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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.17 No.1 pp.30-42

Complementarities in Supply Chain Collaboration

Togar M. Simatupang*, Ramaswami Sridharan
School of Business and Management, Bandung Institute of Technology, Bandung, Indonesia
Newcastle Business School, The University of Newcastle, Newcastle, Australia
Corresponding Author,
October 8, 2016 June 26, 2017 February 9, 2018


Supply chain collaboration often results in better economic value when chain members collaborate with each other on multiple tracks of improvement initiatives. However, there is a lack of previous research explaining the economic impact of various interacting design variables of collaboration. The purpose of this paper is to explain the economic effects of complementarities on a model of supply chain collaboration which demonstrates interactions among design variables of collaboration to the value of collaboration. This research adopts concepts from complementarity theory to explain the economic impact of supply chain collaboration on the value of collaboration through choice of complementary design variables which consist of innovative processes, collaborative decision-making, incentive alignment, collaborative performance system, and information sharing. The findings will help researchers and practitioners build a sound explanation of relationships amongst design variables of collaboration, which is currently insufficiently explained.



    A supply chain system typically consists of different participating actors such as suppliers, distributors, transporters, and retailers. As markets become competitive, each chain member has a stake to be efficient and effective, while at the same time seeking an appropriate level of collaboration with other participating members (Whipple and Russell, 2007). Building collaboration is a challenging task since the parties involved in the supply chain have their own individual objectives and different resources (Lambert et al., 1999; Sepehri, 2012). The participants should arrange levels of collaborative variables, such as incentive alignment and process improvement, to take advantage of the value of collaboration (Dai et al., 2016).

    Supply chain collaboration enables chain members to tap business opportunities and enhance their competitiveness. The members often focus on improving multiple operations activities, such as their agility to respond to consumers, improve service levels, enhance product quality, and improve production efficiency. It is commonly accepted that supply chain collaboration should be used to effectively in order to meet changes in customer preference (Fisher, 1997). For instance, Dell is a prominent exemplar for the success of collaboration which is able to deploy information technology and supply chain competence to customize products in alignment with customer requirements (Dell and Fredman, 1999; Kapuscinski et al., 2004).

    Supply chain collaboration, however, is not an easy task. Its design and implementation requires close attention to the different interests of a variety of players along a supply chain, and to the management of their motivations and expectations (Callioni and Billington, 2001; Lee et al., 1997). Without proper understanding, supply chain collaboration can be a difficult and risky task (Buzzell et al., 1990; Anderson and Jap, 2005; Soosay and Hyland, 2015). Anecdotal evidence suggests that many collaborative initiatives fail to deliver expected outcomes (Kampstra et al., 2006; Lambert et al., 1999). The reason behind the failure stems from the fact that participating members have difficulties in tracing and measuring key design variables that contribute to the payoff of collaboration (Daugherty et al., 2006; Ramanathan et al., 2011). Chain members often do not have a complete understanding of the effect of changes in interorganizational design interfaces on the collaborative payoff. The second conjecture for the reason is that chain members set a target of interorganizational design variables which have little impact on the payoff of collaboration. This is because companies often look out for their own priorities and goals, and ignore those of their partners (Anderson and Jap, 2005; Lehoux et al., 2014). As a consequence, supply chains perform poorly.

    What participating members need is a means of pulling them together in the same direction for a supply chain that delivers products to end consumers quickly and costeffectively. They should coordinate to adopt a set of multiple design variables of collaboration (Lee et al., 1997; Hernández et al., 2014). A design variable is any choice of activity level that can be freely varied by the chain members, so as to encourage them to contribute to the value of collaboration. Analysis of different design variables is complex, since a design variable has special characteristics that differentiate it considerably from other variables, given its intangible nature. Unfortunately, existing models of collaboration do not completely explain design variables of collaboration which contribute to the value of collaboration (Simatupang and Sridharan, 2008; Vinholis et al., 2016). This means that an alternative model must be developed in order to capture and understand the underlying relationships of design variables that lead to successful collaboration.

    A number of studies have emphasized the role of design variables in supply chain collaboration to explain the synergistic relationship between different design parameters to supply chain performance (e.g., Kurtuluş et al., 2012; Sepehri, 2012; Hernández et al., 2014; Lehoux et al., 2014; Palma-Mendozaa et al., 2014; Dai et al., 2016). The results of these previous studies indicate that chain members should consider not only the adoption of a design variable such as information sharing, but also the manner by which this information sharing is combined with other design variables (i.e., business process redesign sign) to produce performance improvement (Sridharan and Simatupang, 2013). However, previous research only addresses a couple of design variables in isolation from other design variables. For example, Kurtuluş et al. (2012) showed that collaborative forecasting could be improved in the presence of coordinating constructs to reduce the cost of supply and demand mismatch. Hernández et al. (2014) proposed a combination of designing the right information and decision flow among chain members to support collaborative processes. Dai et al. (2016) recently developed a supply construct model to reduce late delivery.

    The alignment of different design settings is required as chain members involved both in transactional and collaborative relationships. Soosay and Hyland (2015) found the need for a more holistic approach to developing the necessary complementary capabilities for implementing successful collaboration. Moreover, Christopher and Ryals (2014) argued a shift of attention to the demand chain that exhibits both lean and agile characteristics. Decisions on the joint adoption of multiple design settings have been practiced in different areas of supply chain collaboration due to their interlinked properties. Datta and Christopher (2011) found several combinations of information sharing and coordination mechanisms for reducing the uncertainty in supply chains. More recently, Vinholis et al. (2016) depicted the complementary adoption of feedlot and traceability certification to have greater returns than farmers implementing these strategies separately.

    While a number of previous research have focused on the impact of one or a few particular design variables of collaboration, the way these design variables jointly produce supply chain performance is poorly understood. In this paper, an alternative theoretical foundation is offered based on complementarity theory which provides a more robust explanation of the use of various multiple design variables of collaboration. A complementarity theoretical approach explains the economic value of interaction amongst different key design variables, such as decision authority assignment, innovative processes, and information sharing. We do not propose to predict the value of collaboration; rather, we seek to demonstrate the linkages between the value of collaboration and multiple design variables which can be used in a variety of choices. We explain why all the variables are used in a complementary fashion rather than as substitutes. The application of complementarity theory to supply chain collaboration expands the literature on supply chain management. Specifically, this paper demonstrates a model for identifying multiple design variables and their intermediate variables in contributing to overall profitability. Complementarity amongst multiple design variables thus persists as an understudied area of research within supply chain collaboration.

