Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2021 / Article

Research Article | Open Access

Volume 2021 |Article ID 5518840 | https://doi.org/10.1155/2021/5518840

Jianjun Zhang, Zhigang Song, "Decision Optimization of Four-Level Supply Chain with the Participation of Two-Echelon Logistics Service Providers under Different Power Structures", Mathematical Problems in Engineering, vol. 2021, Article ID 5518840, 22 pages, 2021. https://doi.org/10.1155/2021/5518840

Decision Optimization of Four-Level Supply Chain with the Participation of Two-Echelon Logistics Service Providers under Different Power Structures

Academic Editor: Josefa Mula
Received03 Feb 2021
Revised22 Mar 2021
Accepted03 Apr 2021
Published22 Apr 2021

Abstract

Taking the four-level supply chain participated by two-echelon logistics service providers as the research object, this paper deeply studies the influence of different power structures on the optimal price and logistics service level decisions of the whole supply chain system. On this basis, this paper points out the optimal power structure of the whole supply chain system and then discusses the optimal cooperative decision-making mode to improve the operation efficiency of the supply chain system under optimal power structure. The results show that compared with the two power structures of manufacturer-led and logistics service integrator-led, the retailer-led structure is the optimal power structure, whether from the perspective of maximizing the total profit of the supply chain or the surplus of consumers. When the supply chain is facing consumers who are less sensitive to the retail price of products and more sensitive to the logistics service level, the advantages of retail-led decentralized supply chain are more significant. The centralized decision of product supply chain (PSC) and logistics service supply chain (LSSC) under different power structures is the dominant strategy, and the equilibrium strategy is Nash game adopted by both parties. At this time, the total profit of the supply chain system is the largest and the total social welfare is the largest, while the total profit and consumer surplus of the supply chain under LSSC-led structure are the smallest. When the supply chain is facing consumers with low sensitivity of logistics service level and product retail price, PSC and LSSC have more significant advantages in Nash game rather than Stackelberg game.

1. Introduction

Logistics is the source of the germination of supply chain ideas and the pillar of the in-depth development of supply chain practices [1]. Therefore, logistics service providers play an important role in the research of supply chain management and decision-making. That is to say, in the operation management and decision-making of supply chain, the logistics service and the entities that provided logistics service are included in the supply chain to have an overall consideration in order to achieve a more realistic research conclusion. However, most of the current academic research on supply chain decision-making and coordination lacks consideration and attention to logistics service providers. The specialized division of labor and rapid development of logistics make the application of logistics service supply chain (LSSC) emerge, which can provide integrated logistics solutions based on the complexity of product supply chain (PSC) logistics services; that is, due to the diversity and complexity of the demand for logistics services in the product supply chain, the logistics services provided by a single logistics company obviously cannot better meet customers’ needs [2]. At this time, it is necessary for the logistics service integrator (LSI) to integrate the functional logistics service provider (FLSP) to meet the customers’ customized logistics service needs, thus forming a supply chain system with the participation of two-echelon logistics service providers, as shown in Figure 1.

The supply chain system participated by the two-echelon logistics service providers includes both the PSC composed of manufacturer and retailer, and the LSSC composed of LSI and FLSP. The goal of LSSC is to provide integrated logistics services for PSC by integrating various scattered logistics organizations [3]. As a PSC subchain, LSSC must be fully integrated into PSC, only by doing so can it better improve the logistics service level (including lead time [4], rapid response capacity, and logistics service types and quality) and overall competitiveness of the entire supply chain system and maximize the economic benefits of the entire supply chain system. Therefore, it is necessary to take the entire supply chain system composed of PSC and LSSC as the research object, while this paper focuses on the optimal decisions of the supply chain system participated by the two-echelon logistics service providers under different power structures (a system composed of two-echelon product supply chain and two-echelon logistics service supply chain).

For example, JD logistics uses logistics network and logistics cloud, logistics technology, logistics data, and other resources to provide transportation, storage, packaging, distribution, customer service, information, and comprehensive solution of after-sales integration of forward and reverse supply chain for the retailer’s supply chain. The construction of its supply chain logistics system has united many partners, for example, it established a joint venture company with COSCO to build a comprehensive international supply chain service platform. And it signed cooperation agreements with Huamao International Logistics Co. Ltd., Jiangsu Xinning Modern Logistics Co. Ltd., and Beijing Huahong Co. Ltd. in order to carry out all-round cooperation on intelligent logistics and logistics platform ecology, which can provide retailers and their downstream customers with high-quality supply chain integrated logistics services. For another example, as a professional logistics service integrator, Xiamen Hongxin International Logistics Co. Ltd. has built a relatively complete regional logistics service network through the integration of logistics resources, which can provide storage, transportation, distribution, and dispatching service for the customer’s product supply chain [5]. Thus, it forms a supply chain system participated by the two-echelon logistics service providers.

