MN ($T_{MN}^{*}>T_{M1}^{*}).$ Therefore, the franchisor’s profit is higher in Case MN, whereas the restaurant’s profit is higher in Case M1. That is, ${\pi }_{MN}^{f*}>{\pi }_{M1}^{f*}$ and ${\pi }_{M1}^{r*}>{\pi }_{MN}^{r*}$.

However, this result may be due to this specific parameter setting in this basic numerical example, and hence we will check it through comparative static analyses in Section 5.2. We can also observe that the double marginalization in the decentralized systems of Cases M1 and MN always makes the supply chain’s overall profits much lower than the first-best supply chain profit of Case MF, as in the single brand supply chain.

Comparing the profit performance of single-brand and multi-brand supply chains, we observe that the multi-brand strategy can enhance the profits not only of the supply chain but also of individual players, regardless of whether the supply chain is integrated or decentralized. See in Table 5 that ${\pi }_{MF}^{*}>{\pi }_{SF}^{*}$ and (${\pi }_{MN}^{*}$ or ${\pi }_{M1}^{*}$) > ${\pi }_{SD}^{*}$ for the supply chains, ${\pi }_{MN}^{f*}>{\pi }_{SD}^{f*}$ for the franchisor, and (${\pi }_{MN}^{r*}$ or ${\pi }_{M1}^{r*}$) > ${\pi }_{SD}^{r*}$ for the franchisee restaurant. These results can be mainly due to the adoption of multiple brands and a subsequent increase in demand requests. We can also find that the royalty r is lower in multi-brand cases than in single-brand cases. It is inferred that the royalty burden on the restaurant can be alleviated under the multi-brand systems, leading to a lower set price of the restaurant and significantly higher demand.

Notably, the multi-brand strategy allows the supply chain to significantly improve its profit (${\pi }_{MN}^{*} = 3789.82$, while ${\pi }_{SD}^{*} = 3207.84$), approaching the first-best ideal profit level of the single-brand restaurant supply chain (${\pi }_{SF}^{*}$ = 4310.45). This result makes us expect that the multi-brand strategy can offer a great opportunity to outperform the ideal first-best single-brand supply chain in some business environments even though the double marginalization issue exists in a decentralized franchise system. Therefore, in the next section, we conduct comparative static analyses to provide important business implications for the adoption and management of the multi-brand strategy by comparing the performance of single-brand and multi-brand restaurant supply chains.

5.2. Comparative Static Analysis

5.2.1. Profit Comparison

In addition to the basic numerical example, we examine how changes in the business environment influence the profits of the restaurant, franchisor, and supply chain. Market factors include demand potential ($\alpha \in \left[\mathrm{700,1300}\right]$), demand sensitivity to price and delivery cost ($\beta \in \left[\mathrm{19,25}\right]$), and market size of multiple brands ($\theta \in [0.5,1.1]$). Cost factors are delivery cost (d∈[9,15]), inefficiency cost ($\eta \in \left[\mathrm{0.001,0.6}\right]$), franchise fee ($f\in \left[\mathrm{70,130}\right]$), and brand development and management cost ($\lambda \in \left[\mathrm{140,260}\right]$). Figure 2 and Figure 3 illustrate how profit performance changes in response to changes in market and cost factors, respectively, and

Table 6. How profitability across cases changes with market conditions.

Parameter	Player	Parameter Level	Case Profit Comparison
$\alpha$	Restaurant	Low	SD > MN > M1
		High	M1 > MN > SD
	Franchisor	Low	SD > M1> MN
		High	MN > M1 > SD
	Supply chain	Low	SF > SD > MF > MN > M1
		High	MF > MN > M1 > SF > SD
$\beta$	Restaurant	Low	M1 > MN > SD
		High	SD > M1 > MN
	Franchisor	Low	MN > M1 > SD
		High	SD > MN > M1
	Supply chain	Low	MF > MN > SF > M1 > SD
		High	SF > SD > MF > MN > M1
$\theta$	Restaurant	Low	SD > MN > M1
		High	M1 > MN > SD
	Franchisor	Low	SD > M1 > MN
		High	MN > M1 > SD
	Supply chain	Low	SF > SD > MF > M1 > MN
		High	MF > MN > M1 > SF > SD

and

Table 7. How profitability across cases changes with cost conditions.

