Ata Allah Taleizadeh 1, , Leopoldo Eduardo Cárdenas-Barrón 2,, and Roya Sohani 3,
School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
School of Engineering and Sciences, Tecnológico de Monterrey, E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, Nuevo León, México
Department of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran
* Corresponding author: Tel. +52 81 83284235, Fax +52 81 83284153. E-mail address:lecarden@itesm.mx (L.E. Cárdenas-Barrón)
Received May 2017 Revised January 2018 Published August 2018
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.
Keywords: Pricing, Inventory; supply chain coordination, risk and profit sharing.
Citation: Ata Allah Taleizadeh, Leopoldo Eduardo Cárdenas-Barrón, Roya Sohani. Coordinating the supplier-retailer supply chain under noise effect with bundling and inventory strategies. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1701-1727. doi: 10.3934/jimo.2018118
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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] Bundling Bundle price Selling price Decentralized supply chains
Li et al. [25] Mix bundling Bundle price Selling price Bi-level programming
Yan et al. [51] Bundle pricing and advertising Bundle price Selling price Product complementary and advertisement of bundle product
Wang et al. [47] Service bundling — Service and Price bundling Duopoly competitive environment
Banciu and ∅degaard [3] Different bundling — — Simulation technique
Giri et al. [20] Pricing Bundling price Linearly dependent on price Duopoly market
Vamosiu [43] Imperfect Competition Mixed bundling — Pure bundling
This paper Bundling Bundle selling price Uncertain, selling price and random noise effect on market Centralized and decentralized supply chains
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} $ $F(s_{1} )$
500 237 151 133.50 2.64 316 0.887
700 326 192 178.00 -0.50 424 0.915
819.9 380 218 205.00 -2.36 487 0.927
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} $ $F(s_{1} )$
820 405 231 217.50 -1.50 0.975
1000 541 298 285.50 -2.46 0.855
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} $ Capacity Supplier profit Retailer profit Total profit
163 449 142000 123210 265210
250 401 10954 90740 101694
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} $ $F(s_{B} )$
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} $ $F(s_{B} )$
850 474 298 272.0 -5.90 0.750
Table 7. Profit with bundling policy, Proposed contract: $M_{B}^{c} $ = 867 and total profit = 260621
$w_{B} $ Capacity Supplier profit Retailer profit Total profit
259 794 126730 87871 214601
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 profit Supplier profit
$a_{2} =0.5$ +50 52.8 52.48 38.44 6.02 -29.97 33.09 -279.44 33 -7.07 -4.66
+25 25.83 26.03 18.63 3.12 -12.82 15.83 -121.39 15.99 4.00 3.47
+15 15.42 15.70 11.08 2.04 -7.05 9.35 -68.06 9.51 3.99 3.13
-15 -15.42 -15.29 -10.61 -2.28 6.09 -8.99 51.94 -9.11 -7.31 -5.91
-25 -25.42 -25.62 -17.22 -4.08 9.29 -14.03 90.83 -14.98 -14.60 -9.97
-50 Infeasible
$\theta=0.25$ +50 10.42 10.33 1.65 0.36 2.08 1.08 17.78 1.42 4.89 3.53
+25 5.00 4.96 0.94 0.24 0.96 0.72 8.33 0.81 2.29 1.86
-15 -3.33 -3.31 -0.71 0.00 -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
$\lambda =0.35$ +50 Infeasible
+25 0.00 0.00 13.21 2.40 -7.05 11.15 -66.39 11.34 6.83 5.81
+15 0.00 0.00 8.25 1.56 -4.01 6.83 -39.44 6.88 5.11 4.10
-15 0.00 0.00 -8.25 -1.68 4.17 -6.47 36.67 -7.29 -7.63 -4.22
-25 0.00 0.00 -13.44 -3.00 5.61 -11.15 55.83 -11.74 -12.06 -8.73
-50 0.00 0.00 -25.71 -6.83 8.33 -20.86 91.67 -22.06 -27.45 -19.74
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Ata Allah Taleizadeh Leopoldo Eduardo Cárdenas-Barrón Roya Sohani