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A Bertrand model of pricing of complementary goods under information asymmetry
Abstract
Parties in a supply chain, being independent firms, have private information about various aspects of the business not normally available to other parties. We consider a market where customers need to buy two complementary goods as mixed bundle, offered by two separate firms. The demand for each firm is dependent on the pricing strategy of both firms, which, in turn, depends on the quantities offered as per their own forecasts. We present a profit maximization model to obtain optimal strategies for a firm making decisions under information asymmetry. The model follows a simultaneously played Bertrand type game. We contrast and compare three scenarios: (1) when forecast information is asymmetric between the firms; (2) when forecast information is shared between the firms; and (3) when the firms form a strategic alliance.
... They concluded that introducing complementary products into the firm's product line yields more profit. Following Chansa-Ngavej [17] work, Yue et al. [18] formulated a duopoly for complementary products in the presence of two firms. They formulated their model to understand the importance of information sharing in a duopoly market while dealing with two complementary products under the Bertrand game strategy. ...
... For unique integer value * , the relation TP ( * − 1) ≤ TP ( * ) ≥ TP ( * + 1) satisfies. The relation holds for all unique solutions from equations (15) to (18). ...
... Step 3.3. Find the value of * from equation (18). ...
The nature of complementary products is the dependency of one product on the other for utility. Further, the complementary products with deteriorated nature create a challenging environment for a suitable strategy. How does an industry deal with complementary deteriorated products at the retailer's house? The present study deals with two complementary deteriorating products in a two-echelon supply chain management. The deterioration of complementary products increases with time, and the deterioration rate is taken as the function of time. Complementary deteriorating products are manufactured by two manufacturers and sold to a common retailer. Manufacturers use a flexible production system to produce products and a single-setup-multiple-delivery policy to deliver those products. Under the flexible production system, emissions from setup, holding products, disposal, and transportation of products are considered. A carbon tax policy is used to reduce emissions. This study aims to optimize the total profit of the supply chain by finding a suitable sales strategy. The total profit is maximized by acquiring the optimal values of the retail price, cycle time of the retailer, production rate, and number of shipments. The numerical result shows that the profit becomes maximum when complementary products are less dependent on each other. The result indicates that adapting the flexible production system increases the total profit by 1.86 % and decreases total emissions by 5.36 % than a traditional production system.
... Li et al. [24] researched whether the policy of markdown pricing in the sales cycle is inferior to bundling complementary products. Yue et al. [11] and Wei et al. [25] studied the information sharing of two duopoly companies providing complementary products. Only a few papers have investigated the pricing decisions of complementary products [26][27][28][29], but they either focused on channel members' different powers regarding the complementary products in the traditional channel [26], or considered the power structure of supply chains [30][31][32]. ...
... We can write the first-order partial derivatives of π E r (p 1 , p 2 ) with reference to p 1 and p 2 from Equations (7), (8), (11), and (21) as follows δπ E r (p 1 , p 2 ) δp 1 = c 11 p 1 + c 12 p 2 − c 13 (A15) δπ E r (p 1 , p 2 ) δp 1 = c 21 p 1 + c 22 p 2 − c 23 , (A16) and the Hessian matrix: ...
This study considered the supply chain that two manufacturers sell green complementary products to a dominant offline retailer. We investigated whether a manufacturer (the integrated manufacturer) should add an online channel and examined how it affects channel members’ decisions and profits. We formulated the power structure as the retailer-Stackelberg model and analyzed the pricing decisions for the supply chain. The results demonstrate that the integrated manufacturer prefers not to add the online channel when online and offline market bases are comparable and the level of complementarity is moderate. The integrated manufacturer gains more power at the expense of the offline retailer and the other manufacturer (the traditional manufacturer) when the complementarity between the offline and online channel is the same as offline channels with the addition of a new online channel; furthermore, the retailer earns less, while the traditional manufacturer’s profit hinges on the complementarity between the online and offline channels. It is beneficial for the offline retailer to balance the online and offline market bases of product 1 by improving the sales environment of the physical store. The integrated manufacturer can benefit from varying their marketing actions to decrease the degree of complementarity between the retail and online channels for the two products, while the traditional manufacturer can be better off from the online channel introduction by taking steps to increase the complementarity of the two products between the offline channels.
... They proposed a search method which gives a global optimum solution. Yue et al. [14] investigated a duopoly market dealing with complementary products. ...
... Smith et al. [7] √ √ Wei at al. [9] √ √ Mcgillivray and Silver [11] √ √ Yue et al. [14] √ √ Balkhi and Benkherouf [19] √ √ ...
A combination of substitutable and complementary products is very important for any business industry to make all-round profit from different aspects. How deterioration affects complementary products or substitutable products is discussed in this study. This study investigates the pricing and inventory decisions for complementary and substitutable items which are deteriorating in nature. Four models are analyzed where the demand of one product is dependent upon the selling price and the price of another product. This paper tries to compute the optimum prices and order quantities to optimize the total profit, which is the main aim. Theoretically, this model is solved by a classical optimization method. Numerical examples demonstrate the applicability of this model. Results conclude that the total profit is dependent on the degree of substitutability and complementarity. A sensitivity analysis of optimal solutions is given to test the stability of the proposed model.
... In many cases, small change in the demand may result the large change in the decision. So, a manager investigates the factors that influence the demand, because customers' purchasing behavior may be affected by the factors such as selling price, inventory level, seasonality, etc. Yue et al. (2006) and Mukhopadhyay et al. (2011) considered two separate firms for game theoretic models, which had private forecast information about the market uncertainties and offered complementary goods. Yue et al. (2006) showed that it is beneficial to share information in a Bertrand game, whereas Mukhopadhyay et al. (2011) demonstrated that, in a Stackelberg game, information sharing could benefit the leader but hurt the follower as well as the total profit. ...
... So, a manager investigates the factors that influence the demand, because customers' purchasing behavior may be affected by the factors such as selling price, inventory level, seasonality, etc. Yue et al. (2006) and Mukhopadhyay et al. (2011) considered two separate firms for game theoretic models, which had private forecast information about the market uncertainties and offered complementary goods. Yue et al. (2006) showed that it is beneficial to share information in a Bertrand game, whereas Mukhopadhyay et al. (2011) demonstrated that, in a Stackelberg game, information sharing could benefit the leader but hurt the follower as well as the total profit. ...
In this paper, we consider a duopoly market where two manufacturers separately produce and sell two complementary products through a common retailer as a leader–follower movement. The competition has been studied in two-echelon supply chain system and all produced products are sold by the retailer with individual product prices or with pure products’ bundling price in the non-cooperative market. The demand of each product linearly depends on prices of these two products as per their nature. Here, model for two different cases (without and with pure products’ bundling) are developed mathematically to maximize the profit of each participant of the supply chain and then corresponding optimal pricing strategies are worked out for the manufacturers and retailer. It is shown that supply chain profit for the pure bundling is better than the profit when products are sold at individual prices. Finally, the model is illustrated with numerical data to study the effects of models’ parameters in the pricing strategies and some marketing decisions are explored.
... Here, we are more concerned about the application of the bundling pricing strategies for complementary products. Yue et al. [112] developed a game model to obtain optimal pricing strategies for two complementary products where customers buy them as a mixed bundle in the scenario of information asymmetry. Yan & Bandyopadhyay [106] investigated the influence of product complementarity and advertising on the success of bundling. ...
In a dynamically changing environment of post-pandemic, uncooperative investment of multiple tourism product suppliers’ service efforts and non-synergistic bundled pricing of multiple complementary tourism products lead to poor consumer experiences and satisfactions and low operational performance of tourism omnichannel. This study takes a game-theoretical approach to explore and understand the business dynamics regarding the investment of service efforts and bundled pricing mechanism of multiple suppliers’ complementary products in a tourism omnichannel, evolving rapidly in the tourism industry with still rare research literature. A generic tourism omnichannel structure with multiple complementary tourism product suppliers is conceptualized and formulated into game-theoretical models to investigate the optimal operational decisions on the service efforts investment and bundled pricing approach considering centralized, decentralized and cooperative decision scenarios. The derivation and comparison of the optimal decisions and outcomes for these models have shown that the cooperative strategy regarding the investment of service efforts and the bundled pricing of complementary products creates better operational performance than those of the decentralized ones in a tourism omnichannel. The findings of the numerical and sensitivity analyses offer valuable strategic insights to tourism omnichannel practitioners. The tourism omnichannel study also provides a better theoretical foundation for future tourism omnichannel research.