Parameter	Player	Parameter Level	Case Profit Comparison
$\eta$	Restaurant	Low	M1 > MN > SD
		High	M1 > MN > SD
	Franchisor	Low	MN > M1 > SD
		High	SD > MN > M1
	Supply chain	Low	MF > MN > M1 > SF > SD
		High	MF > SF > SD > MN > M1
$d$	Restaurant	Low	M1 > MN > SD
		High	SD > M1 > MN
	Franchisor	Low	MN > M1 > SD
		High	SD > MN > M1
	Supply chain	Low	MF > SF > MN > M1 > SD
		High	SF > MF > SD > MN > M1
$f$	Restaurant	Low	M1 > MN > SD
		High	M1 > MN > SD
	Franchisor	Low	MN > SD > M1
		High	MN > SD > M1
	Supply chain	Low	MF > SF > MN > M1 > SD
		High	MF > SF > MN > M1 > SD
$\lambda$	Restaurant	Low	M1 > MN > SD
		High	M1 > MN > SD
	Franchisor	Low	MN > M1 > SD
		High	SD > MN > M1
	Supply chain	Low	MF > MN > M1 > SF > SD
		High	MF > SF > SD > MN > M1

help identify which cases yield greater benefits for different business environments and individual supply chain players.

The findings in Figure 2 and Figure 3, as well as Table 6 and Table 7, align with those in Table 5, indicating that multi-brand cases generally lead to higher profits than single-brand cases in many cases. However, the preference for multi-brand strategies depends on specific market and cost conditions, as parameter levels may make them less favorable sometimes.

Regarding the impact of market factors in Figure 2 and Table 6, we find that as market potential α increases, profits of the restaurant, franchisor, and supply chain from multi-brand kitchens rise significantly as shown in Figure 2a–c. The increasing trend in profits for multi-brand kitchens closely mirrors those of restaurants and franchisors, indicating that higher market potential plays a particularly crucial role in the resilient and sustainable operations of multi-brand kitchen as shown in Table 6. In contrast to the effect of market potential $\alpha$, we observe a negative relationship between demand sensitivity to price and delivery cost β and profits in Figure 2d–f. Specifically, high demand sensitivity to price and delivery cost β discourages the adoption of multi-brand kitchens, leading to lower profits. Restaurants are more inclined to adopt multi-brand kitchens when price sensitivity is low as shown in Table 6. Additionally, an increase in the relative market size of multi-brand kitchens $\theta$ enhances profits from multi-brand kitchens. Interestingly, unlike other business environmental factors, the threshold at which multi-brand profits surpass single-brand profits is similar from both the restaurant and franchisor perspectives. This indicates that restaurants and franchisors can more easily reach an agreement on adopting multi-brand kitchen operations. Since these three market factors directly influence the demand for multi-brand kitchens as shown in Figure 2, our findings confirm that market conditions should be carefully taken into account for maximizing profits when implementing multi-brand kitchen strategies.

Figure 3 and Table 7 illustrate the impact of cost factors on the profits of different cases. Among the cost factors, delivery cost d has the most significant influence as shown in Figure 3a–c. Its increase leads to substantial profit declines, regardless of whether supply chains are based on a single brand or multiple brands. In particular, multi-brand kitchen profits decrease more rapidly compared to single-brand kitchens. While restaurants may continue adopting multi-brand kitchens unless the delivery cost d becomes high, franchisors are more likely to revert to single-brand kitchens when delivery costs $d$ rise, indicating that delivery costs d impose a greater financial burden on franchisors. In Figure 3d–f and Table 7, an increase in the inefficiency cost $\eta$ also reduces the attractiveness of multi-brand kitchens. However, restaurants are more likely to continue preferring multi-brand kitchens if inefficiency costs are not extremely high. In contrast, as inefficiency increases, franchisors may find single-brand kitchens more profitable. Across the supply chain, multi-brand kitchens remain preferable unless inefficiency reaches a significantly high level. An increase in franchise fee f does not appear to significantly affect the supply chain’s overall profits as shown in Figure 3i. This is because the fee f is exchanged directly between the restaurant and franchisor, leaving total profits unchanged. However, the changes in franchise fee f affect the profit allocation as shown in Figure 3g,h. An increase in $f$ raises the franchisor’s profit, while it induces a decrease in the restaurant’s profit. Meanwhile, higher brand development and management costs λ negatively impact the profits of multi-brand kitchens as shown in Figure 3j–l and Table 7. The patterns of profit variation for restaurants, franchisors, and the overall supply chains in response to brand development and management costs λ closely mirror those observed for inefficiency costs.