    The paper is structured as follows. The next section is a review of the contributions of complementarity theory to the study of a key approach in order to understand the complementary effect of design variables. The following section contains a stylized model of collaboration, which provides key concepts to reveal the great importance of interaction among different design variables. After the model has been developed, the main conclusions and discussion derived from the analysis are given in the final section.


    The notion of complementarity originates from Edgeworth (1881), in which he defined that activities (i.e., practices, factors, control modes, drivers, choices, or design variables) are complementary if performing any one of them improves returns when performing others. Complementarities (or synergies) are present whenever having a bundle of activities together provides more value than the total value of having each of the activities separately. The complementary concept provides a basis for understanding how various activities in an organization are interrelated to produce greater impact than the sum of its parts because of the synergistic effect of integrating activities together. Complementarity theory addresses how activities in an organization are fit for interpreting the need of having strategy and structure fit one another (Milgrom and Roberts, 1995). The notion of fit is defined as both consistency amongst choices and the appropriateness of a set of choices to the given environmental conditions. This theory explains that some organizational activities or practices are mutually complementary and often adopted together to enhance the contribution from each other (Milgrom and Roberts, 1990). Complementarity theory thus can be used to explain how one activity may influence another and how the interaction between them affects overall performance. Complementarity theory implies that it is necessary for a company to couple many choices simultaneously to be more sensitive to environmental changes. For example, Milgrom and Roberts (1990) used complementarity theory to draw conclusions about observed changes in the strategies and structures of manufacturing firms in response to environmental changes.

    The synergistic effect of a set of practices occurs because the adoption of one practice has externalities for the adoption of other practices (Athey and Stern, 1998). Black and Boal (1994) argued that there are three possible relationships as one practice influences another. First, a compensatory relationship exists when a change in the level of one practice is offset by a change in the level of another practice. Second, an enhancing relationship exists when one practice magnifies the impact of another practice. Third, a suppressing relationship exists when the presence of one practice diminishes the impact of another.

    The strength of complementarity theory resides in its ability to identify and explain complementarities among multiple activities when they are coordinated together. The necessary condition for the existence of complementarity is that participating members of collaboration act rationally to coordinate multiple activities. The mathematical theory states the necessary conditions for activities to be complementary. Suppose there are 2 activities, a1 and a2, and a performance function, Π(a1, a2). Each activity can be performed by the firm (ai = 1) or not (ai = 0) and i ∈ {1, 2}. The function Π(a1, a2) is supermodular and a1 and a2 are complements only if: Π(1, 1) - Π(0, 1) ≥ Π(1, 0) - Π(0, 0), i.e. adding an activity while the other activity is already being performed has a higher incremental effect on performance than adding the activity in isolation.

    The study of complementarities between activities can be traced back to the theory of supermodularity and builds upon the work of Topkis (1978, 1995), Milgrom and Roberts (1990, 1995), Milgrom and Shannon (1994), and Holmström and Milgrom (1994). The mathematical foundation of complementarity theory can be found in Topkis (1998) and is not repeated here. The application of complementarity theory allows explanation of the complex interaction among design options for given contexts. Extension of the theories and applications in management have grown recently - including knowledge management (Choi et al., 2008), Enterprise Resource Planning (ERP) implementation (Grabski and Leech, 2007), information technology and supply chain (Setia et al., 2006), inventory management (Netessine and Zhang, 2005; Netessine et al., 2006), mass customization and electronic commerce (Lee et al., 2000), business process reengineering (Barua et al., 1996), decision support system (Barua and Whinston, 1998), and team-based organization (Barua et al., 1995), to mention a few.

    Previous research in supply chain collaboration suggests that participating members need to consider different types of collaborative design variables which are mutually supportive and, by adopting them together, have a greater impact on overall supply chain performance (Bharadwaj et al., 2007; Wong et al., 2009; Datta and Christopher, 2011). This perspective is consistent with Milgrom and Roberts (1995) who argued that different types of activities are complementarities if doing one activity increases the overall value in doing more of other activities. Complementarities that define value creation system form a piecemeal or linear approach that suggests independently selecting decision variables to maximize profit and assuming that other choice variables are fixed at present levels to a network approach of interrelationships of activities that focuses on maximizing ultimate customer value, as well as a mechanism for sharing generated revenues among participating members. A coordinated choice of design variables should result in higher gains than a series of uncoordinated variables (Lee et al., 1997; Lehoux et al., 2014). If participating members adopt a set of variables that are not complementary, it would likely suffer a reduction in overall profitability. According to Fisher (1997), chain members who have a choice of supply chain system which is not aligned with their supply chain strategy are less successful than chain members that have aligned their supply chain choice with strategy.

    The nature of interdependency of design variables in supply chain collaboration (Simatupang and Sridharan, 2005; Wong et al., 2009) provokes the appropriateness of the application of complementarity theory. The chain members must recognize complementary relationships presented among various design variables to attain superior interorganizational architecture (Lehoux et al., 2014). They have to ensure that all of these complementary design variables fit with each other to form a coherent operating system which leads to an increase in overall profitability. However, complementarity theory has not been used before to explain the complex relationship among design variables in a collaborative setting for the success of supply chain collaboration. The application of complementarity theory is thus proposed to explain why multiple design variables need to be adopted in supply chain collaboration. In the next section, complementarity theory is utilized for explaining how different design variables can work together to contribute to the success of supply chain collaboration.


    In this research, supply chain collaboration is a network consisting of key players, such as a retailer and a supplier who partner with each other to improve the value of the entire system. Collaboration value refers to the value accrued by the participants of collaboration. The measurement of value creation is constrained to the financial indicators of each participant. The main purpose of the model formulation is to specify the concept of complementary changes in a set of relationships among design variables in relation to the payoff function of the participant.

    The concept of collaboration model provides a basis for understanding linkages between design variables, interorganizational parameters, and performance measures. Design variables serve as relevant value drivers which contribute to the attainment of collaborative performance measures. A set of design variables has to be carefully selected based on its role of influencing collaboration value directly and significantly. Complementarities among design variables provide a new relationship between a retailer and a supplier which enables both parties to collect and store more information about each other and their customers, and provide products according to customer preference. As a result, customers will shop more for the best buy with minimum mismatch costs of supply and demand. In this research, a set of design variables is adopted from a framework of collaboration developed by Simatupang and Sridharan (2005; 2008). A framework of collaboration consists of key design variables, including collaborative decision making, integrated process capability that provides products or services, information sharing associated with these processes, incentive alignment, and a collaborative performance system. A collaboration model is then defined as a description of key design variables and their linkages to intermediate variables, and finally to profitability.

