# Research on Risk Diffusion Mechanism of Logistics Service Supply Chain in Urgent Scenarios

Authors: Guangsheng ZHANG; Xiao WANG; Zhijun GAO; Tianyu XIANG
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

Although there are some studies on the risk management of logistics service supply chain (LSSC), we still know little about the effects of risk evolution and interactional mechanism of subjects in different urgent scenarios of logistics service supply chain from a micro perspective. Based on the structures of the LSSC, this study thus analyzed the risk evolution and the main actors’ reactions in the LSSC, including categorizing the urgent scenarios, analyzing their impacts on the diffusion intensity of pricing, profit and demand, and verifying the models’ validity with the numerical analysis. The results indicate divergent impacts of the different urgent scenarios on the logistics service supply chain: the price fluctuation can cause similar profit declines of the supplier and integrator, the reduced capacity can cause the supply chain’s price increase by 50%, and the demand risks can lead to similar changes of the upstream orders, prices and profits. The findings may provide clues for firms to develop effective countermeasures against the risks.


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## Body

## 1. Introduction

To cope with increasingly fierce competition, supply chain firms in Japan, Europe, and the U.S. have taken the lead in switching to Just-in-Time production and lean management, adopting the model of centralized production and distribution. Companies have outsourced their internal logistics business to professional and highly efficient logistics service providers, with lower cost and higher efficiency, thus focusing more on gaining and maintaining its core competitiveness. Different from a product supply chain, logistics services have to be delivered to customers in real time according to their final needs, and logistics outsourcers thus have to be able to adjust their service strategies in time according to the production pace of their customers (enterprises). Logistics Service Supply Chain (LSSC), a new management model with the basic structure of “functional logistics service provider ⟶ logistics service provider ⟶ logistics users,” facilitates the efficient operation of product supply chain by coordinating the supply and demand mechanism of logistics services [1]. However, with intensifying market competition and the trend of globalization and personalized development, logistics services can be easily affected by internal and external factors, and the urgent scenarios may inevitably interfere the implementation of service plan, causing failure in the interenterprise services delivery [2]. Although the lean, just-in-time system can effectively improve operational efficiency, reduce cost, and encourage closer cooperation among enterprises, it has also increased the vulnerability of a supply chain system: a single enterprise’s urgency tend to affect any related nodes, bringing great losses to the supply chain system by impeding promised logistics service provision and thus causing great losses to all of the related enterprises. In particular, in the highly volatile internal and external business environment of China, with the urgencies enterprises are prone to face greater challenges of risk management. Studying the risk diffusion mechanism of the logistics service supply chain in the urgent scenarios thus is of critical significance.In recent years, with the intensifying globalization, deteriorating economic environment, and popularizing lean management in enterprises, the supply chain structure of enterprises is quite fragile in various urgencies. Gedik et al. [3] and Paloviita et al. [4] pointed out that the increasingly lean and agile trend of supply chain aggravates the vulnerability of the supply chain network. Firstly, on the basis of the risk transmission mechanism of the supply chain in urgencies, many researchers have investigated the transmission and diffusion effect of the demand fluctuation and supply interruption in a supply chain. Christopher [5] studied the logistics service elements of the supply chain, pointed out that logistics is an important strategy to realize the supply chain value, and analyzed the diffusion intensity of supply and demand risks from the perspectives of cost, service and customer value. Ivanov [6] covered recent developments in supply chain risk management and resilience from the position of structural dynamics focusing on the disruption propagation and the ripple effect. Qazi et al. [7] developed a supply chain risk network management process that captured interdependencies between risks, multiple performance measures, and risk mitigation strategies within a network setting. Ojha et al. [8] attempted to measure risk-taking following the assessment of supply chain risk propagation, and bayesian network theory is used to analyze the multiechelon network faced with simultaneous disruptions. Liang’an et al. [9] proposed a new model for supply chain risk propagation considering herd mentality and risk preference under warning information on multiplex networks, in which one layer is used to denote the risk propagation and the other one represents the warning information propagation network. The above research results systematically analyzed the generation and diffusion of supply chain urgencies, which helped us to understand diffusion intensity and evolution effect of urgency risks in the logistics service supply chain from different perspectives. Nevertheless, there is still lack of insights pertaining to supply chain enterprises’ behaviors on a micro level, especially what influences different variables (e.g., different transmission time and scope) would have on the major players of a supply chain.Although scholars have developed many strategies for handling the issues caused by the urgencies, they mainly focus on implementing multisource procurement, strengthening supplier tracking, optimizing cooperative relations, establishing spare production lines, and improving the supply chain transparency. In the early stage, Berger et al. [10] studied the single supplier disruption and all supplier disruptions, and adopted the decision tree model to determine the optimal number of suppliers. Kumar et al. [11] studied how a retailer can use pricing decisions along with sourcing strategies under disruption risk while competing against another retailer with a more reliable supply chain. Bimpikis et al. [12] provided an explicit characterization of equilibrium profits, which allows us to derive insights into how the network structure, that is, the number of firms