Overall, despite the different business environment effects, four consistent patterns emerge: (1) franchisors consistently achieve higher profits than restaurants; (2) except some extreme cases, franchisors benefit from multiple franchise fees proportional to the number of brands, while restaurants prefer a single franchise fee; (3) the profit fluctuations in multi-brand cases are larger than those in single-brand cases as market and cost conditions change; (4) in some business environments, the multi-brand strategy can provide a great opportunity to surpass the ideal first-best profit of the single-brand restaurant supply chain even in decentralized supply chain systems.

The first result can be explained by the fact that many restaurants are motivated to become franchisors and launch their own franchise chains in practice. Devising multiple franchise fees helps franchisors enhance their profit performance as shown in the second result, while restaurants prefer a single franchise fee regardless of the number of brands. However, we need to note that the profit difference between these two cases is relatively small, and from the supply chain perspective, the gap becomes even less significant. The larger profit fluctuation observed in the multi-brand supply chains shown in the third result is the key factor affecting the preference for multi-brand strategies, emphasizing the need for caution when adopting the multi-brand strategy. This is because adopting multi-brand strategies in an unsuitable business environment can devastate the profits of the overall supply chain. However, as shown in the fourth result, this large profit fluctuation also provides a great opportunity for the multi-brand restaurant supply chain to achieve superior profit performance. Therefore, it is essential to have a thorough understanding of the impact of business environment changes when adopting and managing the multi-brand restaurant supply chains.

5.2.2. Resilience and Sustainability Performance

In this section, we investigate the resilience and sustainability of five restaurant supply chain models. We first compare the resilience performance. Supply chain resilience can be conceptualized along two distinct, yet complementary, dimensions of performance under volatile demand conditions. The first dimension focuses on the capacity to capitalize on fluctuations in market demand. That is, when external demand becomes volatile, a resilient supply chain is able to convert demand potential into realized sales, thereby fulfilling a greater portion of market demand when compared to less resilient systems [65,66]. In this sense, resilience is reflected through higher realized demand served under disruption, indicating the firm’s superior ability to maintain sales continuity and minimize lost sales [67]. The second dimension defines resilience as the capacity to buffer and absorb volatility, thereby stabilizing customer-facing service outcomes. Even when demand itself fluctuates severely, resilient systems exhibit lower variability in realized sales, indicating effective shock absorption through redundancy, flexibility, and operational agility [65,67].

Therefore, as an indicator of supply chain resilience, we compare demand performance in response to changes in the external business environment. Figure 4 graphically illustrates demand changes according to three market factors.

As shown in Figure 4, except for the extreme ranges, we observe that multi-brand kitchen cases maintain higher demand q than single-brand cases. This result is regardless of the degree of integration. That is, in Figure 4, q^MF > q^SF, and q^MN > q^M1 > q^SD in most ranges of market parameters. We also observe in Figure 4c that this result holds even when the consumer base of multi-brand kitchens (θ) decreases if θ is not extremely low. Also note that the demand performance of decentralized multi-brand kitchen supply chains can be better than the integrated single-brand supply chain. That is, in Figure 4, q^MN > q^M1 > q^SF in many cases. These results demonstrate that multi-brand kitchen operations are more likely to achieve better supply chain resilience performance in today’s changing business environment by meeting a greater portion of market demand. This is possible by pooling demand risks and enabling substitution across brands within a shared operational platform [16]. However, in Figure 4, we also need to note that the variability of realized demand is much lower in the single-brand cases. This indicates that single-brand supply chains can better stabilize consumer-facing service outcomes by absorbing market volatility. Therefore, practicing managers need to note that multi-brand kitchen operations can be a more resilient option that fulfills greater market demand under volatile demand conditions, but multi-brand operations can also have drawbacks in terms of absorbing volatility.

