Introducing a novel revenue-sharing contract in media supply chain management using data mining and multi-criteria decision-making methods

Despite all the advances in supply chain coordination, some businesses are still coordinated traditionally, including the media supply chain, in which the actor’s efficiency or deficiency is not considered in their wage determination. It means the success or failure of the project is nothing to do with the actor’s revenue. This article proposes a novel revenue-sharing coordination contract that benefits from text mining and the best–worst method to address this problem. We aim to determine a fair share of profit or loss of a movie for each of its actors based on their performance and efficiency on the success or failure of the project. One of the Iranian latest movies is considered as a case study, and its lead actor’s wage is determined under this contract. The sentiment analysis technique investigated the viewers’ opinions about the movie and the actor’s performance. Since the reviewers mainly are the people who have no expertise in cinematography, they cannot discern the influence of other participants on the actor’s performance. So the proposed method used experts’ opinions through the fuzzy DEMATEL method to consider the overlapping effect besides enhancing the validity of the reviewers’ opinions. The results of this paper assert that the actor’s performance will improve under the proposed method and therefore the movie will be more successful and profitable.


Introduction
Despite the advancement of human science in supply chain management, some businesses are still run traditionally, among those are the businesses operating in the media field (WebFX 2020). For example, we can refer to the cinema industry. There is no scientific or fair way to pay a movie's participants, especially the actors and actresses. The question that arises here is whether a method can be devised that equates the wage of each actor to the efficiency of his activity on the product, fairly and based on the viewer's opinion (consumer). In this study, we tried to answer this question.
All members of a supply chain (SC) are linked to each other, and their influence on each other performance is undeniable (Wisner et al. 2014). It's worth saying that a lack of coordination in the system between its actors usually causes uncertainties (Konstantelos et al. 2017). These uncertainties are particularly tangible in cases such as wages and the lead times for receiving a product. As you may know, SCs are defined by a variety of activities and different actors (disparate but interdependent members). If any system wants to reach its objectives, it seems reasonable that individuals might align their goals with those of the organization (system). With this in mind, coordination between activities and actors is necessary to coordinate individual objectives with SC global goals to make optimal performance more reachable (Cachon 2003). It should be noted the efficiency of supply chain depends on the flexibility and coordination of its various components (Rezaei et al. 2021).
Contracts have been used as a tool for coordination between two or more independent partners (manufacturer, retailer, supplier, etc.) for so long (Chao et al. 2009). The classic revenue-sharing coordination contract addresses the occasion the retailer is reluctant to raise its service level, especially in uncertain situations (due to the risk of excess inventory), thereby reducing the possibility of increased shortages and reduced SC total profits (Dehghan-Bonari et al. 2021). The revenue-sharing contract helps both retailers and suppliers to cover this drawback. Under these coordination contracts, the retailer offers the supplier less than the wholesale price for each product's purchase. Instead, the retailer shares revenue and profit from the sale with the original supplier (Tsao and Lee 2020).
Wage determination (WD) has a bold influence on SC's coordination (Kenworthy 2001;Manow 2004). But despite all the methods for coordinating the SC, including the coordination contracts, never in any industry, WD was based on efficiency.
In this article, we proposed a novel revenue-sharing contract based on fuzzy decision-making trial and evaluation laboratory (Fuzzy DEMATEL), text mining (TM), and the best-worst method (BWM) for media SC coordination. The main objective of this research is to propose a scientific way for fair WD, and its focus is on media SC and the cinema industry. To reach this goal, it seems rational to investigate costumers' opinion (viewers' opinion). A viewer's comments on the internet (famous websites, Twitter, etc.) are a reachable source of his genuine opinion. The best method to investigate this valuable source is TM. Furthermore, all three methods used in this research are among the most recent techniques that benefit from a highspeed calculation and ease of application.
The results of this research proved that applying proposed contract in for fair WD can elevate the actors' productivity and therefore the movies profitability. Also, it's worth mentioning that this article's findings can be used in any industry for fair WD and revenue-sharing. The reason that in this article, the cinema industry has been considered as the case study is that from the advent of the camera until now, no scientific method is applied in media SC management for fair WD. So the proposed method is so much needed in there.
The rest of the article is organized as follows. Reviewed articles are reported and classified into two categories in Sect. 2: (i) revenue-sharing contract and (ii) text mining & sentiment analysis. Also, a comprehensive literature review table and significant research gap are proposed in this very section. Section 3 describes the problem and our two-stage methodology. Each stage's steps are explained clearly. Furthermore, in stage 4, a real-life case study has been investigated to better understand the proposed methodology. Section 5 has been dedicated to sensitivity analysis and numerical examples, which give us valuable managerial insights. The discussion and managerial insights have been listed succinctly in the sixth section of this article in order to clarify the application of the proposed model. In the seventh section, a brief conclusion has been conducted that finalized paper. This study reaches its end with a short acknowledgment to show our gratitude toward experts and the producers of the investigated case study.

