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Coordinating the supplier-retailer supply chain under noise effect with bundling and inventory strategies

  • * Corresponding author: Tel. +52 81 83284235, Fax +52 81 83284153. E-mail address:lecarden@itesm.mx (L.E. Cárdenas-Barrón)

    * Corresponding author: Tel. +52 81 83284235, Fax +52 81 83284153. E-mail address:lecarden@itesm.mx (L.E. Cárdenas-Barrón) 
Abstract Full Text(HTML) Figure(2) / Table(8) Related Papers Cited by
  • In current competitive market, the products and their demand's uncertainty are high. In order to reduce these uncertainties the coordination of supply chain is necessary. Supply chain can be managed under two viewpoints typically: 1) centralized supply chain and 2) decentralized supply chain, and the coordination can be done in both types of chains. In the centralized supply chain there exists a global decision maker who takes all the best decisions in order to maximize the profit of the whole supply chain. Here, the useful information required to make the best decisions is open to all members of the chain. On the other hand, in the decentralized supply chain all members decide in a separate and sequential way, how to maximize their profits. In order to coordinate efficiently the supply chain, both supplier and retailer are involved in a coordination contract that makes it possible for the decentralized decisions to maximize the profit of the entire supply chain. In this context, the situation that the supplier-retailer chain faces is a two-stage decision model. In the first stage the supplier, based on former knowledge about the market, decides the production capacity to reserve for the retailer. In the second stage, after that demand information is updated, the retailer determines the bundle price and the quantity of bundles to order. This paper considers a supply chain comprised of one supplier and one retailer in which two complementary fashion products are manufactured and sold as a bundle. The bundle has a short selling season and a stochastic price dependent on demand with a high level of uncertainty. Therefore, this research considers that the demand rates are uncertain and are dependent on selling prices and on a random noise effect on the market. Profit maximization models are developed for centralized and decentralized supply chains to determine decisions on production capacity reservation, order quantity of bundled products and the bundle-selling price. The applicability of the developed models and solution method are illustrated with a numerical example.

    Mathematics Subject Classification: 90B05.


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  • Figure 1.  Impact $a_1$ between two products on the retailer's pricing strategy

    Figure 2.  Impact $a_1$ between two products on the wholesale pricing strategy

    Table 1.  Some recent works related to bundling strategy

    Literature Strategies Selling price Demand rate Situation
    Chakravarti et al. [12]BundlingBundle priceSelling priceDecentralized supply chains
    Li et al. [25]Mix bundlingBundle priceSelling priceBi-level programming
    Yan et al. [51]Bundle pricing and advertisingBundle priceSelling priceProduct complementary and advertisement of bundle product
    Wang et al. [47]Service bundlingService and Price bundlingDuopoly competitive environment
    Banciu and ∅degaard [3]Different bundlingSimulation technique
    Giri et al. [20]PricingBundling priceLinearly dependent on priceDuopoly market
    Vamosiu [43]Imperfect CompetitionMixed bundlingPure bundling
    This paperBundlingBundle selling priceUncertain, selling price and random noise effect on marketCentralized and decentralized supply chains
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    Table 2.  Effects of basic demand size $a_1$ to the contract for product 1 when $Q_{1}^{c} <M_{1}^{c} = 487$

    $a_1$ $p_{1} $ $w_{1} $ $d_{1} $ $\alpha _{1} $ $Q_{1}^{c} $ $F(s_{1} )$
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    Table 3.  Effects of basic demand size $a_1$ to the contract for product 1, $ Q_{1}^{c} = M_{1}^{c} = 487$

    $a_1$ $p_{1} $ $w_{1} $ $d_{1} $ $\alpha _{1} $ $F(s_{1} )$
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    Table 4.  Comparison between coordination contract vs price-only contract for profit of product 1, Coordination contract: $M_{1}^{c} $ = 487 and total profit = 279270

    $w_{1} $CapacitySupplier profitRetailer profitTotal profit
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    Table 5.  Effects of basic demand size to the contract under bundling policy, $ Q_{B}^{c} <M_{B}^{c} = 867 $

    $a_1$ $p_{1B} $ $w_{B} $ $d_{B} $ $\alpha _{B} $ $Q_{B}^{c} $ $F(s_{B} )$
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    Table 6.  Effects of basic demand size on the contract under bundling policy when, $ Q_{B}^{c} = M_{B}^{c} = 867 $

    $a_1$ $p_{2B} $ $w_{B} $ $d_{B} $ $\alpha _{B} $ $F(s_{B} )$
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    Table 7.  Profit with bundling policy, Proposed contract: $M_{B}^{c} $ = 867 and total profit = 260621

    $w_{B} $CapacitySupplier profitRetailer profitTotal profit
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    Table 8.  The results in numerical analysis

    Percent change $p_{1} $ $p_{2} $ $p_{B} $ $F(s_{B} )$ $Q_{B}^{c} $ $w_{B} $ $\alpha _{B} $ $d_{B} $Retailer profitSupplier profit
    $a_{2} =0.5$+5052.852.4838.446.02-29.9733.09-279.4433-7.07-4.66
    $\lambda =0.35$+50Infeasible
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