Since there are many companies involved in the supply chain system with the participation of two-echelon logistics service providers, different cooperative decision-making modes exist among companies, including decentralized decision-making mode and partial cooperative decision-making mode. For example, there exist many decision-making situations such as manufacturer-retailer cooperative decision-making mode, LSI-FLSP cooperative decision-making mode, and the decentralized decision-making mode. The difference of cooperative decision-making modes plays an essential role on the operational efficiency of the entire supply chain. At the same time, since each enterprise is an independent decision maker and has their own “power,” they are willing to obtain more profits through their dominant power. EI-Ansary and Stern [6] define this power as “a member controls the decisions of other members in market competition.” At present, in the entire supply chain system, there is a power structure dominated by manufacturing companies (such as Lenovo, Xiaomi, and Haier) earlier, and there exist situations where the dominant position of manufacturing companies is balanced and surpassed by large retail companies, that is, the power structure dominated by retail giants (such as Gome and Wal-Mart). And there is also a situation in which large LSIs have gradually changed from an auxiliary role in the past to a new leading force in the supply chain. That is to say, the power structure is dominated by logistics service integrators such as JD Logistics, Cainiao Logistics, UPS, and other emerging market entities. Their logistics service level and operational capabilities affect the decision behavior of upstream and downstream members of the supply chain [7].

Therefore, based on the above observations, this paper will mainly discuss the following questions:(1)Changes in the power structure of the supply chain have an important impact on the profitability, market competitiveness and social welfare of decision makers, and the entire supply chain system [810]. Which type of power structure can better improve the profit level of the entire supply chain system?(2)Which cooperative decision-making mode is conducive to improving the operational efficiency and competitive advantage of the entire supply chain system?(3)To what extent does consumers’ sensitivity coefficient of retail price and logistics service level influence the optimal power structure and the optimal cooperative decision-making mode?

Addressing the above important research questions highlights the research objectives and contributions of this paper. To the best of our knowledge, this is the first paper which will focus on multiple power structures and deeply study the optimal decisions of the supply chain involving two-echelon logistics service providers under different cooperative decision-making modes. Our approach, in this paper, is essentially different from those presented in previous models in which the channel is controlled only by the manufacturer or the retailer, such as Nikunja et al. [11] and Yu and Xiao [12]. This paper will study multiple power structures, analyze the influence of power structures on the optimal decisions of each participant in the supply chain, the total profit of the supply chain, and consumer welfare, and clarify the optimal power structure of the entire supply chain system. In the meantime, different from Li et al. [13] and Giri et al. [14], this paper will further discuss the optimal cooperative decision-making mode under the optimal power structure to improve the operation efficiency of the supply chain system with the participation of two-echelon logistics service providers.

The remainder of the paper is organized as follows. In the following section, this paper will briefly review the relevant literature and introduce the conceptual model of the four-level supply chain participated by the two-echelon logistics service providers in Section 3. Section 4 analyzes the optimal decisions of each decision maker under different power structures. Section 5 analyzes the impact of the difference in power structures on the optimal decisions of the supply chain, and numerical examples are provided in Section 6 to illustrate the results. The conclusions and some possible directions of future research are arranged in Section 7.

2. Literature Review

The literature related to this research mainly includes two aspects: the optimal decisions of the supply chain involving logistics service providers and the optimal decisions of the multilevel supply chain.