Literature review
Coordination plays a vital role in SC management (Fugate et al. 2006). In this section, a review of several important articles that examined coordination contracts will be proposed. There are many worthy studies about classic coordination contracts (such as Cachon and Lariviere 2005;Lariviere 1999;Ma et al. 2020;Tsay et al. 1999;Wang et al. 2020) that the readers can use to find more information about coordination contracts.
For better comprehension, reviewed articles are sorted into two main groups: revenue-sharing contracts and social media TM and sentiment analysis (SA).

Revenue-sharing contract
In Hsueh (2014) research, the author aimed to integrate corporate social responsibility with the SC's coordination. For this cause, a new revenue-sharing contract was introduced in the two-echelon SC. For determining the optimal corporate responsibility investment, a mathematical model has been proposed by researchers. Arani et al. (2016) aimed to cover the flaws in classic coordination contracts, integrated a European call option contract with a revenuesharing contract. The authors modeled their novel method through a game-theoretic technique that considers and tests different scenarios the retailer or manufacturer may cope with. Liang et al. (2017) investigated the revenue-sharing mechanism along with the aftermarket service of wind turbines in a closed-loop SC. Hu and Feng (2017) investigated the optimization and coordination of an SC consisting of one supplier and one buyer. They modeled the mentioned SC by revenue-sharing contract and service requirement under an uncertain situation. Benefiting the revenue-sharing coordination contract, Yan et al. (2017) coordinates a three-echelon fresh agricultural product SC that runs through the internet of things. Raza (2018) proposed a new quantitative model that discussed joint pricing and socially responsible investments. Demand has been investigated in both stochastic and deterministic scenarios. The game-theoretic approach has been used in this article to analyze the decentralized, centralized, and agreement based on revenue-sharing coordination contracts. According to the enormous growth of e-commerce, Wei et al. (2019) designed a model for cost reduction of a two-echelon SC, based on both revenue-sharing and cooperative investment contracts. Zhao et al. (2019) proposed a conditional probability of the market situation. Authors considering an SC including two retailers (downstream) and a mutual manufacturer (upstream) used revenue-sharing coordination contracts for information sharing. Li et al. (2019) used both revenue-sharing and cost-sharing coordination contracts for investigating the impact factor on carbon emission reduction and profitability. Xia et al. (2019) proposed a framework for the revenue-sharing mechanism among an airline and a high-speed rail operator. Various situations have been considered in their research. The results show if the high-speed rail operator is social welfare-oriented or in the multi-airport system, the airlines are a monopoly, the revenue-sharing coordination contract is more reachable. Considering government subsidy and demands ' uncertainties, Lingcheng et al. (2019) proposed a revenue-sharing that coordinates upstream and downstream firms and solves the power grid-connection problem. Liu et al. (2019) proposed an integrated revenuesharing and service cost allocation contract for the port service chain coordination. Due regard to uncertainties, Aghajani et al. (2020) proposed a mixed possibilisticstochastic model that integrated a two-period option contract. The essence of their work can be described as supplier selection and inventory prepositioning. They defined a two-stage scenario as the foundation of their model. In the first stage, the optimal supplier is selected and in the second stage, the decision on when and how much to use is made. Panja and Mondal (2020) analyzed two game-theoretic models in a two-layer single manufacturer single retailer green SC. In the first model, market demand is dependent on the green degree of product and the selling price. In the second model, demand depends on the credit period that retailer offered and the green degree of product and selling price. Considering a decentralized SC including one retailer and one manufacturer, Tsao and Lee (2020) determined how revenue-sharing coordination contracts affect decision-making and profits. Canbulut et al. (2021) addressed revenue-sharing coordination contracts as twoperson non-constant sum games that each one wants to maximize their profit; So in a supply chine coordinated with a revenue-sharing contract, the supplier determines wholesale price which retailer respond with revenue-sharing rate. In their study, the profit function of the SC actors has been calculated using game theory. Nisa and Qamar (2015) benefited from TM for web services classification and determining key concepts from textual data in the web domain. Li et al. (2016) benefited from hierarchical classification (several classification models and three filters) as TM techniques for online news sentiments analysis. Araque et al. (2017) enhanced the ensemble classification algorithms for SA by deep and surface features integration. Amrit et al. (2017) applied TM to identify child abuse. Using a massive dataset related to children's health, they implementing machine learning methods for their research. Monkman et al. (2018) used a TM method in social media for information gathering about wildlife recreation activity. They used an automated scraping method for mining the generated data (content) by online users. Based on TM capabilities, Yu and Guo (2018) designed a model composed of domain dictionary construction, market convergence time calculation, and dimensionality reduction, integrating semantic analysis for news analysis to predict the medical material price. Fu et al. (2018) introduced a new data-driven MCDM method in an evidential reasoning platform. The diagnosis of thyroid cancer is the perfect application of their model and study it, also generating data-driven diagnostic results. Serna and Gasparovic (2018) tried to investigate the tourists' satisfaction with their used transportation model. For this reason, they applied a TM method to assess the tourist's opinion about success factors. Their study shows the vital role of social media data mining in transport and tourism planning. Ismail et al. (2018) used a fuzzy thesaurus for SA and sentient replacement in Twitter to reduce the dimensionality of the feature space. Their method is completely domain-independent. Greco and Polli (2019) proposed their research on emotional text mining (ETM) application on brand management based on a bottom-up technique that is an approach for classifying unstructured data to identify social media users' sentiment about a subject.  Tan et al. (2020) presented a learning method according to the aspect categories and the aspect terms relation can learn aspect embedding. The objective is to address the relation between the two subtasks of aspect-based sentiment analysis (ABSA): aspect category sentiment analysis (ACSA) and aspect term sentiment analysis (ATSA). Ye and Lee (2020) used TM to analyze the customers' sentiment tendency over time. Their three-step method is commenced with a model for feature words extraction and leads to the second step which is converting costumers' reviews into a sentiment graph. The last step summarizes the reviews that will divulge the customers' tendency.