in each tier, production costs, and disruption risk-affect firms’ profits. Wang and Yin [13] considered three common backup strategies between the firm and the backup supplier: advance purchase, reservation, and contingency purchase. In the traditional supply chain risk research, using mathematical optimization to solve the problem of supply risk has a good research foundation, but it does not involve relevant research on the risks of logistics services supply chain, which is more aligned to our research theme.Since the supply chain is an integrated system composed of various node-based member enterprises, some scholars have studied supply chain issues based on the urgencies’ impact on the internal operation risk of the supply chain. Fattahi et al. [14] proposed the scheme of an elastic network strategy for the internal operation risk in the multiphase supply chain network design. Kwak et al. [15] proposed and validated a theoretical model to investigate whether supply chain (SC) innovation positively affects risk management capabilities, such as robustness and resilience in global SC operations, and to examine how these capabilities may improve competitive advantage. Ivanov et al. [16] studied the impact of digitalisation and Industry 4.0 on the ripple effect and disruption risk control analytics in the supply chain. However, studies based on the urgency risk of supply chain operation are relatively insufficient, where structuring a system of the LSSC comparatively still lacks investigation. Largely, the supply chain operation mechanism can reveal the developmental interactions between microscopic behaviors and macroscopic phenomena and can depict the main heterogeneity and different dynamic behaviors to reveal the essence behind the evolution of risks.Furthermore, the urgency risk caused by sudden demand has always been a hot and difficult issue in the supply chain field. Qi et al. [17] carried out research early and suggested “supply chain coordination with demand disruptions.” Following this research, Huang and Wang [18] investigated disruptions of market demand and supply quantity of used products in a closed-loop supply chain where the manufacturer licenses the third party to undertake remanufacturing activities. Yan et al. [19] showed that the amount of change in decision-making is a linear function of the amount of demand disruption, and it is independent of the risk-averse coefficient. Rahmani and Yavari [20] investigated the demand disruption management in a dual-channel supply chain producing and selling green products and examined the pricing and green issues for a dual-channel green supply chain when the market demand is disrupted. They are based on the simplified contract mechanism to coordinate supply chain optimization, where the existing gap between simplified conditions and the reality may affect the feasibility of solutions. There is little literature that adopts multiagent modeling and contract mechanism to study these problems of logistics service supply chain. However, adopting option contract to effectively analyze urgency risk scenarios of the logistics service supply chain and extracting key risk factor indexes to build a multiagent strategy model can provide effective measures for risk management and urgency response plan.The overall system of the logistics service supply chain should be adaptable, well-organized, and dynamic. The efficient operation of complex system is of great significance for improving efficiency of the logistics service supply chain network. The above research has deeply discussed diffusion effects of supply risk, operation risk, and demand risk in the product supply chain and has laid a foundation for our research on risk diffusion mechanism of the logistics service supply chain. However, the logistics service supply chain is mainly based on coordination of logistics service capability, which is substantially different from the product supply chain. Strategic heterogeneity directly affects formation and development of cooperative alliances under the risk mechanism. This problem also directly affects the operation efficiency of the logistics service supply chain. With increasing dynamics and complexity of the operational environment, the capability to cope with sudden risk of logistics service can facilitate targeted adjustments against potential risks that undermine corporate profitability, which in turn ensures sustainable operation and customer service. So the aim of this study is to analyze the effects of risk evolution and interactional mechanism of subjects in different urgent scenarios of logistics service supply chain from a micro perspective, and explore the risk diffusion of the logistics service supply chain in urgencies, as well as risk management strategies for supply, operation, and demand urgencies, which are important tasks with practical value and theoretical significance.In the decision-making process of Stackelberg’s master-slave game, higher-level decision-makers exercise control and guidance over lower-level decision-makers, and lower-level followers can also deploy decision-making power within their own scope under the guidance. Each level in the master-slave game system has its own objective function, so the final decision result is to enable each decision subject to reach a mutually coordinating scheme. In the logistics service process, the interaction mechanism between functional logistics service providers and logistics service integrators is revealed based on the theory of master-slave game, in which functional logistics service providers are leaders and logistics service integrators are followers. Stackelberg Game theory provides a basic framework for studying diffusion effects of emergency risk. This study mainly focuses on the types of urgencies in the LSSC and constructs the diffusion effect model of the influence of various risk scenarios on the LSSC. Specifically, this study first divided urgent scenarios into supply change, operational failure, and demand change according to the logic of the supply and demand structure of the LSSC. This study analyses the effect of risk evolution and the mechanism of the main actors in the LSSC from a microlevel. Then, the pricing, profit, and demand diffusion intensity at the microlevel of each spot after the occurrence of the urgent risk are investigated. Meanwhile, numerical analysis is used to confirm the effectiveness of the established model. Finally, based on the analytical results, countermeasures are proposed for the prevention and control of urgent risks in the LSSC. Therefore, this research has proved the significance for LSSC enterprises to take effective measures to cope with urgent risks.