2.1. Optimal Decisions of the Supply Chain Involving Logistics Service Providers

Focusing on the optimal decisions of the supply chain with the participation of logistics service providers, Li et al. [13] studied a supply chain composed of a retailer and a manufacturer. Logistics services can be provided in four situations: retailer, manufacturer, manufacturer outsourced by a third party, and retailer outsourced by a third party. The paper analyzes the optimal decisions of each subject under the leadership of the manufacturer. Zhang et al. [15] constructed a two-echelon supply chain composed of online retailers and logistics service providers and studied the optimal retail prices of products led by retailers and the optimal capacity expansion decisions of logistics service providers. On this basis, some scholars have expanded the two-level supply chain to three levels and closed-loop supply chain. For example, Giri et al. [14] constructed a closed-loop supply chain composed of retailers, manufacturers, and logistics companies, in which both the forward supply chain and the reverse supply chain are dual channels, and researched price and product recycling decisions under multiple power structures. Fan et al. [16] constructed a closed-loop supply chain composed of manufacturers, sellers, and third-party logistics providers and studied the optimal price and order quantity decisions based on centralized and decentralized decision-making modes under the leadership of manufacturers. Subrata et al. [17] researched the optimal pricing decisions of a dual-channel closed-loop supply chain composed of manufacturer, retailer, and a third party. Nikunja et al. [11] studied the optimal decisions of the three-level supply chain with the participation of logistics distribution service providers led by manufacturers and analyzed the optimal price and profit decisions of the two retailers under the circumstances of collusive decision, Cournot decision, master-slave decision, etc. Some scholars have also studied the optimal decisions of the supply chain around the characteristics of the product itself. For example, Yu and Xiao [12] built an agricultural product supply chain composed of retailers, suppliers, and logistics service providers based on the characteristics of agricultural products and studied the optimal price and logistics service level decisions under the two power structures led by logistics service providers and suppliers. Some scholars such as Yu [18] studied the optimal pricing decision of the dual-channel supply chain under the leadership of the supplier and TPL. Subrata [19] studied the optimal prices of a dual-channel supply chain composed of the manufacturer, the distributer, and the retailer in three different channel structures. On the basis of the above scholars’ research on a single logistics service company, Gan [20] expanded it into two logistics service companies and studied the optimal decisions of the pharmaceutical supply chain led by the manufacturer with the participation of two competitive logistics service providers.

By systematically combing and reviewing the relevant literature, domestic and foreign scholars have studied the optimal decisions of the two-level supply chain, three-level supply chain, closed-loop supply chain, dual-channel supply chain, and closed-loop dual-channel supply chain involving a single logistics service provider. At the same time, they also studied the optimal decisions of the supply chain with the participation of a single logistics service provider and multiple competitive logistics service providers. However, most of the above studies are based on the perspective of manufacturers or retailers and do not involve the optimal decisions of the supply chain with the participation of two-echelon logistics service providers. They also lack a comparative research on the optimal decisions of the supply chain from the perspective of multiple power structures and multiple cooperative decision-making modes.

2.2. Optimal Decisions of the Multilevel Supply Chain

The research on optimal decisions of supply chain presents a research context from two levels to multiple levels. Shib [21] researched the optimal green quality and sales prices of the manufacturer and the retailer in a two-echelon supply chain. Izabela et al. [22] studied the optimal price and greening level decisions in a three-level green supply chain in both single and two-period setting. Subrata et al. [23] constructed a three-level supply chain with the participation of government, studied the optimal government subsidy strategy. The supply chain system participated by the two-echelon logistics service provider is composed of multiple decision makers at different levels, and it is a complex four-level supply chain essentially. This part focuses on the literature review around the decision optimization of multilevel supply chain.

In terms of research on optimal decisions in the multilevel supply chain, some scholars believe that the supply chain can achieve centralized decision, which is modeled with the goal of maximizing the total profit of the supply chain, minimizing costs, or optimizing service levels. For example, Khalifehzadeh et al. [24] constructed a four-level supply chain structure composed of suppliers, manufacturers, distribution service providers, and consumers and used a mixed-integer linear programming model to construct a network structure design scheme which minimizes the total operating cost of the supply chain. Abolfazl and Seyed [25] constructed a mathematical programming model with the goal of minimizing supply chain inventory costs, and studied the optimal inventory and inventory cycle decisions of a four-level supply chain. On this basis, Hamed et al. [26] constructed a multiobjective integer programming model with the smallest cost and the best service level to study the optimal product quality level decision of the four-level supply chain. Olivares et al. [27] used a mixed-integer linear programming model to study the location selection plan to maximize the profit of the four-level supply chain system from the perspective of distribution center location selection. Hasanov et al. [28] studied the optimal production and inventory decisions of a four-level closed-loop supply chain with the goal of minimizing the total cost of a closed-loop supply chain. The above studies on four-level supply chain decisions have not consider the influence of different power structures and cooperative decision-making modes on the optimal decisions and operational efficiency of the supply chain. Some scholars have also studied the optimal decisions of the four-level supply chain based on the perspective of decentralized decision-making mode. For example, Liu et al. [29] studied the optimal price decisions of the four-level supply chain composed of suppliers, manufacturers, distributors, and retailers. On this basis, Han et al. [30] further studied the quality control decisions of four-level supply chain led by manufacturers. Arnab et al. [31] studied the optimal price decisions of the five-level textile supply chain led by manufacturers and retailers. However, none of the above studies involve the situation led by logistics service providers, and there is also a lack of research about the influence of cooperative decision-making mode on the efficiency of supply chain operation and decision optimization with the participation of logistics service providers.