Research gap
Based on the presented literature review and Table 1, the following research gaps are identified: • Only a few articles used data mining methods to reach coordination in a system (e.g., Wang 2014). • To the best of our knowledge, there is no research article that benefits from data mining or machine learning techniques to design a coordination contract. However, logically it's necessary for the best results. • We found no article that benefits from MCDM methods along with data mining techniques for determining the revenue fraction in the revenue-sharing coordination contracts. • No article uses the revenue-sharing contract to determine project employees' wages according to quality instead of quantity. • There is only a few article that used MCDM alongside with datamining techniques (e.g., Liou et al. 2021). • All three TM, fuzzy DEMATEL, and BWM methods are relatively incipient.
This article covers all of the mentioned gaps by proposing a novel revenue-sharing coordination contract that investigates fair WD in the media SC that uses the TMfuzzy DEMATEL-BWM hybrid method for this reason.

Problem description and methodology
In the last decade, numerous valuable papers have been proposed to coordinate the SC's actors, especially employing coordination contracts. Despite all these researches, many businesses are still coordinated traditionally (if there is any coordination between SC actors). There are lots of businesses that use unscientific methods because there is no proper coordination of WD. These methods almost always lead to injustice.
In the WD process, it's not fair to consider quantity instead of quality and effectiveness. So, it seems more reasonable to determine the effectiveness of each employee, and based on this factor, use a revenue-sharing contract that determines their share from the profit. In the WD, it's more professional to use consumers' opinions about the success and failure factors of the product.
All the mentioned problems in previous paragraphs are easily eliminated by this novel proposed methodology. By applying this contract, all members of the SC will share in the profits and losses fairly, which will enhance the organization's excellence and resilience.
As mentioned before, one of the best options for applying this coordination contract is businesses that run on the media platform, e.g., the cinema industry. There is no applied scientific way in the cinema industry for coordinating the participants of a movie-making project and no fair method for determining their wages.
In order to make the participants' wages fairer, it's needed to be determined how much they affect the success or failure of the film. In the first stage of the methodology, each participants' fraction of revenue-sharing is calculated by determining the effect of his role in the film and his efficiency in that role.
Benefiting the social media environment and employing TM, we can obtain the efficiency degree of each role in the success or failure of the movie from comments of people about the movie, which is reflecting their sentiments. On the other hand, based on the expert's opinion and using a BWM method, the sole efficiency degree of each actor can be obtained. In more accurate words, in the TM step, we understand the efficiency of each role in the success or failure of the project. After that, in the BWM step, we figure out that in success or failure of that specific role, how effective is its actor per se. By multiplying the TM and BWM, the net coefficient degree of each actor can be calculated.
In the second stage, using this factor as the fraction of revenue-sharing, a new revenue-sharing coordination contract will be introduced. It's necessary that using the fuzzy DEMATEL method, each actor's share of the movie budget gets identified as revenue-sharing wage. Figure 1 shows the whole methodology in a glimpse.
It is vital to mention that in this study; we use the opinion of five experts from Iran's national cinema who are familiar with the concept of revenue-sharing coordination contract. They have cooperated with us in both ''determining the impact factor of each actor in the project'' (using fuzzy DEMATEL), and ''Determining the revenuesharing price using the BWM'' steps.
Used notations in this methodology are introduced in Table 2 as follows: 3.1 Stage I: determining the revenue rate of each actor In step one, based on the TM method, considering spectators' comments on the Instagram platform and investigating their sentiment, the efficiency degree of each actor in the success or failure of the movie is obtained. Since most of the spectators cannot distinguish the other participants' work influence on actors' work, in step two, relying on the fuzzy DEMATEL method and benefiting the expert's opinion, we will determine how influential the actor himself was in his role. For example, how much of the success is due to the makeup artist's work and how much due to the actor's work.
In the last step of this stage, by integrating two previous steps results, the revenue rate of each actor can be achieved. This revenue rate is used in the proposed • Both revenue-sharing and cost-sharing coordination contracts have been used in this paper to investigate the impact of carbon emission reduction on the profitability of an SC Xia et al.
• The revenue-sharing mechanism has been used for highspeed railways and airlines Liu et al.
• Revenue-sharing and service cost has been considered for port SC Panja & Mondal (2020) • Two game-theoretic models discussed: demand is dependent on selling price and green degree of product or is dependent on the credit period offered by retailer too • Revenue sharing has been applied in a two-person nonconstant sum game The application of a novel revenue-sharing coordination contract in the media SC has been discussed using BWM, TM, and fuzzy DEMATEL methods Introducing a novel revenue-sharing contract in media supply chain management using data… 2887 revenue-sharing contract to coordinate the media SC fairly scientifically. 3.1.1 Step I: determining the efficiency factor of each actor based on spectators' opinion According to recent research proposed in the literature review section, the application of data mining methods is growing day by day (Alipour- Vaezi et al. 2021;Nisbet et al. 2009). TM is a data mining approach for obtaining information by extracting meaningful numeric indices from the text. This method follows five steps to mine the information (Kumar and Ravi 2016).