... Given the environmental and financial benefits of green innovation and EOU products recovery In addition to product greening and EOU products recovery, another way to the success of any business is the production of complementary products. The notion of complementary products appears when customers have to purchase more than one product to achieve maximum utility (Wei et al., 2013;Yue et al., 2006). In other words, complementary products are those products where the purchase of one of them may require the purchase of another, or they complement each other during their commonplace utilization (Zhao et al., 2017) i.e. one product adds value to another product. ...
... Regarding the influence of information asymmetry on the decision making of complementary firms, Vives [20] studied the decision making of dual occupancy with the Bertrand and Cournot models at the same juncture and indicated that the Bertrand model is more efficient for the analysis of complementarity than the Cournot model in the case of information asymmetry. To follow up, Yue et al. [21] used the Bertrand model to discuss the firms' pricing decisions of two complementary commodities under information asymmetry and compared three different scenarios. Notably, consumers often need to purchase more than one product from varying suppliers to obtain the full benefits of these products, so the concept of "bundled products (Mixed Bundle)" appears. ...
The smartphone is now a widespread trend that causes phone accessory markets to rise. The high penetration rate of smartphones has led to a saturated market. The accessory market not only has tremendous business opportunities but also high potential. In practice, the decision of whether to join the accessory market differentiates by each smartphone firm. This study analyzed and discussed the main product firms’ optimal decisions of whether to enter the accessory market by using game theory as a construct model. Considering the different competition situations, the decision of whether the main product firm invests in the accessory market affected the market demand, pricing, and profit of all firms. Furthermore, we analyzed the differences in the external environment to determine what the best decision for the main product firm was. The results of the research show that complementary effects do not always have a positive influence on firms’ willingness to join the accessory market. When weak main product firms have different market forces in the main product market, the dominant main product firms are not necessarily more willing to join the accessory market than weak firms.
... According to statistics released by the Three Gorges Navigation Authority, the average waiting period for ships has amounted to 2 days or more. Such a long waiting period is not feasible for deteriorating [20] or high-value products. The Three Gorges Transshipment System was designed by the Gorges Navigation Authority to divert ships and thus alleviate congestion, with a deadline of 2035. ...
Transshipment can be a detour for carriers to bypass congested locks. Therefore, the local government provides subsidies to carriers reluctant to adopt transshipment due to high costs. Using the Three Gorges Dam (TGD) as the subject, we address the interaction between the government and carriers and the rational routine choice for carriers when facing severe congestion. Specifically, we investigate pricing competition among carriers under different scenarios. A two-stage game model based on Evolutionary game theory and Bertrand game is used for the study. The results confirm that: (1) Subsidies for the road alternative can alleviate congestion in waterways transport before TGD; (2) Road transport is an efficient way to alleviate lock congestion, especially under emergency states; (3) Public subsidies for road transport support this change of modes at a reasonable price to shippers. Additionally, carriers with transshipment mode can provide more competitive freight prices and more convenient services to customers.
... OvQDQ@ w [1] wvQwm |=ypOt '|Q=PoCt}k w O}rwD Q=Okt pwYLt OwHw =@ pwYLt l} |Q=PoCt}k`w[wt ' , qFt "Ov=xDiQo Q= Qk C=k}kLD VywSB l} QO xv=o =OH CQwYx@ 13 ptmt pwYLt =} 12 u}Wv=H =} u} Ro}=H x@=Wt |xv}tR QO |O=}R C=k}kLD u}vJty "CU= xOW |UQQ@ [3] Rw}w w nv}U \UwD =yv; x@ xt=O= QO xm CU= xDiQo CQwY u}t -=D |xQ}HvR QO pwYLt l} |Q=PoCt}k u=tRsyOwHw=@pwYLtl}|Q=PoCt}kOyO|tu=Wv=y|UQQ@'=t="OwW|txQ=W= xOWv |UQQ@ u}W}B C=k}kLD QO uwvm=D ptmt pwYLt l} w u}Wv=H pwYLt l} ptmt |=yq=m |= Q=O , qwtat CqwYLt '|ak=w |=}vO QO xm [4] u= Q=mty w w} CLD 'OvwW|t O}rwD Cw=iDt |xv=NQ=m wO \UwD xm = Q 14 pwYLt wO Qy Ct}k "Ov=xDiQov Q_v QO = Q |rY= pwYLt OwN |xrUt QO =yv; "Ov=xOQm |UQQ@ Vv pOt wO lQDWt pwYLt l} 15 p=kDv= Ct}k u}}aD |xrUt [5] l=}@wm w |v=NQ=Ry p}rLD |= Q@ Vv pOt l} R= =yv; "Ov=xOQm |UQQ@ = Q |r=tDL= |=[=kD CLD xv=NQ=m Vv |vRxv=J pOt l} '|R=@ QO |Q=mty |UQQ@ R= TB w xOQm xO=iDU= xrUt C=t}tYD [6] |H w w=W "Ov=xO=O x=Q= |Q=mty R= pY=L OwU s}UkD |= Q@ xDi=}xaUwD pwYLt wO Qy |}=yv Ct}k x@ xDU@=w |=[=kD =@ u}Wv=H pwYLt wO |Q=PoCt}k "Ov=xOQm |UQQ@ RmQtDt w Vv |=y|R=@ =@ VQ=iU j@] Q@ S=Dvwt sDU}U l} QO = Q =}H "CU= xDiQo Q= Qk |UQQ@ OQwt R}v u}t -=D |xQ}HvR QO |Q=PoCt}k |xrUt l} pt=W u}t -=D |xQ}HvR l} QO = Q |yOVQ=iU w |Q=PoCt}k C=t}tYD [7] wy w pOt [8] nv=} w w=R "Ov=xOQm |UQQ@ pwYLt l} |= Q@ w VwQixOQN l} w xOvvmu}t -=D w u}Wv=H CqwYLt =@ ?}kQ u}t -=D |xQ}HvR wO QO = Q |yOCtON w |Q=PoCt}k "OvOQm |UQQ@ nQ@rmDU= |R=@ R= xO=iDU= =@ |a]kQ}e |=[=kD`@=D uDiQo Q_v QO =@ l} pt=W u}t -=D |xQ}HvR wO u=}t C@=kQ Vv |R=@ R= xO=iDU= =@ [9] u= Q=mty w |; [10] |wJ "OvOQm |UQQ@ u}Wv=H CqwYLt |= Q@ = Q VwQixOQN l} w xOvvmO}rwD VwQixOQN j} Q] R= VwQi |= Q@ xOvvmO}rwD C=t}tYD Q@ = Q CQOk Q=DN=U C= QF= QO = Q OwU w Ct}k Q@ CQOk Q=DN=U QF= [11] 'u}i}Qo w lDQ= "CU= xOQm |UQQ@ |xrUt QO = Q Q= R=@ * Ct}k * C}U=UL w |UQQ@ |}xrLQt wO u}t -=D |xQ}HvR l} Q=DN=U w CqwYLt |v}Wv=H u= R}t Q}F -=D [12] u= Q=mty w nv=S "Ov=xOQm p}rLD OwN =@ u}t -=D xQ}HvR l} |Q=Po Ct}k C=t}tYD Q@ = Q`}RwD p=v=m QO OwHwt CQOk uwO@ w |Owta Vv |R=@ pO=aD xm OvDi=} QO =yv; "Ov=xOQm |UQQ@ xv=owO`} RwD p=v=m "CU= umtt CQOk Q=DN=U u} QDy@ u}t -=D xQ}HvR pm |= Q@ xiQ]l} CQOk Q=DN=U |xQ}HvR l} QO u}Wv=H pwYLt wO |Q=PoCt}k |xrUt [13] u= Q=mty w w=S QO |v=@D w OvQDQ@ |=y|R=@ =@ = Q lQDWt VwQixOQN l} w xOvvmO}rwD wO pt=W u}t -=D |Q=PoCt}k |xrUt OUQ|t Q_v x@ xOW s=Hv= |UQQ@ =@ "OvOQm |UQQ@ |R=i \}=QW |UQQ@ w KQ]t uwvm=D |rY= ptmt pwYLt l} OwHw =@ u}Wv=H pwYLt wO |xrUt [15] u= Q=mty w |r}a=tU= R}v w [14] u= Q=mty w |QiaH R}v , = Q}N= "CU= xOWv |UQQ@ |L]UxU w |L]UwO |=yu}t -=D |xQ}HvR QO ?}DQD x@ = Q |Q=PoCt}k C=t}tYD uDiQo Q_v QO =@ u}t -=D |xQ}HvR QO |Q=PoCt}k |xrUt 'u}vJty "Ov=xOQm |DU=Q w |NQi "CU= xOW |UQQ@ [16] u= Q=mty w |aQ=R \UwD |OwHwt =@ \@DQt Q_v QO =@ = Q |L]UwO u}t -=D |xQ}HvR l} QO |Q=PoCt}k |xrUt R}v [17] |mRQ@ VQ=iU T=U= Q@ O}rwD sDU}U QO Q= R=@ ?L=YD QO u=oOvvmO}rwD C@=kQ uDiQo |W=O=O \UwD R}v u}t -=D |xQ}HvR QO pkvwptL x@ \w@Qt C=t}tYD "OvOQm |UQQ@ "CU= xOW |UQQ@ [18] u= Q=mty w ...