Based on the above literature research results, it can be concluded that at present, most scholars at home and abroad have studied the decision-making optimization problems of the supply chain with the participation of logistics service providers and the multilevel supply chain based on the perspective of a single power structure. Unfortunately, the two-echelon logistics service provider has not been considered in the whole supply chain system, and the influence of differences in power structures and cooperative decision-making modes are not introduced into the four-level supply chain with the participation of two-echelon logistics service providers. In view of this, this paper builds a supply chain structure model with the participation of the two-echelon logistics service providers based on the reality of layer-by-layer outsourcing in China’s logistics industry. Based on multiple power structures, this paper tries to analyze the optimal decisions of four-level supply with the participation of the two-echelon logistics service providers under the different cooperative decision-making modes. It also analyzes the influence of the power structures on the optimal decisions of the supply chain, clarifies the optimal power structure of the entire supply chain system, and then explores the optimal cooperative decision-making mode for improving the operating efficiency of the supply chain system under the optimal power structure.

3. Research Questions and Hypotheses

3.1. Research Questions

The conceptual model of the four-level supply chain participated by the two-echelon logistics service provider is shown in Figure 2. Suppose that before the arrival of the sales season, the retailer places an order of to the upstream manufacturer based on the customer demand and the manufacturer produces according to the retailer’s order quantity and then sells them to the retailer at the unit wholesale price ; consumers purchase products from the retailer at retail price through online channel; offline logistics services are provided by two-echelon logistics service providers formed by LSI and FLSP. The unit logistics service price that the retailer needs to pay to LSI is , and the unit logistics service price that LSI needs to pay to FLSP is ; obviously, . The logistics service level provided by FLSP is . Consumers can weigh their purchasing decisions based on product retail price and logistics service level comprehensively.

In the four-level supply chain conceptual model shown in Figure 2, there are the following decision-making modes: PSC decentralized/LSSC decentralized decision-making mode (referred to as decentralized decision-making mode), two-party cooperative decision-making mode (including PSC decentralized/LSSC centralized decision-making mode, PSC centralized/LSSC decentralized decision-making mode, and PSC centralized/LSSC centralized decision-making mode), and tripartite cooperative decision-making mode, namely, cooperative decision-making mode between retailer and LSSC.

3.2. Research Hypothesis

This paper assumes that the four decision makers involved in supply chain system are risk-neutral and completely rational. At the same time, the information among the decision makers is symmetrical. Since the logistics services provision of the supply chain is ultimately reflected in the improvement of consumer experience and satisfaction, such as the lead time, which has an important impact on the service level of whole supply chain [32]. The logistics service level in this paper is only for consumers.

At the same time, because retailers sell products directly to consumers, they pay more attention to the logistics service impact of the entire supply chain on consumer satisfaction and their comprehensive experience. Therefore, this paper assumes that the logistics service price is borne by the retailer.

For the entire supply chain, product demand is not only affected by product retail price [33], but also by the level of logistics services [34]. Therefore, this paper assumes that the product demand function is . At the same time, it is assumed that the customers’ demand for the products is equal to the retailer’s product order ; that is, the supply chain can fully meet customers’ demand, where is the market size, is the sensitivity coefficient of product retail price, and is the sensitivity coefficient of logistics service level. The marginal logistics service cost of FLSP is , and the logistics service cost related to the logistics service level is . Most literature studies generally use the form of a quadratic function to express the nonlinear relationship between service cost and service level, such as Jafar and Javad [35], Andy and Narendra [36], Hsieh and Liu [37], Jafar and Pooya [38], and Saeed et al. [39]. The relevant parameters and decision variables in the model are shown in Table 1.