(I) Text preprocessing: It involves text cleanup (removing unnecessary information), tokenization, and part of speech. (II) Text transformation: also known as attribute generation. There are two ways for transforming text documents, the bag of words and vector space.
Feature selection: also known as attribute selection or variable selection. In this step, a proper subset of bold features for model creation.
(IV) Data mining: using classic data mining methods is merged with the TM in this step. (V) Evaluation: evaluating the results is one of the most important steps in the TM technique. (VI) Application: there are many areas that TM may be applied to, web mining, medical, resume filtering, etc.
One of the most efficient branches of TM is SA. SA is a tool that uses TM to extract and classify opinions and emotions within the text. It could be used for understanding customers' feelings and opinions about the product and to hear the voice of the customer (VOC).
SA uses various natural language processing (NLP) algorithms including (Alsaqer and Sasi 2017;Dreisbach et al. 2019): • Rule-based systems that are based on a set of rules which are manufactured manually. • Automatic systems that benefiting machine learning techniques. • Hybrid systems are a combination of both rule-based and automatic systems.
Determining the wages of suppliers and manufacturers without considering consumers' opinions is neither fair nor scientific. Hence, it's necessary to investigate consumers' sentiments about the product. In this article, considering its scope of research (cinema industry), we used the TM approach to analyze the spectators' sentiments and gain their opinion about actors. We want to understand how influential each actor has been on spectators' opinions about the success or failure of the project. Because of the Rule-based systems' high precision, this method is used for modeling this article. To the best of our knowledge, most of the spectators of a movie cannot discern the impact of other people's work on each other, and if they asserted that they think that one of the actors did a great job on the movie and made that film successful, they simply didn't consider the influence of makeup artists, screenwriters, etc. This is not just for cinema actors. In any SC, participants have an undeniable effect on each other work. So in this article, the fuzzy DEMATEL method is used to obtain the impact factor of each actor in the project. In more accurate words, in this step, we considered participants of a movie-making project as criteria of fuzzy DEMATEL technique to determine how much success or failure of a movie belongs to the actor himself. Fuzzy DEMATEL proposed by (Wu and Lee 2007) is one of the most renowned methods of MCDM using the following steps: Form a group of experts.
Define the decision criteria and determining the linguistic scales.  In the above model,Z k ð Þ represents the initial directrelation fuzzy matrix of kth expert (out of p experts) wherẽ ij is a triangular fuzzy number). Also,X k ð Þ denotes the normalized direct-relation fuzzy matrix of expert k wherex The overall profit or loss from the sale of the movie b Predefined movie budget for acting services a i The factor that shows how much of the movie budget is paid to each actor as revenue-sharing price. a 1 is the factor that is relevant to the discussed actor (BWM weights) P B Project total budget P I Project total income Variables E r The efficiency factor of the actor which is determined by the TM-fuzzy DEMATEL mixed method in the first stage p S supplier's (actor's) revenue Introducing a novel revenue-sharing contract in media supply chain management using data… 2889 (V) Calculate the fuzzy matrix of the total relationship. First, the inverse of the normal matrix has to be calculated, then subtract from matrix I, and finally multiply the normal matrix in the resulting matrix. In this step,T represents the total-relation fuzzy matrix, (VI) Create and analyze the casual Chart. For this purpose, first, the sum of the elements of each row (Di) and the sum of the elements of each column (Ri) of the fuzzy matrix have to be calculated. The sum of the elements in each row (D) for each factor indicates the extent to which that factor affects other system factors. The sum of the elements of the column (R) for each factor indicates the degree of influence that factor has on other factors in the system. Then the values of (D þ R) and (D À R) can be obtained easily. To draw a causal diagram, like the DEMTEL method, we have to defuzzify these two values the horizontal vector (D þ R) is the degree of influence of the desired factor in the system. In other words, the higher the (D þ R) factor, the more it interacts with other system factors. After defuzzifying the numbers, a Cartesian coordinate system is drawn. In this device, the longitudinal axis represents the values of (D þ R), and the (D À R) is the transverse axis. If the value (D À R) is positive, the factors are causal, whereas if the value (D À R) is negative, the factors belong to the effect group. Since fuzzy DEMATEL will not give us weights for criteria, based on the method presented by Tian et al. (2019), the criteria weights are found using fuzzy DEMATEL. Table 4 lists the defined criteria of this step. 3.1.3 Step III: obtaining net coefficient rate of each actor Now that we obtained the spectators' opinion about the actor's efficiency and determined the impact factor of the actor in the project, it is time to gain the net efficiency factor of the actor. Equation (4) is found for this purpose.
Equation (5) asserts that the absolute value of the net efficiency factor of the actor has to be considered as the fraction of revenue-sharing.