... Price sensitive linear demand functions can be referred to the literature (Gupta & Loulou, 1998;Martin, 1999;Mukhopadhyay et al., 2011;Raju & Roy, 2000;Wee, 1999;Yue et al., 2006;Zhang, 2002). 12. ...
Economic, environmental, and social criteria are all being taken into consideration simultaneously when determining pricing policies or inventory levels in sustainable production management. The combination of pricing and inventory policies is an important source of leverage for the efficient management of perishable products. This paper, among the first studies, proposes the problem of devising optimal pricing and inventory management decisions simultaneously where the environmental and social criteria are contributed for perishable complementary products replenished and sold by the same company. This study considers two interrelated price-sensitive linear demand functions to consider the possibility of shortage with both budget and warehouse capacity constraints. Another contribution of the proposed model is to consider an upper bound for environmental pollution and a lower bound for job opportunities as the constraints to the model. As a complex optimization model, the challenge of complexity is addressed by a heuristic algorithm for finding an optimal solution. After an extensive analysis using numerical examples, some managerial insights are concluded from the results. One finding from these analyses confirms that the total capacity of the warehouse, the total available budget, carbon emissions, and variable job opportunities have a high impact on the optimal solution to find a balance between sustainability criteria for making pricing and inventory policies.
... In 1981, Winkler studied the uncertainty of the market and demand and proposed to use the normal distribution of random variables to build the model [7]. In 2006, Yue et al. studied the pricing of complementary goods under asymmetric supply chain demand information using the Winkler model [8]. In 2011, Mukhopadhyay et al. discussed the pricing strategy of complementary goods using the Stackelberg game in the case of information asymmetry [9]. ...
Based on the uncertain market demand, this paper studies the sharing strategy of each main body of the closed-loop supply chain for demand prediction information and introduces the variable of advertising effect into the model. Firstly, this paper constructs a manufacturer-led Stackelberg game model based on a two-level closed-loop supply chain. Secondly, the manufacturer advertising mode and the retailer advertising mode are set up, and the influence of information sharing is discussed in each advertising mode. Finally, the conclusion and the proposition are verified by example analysis. The results show that in terms of advertising, manufacturers prefer retailers to undertake, and retailers’ willingness is related to the mode of information sharing. In order to achieve a “win-win” situation by sharing information, certain conditions should be met. The advertising effect is helpful to increase product demand, retail price, advertising investment level, and profits of manufacturers and retailers and also promote recycling activities. However, the impact on wholesale price will vary with different advertising subjects.
... Another stream of the studies focuses on the pricing strategy, which is a vital economic decision for CLSC systems (Yue et al., 2006;Mukhopadhyay et al., 2011;Liu et al., 2012;Gan et al., 2016;Abbey et al., 2015;Lu et al., 2016;Gupta et al., 2019;Johari and Hosseini-Motlagh, 2019;Li et al., 2019;Shen et al., 2019;. Given that the customer demand for new or remanufactured products and CLSC operations are affected by price, a price increase further induces customers to buy fewer products. ...
Remanufacturing and recycling of end-of-life products have changed the structure of supply chain networks, and the option of closed-loop supply chains gains popularity. Growing strict environmental and social legislations are expected to enhance sustainability of closed-loop supply chains. This study focuses on the pricing and advertising decisions in a closed-loop supply chain network. Although pricing decisions have been well-studied in this area, there is a little attention to advertising decisions. It is well-known that advertising plays a significant role in influencing customer behavior in returning end-of-life products for the closed-loop supply chain. Therefore, this research develops an operational and tactical plan for promoting advertising programs considering different elasticity effects. As such, the proposed optimization plan considers the pricing decisions in a more comprehensive view, where the price of similar products in the market and their substitution degree have a high impact on the profitability of manufacturers in a direct-sales closed-loop supply chain. Hence, the main novelty of this paper is to develop a new optimization model with pricing and advertising decisions in a direct-sales closed-loop supply chain. Since the proposed model is more complex than the majority of existing optimization models in the area of closed-loop supply chains, another novelty of this paper is to propose an improvement to the standard particle swarm optimization algorithm using the crowd-learning theory. The developed algorithm is validated by the exact solver and compared with the state-of-the-art algorithms in this research area. An extensive computational experiment is performed considering a number of comparative metrics. The findings show the superior performance of the proposed metaheuristic against the alternative solution approaches in terms of computational time and solution quality. Moreover, some important insights are obtained from this research, which could provide a basis for configuration of pricing schemes and advertising campaigns to improve the efficiency of closed-loop supply chains.
... Finally, it is a dominant strategy for firms to choose quantity as a strategic variable when goods are substitutable, and prices when they are complementary. Yue et al. (2006) presented a model of profit maximization in order to obtain optimal strategies in conditions of information asymmetry. The model follows a Bertrand-type game with players having private information. ...
... A product has a high degree of complementarity with others when it is sold together with another product i.e., a bed and a mattress, a computer and the operating system, a computer and a printer, just to name a few examples. Yue et al. [45] modeled a mixed bundling policy to sell two complementary products in a market with two independent firms. The model determined the optimal pricing strategy by maximizing the total profit. ...
In online purchasing, customers may return products due to dissatisfaction with the quality of the product, and receive a refund based on the return policy, which is determined by online distributors. Online distributors can offer generous policies to attract more customers, but at the cost of reducing total profits. In this paper, the effect of the pricing and quality of complementary products (products sold together with other items) in online selling under the return policy is investigated. For this purpose, a mathematical model is developed to obtain optimal values for selling price, refund amount, and quality of products. Based on analytical results, a solution algorithm is proposed to solve the numerical examples and perform sensitivity analysis. Findings reveal that, while increasing the sensitivity of demand with respect to the refund amount, the price, quality, and refund on returned products should be increased. In addition, the online distributor should increase the quality of products when customers are more sensitive to the quality of products. Among other results, the selling price is shown to be negatively affected by demand elasticity with respect to price. In this situation, the online distributor should reduce the quality level and the refund amount for returned products to avoid a sharp decline in profit. In addition, when the quality cost is high, the price and quality should be decreased and the refund amount unchanged.
... We further review relevant literature on complementary goods pricing. The concept of complementary goods arises when customers need to buy more than one product to obtain the full utility (Yue, Mukhopadhyay, and Zhu 2006). The markets for such goods are interlinked since the demand for one product could affect that for the other (Wei, Zhao, and Li 2013). ...
Healthcare services are customer-intensive services and usually accompanied by other treatment-related consumptions, e.g. medications. Traditionally in China, prescribing and dispensing are both made by hospitals, which causes high drug expenses. To solve this problem, the Chinese government has begun exploring the separation of prescribing and dispensing. Against this background, this paper analyses the optimal designs for healthcare services considering separated medications. We consider a service system with one monopolistic healthcare service provider, which could be a revenue-maximiser or social-welfare maximiser, and assume patients are bounded-rational with demands affected by price and quality of both service and medications. We analyse the optimal service price and service rate for cases involving either single or multiple medications. Revenue-maximiser usually prefers cost-effective medications, and when its service quality is low, more irrational patients are preferred. Its revenue increases with the number of medication types. For the social-welfare-maximiser, as the number of medication types or improved quality of certain medications does not ensure greater social welfare, its benefits depend on the prices and quality of the entire medications. For a social planner, it is effective to institute price caps to achieve socially optimal results. This paper lays theoretical foundations for price regulations of public healthcare systems.
... If products are complementary, then a positive correlation exists between the demands of these complementary products. Buying one of the complementary products requires or persuades the buying of the other to achieve the full utility of the products (Yue et al. 2006). The demand model for complementary products can be either in sets of one unit of each or jointly. ...
