Quality Visibility Improvement with Effort Alignment and Cost-Sharing Policies in a Food Supply Chain

Improving quality visibility along a food supply chain has been considered as a critical driver of quality risk mitigation, safety and security assurance, and performance sustainability. *is paper explores the coordination mechanisms in a food supply chain, where the demand and costs are sensitive to the supply chain quality visibility that depends on an upstream supplier and a downstream retailer jointly, and the effort to improve quality visibility is increasingly expensive. After comparing the centralized and decentralized supply chain models to discover an opportunity for Pareto improvement, it is proved that a pure revenuesharing contract fails to coordinate the supply chain, while the price discount contract with effort alignment policy or effort costsharing policy works. *e two coordinating contracts’ boundary conditions of excluding deviated actions are presented. It is shown that the contract with effort alignment policy is cheaper but more rigid, whereas the cost-sharing one allows us to arbitrarily allocate the supply chain’s profits despite more information being collected.*emodels are applied to a fresh chicken supply chain in order to verify their effectiveness and robustness in reality.*e impacts of several specific parameters on supply chain decisions and performances are analyzed, and the results reveal some meaningful managerial implications regarding supply chain quality visibility.


Introduction
A series of food recalls and destructions worldwide due to poor quality or safety and security have aroused intensive attention on supply chain vulnerability versus sustainability in food industry and academia. Recently, in July, China Customs detected the novel coronavirus that causes COVID-19 on the packages of frozen South American white shrimp produced by Ecuadorian enterprises and returned or destroyed the batches of risky food soon afterward. Unclear contamination source is attributed to the inadequate quality management and visibility in the producer's supply chain, which brings huge health threats and market losses. Global sourcing and outsourcing stretch supply chains, where quality information becomes opaque, leading to unexpected supply chain disasters, even if one plant is contaminated [1][2][3]. Fortunately, it is possible to make supply chains more visible given the prevalence of information technologies such as radio frequency identification (RFID) technology, global positioning system (GPS), quick response (QR) code, and blockchain technology. Increasingly more enterprises consider supply chain visibility as a critical solution to assure product quality and safety, reduce food spoilage and waste [4], enhance operations efficiency, and mitigate supply chain risks [5]. Walmart developed a food traceability initiative with IBM's Food Trust Platform based on blockchain technology and required all his leafygreens suppliers to use this system starting in September 2019. It allows one to trace a food product back to the farm within seconds, rather than days as before, which will help Walmart confirm that products are certified in every exchange, thus mitigating the propagation risk of food-borne diseases along the supply chain and avoiding the losses that he and his partners may suffer in food recalls (source: https://www.nasdaq.com/articles/walmart-embraces-ibmsblockchain-tech-2018-09- 25). e 2017 Supply Chain Worldwide Survey conducted by GEODIS reveals that "Improve end-to-end Supply Chain visibility" has become the third most important supply chain objective behind only two delivery indices [6].
Another stimulus for supply chain quality visibility comes from consumers. e anxiety for quality conditions to be inspected anytime and anywhere via the ubiquitous mobile network and the awareness of sustainable consumption responding to environmental preservation and humanitarian production induce people to request complete quality and health information in order to make sure it meets their exceptions [7]. Specifically, one reviews ingredients, production, and expiration dates on food labels and further wants to know where and how the product was planted or fed, whether the materials involved are organic or environmentally friendly, whether the relevant companies have quality certifications, and whether the product was transported in an uninterrupted cold chain. When it is easy to track these data within seconds, for example, by just scanning the QR code on the package using a smartphone, consumers are willing to buy such high-visibility products with traceable codes or PDO (EU's Protected Designation of Origin) labels and even pay a considerable premium [8].
In addition, there are pressures from regulation and the public. Food visibility that proves good quality and safety has been a legal requirement or best practice in many regions, referring to US Quality System Regulation (see FDA 21 CFR Part 820 at https://www.accessdata.fda.gov/scripts/cdrh/ cfdocs/cfcfr/CFRSearch.cfm?CFRPart�820), EU's General Food Law (see Regulation (EC) No. 178/2002 at https://eurlex.europa.eu/legal-content/EN/TXT/?uri�celex:32002R0178), China's Food Safety Law (see the original version (in Chinese) at http://www.gov.cn/zhengce/2015-04/25/content_ 2853643.htm. For an unofficial translation version (in English) from the United States Department of Agriculture (USDA), see https://apps.fas.usda.gov/newgainapi/api/report/ downloadreportbyfilename?filename�Amended%20Food% 20Safety%20Law%20of%20China_Beijing_China%20-% 20Peoples%20Republic%20of_5-18-2015.pdf), etc. Comments and complaints about food quality on social networks and the media, sometimes not sent by the target consumers, lead companies to invest more in quality visibility to promote public trust and confidence, not merely legal compliance. More and more food companies are integrating with Alibaba Health's "Trust on the Code" platform under the guidance of the local government. is platform helps regulators and consumers to identify the authenticity of the provenance and quality of imported foods (see "Trust on the Code" website (https://www. mashangfangxin.com), which is initially designed for pharmaceutical traceability but now also available for food traceability).
Although supply chain quality visibility benefits companies in proactive quality risk control, operations efficiency, and consumer trust, the motivation to improve quality visibility is still scant. GEODIS reports that 77 percent of supply chain companies have no or very restricted visibility [6]. e few visibility examples at present mostly appear in apparel companies like H&M and Swiss Heidi who have disclosed their entire supply chain information from the cotton source to the distribution center through the label of each garment [5]. However, in the food domain, there are not so many examples as we might think even it should be more reasonable to disclosure information tightly related to health.
Two reasons may explain the status quo. First, technical difficulties and expensive costs of building quality visibility are growing exponentially in food supply chains, often affordable for only large-scale companies. It requires access to more subjects, processes, and items following the "waterfall flow" from farm to table [5] and needs more hard work to collect, standardize, communicate, analyze, store, and visualize quality data, as compared with well-quantified information such as price, demand, and inventory. Besides, the quality of food, especially fresh or perishable food, is always in continuous degradation between two adjacent processing [9], so periodic or real-time monitoring of quality changes is necessary in food supply chains and of course quite expensive. In contrast, product quality is generally constant during each company who gathers quality information only once with a quality inspection in other supply chains. Second, companies' quality visibility decisions are trapped in "double marginalization" and lack an overall coordination. Companies keep the inertia of saving the expense and protecting private information with the expectation of an advantage in competition or games, and they fail to balance information cost, information confidentiality, and information value. eir decisions tend to maximize one's own interest, which makes supply chain revenue and quality visibility suboptimal. eoretical works surrounding supply chain quality visibility are mostly conceptual, technical, or empirical at present, and the model research ignores the expensive cost of building quality visibility and consumer sensitivity to quality visibility in food supply chains. erefore, it is quite necessary to further explore the impacts of quality visibility in the food supply chain and use the approach of coordinating supply chain to reduce companies' cost pressure in quality visibility investment, thus achieving multi-win outcomes for the whole supply chain including the consumer.
is paper seeks to answer the following research questions: (1) What are the optimal strategies in the centralized and decentralized food supply chains with demand and cost dependent on quality visibility? Whether the cooperative decision-making benefits the supply chain profit and quality visibility? To address these research questions, this study constructs models to investigate the centralized and decentralized decision-making scenarios and the feasibility of a common revenue-sharing contract. Based on that, two modified contracts with effort alignment and cost-sharing policies that coordinate the supply chain with quality visibility effort are proposed. Next, the effectiveness and robustness of the contracts in reality are verified with a practical chicken supply chain case. Finally, suggestions for performance improvement and managerial insights are offered. e contributions of this paper are mainly manifested in three aspects: (i) We build an analytical model assuming demand and cost are sensitive to quality visibility of the upstream and downstream companies and provide a useful way to capture the optimal price and quality visibility strategies in the food supply chain. (ii) e positive impacts of food quality visibility spectrum on supply chain players are quantitatively demonstrated, and the opportunity for Pareto improvement is revealed, theoretically enabling companies to improve their quality visibility. (iii) Two contract mechanisms based on the price discount contract are designed to address the coordination problem with dual quality visibility efforts. Both contracts align the decision motivations of the supply chain players and show a strong robustness. To the best of our knowledge, there are no other coordination research studies about quality visibility in the supply chain context. e rest of the paper is arranged as follows. e second section reviews the relevant literature. Afterward, the third section describes the basic model and compares the centralized decision-making supply chain with the decentralized one. In the fourth section, several contracts are discussed to coordinate the supply chain, which is followed by a practical case that applies the model in the fifth section. Finally, this paper concludes with the research limitations and future directions.

