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

Ata Allah Taleizadeh; Leopoldo Eduardo Cárdenas-Barrón; Roya Sohani

doi:10.3934/jimo.2018118

Article Contents

2019, Volume 15, Issue 4: 1701-1727. Doi: 10.3934/jimo.2018118

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

Ata Allah Taleizadeh^1,,
Leopoldo Eduardo Cárdenas-Barrón^2, , and
Roya Sohani^3,

1.
School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
2.
School of Engineering and Sciences, Tecnológico de Monterrey, E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, Nuevo León, México
3.
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)
* 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

Early access: August 2018

Published: July 2019

Abstract Full Text(HTML) Figure(2) / Table(8) Related Papers Cited by

Abstract

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:

Mathematics Subject Classification: 90B05.

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

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

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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

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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} $	$F(s_{1} )$
500	237	151	133.50	2.64	316	0.887
550	259	161	144.50	1.85	343	0.896
600	282	172	156.00	1.08	369	0.903
650	304	183	167.00	0.29	397	0.910
700	326	192	178.00	-0.50	424	0.915
750	348	203	189.00	-1.29	450	0.920
800	371	213	200.50	-2.50	477	0.925
819.9	380	218	205.00	-2.36	487	0.927

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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} $	$F(s_{1} )$
820	405	231	217.50	-1.50	0.975
850	427	242	228.50	-1.68	0.965
880	449	253	239.50	-1.86	0.950
910	472	264	251.00	-2.04	0.940
940	495	275	262.50	-2.16	0.905
970	518	287	274.00	-2.31	0.880
1000	541	298	285.50	-2.46	0.855

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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} $	Capacity	Supplier profit	Retailer profit	Total profit
163	449	142000	123210	265210
199	426	125720	105810	231530
250	401	10954	90740	101694
290	378	95801	75437	171238
320	356	81918	62549	144467

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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} $	$F(s_{B} )$
500	279	216	174.50	8.00	564	0.799
550	303	225	186.50	6.10	592	0.812
600	327	234	198.50	4.20	644	0.823
650	350	244	210.00	2.27	696	0.833
700	374	255	222.00	0.41	746	0.842
750	398	264	234.00	-1.48	796	0.850
800	421	273	245.50	-3.46	847	0.857
819.9	431	278	250.50	-4.18	867	0.860

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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} $	$F(s_{B} )$
820	437	279	253.50	-5.92	0.752
850	474	298	272.0	-5.90	0.750
880	510	315	290.00	-5.86	0.747
910	546	333	308.00	-5.60	0.742
940	585	353	327.00	-5.96	0.740
970	621	371	345.50	-6.25	0.739
1000	658	389	364.00	-6.35	0.736

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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
234	838	142490	104540	247030
259	794	126730	87871	214601
299	745	112410	72037	184447
352	668	96453	60367	156820
386	630	85792	45607	131399

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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 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	2.92	3.31	0.47	0.12	0.64	0.36	6.39	0.40	1.34	1.55
	-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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