Next, we compare the sustainability performance of five supply chain cases. In multi-brand kitchen operations, an increase in the number of brands can inherently enhance sustainability, provided that the brands share overlapping raw materials, kitchen equipment, and labor resources [22]. Moreover, multi-brand configurations facilitate higher overall kitchen utilization, smoothing demand variability across brands and reducing idle capacity, which is recognized as a critical sustainability driver in service operations [67]. From a supply-chain perspective, increased brand count within a shared infrastructure reduces the unit environmental footprint per product line, as common logistics and procurement networks distribute carbon and waste burdens over a broader sales base, improving ecological efficiency [66]. Thus, we regard the number of brands (n) as the indicator of sustainability performance. Figure 5 illustrates the changes in the number of brands of multi-brand kitchen cases, while the single-brand supply chains (Cases SF and SD) always have a single brand.

As shown in Figure 5, we observe that the relationship of n^MF > n^MN > n^M1 always holds. This result verifies the result of Proposition 2 and Table 5. Therefore, to enhance the environmental performance, it is recommended to adopt the multi-brand kitchen concept rather than the single-brand one, and to adopt a franchise contract with multiple fixed fees rather than a single fee regardless of the number of brands.

6. Discussion

In this study, we interpret the multi-brand kitchen structure through the lens of a restaurant supply chain, where the franchisor and the individual restaurants (franchisees) jointly make strategic decisions that affect overall system performance. The franchisor acts as the upstream coordinating agent, setting brand portfolio policies and fee structures, while the restaurant functions as the downstream operator managing demand realization. Unlike previous studies that focused on individual restaurants or brand-level operations, our approach explicitly considers how profit alignment and decision incentives differ between the franchisor and the restaurant under various contractual and environmental conditions. This framing allows us to evaluate the adoption and performance of multi-brand kitchens not only from a unit-level operational perspective but also from a system-wide, cross-organizational perspective that is characteristic of supply chain analysis.

6.1. Managerial Implications

Implication 1.

The multi-brand kitchen adoption enhances the resilient and sustainable operations of the franchise restaurant supply chain, compared to the traditional single-brand franchise supply chain. Among multi-brand strategies, for the supply chain resilience and sustainability, imposing multiple franchise fees proportional to the number of brands is a better choice than a single franchise fee regardless of the number of brands.

As observed in Proposition 2, Table 5, and Figure 4 and Figure 5, a multi-brand franchise system enhances supply chain resilience by pooling demand risks and enabling substitution across brands within a shared operational platform. Shared resources allow franchise supply chains to dynamically reallocate inventory or production among brands and menus to buffer stochastic demand shocks. Compared to traditional single-brand restaurants, multi-brand strategies also contribute to environmental sustainability by reducing energy and water consumption as well as food waste, thereby offering meaningful environmental benefits. Among the multi-brand strategies, the strategy with multiple franchise fees proportional to the number of brands can develop and hence consolidate more brands compared to the multi-brand strategy with a single franchise fee regardless of the number of brands. Therefore, it can strengthen supply chain resilience through broader demand-risk pooling and promote sustainable operations by integrating restaurant activities across brands and optimizing ingredient use and delivery processes. However, practicing managers need to note that even though multi-brand kitchen operations can be a more resilient option that fulfills greater market demand under volatile demand conditions, but multi-brand operations can also have drawbacks in terms of absorbing volatility.

Implication 2.

The multi-brand kitchen adoption decisions would be consistent for the restaurant, franchisor, and supply chain under the same business environment.

As observed in Figure 2 and Figure 3 and also Table 6 and Table 7, the profit trends of the different cases are similar in the restaurant and franchisor, resulting in similar profit trends in the supply chain. This implies that less conflict is expected between the supply chain players in a certain business environment. Thus, they can easily reach an agreement on whether to adopt multi-brand kitchens when the circumstances are favorable. This is a valuable finding as we investigate the supply chain profits instead of focusing on single players.

Implication 3.

Franchise restaurants and franchisors do not have to differentiate single and brand-specific franchise fee structures from each other, at least for the supply chain profit.

The impact of franchise fee structures on profits in multi-brand kitchens follows a consistent pattern across all business environments as shown in Figure 2 and Figure 3. The restaurant’s profit is higher when franchise fees are paid per shop, regardless of the number of brands, whereas the franchisor generates greater profit when the fees are charged separately for each brand. In practice, a per-shop fee structure is more likely to be adopted when restaurants have stronger bargaining power in contract negotiations, whereas a per-brand fee structure is preferred otherwise. However, the difference in profits between these two cases is relatively small, and from the supply chain perspective, the gap becomes even less significant. Therefore, to maximize supply chain profits, the choice of franchise fee structure is relatively less critical compared to other factors. This is another finding and implication that we benefit from a franchise supply chain-focused multi-brand kitchen study.