Supply Chain Quality Visibility: Concept.
Although scholars have focused on supply chain visibility for years, there seems no clear consensus on its definition and position [10]. It is early viewed as the extent of information sharing in the supply chain based on the transparency concept (Lamming et al. [11] and Bartlett et al. [12]) and later described as something similar to traceability based on RFID technology (Holmström et al. [13]), the capacity of the supply chain to have a view of the product life cycle (Musa et al. [14]), or the lower uncertainty of the company's social responsibility effort outcomes based on a CSR perspective (Kraft et al. [15]). In contrast, the definition proposed by Barratt and Oke [16] is more widely accepted: the extent to which supply chain actors have access to or share key or useful information with mutual benefits to their operations.
It is still necessary to distinguish "supply chain visibility" from several intertwined concepts before we discuss its derivative "supply chain quality visibility." Based on the existing discussions, we contend that information sharing among the related companies is a prerequisite for supply chain visibility, and traceability means a visibility of information provenance and dissemination process. Supply chain visibility is considered to meet the information needs of stakeholders internal to the supply chain, and it is named mostly from the perspective of the information user, while supply chain transparency, from the information provider's perspective, comes up only when supply chain companies share or disclose visibility to the external stakeholders [5]. When the consumer is treated as an outsider of the traditional supply chain, supply chain transparency perceived by them can be understood as the minimum of supply chain visibility in terms of information transferred. However, the consumer has been an insider of the modern supply network with engaging more and more in product design, quality supervision, and brand advocacy, etc. erefore, from the perspective of the whole supply chain, we can use "supply chain visibility" and "supply chain transparency" interchangeably to describe the extent to which the consumer gets the desired information from the upstream supply chain.
Supply chain quality visibility then can be concisely defined as the extent to which supply chain actors have access to high-quality information related to product (service) quality. High-quality information means the information rich in "information quality," i.e., accuracy, timeliness, completeness, trustworthy, usefulness, and ease of use. Information quality represents the level of supply chain visibility [17] and depends on the efforts to collect and integrate relevant information from the upstream and downstream supply chain [5]. Quality information of product or service involves not only inherent characteristics of the product or contents of the service, but also all the processes, operations, and factors that may have an impact. Traceability systems that aim to provide such quality visibility have gradually been opened up to consumers especially in food supply chains. Similar to supply chain transparency [18], supply chain visibility can be categorized into price, demand, quality, cost, inventory, and process visibility by information element. It is noticeable that some process information may contribute to both quality and process visibility, but process visibility prefers information about production, transaction, and management processes for operational or strategic considerations, which is different from quality visibility.
As for measuring supply chain quality visibility, Caridi et al. [19,20] suggest a structured assessment model of supply chain visibility using a weighted sum of all the node companies' visibility, which is calculated by the geometric mean of three scales: information type, information quantity (which can be regarded as the completeness dimension of information quality), and information quality. Bartlett et al. [12] link information type to the following quality criteria: scrap levels, rework levels, process repeatability, supplier Mathematical Problems in Engineering quality, quality system audit, and continuous improvement. Tse and Tan [17] believe that product quality (risk) visibility comes from the number of product transitions and the disclosure level of suppliers' information that refers to suppliers' conformity, reliability, safety, and quality standards. For the sake of usefulness to the consumer, we summarize and refine the following types: (i) product provenance; (ii) supplier quality, about quality details in production process; (iii) transport conditions; (iv) retailer quality, about quality details in selling process; (v) quality audit and certification, about third-party or self-certification of food and companies; and (vi) product quality, about details on food labels as regulated. en, their information quality ratings are processed to get the supply chain quality visibility referring to Caridi et al. [19].