Interaction effect across complementary products plays an important role in characterizing the optimal inventory policy. The inventory levels of complementary products are interrelated due to interaction between demand streams. In this paper, we consider a periodic review base-stock policy in the presence of two complementary products with interrelated demands and joint replenishment. Demands are modeled by a Poisson process and any unmet demand is lost. Demands can be in sets of one unit of each or jointly. If an arrival demand requests two products jointly and one of the products is not in stock, then the whole demand is lost. We aim to investigate how this interrelated demand phenomenon influences the optimal base-stock levels and the period length of a periodic review policy. We utilize the renewal reward theorem to derive the explicit expression of the expected profit rate in the system. The goal is to determine the optimal period length and the base-stock levels such that the expected profit rate is maximized. Enumeration and approximation algorithms are employed to find the optimal and near-optimal solutions, respectively. The approximation algorithm is based on a scenario with independent demand processes which results in an explicit expression for the long-run profit per time unit and leads to analytical solutions for optimal policies. Our numerical results reveal that the solutions obtained by the approximation algorithm are close to optimal solutions. Numerical experiences show that the maximum profit in the system is achieved if the proportion of customers with jointly demand increases. Moreover, the interaction effect between demand processes has a significant impact on the control policy performance when the units lost sales and unit holding costs are high, and the demand rare is low.
... al (2005) studied a dynamic lot-size model under one-way item and full substitution where the items are indexed in such a way that a lower-index item may be used to substitute for the demand of a higherindex item while, Tang and Yin (2007) studied joint ordering and pricing strategies for two substitutable items under two-way and full substitution. Yue et al. (2006) studied a duopoly market dealing with complementary items and Wei et al. (2013) studied the pricing decision models with two complementary items in supply chain management consisting of two manufacturers and one common retailer and developed five pricing inventory models: MS-Stackelberg, MS-Bertrand, RS-Stackelberg, RS-Bertrand, and NG models. Salameh et al. (2014) studied the EOQ model for two substitutable items with partial substitution and joint replenishment policy and the work of Salameh et al. (2014) is the extension of the research of Drezner et al. (1995) by taking two-way and partial substitution. ...
p>In this paper, impact of cost of substitution and joint replenishment on inventory decisions for joint substitutable and complementary items under asymmetrical substitution has been studied. The phenomenon of substitution is considered in a stock-out situation and when items become out of stock due to demand then unfulfilled demand is asymmetrically substituted by another item. We formulate the inventory model mathematically and derived optimal ordering quantities, optimal total costs and extreme value of substitution rate for all possible cases. Moreover, pseudo-convexity of the total inventory cost function is obtained and the solution procedure is provided. Numerical example and sensitivity analysis have been presented to validate the effectiveness of the inventory model and substantial improvement in total optimal inventory cost with substitution with respect to optimal total inventory cost without substitution is seen.
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... Complementary goods have been extensively explored in numerous studies. Literature on this topic proceeds from various perspectives, such as information sharing (e.g., [13,17,18]), product promotion (e.g., [19,20]), joint selling (e.g., [21][22][23]), recycling channel decision (e.g., [24]), mechanism design (e.g., [25]) and pricing problems (e.g., [10,26,27]). Our study is situated in the research stream of pricing problems. ...
Although suppliers can sell their goods on e-retailers’ e-platforms through either a wholesale or agency contract, suppliers that produce complementary goods and have different channel roles have been confused as to how to choose an optimal distribution contract. This paper aims to study this problem by considering the combined impacts of suppliers’ channel roles, e-retailer’s referral fees, goods’ differences in the level of complementarity and goods’ differences in potential demand. Our results show that, regardless of one supplier’s distribution contract choice, the other supplier always prefers agency contract, which is independent of two suppliers’ channel roles, the e-retailer’s referral fees, two goods’ differences in the level of complementarity and two goods’ differences in the potential demand. Moreover, when two suppliers use different distribution contracts to sell goods with different levels of complementarity on the same e-retailer’s e-platform, low-complementarity goods have a larger optimal retail price only if the two goods’ differences in the level of complementarity are sufficiently high, and the supplier can obtain more profits by producing low-complementarity goods regardless of the supplier’s distribution contract and channel role.
... Discrete Dynamics in Nature and Society As we stated in the last part of the discussion of the first stream of the literature, few studies have discussed decisions related to complementary products. For example, Yue et al. [61] indicated that the concept of complementary products emerges when customers need to purchase multiple products at the same time to obtain the full utility of the product. ey also built a profit maximization model to obtain an optimal pricing strategy in which two complementary products that customers need to purchase were provided by two different companies. ...
This paper investigates a pricing game and service cooperation for complementary products in a dual-channel supply chain composed of two manufacturers and one retailer. The products of the two manufacturers are complementary products. One manufacturer sells products simultaneously through its own online channel and the traditional retailer, and the manufacturer delivers the product’s service to the retailer in its network direct sales channel by cooperating with the retailer in the form of service cost sharing. Considering the different market power structures of channel members, we establish three different pricing game models. By using the backward induction method and game theory, we obtain the corresponding analytical equilibrium solutions. Then, the service cooperation strategy of using the channel service sensitivity coefficients to construct the weight to share the service cost is proposed. Finally, numerical examples of optimal pricing strategies and profit conditions in different game situations are given, and sensitivity analysis of some key parameters is selectively performed, in which some valuable management insights are obtained.
... Let be the demand for product when using collection option ∈ . We model the demand for the two products as follows (Ceryan et al., 2013;Dong et al., 2009;Mukhopadhyay et al., 2011;Yue et al., 2006;Wei et al., 2015a): ...
In this paper, we search for the best configuration for a closed-loop supply chain (CLSC) dealing with complementary goods. In our model, a manufacturer sells two complementary goods to a retailer, which sells both products in the market. When the products reach their end-of-use stage, the manufacturer has several options for the CLSC: (i) Collect both products (exclusive collection), (ii) collect only one product while outsourcing the other product collection to the retailer (partial outsourcing), and (iii) fully outsource the collection process to the retailer (full outsourcing). Our findings demonstrate that the presence of complementary products makes the CLSC selection extremely difficult. For instance, we demonstrate that the CLSC structure with maximum returns does not necessarily possess the minimum or the maximum wholesale price. Analogously, the minimum retail price (i.e., maximum sales) and maximum return rate often occur in different collection options. We also show that the best collection option for the manufacturer seldom leads to the maximum profit for the retailer. Moreover, often the CLSC option that maximizes the manufacturer’s profit leads to lower returns. Therefore, the presence of complementary products entails several trade-offs among collection performance, prices, and profits.
... In the market, sometimes consumers may have to purchase more than one product at the same time to gain the full utility of the products, and these are referred to as complementary products [5]. On the one hand, with more and more attention paid to green supply chains, traditional manufacturers can gain a competitive advantage by ecological transformation (i.e., the upgrading of equipment and technology), but also need to undertake the corresponding costs at the same time. ...
Retailers usually sell complementary products jointly with a discounted price to attract more consumers. However, the difference of complementary degree between products leads to the diversity of pricing. In parallel, with the development of green supply chains, the extra cost of manufacturers to conduct ecological product design makes the pricing of complementary products further complicated. Thus, it is important to clarify the pricing strategy for complementary products in a green supply chain. Based on the Stackelberg games between two manufacturers and a retailer, this paper constructs three pricing models to simultaneously analyze the changes in the optimal profits of supply chain members and the optimal green manufacturing degree of complementary products. The results demonstrate that: (i) In most cases, two manufacturers prefer the pure bundling pricing strategy, but the strategy preference of the retailer is complex. (ii) The green manufacturing is mutually beneficial for complementary manufacturers and worth advocating. (iii) The increasing sensitivity of consumers to the green manufacturing level of one product will also be detrimental to the improvement of the optimal green manufacturing level of its complementary products.
... Pricing is a critical decision in economic systems Chiu and Choi, 2009;Liu et al., 2012;Yue et al., 2006;Wang et al., 2016;Mukhopadhyay et al., 2011;Li et al., 2019), and it is especially crucial in green-product operations. In the literature, Li et al. (2016) study the pricing decisions for green products when there are two competing retailing channels, one is the direct channel owned by the manufacturer and the other is the indirect channel operated by the retailer. ...
In the circular economy era, environmental sustainability is critical, and both green and non-green products with similar functions co-exist in practice. There is little doubt that these two types of products are competing and may substitute one another even though one is more environmental friendly than the other. In this paper, we build analytical models to explore the optimal advertising and pricing decisions for a green product in the presence of a non-green product substitute. We investigate both simultaneous and sequential pricing strategies under which there are three possible pricing scenarios, namely: 1) both prices of green and non-green products are determined simultaneously (Strategy IP), 2) the green product's price is decided first and then the non-green product's price is determined (Strategy GL), and 3) the non-green product's price is decided first and then the green product's price is determined (Strategy NL). We find that the sequential pricing strategy is more profitable than the simultaneous pricing strategy for both green and non-green supply chains. It is interesting to prove the existence of "second-mover advantage" in the pricing game. Moreover, we identify that if the green supply chain uses Strategy NL, it could achieve a better performance in profit and minimize the corresponding environmental impact. If the green supply chain is truly socially responsible, it should design a product with low substitutability, so that the environmental impact can be enhanced. Furthermore, our numerical results indicate that Strategy IP never performs the best in terms of consumer surplus and social welfare when the product substitution level is sufficiently high. Findings of this paper contribute to the literature on cleaner production systems in the circular economy era.