Stage II: defining a novel revenue-sharing contract
The general purpose of the revenue-sharing contract is to minimize the impact of uncertainty on the SC and motivate the retailer to order and hold a higher level of inventory. Since it's not probable that market periodic demand is exactly the same as the retailer's order quantity, it is easy to conclude that either an excess or a shortage of inventory will take place. Under a revenue-sharing contract, the supplier will commit to delivering the order quantity requested by the retailer at a price lower than the usual wholesale price. In return, the retailer commit that pays a share of the overall sale of the goods at the end of the period to the supplier. (Cachon and Lariviere 2005). As it has mentioned, this article focused on the cinema industry, so we consider the film actors as suppliers and the management team as the retailer. According to the definition of revenue-sharing contracts, the actor receives less than the usual wholesale price in the proposed contract, and the project management team commits to sharing a percentage of the overall movie profit with the actor. Using (0.5, 0.7, 0.9) Moderately high influence 5 (0.7, 0.9, 1) High influence 6 (0.9, 1, 1) Very high influence 7 fuzzy DEMATEL in step I (Sect. 3.2.1), the revenuesharing price will be determined.
In the second step, the mathematical formulation of the proposed coordination contract has been explained.

3.2.1
Step I: determining the revenue-sharing price using the BWM The BWM is one of the novel techniques in multi-criteria decision-making (MCDM), which has been proposed by Rezaei (2015Rezaei ( , 2016. The advantage of this method is that it requires fewer comparative data than similar methods, and its reliability is much higher. The steps of the BWM method are as follows: (I) Determine the set of decision criteria. Needless to say that the criteria of this step are different actors in the project. Because of the large number of criteria that have not been mentioned. (II) Determine the best and the worst criteria (without comparison). (III) Determine the best criteria preference over all the others, using 1-9 numbers. (IV) Determine the worst criteria preference over all the others, using 1-9 numbers. (V) Compute the optimized weight of each criterion. Model (6) is the linear best-worst method. Benefiting this model, the optimized weight of criteria can be calculated.
S.t w B À a Bj w j e l 8j w j À a jW w W e l 8j X j w j ¼ 1 In the above model, a Bj :a jW : w B :w W :w j shows the relative preference of the best criteria to criterionj, the relative preference of criterion i to the worst criteria, the weight of best criteria and the weight of the worst criteria, and the weight of the criteriaj, respectively. Also, the e l represents the consistency index as the decision variable of BWM (Mohammadnazari and Ghannadpour 2018;Tavakkoli-Moghaddam et al., 2020).

3.2.2
Step II: mathematical formulation of the proposed contract Equation (7) is the actor's determined wage. At first, before the filming, the actor will receive the revenuesharing wage, and after the screening and determining the amount of profit or loss of the movie based on stage I steps fraction of revenue-sharing will be identified. If the actor was efficient in the success of the movie, according to the fraction of revenue-sharing, he gets his share of the film's profits. But if the actor was one of the failure factors of the movie, he has to compensate his share of the film's loss.
Relation (8) asserts that revenue-sharing wage is less than wholesale wage. Although this relation is self-evident, we are reasonably obliged to mention it.
As shown in Eq. (9), to obtain the revenue-sharing price of each actor, we used an MCDM method once more. This time, using the fuzzy DEMATEL technique, considering the interaction of actors, each actor's share of the film's budget is determined and paid as the revenue-sharing price to the actor. It has to be mentioned that the predefined movie budget for acting services (b) is determined by the SC decision-makers (producers). Introducing a novel revenue-sharing contract in media supply chain management using data… 2891