    The motivation for collaboration amongst the chain members mainly stems from the potential profit from better match supply with demand at lowered operating costs. The main determinant of supply chain revenue is the size of the customer base. A customer base represents the current flow of customers who reasonably expect the goods or services of a business when planning a purchase. It is common that chain members offer a value proposition that serves as a statement of the functional, emotional and self-expressive benefits of goods and services that provide value to the target customer. The better the chain members offer value proposition manifesting in goods or services attributes that fits to customers’ preferences, the larger realized revenue. The underlying assumptions of the direct relationship between customer base and revenue include customers buying the product if they perceive that its value is greater than the product’s price; customers buying if the supply chain matches customer preferences with appropriate product offerings; the supply chain has the ability to create customized offers that steer consumers to the right goods or services goods at the right moment, at the right price, and in the right channel; and the customer base is composed of customer loyalty and future monetary value. As an illustration, Dell tracks sales and customer feedback data from online sales that enable Dell to discover new ways of offering consumers a chance to configure PCs according to their specific computing needs and a better price on their PCs (Strickland, 1999).

    3.1 A two-Echelon Collaborative Model

    We consider our supply chain as a two-echelon supply chain consisting of one upstream member and one downstream member. The upstream member (i.e., a supplier) is responsible for building production capacity and delivery capability. The supplier sells a common generic product to the downstream member (i.e., a retailer or an assembler) at the wholesale price. Afterwards, the retailer adds service values to the product and decides on the retail prices to the customers. Here the retailer shares his own private information about demand and other sensitive data such as forecast, cost structure, and market promotional strategy with its supplier. Furthermore, we assume each party engages in process innovation to provide products according to customer preference at the right quantity. Chain members also discuss and arrange incentive schemes for balancing risks and benefits associated with collaboration. This includes how they monitor a common platform of performance metrics for fostering accountability and administering incentives according to participant contribution. The collaborative supply chain works well only if the risks, costs, and rewards of doing collaborative business are distributed equitably across the network.

    In fact, in a real situation, the assembler and the supplier collaboratively develop demand forecasting and inventory management (Callioni and Billington, 2001; Kapuscinski et al., 2004). For example, CPFR (Collaborative Planning, Forecasting, and Replenishment) is a collaborative model shared by the buyer and supplier through which private information, such as inventory status, demand forecast, and promotion orientation, is shared and replenishment decisions are generated (Danese, 2007; Derrouiche et al., 2008). The application of complementarity theory to this typical problem setting is illustrated based on real world examples drawn from the practice of supply chain collaboration. This is consistent with the approach taken by Barua et al. (1996). They developed a model of business value for business process reengineering. The model suggests that the value is a function of a set of hierarchical variables starting from design variables to intermediate variables. The value is judged by traditional performance measures such as profitability, unit operating cost, and capital and non-capital costs. The model also implies that improved financial performance is a result of operational excellence based on a business process reengineering initiative.

    The payoff of collaboration depends on the combination of efforts of the upstream and downstream members of the supply chain. The payoff of collaboration is a reduced form of profit function of collaboration (Milgrom et al., 1991). The supply chain faces three factors of profit maximization, including the customer base (B), the net profit per unit sold (π), and capital investment (K). The collaborative payoff function is shown in Figure 1 and denoted by

    Π(p, I, D, P, M, C) = Bπ – K = B(dûu(S, T, p), dâa(F, Q)) (p – o(I, D, P, M, C)) – K(I, D, P, M, C)

    with the following notation:

    • p: unit price;

    • I: level of information-sharing which involves the extent to which chain members will freely and actively provide useful information with a common data model and semantics to each other;

    • D: scope of collaborative decision-making which assigns proper decision rights and delegation, including decision support systems;

    • P: level of process innovation consisting of common supply chain and product development processes to deliver right products at the right time;

    • M: level of collaborative performance system which is composed of common performance metrics and monitoring across chain members for performance accountability;

    • C: level of incentive redesign, i.e. the extent to which applications help and identify and record chain member contribution to value creation for the purpose of sharing risks, costs, and benefits;

    • K(I, D, P, M, C): capital cost of collaboration;

    • B(dûu, dâa): size of customer base;

    • dûu: the capability of market mediation, i.e. the ability to understand demand patterns and then influence customers’ demand toward available supply using the levers of price, promotion, and product;

    • dâa: level of product desired attributes, such as the ability to match product attributes and customer preference;

    • S: level of demand sensing, such as the ability to capture and comprehend structured and unstructured data from customers and partners in order to identify demand patterns and exemptions;

    • T: timeliness;

    • F: product features;

    • Q: product quality;

    • o(I, D, P, M, C): unit operating cost.

    cost. A key determinant of profitability in Figure 1 is the size of the customer base. The customer base provides the basis for predicting revenues and is often expressed as a function of product attributes and how well the chain members satisfy demand realization. It is assumed that the customer base has an ideal product as well as an ideal demand. Customers choose products and services based on product features, delivery and flexibility, quality, aesthetics, and price attributes (Hayes and Wheelwright, 1984). The function of the customer base is similar to the model presented by Lee et al. (2000), who proposed that the customer base depends on the proximity of estimated customer demand to the actual customer demand. The actual customer demand reflects customer preference. Preferences are the main factors that influence consumer demand. The customer base increases when chain members’ ideal product attribute is closer to the ideal demand attribute. It is assumed that the collaborative arrangements enable chain members to learn customer preferences and express the customer’s needs and use various methods to anticipate their interests and to offer customized service. Preferences refer to certain characteristics any consumer wants to have in a product to make it preferable to them. Customer preferences are expectations that drive customer purchasing decisions (Sudharshan and Mild, 2017). Purchasing expresses closeness of customer preferences and offering attributes. Offering attributes in the model are not limited to quality, flexibility, and variety, but also include aesthetics, pleasure, fantasy, and fun.

    The level of product desired attributes addresses customer preferences to accurately reflect choice behavior for product attributes that customers care about. For a product to succeed, it must be unique and have desirable attributes that are communicated to the consumer. A set of ideal product attributes is denoted as a = [aF, aQ] for features and quality. Chain members produce a product denoted as â = [âF, âQ]. The distance between a and â denoted as dâais a measure for the level of product desired attributes. Similarly, chain members use demand signal û = [ûS, ûT, ûP] for demand sensing, timeliness, and price to estimate ideal demand u = [uS, uT, uP]. The distance between u and û denoted as (dûu represents chain members’ capability of market mediation to produce and deliver products in order to match the estimated customer demand.

