Filled function method to optimize supply chain transportation costs

Deqiang Qu; Youlin Shang; Dan Wu; Guanglei Sun

doi:10.3934/jimo.2021115

Article Contents

2022, Volume 18, Issue 5: 3339-3349. Doi: 10.3934/jimo.2021115

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Filled function method to optimize supply chain transportation costs

1.
School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471000, China
2.
School of Information Engineering, Henan University of Science and Technology, Luoyang 471000, China

^* Corresponding author: Youlin Shang
^* Corresponding author: Youlin Shang

Received: September 30, 2020

Revised: January 31, 2021

Early access: July 2021

Published: November 2022

The first author is supported by NSF grant of China (Nos.12071112, 11701150, 11471102); Basic research projects for key scientific research projects in Henan Province of China (No.20ZX001)

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Abstract

The transportation-based supply chain model can be formulated as the constrained nonlinear programming problems. When solving such problems, the classic optimization algorithms are often limited to local minimums, causing the difficulty to find the global optimal solution. Aiming at this problem, a filled function method with a single parameter is given to cross the local minimum. Based on the characteristics of the filled function, a new filled function algorithm that can obtain the global optimal solution is designed. Numerical experiments verify the feasibility and effectiveness of the algorithm. Finally, the filled function algorithm is applied to the solution of supply chain problems, and the numerical results show that the algorithm can also address decision-making problems of supply chain transportation effectively.

Keywords:

Mathematics Subject Classification: 90C30.

Citation:

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Table 1.

	The proposed Algorithm	Algorithm in [10]
	$ f({x^*}) $	$ f({x^*}) $
Problem 1	-1.0316	-1.0316
Problem 2	0	0
Problem 3	1.513e-08	0
Problem 4, n=10	4.4277e-43	1.3790e-14
Problem 4, n=20	3.2490e-44	3.0992e-14
Problem 4, n=50	1.8410e-43	9.85.1e-13

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Table 2.

	The proposed Algorithm		Algorithm in [10]
	CPU run time(s)	Total times(times)	CPU run time(s)	Total times(times)
Problem 1	19.1964	1986	26.3325	2453
Problem 2	15.1005	1537	18.8756	1421
Problem 3	10.8827	961	14.3194	1227
Problem 4, n=10	16.0294	1920	70.5483	8895
Problem 4, n=20	24.6212	4696	91.3288	18242
Problem 4, n=50	34.9223	6728	195.3385	43232

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Table 3. Transporter to seller unit cost and maximum transport volume

		Transporter 1		Transporter 2
Mode of generalized transport		unit cost(＄/t)	maximum amount(t)	unit cost(＄/t)	maximum amount(t)
	Seller 1	220		200
Transporter 1	Seller 2	250	1000	220	1500
	Seller 3	210		210
	Seller 1	180		200
Transporter 2	Seller 2	200	1200	210	1000
	Seller 3	210		220

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Table 4. Transporter to supplier unit cost and maximum transport volume

		Transporter 1		Transporter 2
Mode of generalized transport		unit cost(＄/t)	maximum amount(t)	unit cost(＄/t)	maximum amount(t)
Transporter 1	Supplier 1	180	2000	190	2500
Transporter 2	Supplier 2	210	2200	220	2000

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Table 5. Seller's unit product cost and demand

	Seller 1	Seller 2	Seller 3
Unit product sales cost (＄/t)	80	90	85
Product demand (t)	1000	1200	800

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Table 6.

$ {x^*} $	$ {\beta ^*} $	$ f({x^*}) $
(0 0 800 0 1000 200 0 0 0 0 1000 0)	(0.556 0 0.444 0)	1171.8

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