Case study
For a closer look at the presented model's application, we used a case study. In this section, the information of this case study is provided. To avoid any further conflict about the movie, here we do not mention the movie's name, actors, or decision-makers (DMs) to avoid any conflict. The movie in question which Iran's national cinema has produced is one of the most controversial movies in the last years. There were so many negative critics from famous experts and magazines. But, according to the fact that it grossed about 8.561 million $, it is obvious that it made its way to its spectators' heart. With a 1-1.16 million $ budget, this movie became the sixth most profitable release of that year.
The lead role of this movie had a critical effect on the movie's profitability. Despite the fact that that many people believe the actor has saved the movie, there is no significant change in his revenue. As mentioned in the above paragraphs, the main idea of this article is to decrease the unfairness in the media SC and cinema industry. So we decided to investigate our new coordination contract on the lead actor's performance and revenue. All the steps of the proposed methodology will be examined in this section.

Determining the revenue fraction factor of the lead actor
In this stage, after discovering and analyzing the viewers' opinion about the lead actor's attendance in the movie and normalizing the result by multiplying it into experts' opinions, we obtain a revenue fraction factor of the lead actor.

4.1.1
Step I: determining the efficiency factor of the lead actor based on spectators' reviews To obtain viewers' opinions about the lead actor's efficiency on the movie's profit, we mined for people comments on Twitter, Instagram posts (the movie's official account), and also reviews on famous web pages including IMDb, rotten tomatoes, and google audience reviews. Using rapid miner, SA of the comments took place. Figure 2 shows the process that has been exerted to analyze the sentiment polarity of the reviewers' comments. Just as shown in Fig. 2, two excel sheets have been created. The first one contained the sentiment of spectators about the movie in general, benefitting analyze sentiment (1) operator, and the second one shows the result of analyzing sentiment (2) operator after filtering the comments and obtaining ones that were related to the lead actor's performance.
The Analyze sentiment operator gives the polarity and polarity confidence level (0-1). Each comment can be identified as positive, neutral, or negative. A number (1, 0, -1) has been dedicated to each comment. 1 for positive, 0 for neutral, and -1 for negative. To calculate the efficiency factor, we multiplied this number to polarity confidence level number and the number of importance (the number of likes that comment collected or the number of retweets).
The total efficiency factor of the film, in general, was calculated 278,460, and the total efficiency factor of the lead actor's performance was calculated 33,214.8. Dividing these two numbers, according to Sect. 3.1.1. shows the efficiency factor of the lead actor in the movie's success.
Total efficiency factor of the lead actor's performance Total efficiency factor of the film in general = Efficiency factor of the lead actor in the movie success To the best of our knowledge, most of the comments were sent by people who don't have any expertise in the cinema industry, as mentioned in Sect. 3.1.2. Using the fuzzy DEMATEL method, we extracted experts' opinions about how much the lead actor's performance was influenced by other participants. In other words, how much of people's opinion was because of the lead actor's performance in his role. Table 5 asserts the weights calculated through the fuzzy DEMATEL method. These weights are named as the sole responsibility degree of different participants. Further information about the initial matrix of this step has been provided in the appendix section (Table 10).

