Optimization of the product service supply chain under the influence of presale services

Xiaohui Ren; Daofang Chang; Jin Shen

doi:10.3934/jimo.2021130

Article Contents

2022, Volume 18, Issue 5: 3679-3699. Doi: 10.3934/jimo.2021130

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Optimization of the product service supply chain under the influence of presale services

1.
Institute of Logistics Science and Engineering, Shanghai Maritime University, Shanghai 201306, China
2.
School of Business, Shanghai Dianji University, Shanghai 201306, China

^* Corresponding author: Jin Shen
^* Corresponding author: Jin Shen

Received: November 2020

Revised: April 2021

Early access: August 2021

Published: November 2022

This research is supported by Natural Science Foundation of Shanghai (No: 18ZR1413200), Science and Technology Ministry of China for Cruise Program (No: MC-201917-C09), Shanghai Philosophy and Social Science Planning Project (No: 2020BGL030), Humanities and Social Sciences Project of the Ministry of Education (No: 20YJCZH027)

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Abstract

For some high-value and technology-intensive products, customers first ask service integrators to provide presales consulting services for products with potential demand. Improving the service level of presales service will increase service costs and reduce profits, but it can also increase the demand for products. The change in market demand under the influence of services will result in a series of chain reactions, such as changes in supply chain inventory costs and distribution costs. Thus, this paper considers the changes in the product service supply chain (PSSC) network caused by changes in presale service levels and service prices from the overall perspective of the supply chain and chooses a reasonable service level and price so that service integrators and product suppliers in PSSCs can achieve a win-win situation while meeting customer needs. First, a PSSC network optimization model is established considering the presale service level and price. Then, a double-layer nested genetic algorithm with constraint reasoning is proposed to solve this problem. Finally, by calculating the PSSC case of a building material company that produces a water mist spray system for ships, the feasibility and practicability of the algorithm was verified.

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Mathematics Subject Classification: 90B06.

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Figure 1. Large complex equipment PSSC

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Figure 2. GA encoding for PSSC

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Figure 3. Algorithm flowchart

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Figure 4. Searching process of optimal solution by genetic algorithm

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Figure 5. Searching process of optimal service price and level of genetic algorithm

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Figure 6. Brief PSSC network diagram

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Figure 7. Search process of the classic double nested genetic algorithm

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Figure 8. Search process of the adaptive genetic algorithm

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Table 1. Supply chain nodes and main function

Node	Main Function
product supplier	Providing products, meeting the product demand of the regional warehouse node
service integrator	Setting up offices at the service warehouse node to provide services, selling products and giving product demand order to product supplier
regional warehouse	Meeting the needs of service warehouse node products
service warehouse	Distributing products to customers, provide customers with presale services

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Table 2. Regional warehouse node parameter table

Parameters	Regional Warehouse
Node	1.5	1	1	1.3	1
Unit inventory cost	38	42	40	35	45
Mean demand	1	1	1	1	1
Lead time	2	2	2	2	2
Counting cycle	4	4.5	5.5	5	5
Distribution cost	155	156	200	160	170
Facility fixed cost	1.5	1	1	1.3	1
$ Z_{\alpha} $	0.9	0.9	0.9	0.9	0.9

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Table 3. Service warehouse node S1-S7 parameter table

Parameters	Service Warehouse
Node	S1	S2	S3	S4	S5	S6	S7
Unit inventory cost	1.2	1.5	1.5	1	1.1	1.7	1.5
Unit replenishment cost	2.7	2.7	2.7	2.9	2.9	2.9	3
Mean demand	15	14	16	20	18	17	15
Lead time	1	1	1	1	1	1	1
Counting cycle	2	2	2	2	2	2	2
Facility fixed cost	150	157	160	155	160	170	190
$ \beta $	1	1	1	1	1	1	1
$ Z_{\alpha} $	0.9	0.9	0.9	0.9	0.9	0.9	0.9
$ \mu $	0.65	0.65	0.65	0.65	0.65	0.65	0.65

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Table 4. Service warehouse node S8-S14 parameter table

Parameters	Service Warehouse
Node	S8	S9	S10	S11	S12	S13	S14
Unit inventory cost	0.9	1	1	1.5	1.3	1.3	1
Unit replenishment cost	3	3	2.9	2.9	3	3	3
Mean demand	16	14	15	17	15	20	18
Lead time	1	1	1	1	1	1	1
Counting cycle	2	2	2	2	2	2	2
Facility fixed cost	157	160	180	170	165	170	160
$ \beta $	1	1	1	1	1	1	1
$ Z_{\alpha} $	0.9	0.9	0.9	0.9	0.9	0.9	0.9
$ \mu $	0.65	0.65	0.65	0.65	0.65	0.65	0.65

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Table 5. Unit delivery cost from regional warehouse node to service warehouse node

Node	R1	R2	R3	R4	R5	Node	R1	R2	R3	R4	R5
S1	1	4	2.3	3	3.5	S8	4.3	2.5	5	4	2.5
S2	2	3.5	3	4	3	S9	3	4	2.5	3.5	2
S3	1	2	3.5	1.3	4	S10	1.5	3	1.5	2.6	4
S4	1.3	3	2	5	4	S11	2.3	3	1.5	4	5
S5	3.5	2	1.3	4	5	S12	4	3	1.5	1.5	1.5
S6	3	1.5	2	2.6	1	S13	2	4	2.6	3	1.6
S7	2	2.6	1	3.3	4	S14	4	2.5	3	5	1

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Table 6. Algorithm result analysis table

Population size	Genetic algebra	The optimal value	Optimal value first out of modern number	Operation time/s
10	400	643	365	1.283
	500	643	365	3.568
	600	643	415	5.433
20	400	643	370	0.711
	500	643	427	2.546
	600	643	227	4.653
30	400	586	130	1.263
	500	643	380	2.374
	600	643	370	4.538
40	400	643	270	0.843
	500	597	355	2.176
	550	643	343	4.136
50	400	643	350	0.834
	450	643	275	1.571
	500	643	325	2.283

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