Implication 4.

Franchise companies should be aware of business environmental changes to benefit from multi-brand kitchens.

As shown in Table 3 and Table 4, multi-brand kitchens tend to experience greater profit fluctuations than single-brand kitchens, depending on parameter variations. This indicates that multi-brand kitchens are particularly sensitive to changes in the business environment, meaning their profits relative to single-brand kitchens can vary with the circumstances. This trend is observed in the restaurant, franchisor, and supply chain. Franchise companies should develop a thorough understanding of the current market conditions and cost factors to benefit from multi-brand kitchens. Additionally, if they can anticipate the business environment changes, they will be able to assess whether profits in their existing kitchen system are likely to increase or decline over time, allowing them to devise suitable operational strategies. When predicting business environment changes is challenging, franchise companies can focus on delivery costs, which they have control over. Depending on the decisions on the level of delivery costs, franchise companies can evaluate the feasibility and potential benefits of multi-brand kitchen operations.

Implication 5.

The success of multi-brand kitchens in the supply chain is contingent on favorable market conditions.

As shown in Figure 2, the market potential and multiple-brand market size are key drivers of profitability in multi-brand kitchens. It emphasizes the critical role of favorable market conditions in ensuring the success of multi-brand kitchens. Since market factors are largely beyond companies’ control, businesses should focus on accurately assessing market conditions to make informed decisions about adopting multi-brand kitchens. Interestingly, even though the market potential is low so that single-brand kitchens yield higher profits than multi-brand kitchens, the difference in profits remains relatively small. It indicates that multi-brand kitchens can serve as viable alternatives to single-brand kitchens regardless of the market potential level.

Implication 6.

Franchise companies should develop a deep understanding of consumer characteristics to maximize profits.

In Figure 2 and Figure 3, price sensitivity and rising delivery costs are identified as the most significant factors contributing to profit declines in multi-brand kitchens across the restaurant, franchisor, and overall supply chain. Since these business environment factors are closely tied to consumer behavior, understanding the key drivers influencing consumers’ price and delivery cost sensitivity is crucial for effectively managing multi-brand kitchens. These drivers include demographic factors, such as age, income level, and household composition, as well as external environmental factors like regional characteristics and overall economic conditions. Therefore, restaurants and franchisors should carefully analyze these consumer-related factors to determine the feasibility and strategic viability of adopting multi-brand kitchens.

Implication 7.

The key determinant of multi-brand kitchen success is the extent of consumer demand rather than operational efficiency.

In this study, we find that factors directly influencing consumer demand—such as market conditions, price sensitivity, and delivery costs—play a crucial role in maximizing multi-brand kitchen profits. Therefore, before adopting a multi-brand kitchen, franchise companies must first assess whether there is sufficient and stable demand to support their supply chain resilience and sustainable operations. The results also imply that operational efficiency, which has a relatively smaller impact on demand, may be a less critical concern when deciding whether to implement a multi-brand kitchen strategy. This insight provides a meaningful contribution to the existing literature on multi-brand kitchens by emphasizing the primacy of demand-related factors over operational considerations.

6.2. Comparison with Existing Literature

While research directly addressing multi-brand franchise kitchen supply chains remains limited, existing literature in the areas of cloud kitchens, franchise efficiency, and sustainability in restaurant operations offers relevant insights. We draw comparisons with these studies to contextualize our analytical findings and highlight our contributions. Cai et al. [29] investigate consumer perceptions of cloud kitchens, focusing on how knowledge and perceived benefit-risk influence behavioral intentions. Their work reflects growing interest in non-traditional restaurant formats and highlights customer-side considerations. In contrast, our study approaches the issue from an operational and supply chain perspective, analytically modeling how kitchen brand portfolio influences system-wide performance and profit. Roh and Choi [68] examine efficiency differences among multiple brands within the same franchise using a data envelopment analysis (DEA) framework. Their empirical analysis reveals brand-level heterogeneity in performance, pointing to the importance of internal structural decisions. Building on this idea, our study considers how the number of brands and the design of franchise contracts affect strategic alignment and profitability across the supply chain. Park et al. [69] analyze sustainability and efficiency determinants in Korean coffee shop franchises. While their study centers on performance evaluation at the store level, our model incorporates supply-side structural decisions that extend beyond individual outlets. Specifically, we consider how brand diversification and contract mechanisms jointly shape the dynamics between franchisors and franchisees in a multi-brand kitchen setting. Although our analytical model does not explicitly incorporate disruption events or a dynamic recovery process, the comparative statics reveal that multi-brand configurations exhibit lower sensitivity of system profits to adverse changes in market parameters—such as increased delivery cost or reduced demand potential. This reduced sensitivity, combined with risk pooling and cross-brand substitution, constitutes the source of supply chain resilience in our setting.