Step III: obtaining net coefficient of the lead actor
The revenue fraction factor of the lead actor has been defined using the TM and fuzzy DEMATEL technique, as follows. The efficiency factor of the lead actor in the movie success multiplies to the lead actor's solely responsibility degree is equal to the lead actor's net coefficient degree.
It illuminates that our case study actor is responsible for more than 5 percent of the movie's profit. This factor is used in the proposed revenue-sharing coordination contract as the revenue fraction factor.

Defining a novel revenue-sharing contract
Now that we calculated the revenue fraction factor, it's time to define our novel coordination contract. But first, we have to determine the revenue-sharing price calculated by experts' opinions and the BWM technique. Then the mathematical formulation of the proposed contract has to be investigated.

4.2.1
Step I: determining the revenue-sharing price using BWM In this step, we have to assume that the producer dedicates 1 million $ to contract with the mentioned actors in Table 6. Using the BWM technique, each actor's budget share is determined, as shown in Table 6. To receive complimentary information about the initial matrixes of this step, please observe the Appendix section (Table 11). According to Eq. (9), the lead actor's contract's revenue-sharing price is calculated.
Step II: mathematical formulation of the proposed contract As mentioned before, the movie's budget was 1.16 million $, and the box office was 8.561 million $; therefore, it's needless to say that the movie was profitable. So for defining the revenue-sharing coordination contract Eq. (7) is used as follows: p S p r :u ð Þ¼ p r þ u:c p S p r :u ð Þ¼ 57700 þ 0:0288 Â 7401000 ¼ 270848:8$

Sensitivity analysis and numerical examples
To demonstrate the efficiency and sensitivity of the proposed model, in this section, we examine some numerical experiments alongside the investigated real-life case study.
These numerical examples, whose parameters are listed in Table 7, are proposed to study different possible situations other than the one that has occurred in the above-mentioned case study. Needless to say that based on the movie's profitability and actor's efficiency, four different scenarios may occur. Table 8 proposes a comprehensive discussion about these four scenarios and their relevant examples mentioned in Table 7.
Based on the proposed case study, the following diagrams are presented to identify the sensitivity of the model to various parameters. A various possible situation that  Supporting actor 3 0.05368098159509 may occur for the movie has been depicted and examined in the following figures of this section. Based on the changes in the project's income (P I ) and project budget (P B ), the actor's revenue(p S ) is portrayed in Fig. 3. For utter investigation in each layer, different predefined movie budget for acting services (b) has been involved. In other words, each surface represents the dependency of the actor's wage to project income and project budget on a specific predetermined budget for acting services. It's obvious that although changes in project income can make significant changes in the actor's wage, the project budget does not have much influence. Crystal clear the reason for this case is that the actor's budget is predetermined. If b was directly dependent on the project budget (which it is in the real world, but for easier calculating, we presumed it predetermined), then p S was so sensitive against P B just like the way it is sensitive to the b now.
Figures 4, 5, 6 are dedicated to the actor's dependency level to each parameter. In the legend box of each figure, you can find another parameter that is concerned. The star asserts our case study situation, so you can find better information about the movie. Figure 4 depicts the actor's revenue dependency on the project budget for acting services. This figure asserts that the higher the level of the movie's acting services budget, the higher the actor's wage will be. Also, you can see this on the different levels of the movie's income.
In Fig. 5, you can observe the actor's revenue dependency on project income. Besides, there is a direct relationship between the movie's income and the actor's wage. Figure 6 investigates the actor's revenue dependency on the project budget. As you can observe, this figure shows that a higher level of project budget makes a lower level of the actor's revenue. This is because we presumed that the movie's budget is not related to the acting services' budget, which is not like that in the real world.