## 2. Urgency Risk Scenario of Logistics Service Supply Chain

The implementation of logistics services is often interrupted by various urgencies. These uncertainties will have negative impacts on function supply, service delivery efficiency and customer demand, which will increase the failure risks of the logistics service supply chain system. Based on [21] research on logistics service supply chain urgencies, this study categorizes them into supply risk, operation risk, and demand risk, as shown in Figure 1.Figure 1
Structure of LSSC and risk scenarios.The logistics service supply chain is a complex collaborative network that provides logistics service to ensure logistics operation of the product supply chain. The network nodes of logistics service supply chain represent functional logistics service providers of different functions or different regions, such as providers of warehouse, transportation, and other functions. Function providers offer professional logistics service to integrators through their own services. There are several complete business routes within the logistics service supply chain network where functional logistics service providers complete meeting the logistics service needs through logistics integrators, and there is a clear upstream and downstream sequence among enterprises in the same route. Therefore, this shows that the emergency risk of logistics service supply chain will be affected by several variables such as supply, operation, and demand capacity. Taking the logistics service supply chain structure in Figure1 as an example, the structure of logistics service capability supply is “logistics service subcontractor—functional logistics service provider,” and the functional logistics service provider subcontracts to the upstream logistics service subcontractor according to the service demand of the logistics service integrator. The supply risk is caused by insufficient capacity or failure of the functional suppliers, or failure of cooperation intentions. When the upstream enterprises of the logistics service supply chain cannot normally provide effective services to the downstream enterprises, the latter will not be able to purchase the required services, and the negative influence of the supply failure also will be transmitted along the logistics service supply chain.If the logistics service integrators, as the core enterprise of a logistics service supply chain, cannot effectively integrate the logistics capacity to meet the needs of customers, it will lead to the operational risk. This may due to factors such as imperfection of their own system and poor regulation, thus causing sudden failure for logistics services integrator during the process of operation such as planning, organizing, implementing, and controlling logistics service capacities. Given a logistics service integrator is the core enterprise of a logistics service supply chain (Figure1), its failure will lead to paralysis of the whole system of logistics service supply chain, which impedes business collaborations between the upstream and downstream demanders and suppliers of the logistics services.Logistics capacity demand refers to the decision-making process of determining logistics demand by reverse transmission from the service demand of the downstream market to the upstream supply. Demand urgency is the demand risk caused by reverse transfer effect due to large fluctuation of logistics users’ demand caused by factors such as market environment fluctuations, increased competition, lean management of enterprises and increased complexity of outsourcing, which is similar to the situation where the “bullwhip effect” in the product supply chain affects the decision-making parameters of upstream enterprises. It mainly includes two types: sudden increase in demand and sudden decrease in demand. A sudden change of demand caused by unexpected events will break the balance between supply and demand of original services in the logistics service supply chain, thus affecting the pricing and profit of upstream supply enterprises.


## 3. Model Hypotheses and Problem Description

According to the types of LSSC urgencies, the diffusion effect model indicating their effects is established. The premises and basic problems are presented as below.