Supply Chain Quality Visibility:
Effect. Studies about the impacts of supply chain quality visibility (or supply chain visibility) on the decisions and performances of supply chain companies are relevant. Delen et al. [21] explore the extent of the logistics performance improvement in a supply chain influenced by visibility expressed as RFID data, and they assert that the supply chain visibility could make a company distinctive, just as quality was once the differentiator. Based on the theory of organizational information processing, Williams et al. [22] verify that internal integration can positively regulate the relationship between supply chain visibility (demand, supply, and market visibility) and supply chain responsiveness. Tse and Tan [23] provide quality criteria and a multi-outsourcing decision path for focal companies in supply chains using a marginal incremental analysis (MIA) method. Guo [24] discuss the impact of quality information disclosure on companies' profits in a bilateral monopoly and find that indirect disclosure through the retailer is the optimal form of quality information disclosure. Zhao et al. [25] extend Guo's research to the competitive market, and the results indicate that at equilibrium, the high-quality supply chain chooses not to disclose quality while the low-quality one chooses to disclose quality through the retailer. Wu et al. [26] investigate the quality information-sharing problems in a dual-sourcing supply chain and demonstrate that quality information visibility always benefits the cost-disadvantaged suppliers and the downstream retailer. From a "negative quality" perspective, Piramuthu et al. [27] compare the marginal differences of recall costs at different visibility levels based on the accuracy of contamination source identification and determine the best timing of recall polices in a multistage perishable food supply network.
For consumers, supply chain quality visibility is good up to now. Granados and Gupta [7] elucidate the benefits of qualityand price-related visibility (transparency) to consumers with different product features, industry competition, and regulatory intensity through examples. Ghosh and Galbreth [28] find that a greater proportion of partially informed consumers who capture disclosed quality information can decrease their search behaviour and help companies save disclosure cost and increase profit. Both external visibility initiatives (such as proactive labelling strategies of voluntary certification and ingredient replacement [29]) and internal visibility initiatives (such as improving environmentally sustainable manufacturing [30]) can spur consumers to purchase products. El Benni et al.'s [8] survey study indicates that affected by the 2008 melamine incident, Chinese consumers are willing to pay an extra CNY 69∼109 (equivalent to 30∼40% of the retail price) for a 900 g can of infant milk formula with a PDO label, as well as a high premium for anticounterfeiting packaging and a QR traceable code.
We summarize the related literature in Table 1. ese studies confirm that supply chain quality visibility can be beneficial to the entire supply chain, downstream companies, and consumers, while the impact on upstream companies is not quite clear [7,24,26]. It is because that quality visibility in these studies is provided mainly by suppliers who thus bear quality visibility cost and information leakage risk alone. e mismatch between these disadvantages and slashed revenues handed by downstream companies discourages upstream companies and makes outcomes uncertain. Furthermore, most of the model research studies focus on the information structure transformed by quality information disclosure strategies, also named transparency strategies [18]. ey assume quality information is always ready to be shared or not, ignoring the previous processing cost, and few of them are specific to the food supply chain. In fact, every company contributes to the supply chain quality visibility, and everyone needs to pay for it in food supply chains. We thus assume companies' respective quality visibility levels that jointly make up the overall visibility determine their costs, and explore the impacts on supply chain players.