To consolidate these results,

Table 8. Optimal and practical multi-brand configurations under different market conditions.

Market Condition	Level	Supply Chain Optimal Case	Practical Choice
Market potential	Low	SF	SD
	High	MF	MN
Price and delivery-cost sensitivity	Low	MF	MN
	High	SF	SD
Relative market size of multi-brand kitchens	Low	SF	SD
	High	MF	MN
Inefficiency and development cost	Low	MF	MN
	High	MF	SD *

* MF is the best in theory, but when inefficiency and development cost is high, multi-brand options become too costly in decentralized settings. In practice, SD is the most viable choice.

summarizes the supply-chain-optimal configuration and the corresponding practical decentralized choice for each business environment.

Table 8 synthesizes the main results by distinguishing between the supply-chain-optimal configuration and the most viable decentralized choice under each market condition. While MF or SF emerge as first-best benchmarks, these configurations are typically unattainable in practice due to decentralized decision making and contract frictions. The practical choice column therefore highlights which feasible franchise structure (SD, M1, or MN) most closely approximates the supply-chain optimum in each environment.

7. Conclusions

In this study, we examine the profitability of multi-brand kitchens under franchise contracts by modeling five different cases, varying in the number of brands, degree of decentralization, and franchise fee policy. Our analysis identifies the optimal price, royalties, and number of brands that maximize the profits of the restaurant, franchisor, and overall supply chain. We also explore how these outcomes change with shifts in the business environment.

The results reveal that, in general, multi-brand kitchens yield not only better supply chain resilience and sustainability but also higher profits than single-brand kitchens, particularly at the supply chain level. This is mainly due to the increased total demand generated by multiple brands and the efficient utilization of shared resources. However, the profitability of multi-brand kitchens is not always guaranteed, as it is more sensitive to changes in key parameters such as delivery cost, inefficiency cost, and price sensitivity. Depending on the environment, multi-brand kitchens may even result in lower profits compared to single-brand operations. Interestingly, the consistency in profit trends across the restaurant, franchisor, and supply chain suggests that multi-brand kitchen adoption decisions may be aligned among supply chain players, reducing potential conflicts in contract negotiations. Furthermore, the choice between single and brand-specific franchise fee structures does not significantly impact total supply chain profitability, providing flexibility in contract design based on bargaining power.

Overall, the success of multi-brand kitchens depends heavily on demand-related factors rather than operational cost efficiency. To benefit from the resilient and sustainable operations of multi-brand kitchens, franchise companies should carefully assess market potential, delivery economics, and consumer price sensitivity. This study offers practical insights for restaurant operators and franchisors while contributing to the literature by incorporating a supply chain perspective in the analysis of multi-brand kitchen models.

This study has certain limitations. In particular, while our analytical framework captures key aspects of franchise supply chain interactions, it does not explicitly consider the role of third-party delivery platforms, which are increasingly important in practice. Future research could address this limitation by incorporating such platforms into the analytical setting to better reflect real-world operations. In addition, future research may incorporate time-varying demand environments and repeated interactions between franchisors and franchisees, thereby providing a richer understanding of long-term outcomes. Although the influence of online delivery platforms is reflected through delivery-related demand parameters in our model, future research may extend the framework by explicitly modeling platforms as additional strategic players interacting with franchisors and franchisees. Moreover, as this is one of the first studies considering multi-brand restaurant supply chains, our model does not incorporate a dynamic disruption process, but we investigate the supply chain resilience issues based on the comparative static analyses. We are planning a future study that focuses on the supply chain resilience performance under dynamic disruption scenarios. Finally, empirical analyses using industry data would complement the analytical findings and enhance the external validity of the results.