### 3.1. Premises

Premise 1: information of the cost structure and market demand of LSSC is complete, and each player is a rational economic entity aiming to maximize its own profits.
Premise 2: capacity of customer demandCp2 is the function of sales price p2p2>0 of the logistics service integrator, i.e., Cp2=a−bp2+ε, where a and b are constants a>0,b>0 the probability density function ε is a random variable of fε, the mathematical expectation is Eε=ε, and the probability distribution is Fε. Assuming ε and p2 are independent of each other, ε reflects the fluctuation of logistics demand caused by factors other than price, and the change of demand caused by factors related to price is mainly reflected in the parameter p2.
Premise 3: the profits of functional logistics service provider (A) and logistics service integrator (I) are G1 and G2, then the profit functions of functional logistics service provider and logistics service integrator are G1=p1−p0×C and G2=p2−p1×Cp2, where p0p0>0 is the price of logistics service subcontractor, p1p1>0 is the price of functional logistics service provider, and CC>0 represents the purchasing ability of logistics service integrator.
Premise 4: regardless of the logistics service failure, the service capacity of the functional logistics service provider can be completely achieved, and it can also be supplied according to the demand capacity of the logistics service integrator, i.e.,C=Cp2.
Premise 5: the supply function of logistic capacity of subcontractors isS=as+bsp0, and the demand function of logistic capacity of customers is C=ad−bdp2. as and ad are constants (as>0,ad>0), and bs and bd (bs>0,bd>0) are the elasticity coefficients.


### 3.2. Problem Description

Without loss of generality, assuming the research object is three-level logistics service supply chain, the main participants are logistics service subcontractors (S), functional logistics service providers (A), logistics service integrators (I), and logistics customers (C), as shown in Figure 2. Each arrow line corresponds to a different logistics service product Li, and the arrow direction indicates the flow direction of the service. LSSC decision sequence: first, the functional logistics service provider (A) determines the retailer price of the service product p1 according to its own benefit maximization and the service price of the logistics service subcontractor p0; second, logistics service integrators (I) determine the total capacity C of logistics service integrators to purchase from suppliers according to logistics customer (C) demand function Cp2, procurement price p1, and profit maximization conditions. Therefore, it can be seen that this decision is, in essence, a Stackelberg game process. In the process of logistics service provision, the interaction between suppliers and integrators is observed according to the Stackelberg game, in which the functional logistics service provider (A) is the leader and the logistics service integrator (I) is the follower.Figure 2
Game structure of the three-level logistics service supply chain.Firstly, logistics service integrator’s decision-making process is considered first in the solution based on the Stackelberg game. Then the decision-making function of logistics service integrator (I) is(1)maxEG2=Ep2−p1×Cp2,where E⋅ is the expectation of profit and is substituted into Cp2=a−bp2+ε:(2)maxEG2=Ep2−p1×a−bp2+p2−p1×ε=p2−p1×a−bp2+p2−p1×Eε.LetdEG2/dp2=0 to obtain the price of logistics customers p2, we have p2=a+Eε+bp1/2b, while the ability of integrators to purchase from functional logistics service providers is C=a+Eε−bp1/2.Secondly, decision-making of the functional logistics service provider (A) is considered. In order to meet the procurement demand Cp2 of logistics service integrators, functional logistics service providers purchase logistics capacity C from logistics function subcontractors (S), and the provider’s objective function is(3)maxEG1=Ep1−p0×C=p1−p0×C,C=a+Eε−bp12.LetdEG1/dp1=0, obtain the price of the logistics service integrator p1=a+Eε+bp0/2b, the expected profits of functional logistics service providers and logistics service integrators are(4)EG1=a+Eε−bp028b,EG2=a+Eε−bp0216b.Thus, the final capacity price and service demand adopted by the logistics service integrator are(5)p2=3a+3Eε+bp04b,Cp2=a+Eε−bp04.