Supply Chain Coordination Contracts.
Asymmetric information in a supply chain often traps the upstream and downstream companies into a double marginalization, which can be dramatically mitigated by supply chain coordination contracts maximizing supply chain profits [31,32]. is field has accumulated extensive literature. is paper involves several relevant streams, including supply chain coordination with a revenue-sharing contract or a price discount contract, and coordination policies for the supply chain with effort decisions. e revenue-sharing contract is one of the most common supply chain coordination mechanisms. Cachon and Lariviere [33] conduct a comprehensive analysis of it and illustrate its broad applicability with a single retailer in demand or price certainty/uncertainty settings, or with competing retailers in quantity competition. However, it stops functioning when the supply chain needs to deal with the retailer's costly effort. Xiao et al. [34] examine the impacts of product quality and service quality on demand and obtain the optimal decisions and Pareto conditions of the coordination mechanism using a revenue-sharing contract. Kong et al. [35] discuss the information leakage problem from a supplier in a supply chain where the retailers compete, and their results show that a revenue-sharing contract aligns the motivations of suppliers and retailers better and mitigates the supplier's disclosure risk. Bernstein and Federgruen [36] propose a wholesale price contract with a buyback rate, i.e., a price discount contract, that can coordinate the supply chain with uncertain demand, which is proven to be equivalent to a revenue-sharing contract in the price-setting model [33]. Cai et al. [37] demonstrate that in the dual-channel supply chain competition, the price discount contract reduces channel conflict and helps achieve coordination by distributing more profit to the retailer.
To coordinate the supply chain with costly effort, Bhaskaran and Krishnan [38], respectively, assess revenue, investment, and innovation sharing policies in an innovation supply chain. Product innovation revenue only derives from the quality improvement that depends on the innovation effort of both the focal company and the partner company. e results show that although the proposed three mechanisms fail to coordinate the supply chain, they improve supply chain profits compared with the decentralized supply chain when specific conditions are realized. Krishnan et al. [39] pointed out that a single-parameter contract could not correct the distortion caused by the pricing and effort decisions, and they propose effort cost-sharing, unilateral markdown allowances, and constrained buyback mechanisms to address it. Cachon and Lariviere [33] also offer a simple coordinating quantity discount contract based on revenue-sharing. Lambertini [40] extends the traditional two-part tariff contract for quality improvement using a variable linear tariff according to the R&D effort or product quality. For fresh products, Cai et al. [9] consider the impact of distributor's fresh-keeping effort on product freshness and thus on product quality and quantity and develop a price discount sharing contract with compensation contract to make the supply chain coordinated. Extending Cai et al.'s [9] study to the online situation, Gu et al. [41] characterize the online retailer's strategy of fresh-keeping effort under a consumer full-refund policy and present a buyback contract and a revenue-and cost-sharing contract to achieve the cooperative optimization. Table 2 provides an overview of the related literature, omitting the wholesale price contract that cannot coordinate the supply chain in each row of the last column. Most of the effort-related studies deal with the single effort of the downstream company, and the revenue-sharing contract or price discount contract works well by extending with an additional parameter. However, when there are multiple decision variables linked to the efforts of the upstream and downstream, more than one parameter needs to be introduced into simple supply chain contracts [38,40]. Furthermore, there is no model research where the consumer demand is influenced by quality visibility, leaving a missing link between visibility effort and market revenue. In this paper, we consider the demand dependent on supply chain quality visibility and address the coordination problem with dual quality visibility efforts.

Model Settings.
We examine a two-tier food supply chain consisting of a supplier and a retailer who faces a consumer market. At the start of a selling season, the supplier sets a wholesale price w and its own quality visibility level v s . en the supplier invests in quality visibility as it claims and begins to produce after receiving the retailer's order. Once the delivery is ready, the retailer determines a retail price p and its own quality visibility level v r . Subsequently, the retailer invests in quality visibility and sells the food.
e consumer observes the price and the overall quality visibility provided by both companies and decides to buy or not, finally making revenue realize. e timeline of events is outlined in Figure 1. Consumers are assumed sensitive to food price and supply chain quality visibility, d(p, v sc ) � θ − λp + αv sc , where θ is the largest potential demand, λ and α are sensitivity coefficients, λ, α > 0, and θ > λp > 0. Refer to the supply chain visibility assessment method of [19], where the weight ω i measures the importance of the quality visibility provided by company i to consumers. We suppose ω s � ω r � (1/2), indicating equal importance. e demand sensitive to quality visibility is reasonable mostly in food supply chains where consumers are willing to pay a significant premium [8].

Cost Function with Quality
Visibility. e visibility effort cost of the upstream or downstream company is i , a most widely used effort cost function [33,38,40], where β i > 0. e square reflects the diseconomy of visibility systems due to the increased information capacity, efficacy requirement, and management complexity brought by a higher visibility level [42]. e diseconomy occurs in every company no matter upstream and downstream, characterizing the food supply chain. In contrast, except for the focal company, quality visibility cost of the partner company is generally fixed or linear in other types of supply chains. For example, a quality inspection instruction is usually enough for mobile phone components, and the mobile phone retailer rarely needs to invest in quality visibility. e related notations and variables are defined as follows. i � sc, s, r are the subscripts that represent the whole supply chain, the supplier, and the retailer, respectively. j � C, D, R, E, B are the subscripts that represent scenarios of centralized decision-making, decentralized decision-making, a revenue-sharing contract, a price discount contract with effort alignment, and a price discount contract with cost-sharing, respectively.  w is the wholesale price of a food unit p is the retail price of a food unit v i is the food quality visibility provided by the supply chain or company i d is the market demand θ is the largest potential demand λ is the price sensitivity coefficient of demand α is the quality visibility sensitivity coefficient of demand β i is company i's cost coefficient of the quality visibility effort In this supply chain setting, the supplier's profit is as follows: e retailer's profit is given by and the profit of the whole supply chain is given by e channel costs of the supplier and the retailer are omitted; however, by replacing w and p with w − c s and p − c r , respectively, we have the intact costs, where c s is the supplier's production cost per unit and c r is the retailer's retail cost per unit.

