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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) 
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  • 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.

    Citation:

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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} $ $F(s_{1} )$
    500237151133.502.643160.887
    550259161144.501.853430.896
    600282172156.001.083690.903
    650304183167.000.293970.910
    700326192178.00-0.504240.915
    750348203189.00-1.294500.920
    800371213200.50-2.504770.925
    819.9380218205.00-2.364870.927
     | Show Table
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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} $ $F(s_{1} )$
    820405231217.50-1.500.975
    850427242228.50-1.680.965
    880449253239.50-1.860.950
    910472264251.00-2.040.940
    940495275262.50-2.160.905
    970518287274.00-2.310.880
    1000541298285.50-2.460.855
     | Show Table
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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
    163449142000123210265210
    199426125720105810231530
    2504011095490740101694
    2903789580175437171238
    3203568191862549144467
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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} $ $F(s_{B} )$
    500279216174.508.005640.799
    550303225186.506.105920.812
    600327234198.504.206440.823
    650350244210.002.276960.833
    700374255222.000.417460.842
    750398264234.00-1.487960.850
    800421273245.50-3.468470.857
    819.9431278250.50-4.188670.860
     | Show Table
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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} $ $F(s_{B} )$
    820437279253.50-5.920.752
    850474298272.0-5.900.750
    880510315290.00-5.860.747
    910546333308.00-5.600.742
    940585353327.00-5.960.740
    970621371345.50-6.250.739
    1000658389364.00-6.350.736
     | Show Table
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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
    234838142490104540247030
    25979412673087871214601
    29974511241072037184447
    3526689645360367156820
    3866308579245607131399
     | Show Table
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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
    +2525.8326.0318.633.12-12.8215.83-121.3915.994.003.47
    +1515.4215.7011.082.04-7.059.35-68.069.513.993.13
    -15-15.42-15.29-10.61-2.286.09-8.9951.94-9.11-7.31-5.91
    -25-25.42-25.62-17.22-4.089.29-14.0390.83-14.98-14.60-9.97
    -50Infeasible
    $\theta=0.25$+5010.4210.331.650.362.081.0817.781.424.893.53
    +255.004.960.940.240.960.728.330.812.291.86
    +152.923.310.470.120.640.366.390.401.341.55
    -15-3.33-3.31-0.710.00-0.32-0.36-3.06-0.61-1.91-0.08
    -25-5.42-4.96-0.94-0.12-0.96-0.72-6.39-0.81-2.32-1.05
    -50-10-10.33-1.65-0.24-1.06-1.08-14.72-1.42-4.72-3.42
    $\lambda =0.35$+50Infeasible
    +250.000.0013.212.40-7.0511.15-66.3911.346.835.81
    +150.000.008.251.56-4.016.83-39.446.885.114.10
    -150.000.00-8.25-1.684.17-6.4736.67-7.29-7.63-4.22
    -250.000.00-13.44-3.005.61-11.1555.83-11.74-12.06-8.73
    -500.000.00-25.71-6.838.33-20.8691.67-22.06-27.45-19.74
     | Show Table
    DownLoad: CSV
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