... Price sensitivity generally defined as the degree of a product's price impact on consumer behavior. Price sensitive linear demand functions with cross elasticity depending on the degree of complementarity/substitutability of products are commonly used in business and economic literature [10,15,27]. ...
In practice, the holding cost in inventory models can be considered as linear or nonlinear functions. Nevertheless, nonlinear holding cost rarely attracted the attention of the researchers, and to our knowledge, it is novel in the presence of complementary or substitute items. It can also be interpreted as a way to include the perishability of products. Except for the perishability, nonlinear holding cost can be employed for other purposes like cold supply chain. In this paper, a new pricing method based on a multi-product inventory model is presented for complementary and substitute items. This paper aims to find the optimum value of the replenishment cycle and prices for the products supplied together (complementary) or interchangeable (substitute), such that the total cost of the inventory system is minimized. Demand is assumed as a price sensitive function while the proposed model is trying to obtain the optimal values of prices and the replenishment cycle simultaneously.
... Estelami [11] calculates the consumer's savings when they buy the bundling with a combined price, finds that the consumers will pay higher prices by purchasing the bundle while on average save about 8%. Yue et al. [12] study that customers buy the bundling goods consisting of two complementary goods offered by two separate firms. They obtain optimal strategies for the two firms when making decisions under information asymmetry and compare the difference between three scenarios according to the degree of the information sharing. ...
In this paper, we study the pricing decisions stability when a retailer adopts bundling strategy for complementary products. We firstly explore whether or not the decision maker will adopt bundling strategy, finding that bundling strategy benefits retailer’s profit by improving sales of both products. Considering demand uncertainty, we focus on a bounded rational decision maker adjusting decisions in each period, build a dynamic pricing system and study its stability based on chaos theory. According to different pricing strategies for the bundling products, we propose two game models, i.e., simultaneous and sequential game, and compare the performance on the bundling strategy and system stability. The results show that both game models can reach the same optimal decisions, but sequential game has a better performance in keeping system stable. We also show the joint influence of parameters on the system stability and find that the retailer can control a chaos system caused by uncertain demand by slowing down the speed of decision adjustment. This paper’s theoretic contribution is to compare the performance of two or more systems’ stabilities based on Jury criteria.
... For example, Winkler (1981) developed a mathematical model to combine information from different sources to facilitate information sharing and information update. Following the lead of Winkler (1981), Yue et al. (2006) investigated the pricing decision for the complementary product sale using the Bertrand game and Zhu et al. (2011) studied the same issue using the Stackelberg game. Cachon and Lariviere (2001) explored contracts that allow the supply chain to share demand forecasts credibly. ...
Nowadays, in business operations achieving sustainable development goals is critically important. With the proper use of information, supply chain management can significantly help enhance sustainability. In this paper, we analytically study a supply chain model where a manufacturer produces a green product and sells it to the end consumers through a retailer. We formulate the analytical model as a Stackelberg game. In the game, the manufacturer is the Stackelberg leader who decides the wholesale price and product sustainability level, and the retailer is the follower who reacts by setting the retail price. After deriving the Stackelberg equilibrium of the wholesale price, the product sustainability level, and the retail price in the closed form expressions, we compare the manufacturer’s, the retailer’s, and the whole supply chain’s performances. We derive and compare the equilibria under three business scenarios, including Decentralized Supply Chain with Non-information Sharing (Scenario N), Decentralized Supply Chain with Information Sharing (Scenario I), and Centralized Supply Chain (Scenario C). We give managerial suggestions to the manufacturer and the retailer on how to promote the green products and achieve organizational sustainability goals. We also analytically illustrate how to coordinate the channel, and highlight the crucial role played by information in the green product supply chain.
... The retailer can share his demand information with the manufacturer and the paper identifies the optimal time to share information for the retailer. Yue, Mukhopadhyay, and Zhu (2006) study demand information asymmetry under the non-cooperation and cooperation scenarios. They argue that information sharing is easy to implement under cooperation scenarios but not always good for both members. ...
Supply chain contracting and the use of information are undoubtedly two critical and influential areas in modern supply chain management. However, relatively little is known about supply chain contracting mechanisms with different information settings. To fill this gap, we review and classify the related supply chain contracting literature into three categories with respect to different kinds of information considerations, namely (i) demand information updating, (ii) supply information updating and (iii) information asymmetry. We report the publication trend and classify the commonly studied supply chain contracts with the use of information such as pricing contracts, commitment contracts and menu of contracts. We discuss how contracting and the use of information influence each other in the supply chain. Moreover, we review the major application areas of information usage and report the historical development of major related topics. Finally, we propose several important future research directions.
... Many examples can be listed where firms agree to adopt the cooperation alliance with the intention to benefit from unique advantages of their counterparts. For example, SBC communications and HP announced cooperation alliance for integrated IT and Telecom managed services; Apple Inc. and HP.com announced a cooperation alliance to deliver an HP-branded digital music player based on Apple's iPod [8]. ...
This paper investigates the green supply chain pricing problem when two manufacturers sell complementary products to one retailer. Considering the manufacturers’ cooperation or noncooperation strategies, we first give the centralized pricing model as a benchmark. According to market power among the supply chain, we analyze two types of supply chains: supplier-led type where the green driving factor comes from the suppliers and retailer-led type where the core member retailer leads the green supply chain. We then give two decentralized pricing models through considering strategic cooperation between two manufacturers and different structures. Corresponding closed-form expressions for equilibrium pricing strategies are established. Finally, many valuable managerial results are acquired through comparing the profits and equilibrium decisions of these models. Our paper shows that consumers are indifferent as to who is the leader of the two echelons when the manufacturers adopt non-cooperative action; the two complementary products get the same optimal wholesale/retail prices, maximum retail margins, and maximum demands regardless of the manufacturers’ cooperation or noncooperation strategies.
... Our work contributes to the bundling literature on competition and complementarity because we examine a firm's bundling strategy when the information product and the premium service exhibit complementary effects in the duopoly setting. A great number of studies focus on the bundling strategy of complementary goods (Bakos and Brynjolfsson 1999;Halmenschlager and Mantovani 2017;Mukhopadhyay, Yue, and Zhu 2011;Yan et al. 2014;Yue, Mukhopadhyay, and Zhu 2006). Recently, Taleizadeh et al. (2017) examine the optimal problem for two complementary goods under three business strategies (i.e. ...
In this paper, we model a fully covered duopoly market in which two firms offer a differentiated information product that exhibits positive network effects and a complementary premium service to consumers. For each firm, there are two marketing strategies: the freemium strategy and the bundling strategy. We find that, under the market equilibrium, a firms’ decision whether to employ the freemium strategy or not depends largely on the quality of the information product compared to its rival. When the information product quality is similar and the products’ intrinsic values are sufficiently large, both firms will be better off by adopting the freemium strategy, while the bundling strategy will prevail if the products’ intrinsic values are sufficiently small. Additionally, when the magnitude of complementary effects or network effects exceeds a given threshold, both firms’ profit can be enhanced by an increase in the degree of product complementarity or in the intensity of network effects. We also demonstrate that a firm can benefit from an increasing market size only if the intrinsic value of its information product is sufficiently large. Finally, we extend our model to the uncovered market and derive the equilibrium prices and profits.
... While some studies examined the incentive for a firm to share information with its competitors in an oligopoly, Lee and Whang [25] explained the types of information shared such as inventory, sales, demand forecast, order status, and production schedule and discussed how and why this information is shared using industry examples and relating them to academic research. Yue et al. [26] considered a market where customers need to buy two complementary goods as a mixed bundle, which are offered by two separate firms. They presented a profit maximization model to obtain optimal strategies for a firm to make decisions under information asymmetry. ...
This paper studies information sharing in a supply chain where a contract manufacturer (CM) acts as both an upstream partner and a downstream competitor to an original equipment manufacturer (OEM). To better explore the effect of information sharing on a coopetitive supply chain, we consider a sequential game with the OEM as the Stackelberg leader under two different wholesale pricing methods, which is close to practical situation. Our analysis shows that when the wholesale price is exogenously given, information sharing is beneficial for the OEM but hurts the CM and a side-payment contract is designed to induce Pareto-optimal information sharing. When the wholesale price is a decision variable, the CM benefits from information sharing while the OEM doesn’t and a discount-based wholesale price contract is designed to induce truthful information sharing. The numerical examples analysis further finds that the OEM benefits from the exogenous wholesale price scenario while the CM benefits from endogenous wholesale price scenario. The study sheds lights on the decision-making processes for operating and managing the co-opetitive supply chain and extends the research scope of information sharing. Our findings also provide some scientific references about information sharing in daily production.