Centralized Supply Chain.
e supplier and the retailer are integrated when making decisions in the centralized supply chain. Although their own visibility systems are also expected to be integrated into one, the system integration costs and benefits are quite slight compared to the visibility input cost, namely, the effort cost. is is partly because the amounts and types of quality metadata collected from the upstream and the downstream are rarely the same, and thus, the two parts of the integrated visibility system are regarded as still working separately. e profit function of the centralized supply chain is obtained from equation (3): e profit function (4) always has second continuous partial derivatives. In order to avoid not making sense, the function is assumed to have a maximum value in its definition domain θ/λ > p C > 0 and v i,C > 0. erefore, its Hesse Let Δ 1 � 16λβ s β r − α 2 β s − α 2 β r and then we have
Proof. Solve three first-order conditions of equation (4) jointly, as follows: e optimal retail price p * C � (8β s β r θ/Δ 1 ), the optimal quality visibility level of the upstream v * s,C � (2αβ r θ/Δ 1 ), and the optimal quality visibility level of the downstream v * r,C � (2αβ s θ/Δ 1 ) can be easily derived. en, substituting them into equation (4) and v sc � ω i v i simultaneously, we have the optimal supply chain profit v * sc,C � (αθ(β s + β r )/Δ 1 ) and maximal supply chain quality visibility π * sc,C � (4β s β r θ 2 /Δ 1 ) in the centralized supply chain.
From Corollary 1, we can find that the more sensitive consumers are to quality visibility, the greater the incentives that supply chain companies have to improve their quality visibility related to the foods in each stage so that the supply chain can charge a higher retail price and gain a bigger supply chain profit. Conversely, more price-sensitive consumers and a greater marginal cost of the visibility system prevent the previous process.

Decentralized Supply Chain.
In a decentralized decisionmaking supply chain, the supplier firstly determines its own quality visibility level and supplies the retailer at a wholesale price according to the pure wholesale price contract. e retailer then decides its own quality visibility level after receiving the delivery and sells foods at a retail price. e profit function of the retailer is given by and the profit function of the supplier is as follows: Mathematical Problems in Engineering Let Δ 2 � 32λβ s β r − 2α 2 β s − α 2 β r . rough the backward induction of a Stackelberg game, it is easy to find that the Hessian matrixes of equations (6) and (7) are negative definite with 16λβ r − α 2 > 0 and Δ 2 � 2Δ 1 + α 2 β r > 0, which reveals that there exists a maximum solution set of the decentralized supply chain.
Proof. Given w D and v s , the retailer's optimal retail price and quality visibility are acquired by the first-order conditions of equation (6) as follows: We substitute them into equation (7) π s,D w D , v s,D � 4β r λw D αv s, and similarly obtain the supplier's optimal wholesale price w * D and quality visibility v * s,D by solving the first-order conditions of equation (9). en, it is easy to get p * D and v * r,D by a substitution into equation (8) and thus the optimal performance variables by a few further substitutions.
Under the optimal equilibriums, by comparing the overall supply chain profits in the two decision-making contexts, Corollary 2 (i) indicates that the overall profit of the decentralized supply chain is strictly less than those of the centralized supply chain. Since the supply chain's revenue completely comes from the retailer, to coordinate the supply chain, the optimal solution p * C , v * r,C of integrated decisions should be optimal for the retailer, and it must satisfy en, we have w D � 0 and v s,D � v * s,C , which mean that the supplier receives nothing from charging a production cost, but bears its own quality visibility cost. erefore, the simple wholesale price contract cannot coordinate the supply chain, which is consistent with many previous researches. From Corollary 2 (ii), the supplier's profit is larger than the retailer's, which verifies the supplier's great firstmove advantage in the Stackelberg game.
In addition, Corollary 2 (iii) and (iv) show that the overall quality visibility level in the decentralized supply chain is lower than that in the centralized one, but the former retail price is higher than the latter. It implies that the centralized supply chain realizes not only greater profit and higher food quality visibility, but also greater consumer surplus, which leads to more social welfare, thus realizing a win-win between the supply chain and consumers. e inspirations from Corollary 3 are similar to those from Corollary 1, i.e., consumers' sensitivity to quality visibility positively influences the prices and performances of the decentralized supply chain, as opposed to the price sensitivity and visibility cost coefficients. Nevertheless, it seems that the extent of the influences they have is less significant than that in the centralized supply chain due to the double marginalization, which will be recognized more intuitively in the subsequent practical case.
is finding indicates that a centralized or coordinated food supply chain is more efficient than a decentralized one in performance improvement. erefore, it is necessary to explore a coordination contract if there is no chance to integrate this food supply chain to a centralized one.

Revenue-Sharing Contract.
e revenue-sharing contract is one of the most used coordination contracts. Suppose that the supplier and the retailer agree on the following exante revenue-sharing contract: the supplier charges a lower wholesale price w R and receives 1 − φ(0 < φ < 1) percent of the retailer's revenue. Assuming φ � 1, the contract becomes a pure wholesale price contract; and if w R � 0, it is equivalent to a price discount contract with w � (1 − φ)p. erefore, for a crisp wholesale price contract and a price discount contract, there is always an equivalent revenue-sharing contract. e retailer's profit function is given by Similarly, by solving the first-order conditions is means that if the supply chain is coordinated, the supplier needs to subsidize the retailer (1 − φ)p * C for each unit of food; however, the revenue that the supplier receives from the retailer is equal to the total subsidy. Just like in the wholesale price contract, the supplier in the revenuesharing contract does not realize any revenue but experiences the losses due to his own quality visibility cost. e revenue-sharing contract, as Cachon and Lariviere [33] assert, cannot coordinate the supply chain with costly effort decisions.