    3.2 Assumptions of the Model

    The model as shown in Figure 1 indicates that higher performance of collaboration is affected by multiple design variables through a set of intermediate variables. Chain members should choose a set of appropriate levels of design variables in order to increase overall performance of collaboration. The nature of changes in design variables depend on the assumption underlying the complementarity of the relationship. Several assumptions relating to complementarity are outlined as follows:

    Assumption 1.The size of customer base B is increasing and supermodular in (-dûu, -dâa).

    Customer base increases when chain members estimate customer demand is closer to actual customer demand (Fisher, 1997) and when chain members deliver product that is closer to customer preference (Govindarajan and Gupta, 2001). The customer base increases as a function of the number of complementary components of the product desired attributes and the collaborative supply chain effect. This supply chain effect on demand is called market mediation, i.e. the matching of quantity of product supplied through the chain to that which is demanded (Fisher, 1997; Kopczak and Johnson, 2003). Chain members leverage the potential for value creation by offering complementary bundles of product attributes matching with customer preference (product development view) and the capability of market mediation (sense and response view). They are often related to the use of supply chain visibility to shape demand and product development to provide suitable products in order to increase revenue.

    The notion of product desired attributes can span different markets and can be a key influence on the likely success of a product offering in a given market. The value of a product is measured by the utility that the customer derives from buying some combination of those attributes. To improve financial performance, a firm must identify and deliver attributes that are valued by customers. Due to standardized platforms, for example, it is technically easy for Dell and its suppliers to integrate product offerings at the service point and market mediation across the supply chain (Dell and Fredman, 1999). This concept is consistent with Simchi-Levi et al. (2007) who defined supply chain management as a set of approaches utilized to efficiently integrate chain members, so that merchandise is produced and distributed in the right quantities, to the right locations, and at the right time, in order to minimize system-wide costs while satisfying service level requirements. This definition suggests that supply chain management is aimed at installing beneficial collaboration and seamless linkages among multiple participants operating at different levels of the supply chain to satisfy customer preference in the right quantities.

    Assumption 2. The capability of market mediation - dûu is supermodular in (S, -T, p).

    The capability of market mediation measures to what extent the chain members are able to match supply with demand using the levers of price, promotion, and product. The focus of market mediation is demand sensing and shaping to reduce the gap between expectation of customer demand (û) and actual customer demand (u). Tactically, the capability of market mediation is to complement market sensing for planning the demand, timeliness of supply by closing the loop through execution, and dynamic pricing. The supermodularity of the capability of market mediation in S, -T, and p implies that the effect of a higher level of demand sensing on the capability of market mediation will be more significant if it is complementary with timeliness of product delivery and the practice of dynamic pricing. For example, Dell maintains realtime visibility in its supply chains about customer orders as well as inventory levels at present and in the immediate future on an hourly basis (Kapuscinski et al., 2004). Dell has a higher level of demand sensing to know customer demand in advance. Dell shares this demand information with its suppliers who take necessary action to deliver products in a timely manner. In case Dell does not have enough stock for customer configuration, Dell informs its customer on delayed shipping or offers the customer alternative components at a discount. Dell is able to persuade its customers to purchase other components that can meet their needs through dynamic pricing.

    Assumption 3.Level of demand sensing S is supermodular in(I, D, M, C).

    Demand sensing becomes critical for a supply chain to understand different factors of existing and potential customers’ choice behavior by capturing different demand signals. The scope of demand sensing can range from demand forecasting for future purchasing, identification of market segmentation, estimation of the price a customer is willing to pay, and identification of events that affect demand. Level of demand sensing refers to the ability of the chain members to capture and comprehend structured and unstructured data from customers and partners in order to identify demand patterns. For example, the advance of Customer Relationship Management (CRM) enables Amazon and its partners to track and trace their consumers' preferences with better accuracy, and use that preference data to provide products and services that create the potential for retaining, cross-selling, and upselling (Simchi-Levi et al., 2007). To better estimate ideal customer demand, chain members are involved in sharing information with their customers and partners (I), assigning decision rights for making accurate estimations (D), monitoring the accuracy of demand sensing (M), and designing incentives to motivate better accuracy in demand decision (C).

    Assumption 4.Product timeliness T is decreasing and submodular in (I, D, P, M, C).

    Timeliness represents a response-time metric as a measure of success in meeting customer commitment. Timeliness is most useful when embedded in a collaborative performance system (M) that represents a supply chain process. Innovations in supply chain processes determine the criticality of timeliness depending on the requirement of fashion or functional products (Fisher, 1997). Timeliness is composed of a series of internal manufacturing and processing lead times and external distribution and transportation lead times found at various stages of the supply chain. Delivery to end customers should be determined with regards to the customer’s specification of timeliness as defined by an on-time delivery window. Since the sum of timeliness is a result of actions taken by chain members from planning time, procurement time, production time, and delivery time, a set of response metrics need to be assigned to key roles of chain members that have process execution, monitoring and tracking responsibilities (Callioni and Billington, 2001). Ultimate payment obtained from end customer for product timeliness should be tied to the level of incentive design (Narayanan and Raman, 2004). Incentive design also relates to penalty costs for early and late deliveries (Fisher, 1997). It can be summarized that changes in collaborative decision- making (D), collaborative performance system (M), process innovations (P), information sharing (I), and incentive alignment (C) have a complementary effect in reducing timeliness.

    Assumption 5.Level of product desired attributes - dâais supermodular in (F, Q).

    The supermodularity of the level of product desired attributes in F and Q implies that the effect of increasing variety of product features on the level of product desired attributes will be more significant if it is matched by a high quality of product (Kopczak and Johnson, 2003). This assumption implies that a collaborative supply chain which can deliver a set of product features and high product quality is likely to have a higher level of ability to meet customer preference (Govindarajan and Gupta, 2001).

    Assumption 6.Product feature F is supermodular in (I, D, P, M, C).

    Chain members exchange information (I) about product features and linking this information to a corresponding chain member (i.e., the upstream member) who has responsibility (D) for product design and development processes (P). The downstream member will be able to identify the optimal level of F through maximizing the expected value of incentive (C). Furthermore, a collaborative performance system (M) needs to be embedded in product development in order to align the actions of chain members to eventual outcomes of product features, not only maximizing fit of product feature to customer requirements but also minimizing time to market of new products (Hauser, 2001).

    Assumption 7.Product quality Q is supermodular and increasing in (I, D, P, M, C).