ParametersImplicationDecision variablesImplication

Marginal production cost of manufacturerProduct wholesale price
Marginal logistics cost of FLSPLogistics services price paid by retailer
Market capacityLogistics service level
Sensitivity coefficient of product retail priceProduct retail price
Sensitivity coefficient of logistics service levelLogistics services price paid by LSI

Based on the above research hypothesis, the profit functions of each decision maker in the supply chain, the profit functions of PSC and LSSC, and the tripartite cooperative body (the cooperative body formed by the retailer and the LSSC) can be obtained as follows. Among them, manufacturer, retailer, LSI, FLSP, PSC, and LSSC are represented by subscripts , , , , , and , respectively, and tripartite cooperative body is represented by subscript :

The total profit function of the supply chain system is

4. The Optimal Decisions under Different Power Structures

This paper will focus on the power structure of manufacturer-led, retailer-led, and LSI-led and deeply study the optimal decisions of each decision maker in the supply chain based on a variety of decision-making modes. Among them, structures of manufacturer-led, retailer-led, and LSI-led are represented by superscripts , , and , respectively. Decentralized decision-making mode, PSC decentralized/LSSC centralized decision-making mode, PSC centralized/LSSC decentralized decision-making mode, PSC centralized/LSSC centralized decision-making mode, and tripartite cooperative decision-making mode are represented by superscripts , , , , and , respectively.

4.1. The Optimal Decisions Led by Manufacturer
4.1.1. Decentralized Decision-Making Mode

The decision sequence of the decentralized decision-making mode led by manufacturer is as follows: firstly, the manufacturer decides the product wholesale price , then LSI decides the logistics service price , and FLSP decides the logistics service level and the logistics service price . Finally, the retailer decides the retail price of the product.

First, the derivative of to is obtained by the inverse induction method, since , so is a quadratic concave function of , making , and we obtain

Substituting (9) into , since is jointly negative for and , the Hessian matrix is as follows:

The above Hessian matrix satisfies the negative definite criterion, when it satisfies .

According to , , it can be concluded that

Substituting (9)–(12) into , since , so is a quadratic concave function of , let , and we obtain

Substituting (9)–(13) into , since , so is a quadratic concave function of , making , the optimal product wholesale price is as follows:

Due to , so .

Substituting (14) into (9)–(13), the optimal decision variables are as follows:

Substituting (15) and (16) into , we can obtain the optimal product demand:

Substituting (14)–(18) into (1)–(8), the optimal profit functions of each decision maker can be obtained as shown in Table 2; among them, and .


Optimal valueDecentralized decision-making modePSC decentralized/LSSC centralized decision-making modePSC centralized/LSSC decentralized decision-making modePSC centralized/LSSC centralized decision-making modeTripartite cooperative decision-making mode

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4.1.2. PSC Decentralized/LSSC Centralized Decision-Making Mode

The decision sequence of the PSC decentralized/LSSC centralized decision-making mode led by the manufacturer is as follows: firstly, the manufacturer decides the wholesale price of the product, and then the LSSC decides the logistics service price and the logistics service level . Finally, the retailer decides the retail price of the product. Using the reverse induction method, the optimal solutions can be obtained as shown in Table 2; among them, and . The specific calculation process is the same as above, which is omitted here.

4.1.3. PSC Centralized/LSSC Decentralized Decision-Making Mode

The decision sequence of the PSC centralized/LSSC decentralized decision-making mode led by the manufacturer is as follows: firstly, PSC decides the retail price of the product , LSI decides the logistics service price , and finally, FLSP decides the logistics service level and the logistics service price . Using the reverse induction method, the optimal solutions can be obtained as shown in Table 2; among them, and .

4.1.4. PSC Centralized/LSSC Centralized Decision-Making Mode

The decision sequence of the PSC centralized/LSSC centralized decision-making mode led by the manufacturer is as follows: firstly, PSC decides the retail price of the product , and then LSSC decides the logistics service price and the logistics service level . Using the reverse induction method, the optimal solutions can be obtained as shown in Table 2; among them, and .

4.1.5. Tripartite Cooperative Decision-Making Mode

The decision sequence of the tripartite cooperative decision-making mode led by the manufacturer is as follows: firstly, the manufacturer decides the wholesale price of the product, followed by a tripartite cooperative body composed of retailers and LSSC jointly decides the product retail price and logistics service level . Using the reverse induction method, the optimal solutions can be obtained as shown in Table 2; among them, and .

4.2. The Optimal Decisions Led by Retailer
4.2.1. Decentralized Decision-Making Mode

The decision sequence of the decentralized decision-making mode led by the retailer is as follows: firstly, the retailer decides the retail price of the product, the manufacturer decides the wholesale price of the product, then LSI decides the logistics service price . Finally, FLSP decides the logistics service level and logistics service price . The optimal solutions are shown in Table 3; among them, and .


Optimal valueDecentralized decision-making modePSC decentralized/LSSC centralized decision-making modePSC centralized/LSSC decentralized decision-making modePSC centralized/LSSC centralized decision-making modeTripartite cooperative decision-making mode

d