Discussion and managerial insights
This novel study benefitting from TM and MCDM can improve many different SCs' profitability. Fair WD can be determined by applying this method. Since there is no similar paper to compare this novel methodology with, we investigated a real-life case study from Iran's national cinema and determined the fair wage of its lead actor. To study this paper's application, in Table 9, we have compared the function of the actor in question in his previous movies (in recent years and the same genre) and his influence on the success of the case study movie under the proposed coordination contract.
As shown in Table 9, before using the proposed method, the actor's income was nearly the same in all the movies no matter whether the project was profitable (Movie no.1 and no. 2) or not (Movie no. 3). Considering the huge difference between the case study movie's income and the other  In this situation, we can't calculate the actor's accurate wage based on the proposed methodology; But as mentioned in Table 7, revenue-sharing price is computed as the upper bound of the third scenario Loss-making Efficient 3rd example In this situation, we can't calculate the actor's accurate wage based on the proposed methodology; But as mentioned in Table 7, the revenue-sharing price is computed as the lower bound of the fourth scenario three's, it is rational to conclude that applying this method will accelerate the productivity level of the actor and therefore the movie's profitability. Also, the total income of the actor has been increased considerably in the case study movie. So it is reasonable to say that this methodology is preferable for both DM and actor.    Furthermore, this study helps DMs of nearly any SC to improve their system's profitability and productivity. Here, few applications of this research are proposed as follows: • Any industry whose customers know different actors of it can benefit from this methodology for fair WD. The cinema industry, which has been investigated by a reallife case study, and health care systems can be named as examples of these industries. • Multi-product factories (or any other entity) can apply this method in order to determine the fair budget for each product. Since based on their customers' opinion they can understand the impact of each product on their profit and brand. • Governments can benefit from this method using the tourists' opinions and fairly determine the tourism budget of different cities.
Also, based on sensitivity analysis, several managerial insights are listed in the following paragraphs for DMs of SCs: • We highly recommend DMs apply this methodology for fair WD and coordination of their systems, since according to Table 9, it benefits both DMs and actors. • Based on Figs. 3, 4, 5, 6, we advise DMs to decrease actors' wholesale price (p w ) and instead raise actors' impact factor on the project (C a ) when the project budget is low. This way, the actors' productivity will still be high. • DMs can use this paper's method for their projects to both increase their profit and reduce their loss. • According to Fig. 3, it is recommended to the DMs to determine the actors' optimal wage based on the different layers of project budget and income. • Based on Fig. 4, it is recommended to DMs to determine the optimal wages of each actor. This can be helpful for them for fair WD considering each actor's effect on the project's success or failure.

Conclusion
To the best of our knowledge, the most eligible way for fair WD is to take a step into SCs coordination. Throughout human history, many tools have been introduced, hoping to coordinate SCs. One of the most efficient tools in this matter is the coordination contract. Each coordination contract has drawbacks that need to be considered and updated. In this research, a novel revenue-sharing coordination contract has been defined, which uses the TM method to extract the efficiency degree of each role in the movie's success or failure to make WD fairer. Meanwhile, the fuzzy DEMATEL technique has been applied to calculate the sole responsivity degree of each actor in their role. By multiplying these factors, we easily got the net coefficient factor we used as the revenue-sharing fraction. By applying the BWM technique, the revenue price got calculated. The movie is considered as the case study and investigated step by step in this very paper. At the end of this study, some brief sensitivity analysis has been proposed that could give valuable managerial insights. The fair WD has been done according to novel methods of decision-making and based on the efficiency of actors. Considering people's opinions along with the expert's opinions made it reliable. The findings of this study confirm the professional reviews of the great critics of the cinema industry. This paper can help media DMs of SC in many aspects. Here we reckon some of its benefits: • Applying this method leads to a fair WD.
• Using this method, the actor does his best to accelerate the movie's income, which is his. • This method prevents the movie from heavy loss, and in case of loss, it will share it with people in guilt.
It's worth mentioning that this research has encountered the following limitations: • We have gathered and investigated a portion of the existing comments. Obviously, by considering a larger portion of the existing comments, the results would be more accurate. • This research benefits from the opinions of a number of experts in Iran's national cinema. For more reliable results, experts should be from related international departments. • This research had the opportunity of investigating its model with a real-life case study provided by Iran's national cinema industry. However, it was one of the limits that this study has encountered that it couldn't use other international case-studies.
Finally, we highly recommend that future researches use bargaining methods or game theory approach to calculate the actor's wage or use a data analytics approach to determine how much profit or loss the question actor has made.