    Chain members of collaboration need to recognize quality requirements of internal and external customers, and define quality metrics which assess quality performance in satisfying their requirements (Deming, 2000). A collaborative performance system (M) is needed to specify and monitor quality metrics to encourage chain members to focus on quality output perceived by end customers (Ramanathan, 2014). Since the market rewards payment of price for higher product quality, successful collaboration depends on the ability of chain members to consistently improve customer requirements for product quality (Callioni and Billington, 2001). Thus, chain members can take advantage by producing product at the level of quality demanded by the consumer at a lower cost. Chain members also need to design their incentive systems to explicitly reward the achievement of quality goals (Narayanan and Raman, 2004). Consequently, quality initiatives increasingly adopt complementarity changes in the design of interorganizational processes (P), autonomy of quality improvement (D), substantial information sharing about quality requirements and metrics (I), higher level of a collaborative performance system (M), and increasing the scope of incentive design (C).

    Assumption 8.The capital cost of collaboration K(I, D, P, M, C) is increasing and submodular in its arguments.

    Supply chain collaboration often incurs investments in interorganizational systems development and training. Developing an information sharing system, innovating supply chain processes, reallocation of decision rights, installing a collaborative performance system, and designing incentive schemes require reorientations, adjustments, and training in order to be able to carry out an effective collaboration (Callioni and Billington, 2001). The submodular effect on collaboration cost implies that the increases with each design variable are compensated by its cost efficiency by increasing all the variables at the same time.

    Assumption 9.The unit operating cost o(I, D, P, M, C) is decreasing and submodular in its arguments.

    Chain members do incur various operating costs of material, labor, rent, or overhead that change in a traceable and measurable way due to changes in the volume of production units or the amount ordered. Many operating costs are often independent of the amount actually sold. Making proper improvements in process design coupled with higher level of information sharing does reduce operating costs as chain members can simultaneously lower inventory and improve customer service. However, the submodularity of operating cost on process redesign and information sharing needs to be bundled with the level of decision rights assignment, performance monitoring, and incentive alignment. For example, assigning the supplier with decision rights for timing and quantity of delivery does improve supply chain efficiency (Lee et al., 1997). Furthermore, the level of incentive alignment encourages the supplier to deliver higher quality at lower cost by improving its production and distribution processes which often take place before demand is realized (Cho and Gerchak, 2005).

    Assumption 10.The assumption of strong supermodularity where it applies.

    Strong supermodularity refers to the conditions where if d(f, g) is supermodular on (f, g), f(x1, …, xn) is supermodular on (x1, …, xn), and g(y1, …, yn) is supermodular on (y1, …, yn), then d is supermodular on (x1, …, xn) (y1, …, yn). It is assumed that strong supermodularity exists in this model for all multi-layered functions. Barua et al. (1996) provided a complete condition and proof.

    3.3 Adaptive, Agile, and Lean Collaboration

    The predetermined assumptions imply that chain members need to choose all design variables in a coordinated manner in order to improve the profit function (Christopher and Peck, 2004). There are three options available for chain members to arrange design variables dependent on the price setting. The first focus is to increase the market base of the supply chain by coordinating all design variables without increasing the price. This supply chain is called adaptive collaboration as it operates in a highly competitive market and the best option to take is to coordinate proper selection of design variables to improve better performance (Lee, 2004). The following theorem shows that design variables (I, D, P, M, C) complement each other to attain better overall performance when the price is fixed.

    Theorem 1. Consider a collaborative supply chain under a fixed market price. Suppose that (i) -dûu is supermodular in (S, -T), (ii) -dâais supermodular in (F, Q), and (iii) p > o, then Π(I, D, P, M, C) is supermodular in (I, D, P, M, C).

    Proof: Since (i) B is supermodular in (I, D, P, M, C), (ii) - o is supermodular in (I, D, P, M, C), (iii) Π is positive, and –K is supermodular in (I, D, P, M, C), then Π is supermodular in (I, D, P, M, C).

    The second theorem operates when the market responds to the higher price for better timeliness, product quality, and product variety. In this case, chain members treat price as a decision variable which is akin to an agile supply chain (Lee, 2004; Christopher and Ryals, 2014). Agility is an ability to have visibility of demand, flexible and quick response, and streamlined supply chain operations. The agile supply chain helps chain members to meet the unpredictable demand of the end customers (Christopher, 2000; Purvis et al., 2014).

    The high level of market mediation and product development can profitably satisfy customer demand because they have the ability to meet the demand of customers for ever-shorter delivery times and to synchronize processes during the peaks and troughs of the demand. The availability of better timeliness and higher quality product to customers result in the increase of demand for high priced products compared to low priced products. The increase in price results in higher demand for high quality products compared to the same increase in price for low quality products.

    Theorem 2. Consider a collaborative supply chain when price is a decision variable. Suppose that (i) -Mdûu is supermodular in (S, -T, p), (ii) -dâa is supermodular in (F, Q), and (iii) p < o, then Π(p, I, D, P, M, C) is supermodular in (p, I, D, P, M, C).

    Proof: Let x = (I, D, P, M, C) then Π = B(p, x)(po(x)) - K(x). B is supermodular in (p, x) and increasing in (p, x), B(p, x) is supermodular in (p, x) by assumption, - k(x) is supermodular in (x), (p – o(x))B(p, x) is supermodular in (p, x).

    The last theorem relates to a lean supply chain which operates in the market which is sensitive to price (Christopher and Peck, 2004; Christopher and Ryals, 2014; Purvis et al., 2014). The customer base increases as the chain members are able to improve product attributes when price is lower than when price is higher. The reduction in price results in a larger customer base when the product quality is higher compared to the same price reduction when the product quality is lower.

    Theorem 3. Consider a collaborative supply chain when there is a decrease in price. Suppose that (i) -dûu is log-supermodular in (S, -T, -p), (ii) -dâais supermodular in (F, Q), (iii) K(I, D, P, M, C) is submodular in (I, D, P, M, C), then (a) π = max(pεP)Π(I, D, P, M, C) is supermodular in (I, D, P, M, C), and (b) p is decreasing in (I, D, P, M, C).

    Proof: Part (a), let x = (I, D, P, M, C) then Π(p, x) = B(p, x)(po(x)) - K(x). If price is a decision variable, then the profit of the collaborative supply chain after optimizing over the decision variables p and x is π = max(pεP)Π(p, x)+K(x) = max(pεP)B(p, x)(po(x)) = exp(log (max(-p: -p<-o, --P)B(p, x)(po(x)))) = exp(max(-p: -p< -o, -- P)(logB(p, x)(po(x)))). Because logB(p, x) is supermodular in (-p, x) from the assumption and o(x) is submodular in x, therefore po(x) is supermodular in (-p, h). Since B > 0, then π > o can be considered to maximize Π(p, x).