... Our work is also related to the literatures on complementary products pricing and bundling, such as Gabszewicz et al. (2001), Yue et al. (2006), Wang (2006), Chris et al. (2013), etc. This research differs from the existing literature, we consider the markdown pricing and bundling strategy of complementary products in multiple periods, the consumer has the option to buy or not, and decide the time of buying with their strategic behavior. ...
... For example demand for printers makes demand for ink cartridges. Some other examples of complementary products are tooth brush and tooth paste, computer and its software, etc. Yue et al. [29] studied two complementary products considering bundling strategy and obtained optimal pricing decision under three different cases. Yan and Bandyopadhyay [30] studied bundling of complementary products in which the demand is sensitive to price of both products. ...
This paper proposes an integrated two-stage model, which consists of one vendor and one buyer for two complementary products. The vendor produces two types of products and delivers them to the buyer in distinct batches. Buyer stocks items in the warehouse and on the shelf. The demand for each product is sensitive to stock levels of both products. A vendor-managed inventory with consignment stock policy is considered. The number of shipments and replenishment lot sizes are jointly determined as decision variables in such a way that total profit is maximized. The numerical study shows that as complementation rate increases, the quantity of transfers and demand of both products increase. Hence, ignoring the complementation between products leads to the loss of some customers.
... The retailer can share his demand information with the manufacturer and the paper identifies the optimal time to share information for the retailer. Yue, Mukhopadhyay, and Zhu (2006) study demand information asymmetry under the non-cooperation and cooperation scenarios. They argue that information sharing is easy to implement under cooperation scenarios but not always good for both members. ...
... A higher (lower) variance implies a less (more) precise forecast. The precision parameter is given by t ¼ V=ðV þ sÞ and is inversely proportional to the error variances (Yue et al., 2006). In line with findings of the existing literature (e.g., Vives, 1984;Roy, 2000 andLi, 2002), all the parameters of the model (except the forecast) are assumed to be of common knowledge to both the firms. ...
In today's volatile global marketplace co-developing of new products is increasingly important, owing to the uncertainties of developing and launching a new product. The collaborative new product development process however, presents a new challenge for the partner firms due to the sharing of information, resources and technology. Literature has not adequately addressed the issues associated with collaborative decision making that has to be robust in an environment with varying performance, quality and timing uncertainties, despite the growing need to collaborate. In our model, we consider a product development company and a technology development company with different but symbiotic capabilities. We analyze various scenarios, assessing the benefits and downsides of demand forecast information sharing on each company and the supply chain as a whole. The scenarios analyzed vary according to the level of technology, innovation and resources shared between the firms.
We develop five methods to determine optimal revenue management policies for related items in a flexible supply chain including one seller and two producer in two tiers. We assume that in each echelon manufacturers produce similar and complementary products with different unit manufacturing costs, so demand leakage may occur between the echelons. The objectives of this paper are to investigate the impacts of various market powers between the members of the chain, determine the quantity of demand leakage under optimal prices, and obtain algebraic functions to compute the overall profit of the developed flexible supply chain. According to the power structures of chain members, five policies such as MS-Stackelberg, MS-Bertrand, RS-Stackelberg, MS-Bertrand and Nash games are developed. Finally, numerical studies are presented to illustrate the applicability of the developed models and solution methods.
This article examines the information acquisition strategy of a dual‐channel supply chain, in which a manufacturer sells a product both through a retailer and through its own direct channel. Either the manufacturer or the retailer can acquire demand information from a third‐party marketing research company. The manufacturer first decides whether or not to acquire such information, and then the retailer decides whether or not to acquire information. This setup implies a signaling game (either the manufacturer or the retailer may have private demand information) with an endogenous information structure. We identify conditions under which neither of the firms will acquire demand information, even when the cost of implementation is negligible. We also show that information acquisition can have a negative impact on the retailer, the supply chain, customers, and society. The manufacturer who acquires information always prefers to share information with the retailer, which benefits the retailer. The retailer who acquires information, however, may not want to share information with the manufacturer. The managerial insight of our paper is that firms that have more accurate demand data must develop strategies for the appropriate use of that information, both in their own planning and within the context of their dual‐channel supply chain.
We study compatibility choices of two competing applications from an alternative perspective that considers demand sharing effect and reduced misfit effect to explain differences between the compatible and incompatible cases. We construct a game-theoretic model in which an application with two main businesses tries to share its exclusive demand of its unique business with its rival application on their competing business. We find that incentives to establish one-way compatibility------the application with exclusive demand grants access to its competitor-----arise from the decrease of the reduced misfit cost while it may either arise or disappear from the decrease of the shared demand. In addition, consumer surplus increases in the reduced misfit cost and the shared demand. Moreover, we find the compatible case generates more social welfare than the incompatible case. And we find when the reduced misfit cost is beyond a threshold, the horizontal differentiation of the two applications is reduced to a lower level in the compatible case and the price competition is intensified in this situation. However, when the reduced misfit cost is less than a threshold, the price competition of the two applications can either be softened or intensified by compatibility, depending on the degree of shared demand.
Investment subsidies and output subsides are two common subsidy schemes used to promote the diffusion of eco-friendly products (EFPs). We adopted an analytical model to study which type of subsidies should be employed in promoting EFP diffusion in a competitive market of traditional products. Considering that there is a pre-investment in producing EFPs and EFP production technology is immature, we assume that a firm that wants to produce EFPs needs to bear both switching costs and higher manufacturing costs. When encouraging firms to produce EFPs, the results show that output subsidies are less costly when the switching costs are in the middle range. Meanwhile, in the case of a large potential market and low EFP manufacturing costs, output subsidies are more likely to be employed in attracting firms to produce EFPs. When encouraging all firms to produce EFPs, output subsidies are less costly, as they face a low switching cost. In the case of a small potential market, however, investment subsidies are more likely to be implemented. Finally, we tested the robustness of these findings in a market composed of more than two firms. We explored the subsidies in a circumstance where only one firm produced EFPs and found that investment subsidies were more likely to be implemented under these circumstances.
To explore the impacts of trade credit on the pricing decisions of complementary product manufacturers, we establish a Bertrand model of two-echelon supply chains. Such a supply chain consists of two duopolistic suppliers that provide complementary products to a monopolistic retailer in three scenarios: 1) no supplier extends trade credit, 2) only one supplier extends trade credit, and 3) both suppliers extend trade credit. We find that the impacts of trade credit on the profit of each supply chain member are dependent on the difference in the opportunity cost between the upstream suppliers that extend trade credit and the downstream retailer. If the value is negative, one supplier will increase its profit by extending trade credit, thereby enhancing the profits of the other supplier and the retailer simultaneously. Further, if the value is negative, both suppliers adopting trade credit will provide more benefits to the whole supply than only single supplier adopting it. On the contrary, if the value is positive, no party extending trade credit will benefit all participants the most.
تبلیغات و قیمتگذاری از موضوعات راهبردی شرکتها محسوب میشوند. سه محصول شامل یک کالای اصلی و دو کالای مکمل آن که جانشین یکدیگر هستند را در نظر بگیرید. در این مقاله برای اولین بار، مسئلهی تعیین همزمان سطح تبلیغات محصول اصلی به همراه قیمتگذاری دو محصول
جانشین مکمل محصول اصلی بررسی شده است. جوابهای تعادلی مسئله بههمراه تحلیلهای پارامتریک بر روی سطح تبلیغات تعادلی با رویکرد استکلبرگ - برترند که در آن محصول اصلی رهبر و محصولات جانشین پیرو هستند، محاسبه و ارائه شده است. تحلیل حساسیت پارامتریک نشان میدهد که تقاضای پایهی بازار بر روی تبلیغات تعادلی بیاثر است. همچنین، کشسانی
قیمت خودی بر روی تبلیغات تعادلی اثر منفی و کشسانی قیمت غیرخودی بر روی تبلیغات تعادلی اثر مثبت دارد. نتایج تحلیلی نشان میدهد قیمت محصول اصلی، اثر مثبت بر روی سطح تبلیغات محصول اصلی دارد.
Purpose
This paper attempts to analyze the relationship between the complementarity degrees of imperfect complementary products and sales strategies and give appropriate sales strategies for a two-stage supply chain.