Effort Alignment Policy.
e contracts with a single parameter could correct the distortion in the pricing decisions of the upstream and downstream supply chain, but they do not address the dual-effort and pricing decisions. Two or more parameters need to be included to align the relevant decision variables, making the profit function of the last-move decision-maker an affine transformation of the profit function of the whole supply chain. In this paper, the profit function of the retailer who plays as the last-mover depends on the effort decisions, that is, the quality visibility decisions of both the supplier and the retailer. Given that effort can be observed, it is feasible to align the supplier's effort with the retailer's, similar to the wholesale price aligned with the retail price in a pure price discount contract.

Theorem 1.
e following price discount contract with effort alignment (E) can coordinate the supply chain: the supplier charges a wholesale price w E � (β r /(β s + β r ))p E and offers quality visibility v s,E � (β r /β s )v r,E . en, the retailer's profit function is π r,E � φπ sc,C and the supplier's profit function is is the optimal solution set of the supply chain, where φ � (β s /(β s + β r )).
Proof. Substitute w E � (β r /(β s + β r ))p E and v s,E � (β r /β s ) v r,E into the retailer's profit function (2): i.e., π r,E (p E , v r,E ) � φπ sc,C (p E , v s,E , v r,E ), and then p * e supplier's profit function is π s,E � π sc,C − π r,E � (1 − φ)π sc,C . □ eorem 1 shows that the price discount contract allocates the supply chain profit to the supplier and the retailer at proportions of 1 − φ and φ, respectively, and coordinates the supply chain. e proportion φ is a fixed value dependent on the quality visibility cost coefficients of both sides. Since the quality visibility cost function is nonlinear, φ has a unique value in order to ensure a linearly affine transform of the profit functions in a threeparameter contract (w, v s , φ). According to the contract, the supplier loses his decision autonomy on quality visibility, which is anchored to that of the retailer via a fixed rate (β r /β s ).
e bigger the rate is, the greater the gap between the supplier and retailer regarding price, quality visibility, and profit. Although the contract does not allow them to freely negotiate on the profit allocation rate, it is cheaper and less tedious under specified conditions due to a reduction of one contract parameter in the determination.

Proposition 3.
e incentive compatibility conditions of the contract (E) are 16λβ 2 r − 16λβ s β r + α 2 β s ≥ 0 for the supplier and (3β s − β r )Δ 2 2 + (β s + β r )α 4 β 2 r ≥ 0 for the retailer when there is an alternative opportunity profit by a pure wholesale price contract.
□ e two inequations in Proposition 3 guarantee that the effort alignment policy is Pareto superior to the decentralized decision-making, and thus, it can strictly coordinate the supply chain coordination.

Effort Cost-Sharing Policy.
e price discount contract with an effort alignment policy may not always match the negotiation power and profit appeal of the two supply chain players because it is unable to arbitrarily allocate supply chain profit, and whether its rigid incentive compatibility conditions could be realized with extreme parameters is doubtful. In order to relax these restrictions and thus enhance companies' motivations for quality visibility, effort cost-sharing is introduced into the price discount contract, where the supplier and retailer proportionately share the total costs of quality visibility.

Theorem 2. A price discount contract with cost-sharing (B)
can coordinate the supply chain: the retailer pays the supplier a wholesale price w B � (1 − φ)p B and shares the total quality visibility cost of the supply chain at a proportion φ (the supplier shares 1 − φ and 0 < φ < 1). en, the retailer's profit function is π r,B � φπ sc,C , and the supplier's profit function is π s,B � (1 − φ)π sc,C . Furthermore, is the optimal decision set of the supply chain.
Proof. With cost-sharing, the retailer's profit function is We substitute w B � (1 − φ)p B into it to get π r,B (p B ,v r,B ) � φπ sc, C (p B , v s,B , v r,B ) and π s,B � (1 − φ)π sc,C . □ Compared with contract (E), the feasible range of φ under contract (B) covers the whole interval (0, 1), and it is determined by the bargaining power of the supplier and the retailer. e stronger the retailer's power is, the greater the φ. When φ equals 0 or 1, the supply chain turns into a centralized one. Similarly, the incentive compatibility conditions (14) must be satisfied when a wholesale price contract is an option. In addition, the information of both contracts (B) and (E) need to include the retail price and the retailer's quality visibility level, while contract (B) needs to include the supplier's quality visibility level as well. e difference in the required information sets dominates the applicability of the two contracts, and the higher information cost of contract (B) contributes to the arbitrarily profit allocation to some extent.