    Since po(x) is a positive increasing supermodular function, then po(x) is also log supermodular in (-p, h) (Topkis, 1995). Therefore, log(B(p, x)(po(x))) = logB(p, x) + log(po(x)) is supermodular in (-p, x). Under the maximization operation, if a group of complementary variables are optimized under a subset of complementary variables, then the remaining variables are still complementary (Topkis, 1978). It can be stated that max(pεΠ)logB (p, x)(po(x)) is supermodular in (x). Since K is submodular in (x), then π(p, x) = max(pεP)Π(I, D, P, M, C) + K(x) is supermodular in (I, D, P, M, C).

    Part (b), logB(p, x)(po(x)) is supermodular in (x) and supermodular in (-p, x), therefore –p in increasing in (x). Since K(x) is not a function of p, argmax(-pε-P)(log(B(p, x)(po(x)))) = argmax(-p:-p<-o, -pε-P)(B(p, x)(p – o(x))) = argmax(-pε-P)Π(p, x).


    The result of this paper provides a new perspective on design decisions in collaboration under condition of fixed and variable prices. Several advantages of the application of complementarity theory to supply chain collaboration are outlined as follows. First, chain members would be informed about the importance of complementary synergy between design variables of collaboration that affect performance. Although previous studies (Callioni and Billington, 2001; Corbett et al., 1999) have recognized the value of this synergy, this research theoretically shows that the interactions of design decisions at different maturity levels have direct and indirect impact on supply chain performance. Designing an information-sharing system is essential to make information available to all participants concerned. Information should be made available for easy access in a desirable form and used to improve the quality of decision- making. For example, the synergy between information- sharing (e.g., demand data, sales data, order status, delivery plan, and inventory level) and coordinated decision-making leads to reduction in the inefficiencies found in the practice of less collaborative relationships. Second, the model involves the choice of incentive redesign for equitably sharing risks, costs, and benefits of collaboration. Chain members might develop toolkits for designing productive incentives that encourage efforts to create savings or increase revenue (Barua and Whinston, 1998).

    In addition, synergy between coordinated decision making and integrated processes enable chain members to achieve on both the costs and services from an operational perspective. Coordinated decision-making can be defined as the extent to which chain members, through face-to-face meetings and virtual discussion, are able to arrange critical decisions at planning and execution levels for achieving efficiency. The enhancement of integrated processes can help the alignment of responsibilities and resources to ensure seamless flow of material to end customers. Chain members with higher levels of collaborative relationships are able to achieve a better overall performance. In addition to this, chain members can anticipate how proposed changes would affect them in terms of costs and risks that might cause them to have little incentive to cooperate as a consequence of the lack of an incentive alignment agreement. The model suggests chain members to negotiate and design commercial issues of sharing costs and benefits, and benefitsharing procedures.

    The practical use of the model addresses how participating members streamline their collaborative practices. The first stage involves the design of a collaborative performance system in terms of tangible and intangible common metrics based on a common strategic intent of the participants. Secondly, the design of the supply chain processes is carried out after taking into account the entire network of activities and the levels of service. In the next stage, chain members can work to develop the capability of market mediation as a basis to design the level of timeliness and demand sensing to determine the quantity and timing of material flow. This is necessary to understand the capabilities required to move materials in a timely fashion. In the third step, opportunities to improve the level of product desired attributes have to be carefully identified after taking into account the production and distribution requirements.

    The implication of this research is on the importance of collaboration payoff function and the practical use of model. Only through explicit choices of design variables embedded in the payoff function can value creation through collaboration be exploited. The contribution of participating members of collaboration in the valuecreating system is a result of creative and innovative decisions. These innovations include the development of new products, new supply chain processes, new transaction exchange mechanisms, as well as new capability of market mediation. The design variables represent key opportunities for creating new value of collaboration and are derived from new relationships among participants in the collaborative supply chain.


    Collaboration value is, to a large extent, determined by the specific design variables employed by participating members of collaboration. Specifically, certain key aspects of the collaboration model play a key role and possess the power of influencing collaboration value directly and significantly. In this research, a collaboration model is offered to value the payoff function of collaboration, taking into account a set of key design variables, namely information sharing, collaborative decision-making, process innovations, a collaborative performance system, and incentive design. We have identified the relationships of these multiple design variables and intermediate variables as well as the effect on the collaboration payoff. The assumption of synergistic effect stems from the combination of information and know-how of participants causing externalities on economies of coordinated decision-making among chain members. This suggests that chain members need to jointly convey the pattern of complementarities that govern the value of collaboration under one of the three types of collaboration, namely adaptive, agile, and lean supply chains.

    Supply chain collaboration represents the selection of design variables that affects the capabilities of chain members to deal with typical problems that cannot be addressed effectively and efficiently alone. The main contribution of this research is to provide a framework for explaining complementary design settings of supply chain collaboration that incorporates price sensitivity to exhibit agile and lean characteristics. The proposed model provides greater insight into how supply chain design can help describe, explain, and predict collaborative activities and outcomes at the supply chain level. The value of supply chain collaboration is the ability to deal with unknown customer expectations and the implications of cost and efficiency. Collaboration makes sense when chain members provide a much better customer service to their customers through information sharing and coordinated decision-making to quickly respond to customer expectations and anticipate customer needs.

    The current research lays the foundation for future work in the area of complementarity in collaboration. In the first step, the design variables can be deconstructed into different parts which belong to each side of participants. Differentiated parts of design variables can be linked more firmly to the collaborative contract by allowing either the upstream member or the downstream member to influence the success of collaboration. This is important with regards to environmental changes that can be encountered by chain members. These changes will impact the participant strategies as well as the payoff function of collaboration. Therefore, new terms and conditions of design variables need to be renegotiated. Secondly, it will be valuable to further analyze the value of collaboration for customers which is not included in the model. The success of collaboration derives from a fit not only between the firm and its collaborating partners, but also between the firm and its customers. The fit is all about identifying customer value creation and defining how customer value creation is affected by collaborative efforts. In the third step, the theoretical work done here should be complemented with more in-depth empirical research on design and implementation of supply chain collaboration.

    With the application of complementarity theory, it is clear for chain members that the improvement of one design variable in the presence of another type of design variable has potential to gain greater returns. However, the model excludes design, monitoring, and compliance costs, as well as different levels of risks of the supply chain (Wakolbinger and Cruz, 2011). The architectural approach could be developed to suit the requirements of collaboration to appropriate design variables. The main effect and interaction effects of design decisions on performance may vary under different conditions of a supply chain. Nevertheless, the critical problem remains with how chain members select appropriate design variables that significantly satisfy customer requirements at the lowest possible cost. No single design variable can be seen disjointedly from others, but they have to be viewed through both the design variable effect and the interaction effect. Failure to solve design decisions results in costly inefficiency. Through more open and frequent exchange of information with the understanding of complementary synergy, chain members can eliminate many misaligned problems of design variables and ensure ongoing improvement.