## 3.1. Premises

Premise 1: information of the cost structure and market demand of LSSC is complete, and each player is a rational economic entity aiming to maximize its own profits.
Premise 2: capacity of customer demandCp2 is the function of sales price p2p2>0 of the logistics service integrator, i.e., Cp2=a−bp2+ε, where a and b are constants a>0,b>0 the probability density function ε is a random variable of fε, the mathematical expectation is Eε=ε, and the probability distribution is Fε. Assuming ε and p2 are independent of each other, ε reflects the fluctuation of logistics demand caused by factors other than price, and the change of demand caused by factors related to price is mainly reflected in the parameter p2.
Premise 3: the profits of functional logistics service provider (A) and logistics service integrator (I) are G1 and G2, then the profit functions of functional logistics service provider and logistics service integrator are G1=p1−p0×C and G2=p2−p1×Cp2, where p0p0>0 is the price of logistics service subcontractor, p1p1>0 is the price of functional logistics service provider, and CC>0 represents the purchasing ability of logistics service integrator.
Premise 4: regardless of the logistics service failure, the service capacity of the functional logistics service provider can be completely achieved, and it can also be supplied according to the demand capacity of the logistics service integrator, i.e.,C=Cp2.
Premise 5: the supply function of logistic capacity of subcontractors isS=as+bsp0, and the demand function of logistic capacity of customers is C=ad−bdp2. as and ad are constants (as>0,ad>0), and bs and bd (bs>0,bd>0) are the elasticity coefficients.


## 3.2. Problem Description

Without loss of generality, assuming the research object is three-level logistics service supply chain, the main participants are logistics service subcontractors (S), functional logistics service providers (A), logistics service integrators (I), and logistics customers (C), as shown in Figure 2. Each arrow line corresponds to a different logistics service product Li, and the arrow direction indicates the flow direction of the service. LSSC decision sequence: first, the functional logistics service provider (A) determines the retailer price of the service product p1 according to its own benefit maximization and the service price of the logistics service subcontractor p0; second, logistics service integrators (I) determine the total capacity C of logistics service integrators to purchase from suppliers according to logistics customer (C) demand function Cp2, procurement price p1, and profit maximization conditions. Therefore, it can be seen that this decision is, in essence, a Stackelberg game process. In the process of logistics service provision, the interaction between suppliers and integrators is observed according to the Stackelberg game, in which the functional logistics service provider (A) is the leader and the logistics service integrator (I) is the follower.Figure 2
Game structure of the three-level logistics service supply chain.Firstly, logistics service integrator’s decision-making process is considered first in the solution based on the Stackelberg game. Then the decision-making function of logistics service integrator (I) is(1)maxEG2=Ep2−p1×Cp2,where E⋅ is the expectation of profit and is substituted into Cp2=a−bp2+ε:(2)maxEG2=Ep2−p1×a−bp2+p2−p1×ε=p2−p1×a−bp2+p2−p1×Eε.LetdEG2/dp2=0 to obtain the price of logistics customers p2, we have p2=a+Eε+bp1/2b, while the ability of integrators to purchase from functional logistics service providers is C=a+Eε−bp1/2.Secondly, decision-making of the functional logistics service provider (A) is considered. In order to meet the procurement demand Cp2 of logistics service integrators, functional logistics service providers purchase logistics capacity C from logistics function subcontractors (S), and the provider’s objective function is(3)maxEG1=Ep1−p0×C=p1−p0×C,C=a+Eε−bp12.LetdEG1/dp1=0, obtain the price of the logistics service integrator p1=a+Eε+bp0/2b, the expected profits of functional logistics service providers and logistics service integrators are(4)EG1=a+Eε−bp028b,EG2=a+Eε−bp0216b.Thus, the final capacity price and service demand adopted by the logistics service integrator are(5)p2=3a+3Eε+bp04b,Cp2=a+Eε−bp04.


## 4. Risk Evolution Model of Logistics Service Supply Chain Involving the Urgencies

This paper discusses the impact of the four kinds of urgencies, including price increase, capacity decrease, demand increase, and demand decrease, on the pricing, profit, and demand intensity of logistics service supply chain, as shown in Figure3.Figure 3
Risk evolution of logistics service supply chain involving the urgencies.