Design/methodology/approach
With respect to two-stage supply chain consisting of two manufacturers who produce imperfect complementary products and one retailer who sells the products, aiming at bundling sales strategy, the authors define complementarity elasticity of products and use it to measure the degree of complementary between two products. Based on Stackelberg game and cooperation, the authors analyze the relationship between the complementarity degrees of imperfect complementary products and appropriate sales strategies.
Findings
As the impact of complementarity degree on sales strategy decision-making is better, the authors can pinpoint out which sales decision-making is optimal and which bundling sales strategy is the best for a two-stage supply chain. Considering that the degree of complementarity has a significant impact on the product sales strategy, the authors can point out which sales decision-making is optimal, that is, which bundled sales strategy is the optimal in the secondary supply chain of selling complementary products.
Practical implications
An innovative bundling can expand the sales of existing products and new products. It helps a retailer transcend and defeat competitors by reducing marketing expenses while increasing profits. Proper use of bundling can improve consumers utility and create an overall positive effect for both the enterprises and consumer.
Originality/value
The research can help some retailers to make many appropriate bundling sales strategies.
Information has become an extremely important commodity nowadays. The privatization of corporate social responsibility cost information has a negative impact on the sustainable development of supply chain. Hence, it is important to set up a reasonable coordination mechanism to encourage the supply chain members to reveal the true corporate social responsibility cost information. This paper investigates corporate social responsibility-sensitive supply chain, where a contract supplier sells products through a brand retailer. The contract supplier can invest in corporate social responsibility activities, but its corporate social responsibility cost information is only privately known to him. According the corporate social responsibility cost information revealed by the supplier, the retailer will decide whether to cooperate with him for a long time. Stackelberg game is used to explore the impact of the cost information asymmetry on the decision of supply chain members. The paper compares the decision effects under information asymmetry and symmetry decision, and designs a coordination mechanism for promoting the supplier to reveal the true corporate social responsibility cost information and achieving the supply chain coordination. The results show that the decision-making effect under symmetric information is better than asymmetric information, and the supplier's profit under the designed mechanism is not lower than that under asymmetric information. Moreover, the designed mechanism can improve the supplier's commitment to corporate social responsibility and eliminate double marginal effect to a certain extend. This paper provides managerial and practical insights for the enterprise adopting sustainable business models.
Information sharing has been regarded as a major way to promote collaboration or to optimize overall supply chain performance. Most of the literature has focused on unilateral information sharing in a supply chain with single or substitutable products. This paper investigates bilateral information sharing in two supply chains with complementary products, and formulates four decision models based on different information sharing patterns. Our results show that (i) information sharing always benefits the manufacturer, and benefits the retailer and the whole supply chain under certain conditions; (ii) information sharing increases/decreases the positive effect of the retailer's/manufacturer's forecast on the optimal pricing strategies in its own supply chain; however, its impact depends on the parameter conditions in the other complementary supply chain.
Due to frequent changes in consumer tastes, manufacturers continuously introduce new products to meet the desires of consumers. As a result, product launching strategies and pricing decisions have a considerable impact on a firm's profits, especially for short-life-cycle products. This study considers pricing competition in a multistage game between two asymmetric firms and examines three scenarios that are developed based on the firms’ product launching strategies under a single-product policy. Specifically, the firms may adopt simultaneous launching strategies and interact with each other in a two-stage game, or they may introduce their new products earlier or later than their rival under a three-stage interaction. We derive the firms’ equilibrium pricing decisions in a dynamic programming approach and analyze the firms’ equilibrium pricing behavior. Furthermore, we investigate the parametric effects on the firms’ profitabilities, performances, and preferences with regard to the product launching strategies. Introducing a new product later than the rival is often a dominant strategy for firms. However, in some cases, the firms may change their preference to launch their new product earlier than their rival to allow for a longer sales period.
In this article, the authors present a model for the pricing of a substitute and complementary products (four commodities) while the seller delivers the products individually, in the form of a package to the final customer, and compares the profits from the sale of each scenario. Also, a comparative study has been completed. In the package sale, two complementary products are delivered in one package, but each item is sold in separate sales. The demand function for each product is a function of the price. To illustrate the validity of the model, numerical examples have been used and a sensitivity analysis has been done on the important parameters in the problem.
This paper studies the manufacturer's and retailer's integration strategies in a supply chain with complementary products and examines the effects of downstream, upstream and vertical integrations on supply chain members' decisions and profits and on supply chain performance. The centralised and decentralised decision models are considered as benchmarks that are compared to downstream, upstream and vertically integrated strategies. Our comparison and analysis show that the total profit of the supply chain increases with the number of integrated players and that vertical integration can be more profitable than that of upstream and downstream integrations. However, to our surprise, the upstream and downstream integration strategies do not affect the total profit.
Purpose
This paper aims to address the following problems: What are the firms’ optimal pricing and quality policies under three scenarios (no bundling, pure bundling and mixed bundling)? In what condition will one bundling strategy dominate the others? How does the degree of complementarity affect the firms’ decision?
Design/methodology/approach
Using the game theory, this study first establishes three models of bundling strategies: no bundling, pure bundling and mixed bundling and then obtains the optimal prices and quality decisions. This study uses numerical analysis to explore the relationships between the prices (demands and profits) and some key parameters and to obtain some valuable management complications.
Findings
Some interesting and valuable management implications are established: regardless of the degree of complementarity, adopting a pure bundling or mixed bundling strategy is better than separately selling an individual product; a high degree of complementarity leads to reduced profit in the no bundling and mixed bundling scenarios, whereas the condition in the pure bundling strategy is the opposite; and when the degree of complementarity is adequately large, choosing pure bundling strategy is more profitable.
Research limitations/implications
On the one hand, this study does not calculate the profit sharing ratio, and hence, the equilibrium profit sharing ratio can be explored in future work. On the other hand, marketing efforts (e.g. advertising and promotion) can be included in the study.
Practical implications
This study derives the necessary conditions for the most effective bundling strategy that maximizes firm’s profits, and these conclusions can provide a decision reference to the bundling decisions of firms.
Originality/value
First, the optimal bundling strategies in a horizontal supply chain consisting of two firms is considered. Under the pure and mixed bundling strategies, the two firms sell the bundled product by building a cooperative program. Second, both the pricing policies and quality decisions of supply chain members under the different bundling strategies are studied.
In this paper, we investigate the price decisions for a seller who provides two complementary products to strategic consumers over two periods under three selling strategies: markdown pricing, second period bundling (SPB) and first period bundling (FPB). We find that the seller’s optimal prices in the second period of SPB and FPB are higher than that of markdown pricing strategy, the seller can obtain the best profit by utilizing the FPB strategy, and obtain more profit in the SPB strategy than that in the markdown pricing strategy with some conditions. The effects of consumers’ patience and complementary coefficient of products on seller’s profit and selling strategies are analyzed by the numeral examples.
Many companies have embarked on initiatives that enable more demand information sharing between retailers and their upstream suppliers. While the literature on such initiatives in the business press is proliferating, it is not clear how one can quantify the benefits of these initiatives and how one can identify the drivers of the magnitudes of these benefits. Using analytical models, this paper aims at addressing these questions for a simple two-level supply chain with nonstationary end demands. Our analysis suggests that the value of demand information sharing can be quite high, especially when demands are significantly correlated over time.
We develop an analytical model of contingent valuations and address two questions of import to a monopolist: (i) should a given pair of complements or substitutes be sold separately (pure components), together (pure bundling), or both (mixed bundling), and at what prices? (ii) How do optimal bundling and pricing strategies for complements and substitutes differ from those for independently valued products? We find that the combination of marginal cost levels and the degree of complementarity or substitutability determines which of the three bundling strategies is optimal. Complements and substitutes should typically be priced higher than independently valued products.
Competitive maneuvering in the information economy has raised a pressing question: how can firms raise profits by giving away products for free? This paper provides a possible answer and articulates a strategy space for information product design. Free strategic complements can raise a firm's own profits while free strategic substitutes can lower profits for competitors.We introduce a formal model of two-sided market externalities based in textbook economics -- a mix of Katz & Shapiro network effects, price discrimination, and product differentiation -- that leads to novel strategies such as an eagerness to enter into Bertrand price competition. This combination helps to explain many recent firm strategies such as those of Microsoft, Netscape (AOL), Sun, Adobe, and ID.The model presented here argues for three simple and intuitive results. First, a firm can rationally invest in a product it intends to give away into perpetuity even in the absence of competition. Second, we identify distinct markets for content-providers and end-consumers and show that either can be a candidate for the free good. Third, a firm can use strategic product design to penetrate a market that becomes competitive post-entry. The model therefore helps to explain several interesting market behaviors such as free goods, upgrade paths, split versioning, and strategic information substitutes.