    Another limitation of the model is to overlook the design of the decentralized model (Schmitt et al., 2015) of a supply chain that requires coordination mechanisms that need to be designed in a decentralized way that authorizes individual members to make their own decisions. The current model is based on the assumption of complementarity of design variables at different levels of maturity that leads to better performance. There is little attention to consider agency costs (Narayanan et al., 2005) associated to decentralized or centralized coordination mechanisms. This warrants further research in order to find an appropriate combination of centralized or decentralized design variables to balance advantages and disadvantages of both approaches for improving supply chain performance and providing better incentive alignment.


    The authors would like to thank Chi-Hyuck Jun as Editor-in-Chief and three anonymous referees who kindly reviewed the earlier version of this manuscript and provided valuable suggestions and comments.



    A value model of complementary design variables of collaboration.



    1. E. Anderson , S.D. Jap (2005) The dark side of close relationships., MIT Sloan Manag. Rev., Vol.46 (3) ; pp.75-82
    2. S. Athey , S. Stern (1998) An Empirical Framework for Testing Theories about Complementarity in Organizational Design., National Bureau of Economic Research,
    3. S. Bharadwaj , A. Bharadwaj , E. Bendoly (2007) The performance effects of complementarities between information systems, marketing, manufacturing, and supply chain processes., Inf. Syst. Res., Vol.18 (4) ; pp.437-453
    4. A. Barua , C.H.S. Lee , A.B. Whinston (1995) Incentives and computing systems for team-based organizations., Organ. Sci., Vol.6 (4) ; pp.487-504
    5. A. Barua , C.H.S. Lee , A.B. Whinston (1996) The calculus of reengineering., Inf. Syst. Res., Vol.7 (4) ; pp.409-428
    6. A. Barua , A.B. Whinston (1998) Complementarity based decision support for managing organizational design dynamics., Decis. Support Syst., Vol.22 (1) ; pp.45-58
    7. J.A. Black , K.B. Boal (1994) Strategic resources: Traits, configurations and paths to sustainable competitive advantage., Strateg. Manage. J., Vol.15 (1) ; pp.131-148
    8. R.D. Buzzell , J.A. Quelch , W.J. Salmon (1990) The costly bargain of trade promotion., Harv. Bus. Rev., Vol.68 (2) ; pp.141-149
    9. G. Callioni , C. Billington (2001) Effective collaboration: Hewlett-packard case study., OR/MS Today, Vol.28 (5) ; pp.34-39
    10. R.K. Cho , Y. Gerchak (2005) Supply chain coordination with downstream operating costs: Coordination and investments to improve downstream operating efficiency., Eur. J. Oper. Res., Vol.162 (3) ; pp.762-772
    11. B. Choi , S.K. Poon , J.G. Davis (2008) Effects of knowledge management strategy on organizational performance: A complementarity theory-based approach., Omega, Vol.36 (2) ; pp.235-251
    12. M. Christopher (2000) The agile supply chain: Competing in volatile markets., Ind. Mark. Manage., Vol.29 (1) ; pp.37-44
    13. M. Christopher , H. Peck (2004) Building the resilient supply Chain., Int. J. Logist. Manag., Vol.15 (2) ; pp.1-14
    14. M. Christopher , L.J. Ryals (2014) The supply chain becomes the demand chain., J. Bus. Logist., Vol.35 (1) ; pp.29-35
    15. C.J. Corbett , J.D. Blackburn , L.N. Van Wassenhove (1999) Partnerships to improve supply chains., Sloan Manage. Rev., Vol.40 (4) ; pp.71-82
    16. T. Dai , S.H. Cho , F. Zhang (2016) Contracting for on-time delivery in the U.S. influenza vaccine supply chain., Manuf. Serv. Oper. Manag., Vol.18 (3) ; pp.332-346
    17. P. Danese (2007) Designing CPFR collaborations: Insights from seven case studies., Int. J. Oper. Prod. Manage., Vol.27 (2) ; pp.181-204
    18. P.P. Datta , M.G. Christopher (2011) Information sharing and coordination mechanisms for managing uncertainty in supply chains: A simulation study., Int. J. Prod. Res., Vol.49 (3) ; pp.765-803
    19. P.J. Daugherty , R.G. Richey , A.S. Roath , S. Min , H. Chen , A.D. Arndt , S.E. Genchev (2006) Is collaboration paying off for firms?, Bus. Horiz., Vol.49 (1) ; pp.61-70
    20. M. Dell , C. Fredman (1999) Direct From Dell: Strategies That Revolutionized an Industry., Harper Collins,
    21. R. Derrouiche , G. Neubert , A. Bouras (2008) Supply chain management: A framework to characterize the collaborative strategies., Int. J. Comput. Integrated Manuf., Vol.21 (4) ; pp.426-439
    22. W.E. Deming (2000) Out of the Crisis., The MIT Press,
    23. F.Y. Edgeworth (1881) Mathematical Psychics., Kegan Paul,
    24. M.L. Fisher (1997) What is the right supply chain for your product?, Harv. Bus. Rev., Vol.75 (2) ; pp.105-116
    25. V. Govindarajan , A.K. Gupta (2001) Strategic innovation: A conceptual road map., Bus. Horiz., Vol.44 (4) ; pp.3-12
    26. S.V. Grabski , S.A. Leech (2007) Complementary controls and ERP implementation success., Int. J. Account. Inf. Syst., Vol.8 (1) ; pp.17-39
    27. J.R. Hauser (2001) Metrics thermostat., J. Prod. Innov. Manage., Vol.18 (3) ; pp.134-153
    28. R.H. Hayes , S.C. Wheelwright (1984) Restoring Our Competitive Edge: Competing Through Manufacturing., Wiley,
    29. J.E. HernA ndez , J. Mula , R. Poler , A.C. Lyons (2014) Collaborative planning in multi-tier supply chains supported by a negotiation-based mechanism and multi-agent system., Group Decis. Negot., Vol.23 (2) ; pp.235-269
    30. B. Holmström , P. Milgrom (1994) The firm as an incentive system., Am. Econ. Rev., Vol.84 (4) ; pp.972-991
    31. R.P. Kampstra , J. Ashayeri , J.L. Gattorna (2006) Realities of supply chain collaboration., Int. J. Logist. Manag., Vol.17 (3) ; pp.312-330