### 4.1. Increase of Supply Price

Under this circumstance, unexpected events lead to the continuous increaseΔp0 of logistics service supply price p0, and the price and profit risk of downstream nodes caused by the sudden price change are focused. In accordance with the decision sequence, the elasticity coefficient of p1 and p2 to the supply price p0:(6)dp1/p1dp0/p0=p0a+Eε/b+p0,dp2/p2dp0/p0=p03×a+Eε/b+p0,p1′=a+Eε+bp0+Δp02b,p2′=3a+3Eε+bp0+Δp04b.Given 0 <dp2/p2/dp0/p0<dp1/p1/dp0/p0 < 1, if the price p0 rises by 1%, causing the increases of p1 and p2 less than 1%, the diffusion intensity will be gradually weakened, and when the price rises Δp0, the optimal price of the sales of functional logistics service providers to the logistics service integrators p1 will increase Δp0/2, while the optimal price of the logistics service integrators p2 will increase Δp0/4. It indicates that the price fluctuation caused by emergencies will be transmitted along the downstream direction of LSSC, and the buffer strength of each node is 50%.Similarly, the elasticity coefficients of the profit of the functional logistics service providerG1 and of the logistics service integrator G2 to price p0 is(7)dG1/G1dp0/p0=−2p0a+Eε/b−p0,dG2/G2dp0/p0=−2p0a+Eε/b−p0,from Cp2>0, we know that dG1/G1/dp0/p0=dG2/G2/dp0/p0<0, suggesting that the fluctuation of supply price caused by emergencies reduces the downstream profits G1 and G2, and both have the same profit change rate.


### 4.2. Decrease of Supply Quantity

Under this circumstance, Stackelberg’s decision-making sequence is as follows: firstly, functional logistics service providers make decisions ofp1 based on the subcontractor supply function and profit maximization; secondly, logistics service integrators determine the optimal price p2 according to logistics customers, providers p1 and profit maximization. In this case, the expected profit function of logistics service integrator is(8)maxG2=p2−p1×Cp2.SubstituteC=ad−bdp2 into equation (8), let dEG2/dp2=0 and obtain p2=ad+bdp1/2bd. Provider profit function is(9)maxG1=p1−p0×C.The results of solving parameters are as follows:(10)p1=ad−2asbd+2adbsbd4bs+bd,p2=12bdad+ad−2asbd+2adbs4bs+bd,C=adbs+asbd4bs+bd,p0=ad−4as4bs+bd,G1=2adbs+asbd2bd4bs+bd2,G2=G12=adbs+asbd2bd4bs+bd2.For the analysis of the sudden decrease in the supply capacity of logistics service subcontractors caused by urgencies, hereby we study a typical case in which bothas and bs decreases. The change of supply curve is shown in Figure 4:Figure 4
Sudden decrease in supply capacity.The sudden reduction of supply capacity can be decomposed into two basic processes: Process 1 refers to that the intercept of logistics subcontractor’s supply capacityS=as+bsp0 drops, as turns to as′, which makes the curve S become S′; Process 2 is a change in the price elasticity of S=as+bsp0 that causes the slope to go down and the supply to go from S′ to S″. This research examines how these two scenarios influence downstream of the LSSC, thus influencing the demand and pricing of it.Process 1:as decreases Δas bs does not change. When supply becomes S′=as−Δas+bsp0, the coefficient of demand elasticity is(11)dC/Cdas/as=asbdadbs+asbd<1.Demand and supply change in the same direction, and the degree of change in demand is less than the degree of change in supply. The results of calculated parameters are as follows:(12)ΔC=Δasbd4bs+bd,Δp0=4Δas4bs+bd,Δp1=2Δas4bs+bd,Δp2=Δas4bs+bd,ΔG1=−2Δasbd2adbs+2asbd−Δasbdbd4bs+bd2,ΔG2=−Δasbd2adbs+2asbd−Δasbdbd4bs+bd2,whereΔC<0,ΔC<Δas, that is, in Process 1, the continuous decrease of supply causes the decrease of demand, Δp0>Δp1>Δp2>0 indicates that the continuous decrease of supply causes the price increase of the downstream in this case, and the lower increase rate of price along the LSSC. The supply chain node plays a buffer role in the price risk transmission.Process 2:bs decreases Δbs, as does not change. That is, the supply capacity is S=as+bs−Δbsp0, and we obtain(13)ΔC=Δbsbd4as−ad4bs−4Δbs+bd4bs+bd.FromΔbs>0 and bs>Δbs, we have 4bs−4Δbs+bd4bs+bd>0. The value of ΔC is determined by 4as−ad, that is when 4as>ad, ΔC>0, whereas when 4as<ad, ΔC<0. The results of parameters are:(14)Δp0=4Δbsad−4as4bs−4Δbs+bd4bs+bd,Δp1=2Δbsad−4as4bs−4Δbs+bd4bs+bd,Δp2=Δbsad−4as4bs−4Δbs+bd4bs+bd,ΔG1=2Δbsad−4asadbdΔbs−2bs+4asbdΔbs−2bs+8adbsΔbs−bs−2bd2as4bs−4Δbs+bd24bs+bd2,ΔG2=Δbsad−4asadbdΔbs−2bs+4asbdΔbs−2bs+8adbsΔbs−bs−2bd2as4bs−4Δbs+bd24bs+bd2.