Data Collection.
We collect data from a practical fresh chicken supply chain, where a fresh retailer orders to its partner farm base. Fresh chicken is not the dominant meat in the local market, and its demand is elastic. e retailer submits the order plan to the farm base regularly. After receiving the plan, the farm base slaughters all the planned chickens and cools them to 0 to 4 degree centigrade in packages for chilled freshness. e fresh retailer is in charge of the delivery using its own whole-process cold chain system from the farm base to all its fresh supermarkets.
Consumers can scan the QR traceable code on the package to obtain the quality visibility from the chicken feeding to the shelf reported by the farm base and the fresh supermarket, and the completeness and accuracy of the available quality information depend on the visibility systems of the two companies. Figure 2 shows the quality visibility displayed on a type of packaging for fresh chicken.
First, we operationalize the supply chain quality visibility assessment model suggested by Caridi et al. [19]. We ignore the mandatory information such as ingredients, product date, shelf life, and quality certification as shown in Figure 2 and focus on the changing quality information linked to QR code and sale scene instead, i.e., the four information types listed at the end of Section 2.1 except the fifth one. Information quality is rated and quality visibility is calculated in (0, 5). e 5 of quality visibility represents that consumers could get all the quality-related knowledge if they want, and this knowledge has an almost perfect quality. e 0 indicates consumers hardly get any additional information except what is on the package.
Second, the value of each parameter is derived based on the sales statistics of the fresh retailer during a quarter in 2019. When the price remains the same for a few days and there is a change in the information system, we obtain the sensitivity coefficient of the demand to quality visibility and the potential market demand using linear fitting; similarly, the sensitivity coefficient of demand to price is obtained when the information system is constant and the price fluctuates. Two sensitivity coefficients of cost to quality visibility are derived by quadratic fitting. Historical records of several other quarters are used as a reference for correction.
For simplicity, we use the integers close to these parameters for case analysis, and the sensitivity analysis in Section 5.3 proves that a slight parameter deviation does not affect the validity of the results. Finally, we have the potential market demand θ � 5000 in the quarter, the sensitivity coefficient of demand to price λ � 100, the sensitivity coefficient of demand to quality visibility α � 700, the supplier's quality visibility cost coefficient β s � 1900, and the retailer's quality visibility cost coefficient β r � 2500.

Contract Discussion.
e optimal decisions and performances of the supply chain in different scenarios are presented in Table 3. In this case, it is obvious that the price discount contract with effort alignment (E) or cost-sharing (B) coordinates the supply chain to an integrated one. In contrast, the total quality visibility and profit of the supply chain in the decentralized supply chain (D) are far lower than those in the other scenarios because of severe double marginalization. It is presumed a higher revenue per unit with an increased retail price and a lower visibility cost with a decreased visibility effort in (D); however, they inhibit consumers' demand, which dominates both companies' profit functions. erefore, there are strong practical interests for both the farm base and fresh retailer, driving them to seek supply chain integration or coordinated decisionmaking.
e outcomes under contract (E) are as good as a centralized supply chain, but the contract distributes supply chain profit at a fixed proportion because it requires a correlation of the visibility efforts between the supplier and the retailer, similar to the pricing. It applies to two companies of similar size with stable partnership, since it does not require integrating the visibility systems of the two companies, leaving them largely independent instead. However, contract (B) applies to a closer partnership because it requires upstream and downstream firms to integrate visibility systems and share effort costs. In this sense, the two contracts are in the middle of the vertical integration spectrum where the decentralized and centralized scenarios are at opposite ends.
Further consider that when the profit allocation rate φ is slightly lower than the lower threshold 0.25 (or slightly higher than the upper threshold 0.55), the fresh retailer (or the farm base) obtains a slightly smaller profit under contract (B) than that under contract (D). It seems that there is no reason for the fresh retailer (or the farm base) to deviate from contract (D) in terms of profit, but his and his partner's quality visibility levels would be significantly improved if they used contract (B). Furthermore, the reduced retail price and higher supply chain visibility offered by contract (B) lead to increased food sales and consumer welfare, as well as predictable improvements in business management and goodwill, which to some extent spur the fresh retailer and the farm base to change their minds. We conclude that there is a strong stability with contract (B).
ere are some existing practices in which retailers or brand owners ally with suppliers to jointly bear the costs of visibility systems. As mentioned earlier, Walmart is believed to accept a large part of the R&D costs of the Food Trust Platform in cooperation with IBM while the leafy-greens suppliers just pay a service fee of 100∼10000 dollars monthly according to their scales. Figures 3-6 show the influence of price sensitivity, quality visibility sensitivity, and visibility cost coefficients on supply chain performances and contract parameters. e shadow in each figure represents the Pareto improvement space in the decentralized supply chain.