    32. R. Kapuscinski , R.Q. Zhang , P. Carbonneau , R. Moore , B. Reeves (2004) Inventory decisions in Dell ?(tm)s supply chain., Interfaces, Vol.34 (3) ; pp.191-205
    33. L.R. Kopczak , M.E. Johnson (2003) The supply-chain management effect., MIT Sloan Manag. Rev., Vol.44 (3) ; pp.27-34
    34. M. Kurtulu Y , S. AolkA1/4 , B.L. Toktay (2012) The value of collaborative forecasting in supply chains., Manuf. Serv. Oper. Manag., Vol.14 (1) ; pp.82-98
    35. D.M. Lambert , M.A. Emmelhainz , J.T. Gardner (1999) Building successful logistics partnerships., J. Bus. Logist., Vol.20 (1) ; pp.165-181
    36. C.H. Lee , A. Barua , A.B. Whinston (2000) The complementarity of mass customization and electronic commerce., Econ. Innov. New Technol., Vol.9 (2) ; pp.81-109
    37. H.L. Lee (2004) The tripe-A supply chain., Harv. Bus. Rev., Vol.82 (10) ; pp.102-112
    38. H.L. Lee , V. Padmanabhan , S. Whang (1997) Information distortion in a supply chain: The bullwhip effect., Manage. Sci., Vol.43 (4) ; pp.546-558
    39. N. Lehoux , S. D ?(tm)Amours , A. Langevin (2014) Inter-firm collaborations and supply chain coordination: Review of key elements and case study., Prod. Plann. Contr., Vol.25 (10) ; pp.858-872
    40. P. Milgrom , Y. Qian , J. Roberts (1991) Complementarities, momentum, and the evolution of modern manufacturing., Am. Econ. Rev., Vol.81 (2) ; pp.84-88
    41. P. Milgrom , J. Roberts (1990) The economics of modern manufacturing: Technology, strategy, and organization., Am. Econ. Rev., Vol.80 (3) ; pp.511-528
    42. P. Milgrom , J. Roberts (1995) Complementarities and fit: Strategy, structure, and organizational change., J. Account. Econ., Vol.19 (2-3) ; pp.179-208
    43. P. Milgrom , C. Shannon (1994) Monotone comparative statics., Econometrica, Vol.62 (1) ; pp.157-180
    44. V.G. Narayanan , A. Raman (2004) Aligning incentives in supply chains., Harv. Bus. Rev., Vol.82 (11) ; pp.94-102
    45. V.G. Narayanan , A. Raman , J. Singh (2005) Agency costs in a supply chain with demand uncertainty and price competition., Manage. Sci., Vol.51 (1) ; pp.120-132
    46. S. Netessine , F. Zhang (2005) Positive vs. negative externalities in inventory management: Implications for supply chain design., Manuf. Serv. Oper. Manag., Vol.7 (1) ; pp.58-73
    47. S. Netessine , N. Rudi , Y. Wang (2006) Inventory competition and incentives to back-order., IIE Trans., Vol.38 (11) ; pp.883-902
    48. J.A. Palma-Mendozaa , K. Neailey , R. Roy (2014) Business process re-design methodology to support supply chain integration., Int. J. Inf. Manage., Vol.34 (2) ; pp.167-176
    49. L. Purvis , J. Gosling , M.M. Naim (2014) The development of a lean, agile and leagile supply network taxonomy based on differing types of flexibility., Int. J. Prod. Econ., Vol.151 ; pp.100-111
    50. U. Ramanathan (2014) Performance of supply chain collaboration: A simulation study., Expert Syst. Appl., Vol.41 (1) ; pp.210-220
    51. U. Ramanathan , A. Gunasekaran , N. Subramanian (2011) Supply chain collaboration performance metrics: A conceptual framework, Benchmarking., Int. J., Vol.18 (6) ; pp.856-872
    52. A.J. Schmitt , S.A. Sun , L.V. Snyder , Z.M. Shen (2015) Centralization versus decentralization: Risk pooling, risk diversification, and supply chain disruptions., Omega, Vol.52 ; pp.201-212
    53. M. Sepehri (2012) A grid-based collaborative supply chain with multi-product multi-period production-distribution., Enterprise Inf. Syst., Vol.6 (1) ; pp.115-137
    54. P. Setia , S. Vickery , C. Droge , S. Vallabhajosyula (2006) Complementarities between organizational IT and supply chain initiatives: An empirical test, Proceedings of the 2006 Academy of Management Annual Meeting,
    55. T.M. Simatupang , R. Sridharan (2005) An integrative framework for supply chain collaboration., Int. J. Logist. Manag., Vol.16 (2) ; pp.257-274
    56. T.M. Simatupang , R. Sridharan (2008) Design for supply chain collaboration., Bus. Process. Manag. J., Vol.14 (3) ; pp.401-418
    57. R. Sridharan , T.M. Simatupang (2013) Power and trust in supply chain collaboration., International Journal of Value Chain Management, Vol.7 (1) ; pp.76-96
    58. D. Simchi-Levi , P. Kaminsky , E. Simchi-Levi (2007) Designing and Managing the Supply Chain., McGraw-Hill Irwin,
    59. C.A. Soosay , P. Hyland (2015) A decade of supply chain collaboration and directions for future research, Supply Chain Management., Int. J., Vol.20 (6) ; pp.613-630
    60. T. Strickland (1999) Strategic Management, Concepts and Cases., McGraw Hill College Division,
    61. D. Sudharshan , A. Mild (2017) Changes in customer preference heterogeneity patterns: A simulation study., J. Model. Manag., Vol.12 (2) ; pp.303-319
    62. D.M. Topkis (1978) Minimizing a submodular function on a lattice., Oper. Res., Vol.26 (2) ; pp.305-321
    63. D.M. Topkis (1995) Comparative statics of the firm., J. Econ. Theory, Vol.67 (2) ; pp.370-401
    64. D.M. Topkis (1998) Supermodularity and Complementarity., Princeton University Press,
    65. M.M.B. Vinholis , H.M.S. Filho , M.J. Carrer , W.B. Junior , F.R. Chaddad (2016) Complementarity in the adoption of traceability of beef cattle in Brazil., Production, Vol.26 (3) ; pp.540-550
    66. J.M. Whipple , D. Russell (2007) Building supply chain collaboration: A typology of collaborative approaches., Int. J. Logist. Manag., Vol.18 (2) ; pp.174-196
    67. T. Wakolbinger , J.M. Cruz (2011) Supply chain disruption risk management through strategic information acquisition and sharing and risk-sharing contracts., Int. J. Prod. Res., Vol.49 (13) ; pp.4063-4084
    68. C.W.Y. Wong , K.H. Lai , T.C.E. Cheng (2009) Complementarities and alignment of information systems management and supply chain management., Int. J. Shipp. Transp. Logist., Vol.1 (2) ; pp.156-171