Impact of cap-and-trade regulation on coordinating perishable products supply chain with cost learning

Qingguo Bai; Jianteng Xu; Fanwen Meng; Niu Yu

doi:10.3934/jimo.2020126

Article Contents

2021, Volume 17, Issue 6: 3417-3444. Doi: 10.3934/jimo.2020126

This issue Previous Article Coordination of a supply chain with a loss-averse retailer under supply uncertainty and marketing effort Next Article Bayesian decision making in determining optimal leased term and preventive maintenance scheme for leased facilities

Impact of cap-and-trade regulation on coordinating perishable products supply chain with cost learning

1.
School of Management, Qufu Normal University, Rizhao, Shandong, 276826, China
2.
Department of Health Services and Outcomes Research, National Healthcare Group, Singapore 138543
3.
School of Management, Wuhan Textile University, Wuhan, Hubei, 430200, China

^* Corresponding author: Fanwen Meng
^* Corresponding author: Fanwen Meng

Received: December 31, 2019

Revised: February 29, 2020

Early access: June 2020

Published: November 2021

The research is partly supported by the National Natural Science Foundation of China under grants 71771138, 71702087 and 71701154, Humanities and Social Sciences Youth Foundation of Ministry of Education of China under grant 17YJC630004, Special Foundation for Taishan Scholars of Shandong Province, China under Grant tsqn201812061, and Science and Technology Research Program for Higher Education of Shandong Province, China under Grant 2019KJI006

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Abstract

This paper incorporates carbon emission regulation and cost learning effects to examine a manufacturer-retailer supply chain for deteriorating items over a multi-period planning horizon. We investigate their impacts on supply chain coordination under the assumption that the product demand is affected by the selling price, promotional effort and inventory level. We first propose two algorithms for determining optimal solutions of the centralized and decentralized models. We show that the decentralized system can be coordinated perfectly with a two-part tariff contract. Further, we study necessary conditions under which members of the supply chain can accept this contract. At last, we conduct numerical experiment to illustrate the obtained theoretical results in impact analysis and the robustness of the coordinated model.

Keywords:

Mathematics Subject Classification: Primary: 90B60, 91A05; Secondary: 90C46.

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Figure 1. Graphical representation of inventory level at the retailer

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Figure 2. Intervals of contract parameters to attain the win-win outcome

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Figure 3. Impacts of $ C $ on profit and total emissions amount

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Figure 4. Impacts of $ c_{p} $ on profit and total emissions amount

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Figure 5. Impacts of $ \phi $ on profit and total emissions amount

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Figure 6. Effects plot for the SN ratio of the coordination system

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Table 1. The optimal solution of the example

Model	$ w $	$ s $	$ p $	$ n $	Retailer's	Manufacturer's	Total	Total emissions
					profit	profit	profit	amount
Centralized	-	12.15	213.75	3	-	-	25589.00	285270
Decentralized	56.76	6.08	256.88	3	3622.10	17045.00	20667.10	142640
TT contract
$ F=9850 $	50	12.15	213.75	3	8539.00	17050.00	25589.00	285270
$ F=12000 $	50	12.15	213.75	3	6389.00	19200.00	25589.00	285270
$ F=14750 $	50	12.15	213.75	3	3639.00	21950.00	25589.00	285270

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Table 2. Calculation results of $ L_{8} $ orthogonal array experiment for the coordination model

No.	A	B	C	D	E	Total profit	SN ratio of	Total emissions	SN ratio of total
	$ h_{r} $	$ \theta $	$ \phi $	$ C $	$ c_{p} $		total profit	amount	emissions amount
1	1	1	1	1	1	43394	92.75	284600	-109.085
2	1	1	1	2	2	38191	91.64	309080	-109.801
3	1	2	2	1	1	15727	83.93	259150	-108.271
4	1	2	2	2	2	6371	76.08	280390	-108.955
5	2	1	2	1	2	39551	91.94	314060	-109.940
6	2	1	2	2	1	32531	90.25	289570	-109.235
7	2	2	1	1	2	15409	83.76	284830	-109.092
8	2	2	1	2	1	13943	82.89	263590	-108.419

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Table 3. Analysis of variance for the total profits and its SN ratio

(a) Analysis of variance for the total profits
Source	df	SS($ \times10^{8} $)	MS($ \times10^{8} $)	F	P
A	1	0.0063	0.0063	0.11	0.776
B	1	13.0604	13.0604	217.25	0.005
C	1	0.3510	0.3510	5.84	0.137
D	1	0.6639	0.6639	11.04	0.080
E	1	0.0461	0.0461	0.77	0.474
Error	2	0.1202	0.0601	-	-
Total	7	14.2480	-	-	-
(b) Analysis of variance for the SN ratio of the total profits
Source	df	SS	MS	F	P
A	1	2.450	2.450	0.43	0.581
B	1	199.178	199.178	34.55	0.028
C	1	9.734	9.734	1.69	0.323
D	1	16.603	16.603	2.88	0.232
E	1	5.109	5.109	0.89	0.446
Error	2	11.529	5.765	-	-
Total	7	244.604	-	-	-

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Table 4. Analysis of variance for the carbon emissions and its SN ratio

(a) Analysis of variance for the carbon emissions
Source	df	SS($ \times10^{8} $)	MS($ \times10^{8} $)	F	P
A	1	0.4432	0.4432	16.84	0.055
B	1	14.9468	14.9468	567.78	0.002
C	1	0.0014	0.0014	0.05	0.837
D	1	0.0000	0.0000	0.00	0.998
E	1	10.4539	10.4539	397.11	0.003
Error	2	0.0527	0.0263	-	-
Total	7	25.8979	-	-	-
(b) Analysis of variance for the SN ratio of the carbon emissions
Source	df	SS	MS	F	P
A	1	0.0411	0.04107	157.77	0.006
B	1	1.3819	1.3819	5307.76	0.000
C	1	0.0000	0.0000	0.01	0.920
D	1	0.0001	0.0001	0.25	0.669
E	1	0.9655	0.9655	3708.69	0.000
Error	2	0.0005	0.0003	-	-
Total	7	2.3891	-	-	-

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