Sensitivity Analysis.
It is easy to find that increased quality visibility sensitivity leads to a higher price (in Figure 4(a)), higher quality visibility (in Figure 4(b)), and greater profit (in Figure 4(c)), regardless of the supply chain or the companies in it, while the other three parameters have the opposite effect (in Figures 3, 5, and 6). erefore, when the negotiating cost of a coordination contract is too high or the supply chain has   been coordinated, for more profits and quality visibility, the companies may consider (i) promoting food positioning and acquiring more price-insensitive consumers, such as by launching "organic chicken" or minipackaging for one meal by the farm base and locating in luxury communities or office buildings for the fresh retailer; (ii) advocating for the traceable and trackable whole-chain quality and safety from farm to table in order to attract consumers focused on quality visibility; and (iii) purchasing or renting a more popular cost-effective visibility system, and improving the interfaces and compatibility of visibility systems.
As shown in Figures 4(a)-4(c), when consumers pay more attention to quality visibility, the company's visibility investment increases demand, which compensates for the demand reduction caused by price inflation. In this respect, higher quality visibility sensitivity rapidly increases the optimal retail price in the supply chain, that is, consumers' willingness to pay for a high-quality visibility food. In this case, for a unit increase in quality visibility, consumers are willing to pay an extra 7 CNY (α/λ) as the food premium for high-quality visibility. e increased quality visibility sensitivity also leads to a broader range of the profit allocation rate (increased φ max and decreased φ min ) from Figure 4(d), while the other three parameters still have the opposite effect and narrow the range. erefore, it is easier to realize supply chain coordination with a high visibility sensitivity, low price sensibility, or low-quality visibility cost coefficient.
In addition, a significant impact of the visibility cost coefficient on the contract (E) is observed in Figures 5(d) and 6(d). e fresh retailer (or the farm base) seizes a larger share of the supply chain profit with its own lower cost coefficient or a higher cost coefficient of the other party. Moreover, a large part of the φ E curve is below 0.5 (by β s � β r ), which suggests that it is prone to contract (E) when the visibility cost coefficient of the fresh retailer is far beyond that of the farm base, according to incentive compatibility conditions in Section 4.2. Indeed, more and more retailers source directly from farms and transport using self-built logistics to mitigate supply risk and quality risk, which makes the retailer's visibility cost coefficient often greater  than the supplier's, and thus, it is more likely to coordinate the supply chain with contract (E).
It is also meaningful to examine the sensitivity of each constraint condition to each parameter. e assumption in Proposition 1 is the condition to ensure a profitable supply chain coordination, denoting as Cdt1, while the incentive compatibility conditions in Proposition 3 guarantees the companies' participation, denoting as Cdt2 for the supplier and Cdt3 for the retailer, respectively. We can get the interval of each parameter with other parameters fixed (the strictest condition where the number is derived is in the parentheses): λ> 56.74 (Cdt1), (Cdt1) 929.32> α >0, (Cdt2) 2849.00 > β s > 811.26 (Cdt1), (Cdt3)5677.35 > β r >903.88 (Cdt1). e result shows that as long as Cdt1 is met, what stops the company is its own cost coefficient of quality visibility. erefore, it could be the most important thing to reduce the unit cost of visibility efforts, and a number of companies good at information systems are working on that. For example, Frigga launches a low-cost real-time and an ultra-low-cost USB temperature recorder for cold chain logistics, and both of them are disposable and can be used for more than 90 days (see its website: https://www.friggatech. com).
Finally, from the perspective of the overall supply chain or the regulators, it is good for improving quality visibility to promote IT innovation, upgrade industries and consumption, and create a conducive environment for sign a contract.

Conclusions
is paper examines a food supply chain decision-making problem in which both the supplier and the retailer determine prices and quality visibility, and both demand and costs depend on each company's quality visibility. We propose two price discount contracts with effort alignment and with cost-sharing to coordinate the supply chain. After discovering a Pareto improvement opportunity by comparing the supply chain performances under the centralized and decentralized (wholesale price contract) situations, we demonstrate that the two modified contracts other than a common revenue-sharing contract could coordinate the supply chain, and we give their boundary conditions excluding the deviated actions. eir strengths and limitations are presented, as well as their feasibility and stability, which are confirmed by a practical case of a chicken supply chain. Sensitivity analysis is conducted to reveal the impacts of four exogenous coefficients on the decisions and performances of the supply chain, which provide some meaningful managerial implications related to supply chain quality visibility. e results prove that the decentralized supply chain is far inferior to the centralized supply chain in terms of both quality visibility and profit due to the existence of double marginalization. Both the supplier and the retailer have enough incentives to realize supply chain coordination from an inefficient wholesale price contract. However, other simple contracts are also invalid unless more than one parameter is introduced when the profit functions of all the players depend on the prices and efforts of both the upstream and downstream supply chains in this model, which is different from most of the existing studies. e effort alignment and cost-sharing policies correct the distortions in the decisions on multiple layers. e former is simpler at a fixed profit allocation rate, whereas the latter can arbitrarily allocate supply chain profits to the supplier and retailer despite a larger information set being needed. In reality, considering that the quality visibility marginal costs of fresh retailers are relatively high, the incentive compatibility condition of the retailer seems to be more easily satisfied when an opportunity profit exits. Furthermore, since the coordination contracts improve everyone's quality visibility considerably, there is still a good chance for the companies to pursue coordination even if either's profit is slightly eroded, which guarantees the practical applicability of the two contracts.
Supply chain coordination not only provides opportunities to improve the performance of supply chain companies, but it also increases sales and consumer welfare at a lower retail price, which implies potential benefits such as higher brand awareness and goodwill. It may be effective to improve supply chain profit and quality visibility using improved food positioning, publicity for quality assurance, or a more costeffective visibility system. Furthermore, IT innovation, industries and consumption upgradation, and contracting convenience also help from the holistic point of view.
Our study has limitations that lead to further research suggestions. e demand function in the model is classically linear, which may be applicable for foods with elastic demand and within certain ranges of price and quality visibility. However, daily consumption products except necessities generally have high elasticities and so do each of the competing brands in the same category of necessities. It would be interesting to discuss different demand functions and pricing models and examine the effects of revenuesharing, buyback, quantity flexibility, and quantity/price discount contracts in the case that quality visibility effort is not observed. Another research direction in the future is to study the quality visibility strategies in the multisupplier, multiretailer, or multistage supply chain.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.