We examine a heterogenous goods duopoly model, wherein governments simultaneously and noncooperatively choose whether or not to provide subsidies for their firms and then firms noncooperatively choose output levels, either sequentially or simultaneously. We find that government trade policy and market structure are interdependent. First, the trade regime alters traditional firm preferences over sequential versus simultaneous play. Second, different market structures influence governments' preferences about free trade versus subsidies. Further, if one of the firms is a potential leader, allowing for endogenous market structure generates equilibrium outcomes that sometimes reinforce, and sometimes counter, traditional results in the strategic trade literature.
Forecast sharing is studied in a supply chain with a manufacturer that faces stochastic demand for a single product and a supplier that is the sole source for a critical component. The following sequence of events occurs: the manufacturer provides her initial forecast to the supplier along with a contract, the supplier constructs capacity (if he accepts the contract), the manufacturer receives an updated forecast and submits a final order. Two contract compliance regimes are considered. If the supplier accepts the contract under forced compliance then he has little flexibility with respect to his capacity choice; under voluntary compliance, however, he maintains substantial flexibility. Optimal supply chain performance requires the manufacturer to share her initial forecast truthfully, but she has an incentive to inflate her forecast to induce the supplier to build more capacity. The supplier is aware of this bias, and so may not trust the manufacturer's forecast, harming supply chain performance. We study contracts that allow the supply chain to share demand forecasts credibly under either compliance regime.
The value of new information depends on how accurate the information is, but it may also depend on the characteristics of the firm and the nature of the industry it operates in. We develop a game-theoretic model to understand how firm and industry characteristics moderate the effect of market information on firm profits. Our results suggest that information is more valuable when product substitutability is higher, suggesting that information is of greater value in more competitive industries. Our results also suggest that although industry size does not affect the value of information, information is more valuable for larger firms. We find that, except under some conditions, more precise market information has a greater impact on profits in a Stackelberg mode of conduct than in a Bertrand-Nash mode.
In traditional supply chain inventory management, orders are the only information firms exchange, but information technology now allows firms to share demand and inventory data quickly and inexpensively. We study the value of sharing these data in a model with one supplier, N identical retailers, and stationary stochastic consumer demand. There are inventory holding costs and back-order penalty costs. We compare a traditional information policy that does not use shared information with a full information policy that does exploit shared information. In a numerical study we find that supply chain costs are 2.2% lower on average with the full information policy than with the traditional information policy, and the maximum difference is 12.1%. We also develop a simulation-based lower bound over all feasible policies. The cost difference between the traditional information policy and the lower bound is an upper bound on the value of information sharing: In the same study, that difference is 3.4% on average, and no more than 13.8%. We contrast the value of information sharing with two other benefits of information technology, faster and cheaper order processing, which lead to shorter lead times and smaller batch sizes, respectively. In our sample, cutting lead times nearly in half reduces costs by 21% on average, and cutting batches in half reduces costs by 22% on average. For the settings we study, we conclude that implementing information technology to accelerate and smooth the physical flow of goods through a supply chain is significantly more valuable than using information technology to expand the flow of information.
This paper analyzes investment decisions that can be made in a modular form. It is motivated by the empirical observation that managements are particularly worried about "downside" risk. With a sequential approach this risk is minimized. An investment in a module produces information as well as profits or losses. In our model a larger investment produces more information in addition to larger profits or losses. Costs for changing the level of the investment from period to period are introduced. The optimal sequential investment policy is studied for a two-period problem. Conditions are presented under which no investment, a partial investment, or a full investment in the first period is optimal.
Inferences or decisions in the face of uncertainty should be based on all available information. Thus, when probability distributions for an uncertain quantity are obtained from experts, models, or other information sources, these distributions should be combined to form a single consensus distribution upon which inferences and decisions can be based. An important feature of information from different sources is the possibility of stochastic dependence, and a consensus model which formally allows for such dependence is developed in this paper. Under normality, the model yields reasonably tractable results, and the consensus distribution is quite sensitive to the degree of dependence.
Electronic Data Interchange (EDI) and related technologies are making it less expensive to frequently transmit demand information up the supply chain from the point of sale. However, little is known about how the various participants in the supply chain might exploit more timely demand information. This research is intended to be an opening contribution to the analytical study of timely demand information. We study a simple two-level system composed of a supplier (or component plant) and a single customer (or final assembly plant). The two factories use a standard periodic base-stock policy for one particular item, but the equal-length production cycles of the two factories do not necessarily coincide. Both participants hold inventories to buffer the effects of uncertain orders and uncertain deliveries. The supplier is in turn supplied by a source with infinite capacity. Final demand occurs only at the final assembly plant, which communicates demand over its order cycle to the component plant. If the component plant begins a production cycle between orders from the final assembly plant, it is uninformed about some number of days' demand which has been observed at the customer but not yet communicated. Any technology, such as EDI, that makes it cheaper for the customer to communicate demand as it occurs allows the supplier to base its decisions on more accurate information. With more accurate demand information the supplier could reduce inventories, or improve the reliability of its deliveries to its customer, or both. The customer, in turn, could reduce its inventories if its supplier were more reliable. We examine the changes brought about by the exchange of timely demand information in inventories and service levels at both the supplier and customer. Our results show that inventory-related benefits are particularly sensitive to demand variability, the service level provided by the supplier, and the degree to which the order and production cycles are out of phase.
A standard oligopoly model of bundling shows that bundling by a firm with a monopoly over one product has a strategic effect because it changes the substitution relationships between the goods among which consumers choose. Bundling in appropriate proportions is privately profitable, reduces rivals' profits and overall welfare, and may drive rivals from the market.
In a duopoly model where firms have private information about an uncertain linear demand, it is shown that if the goods are substitutes (not) to share information is a dominant strategy for each firm in Bertrand (Cournot) competition. If the goods are complements the result is reversed. Furthermore the following welfare results are obtained: 1.(i) With substitutes in Cournot competition the market outcome is never optimal with respect to information sharing but it may be optimal in Bertrand competition if the products are good substitutes. With complements the market outcome is always optimal.2.(ii) Bertrand competition is more efficient than Cournot competition.3.(iii) The private value of information to the firms is always positive but the social value of information is positive in Cournot and negative in Bertrand competition.
This article analyzes the duality of prices and quantities in a differentiated duopoly. It is shown that if firms can only make two types of binding contracts with consumers, the price contract and the quantity contract, it is a dominant strategy for each firm to choose the quantity (price) contract, provided the goods are substitutes (complements).
This paper analyzes a model of duopoly with fixed costs. Leadership by one "established" firm may yield an outcome in which the second is inactive, but entry prevention is not a prior constraint. We find that two aspects of product differentiation have distinct effects: an absolute advantage in demand for the established firm makes entry harder, but a lower cross-price effect facilitates it. In the basic model we maintain the same quantity after entry. An extension of the model deals with the case where the threat of a predatory output increase after entry is made credible by carrying excess capacity prior to entry.
This paper examines the incentives for firms to share information vertically in a two-level supply chain in which there are one upstream firm, a manufacturer, and many downstream firms, retailers. The retailers are engaged in a Cournot competition and are endowed with some private information. Vertical information sharing has two effects: "direct effect" due to the changes in strategy by the parties involved in sharing the information and "indirect effect" (or "leakage effect") due to the changes in strategy by other competing firms (who may infer the information from the actions of the informed parties). Both changes would affect the profitability of the firms. We show that the leakage effect discourages the retailers from sharing their demand information with the manufacturer while encouraging them to share their cost information. On the other hand, the direct effect always discourages the retailers from sharing their information. When voluntary information sharing is not possible, we identify conditions under which information can be traded and show how price should be determined to facilitate such information exchange. We also examine the impact of vertical information sharing on the total supply chain profits and social benefits.
We examine a heterogenous goods duopoly model, wherein governments simultaneously and noncooperatively choose whether or not to provide subsidies for their firms and then firms noncooperatively choose output levels, either sequentially or simultaneously. We find that government trade policy and market structure are interdependent. First, the trade regime alters traditional firm preferences over sequential versus simultaneous play. Second, different market structures influence governments' preferences about free trade versus subsidies. Further, if one of the firms is a potential leader, allowing for endogenous market structure generates equilibrium outcomes that sometimes reinforce, and sometimes counter, traditional results in the strategic trade literature. Copyright 2004 Blackwell Publishing, 350 Main Street, Malden, MA 02148, USA, and 9600 Garsington Road, Oxford OX4 2DQ, UK..
Trusted partners: how companies build mutual trust and win together
- Lewis Jordan
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http://www.sbc.com/gen/press-room?pid=4800 and cdvn=news and news-articleid=21545
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To ally or not to ally? Mark Manage
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To ally or not to ally?
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