### 4.3. Changes in Logistics Demand

Similar to the change of supply capacity, it is necessary to analyze the scenario that both parametersad and bd change in the demand function when LSSC logistics demand changes due to urgencies. Since the increase and decrease of demand are completely reverse processes in the function, this research only needs to study the continuous increase of demand. The change in demand increase is shown in Figure 5.Figure 5
Continuous increase in demand capacity.It can be divided into two basic processes: Process 1 is the change fromad to ad′ in the logistics customer demand C=ad−bdp2, which leads to the change of curve from C to C′; Process 2 is the change in elasticity of C=ad−bdp2 that causes a change in the slope, which moves from C′ to C″. This research studies how these two risks spread to the upstream of LSSC, and then affect the supply and pricing.Process 1:ad changes Δad,bd does not change. That is, when the demand function is C=ad+Δad−bdp2, we have(15)ΔC=Δadbs4bs+bd,Δp0=Δad4bs+bd,Δp1=Δadbd+2bsbd4bs+bd,Δp2=Δad×3bs+bdbd4bs+bd,ΔG1=2Δadbs2adbs+asbd+Δadbsbd4bs+bd2,ΔG2=Δadbs2adbs+asbd+Δadbsbd4bs+bd2,whereΔC>0 and ΔC<Δad/4. In Process 1, the increase in demand causes the increase in upstream orders, but the increase is less than the change in demand. Δp2>Δp1>Δp0>0 shows that the continuous increase of demand in this case causes the upstream price of LSSC to rise, and the further away from the demand increase point, the smaller the price changes. The supply chain node also plays a buffer role.Process 2:bd decreases by Δbd, ad does not change. When the demand function is C=ad−bd−Δbdp2, we obtain(16)ΔC=Δbdbsad−4as4bs+bd4bs+bd−Δbd.Frombd>Δbd, we know 4bs+bd−Δbd>0, the sign of ΔC therefore depends on ad−4as, that is, when ad>4as, ΔC>0; otherwise, ΔC<0. The results of parameters are(17)Δp0=Δbdad−4as4bs+bd4bs+bd−Δbd,Δp1=Δp02+Δbdad2bdbd−Δbd,Δp2=Δp04−Δbdad4bdbd−Δbd,ΔG1=2Δbdbsad−4as4bs+bdadbs+asbd−Δbd+4bs+bd−Δbdadbs+asbdbd−Δbd4bs+bd24bs+bd−Δbd2+2Δbdbdadbs+asbd2bd−Δbd4bs+bd2,ΔG2=Δbdbsad−4as4bs+bdadbs+asbd−Δbd+4bs+bd−Δbdadbs+asbdbd−Δbd4bs+bd24bs+bd−Δbd2+Δbdbdadbs+asbd2bd−Δbd4bs+bd2.


## 4.1. Increase of Supply Price

Under this circumstance, unexpected events lead to the continuous increaseΔp0 of logistics service supply price p0, and the price and profit risk of downstream nodes caused by the sudden price change are focused. In accordance with the decision sequence, the elasticity coefficient of p1 and p2 to the supply price p0:(6)dp1/p1dp0/p0=p0a+Eε/b+p0,dp2/p2dp0/p0=p03×a+Eε/b+p0,p1′=a+Eε+bp0+Δp02b,p2′=3a+3Eε+bp0+Δp04b.Given 0 <dp2/p2/dp0/p0<dp1/p1/dp0/p0 < 1, if the price p0 rises by 1%, causing the increases of p1 and p2 less than 1%, the diffusion intensity will be gradually weakened, and when the price rises Δp0, the optimal price of the sales of functional logistics service providers to the logistics service integrators p1 will increase Δp0/2, while the optimal price of the logistics service integrators p2 will increase Δp0/4. It indicates that the price fluctuation caused by emergencies will be transmitted along the downstream direction of LSSC, and the buffer strength of each node is 50%.Similarly, the elasticity coefficients of the profit of the functional logistics service providerG1 and of the logistics service integrator G2 to price p0 is(7)dG1/G1dp0/p0=−2p0a+Eε/b−p0,dG2/G2dp0/p0=−2p0a+Eε/b−p0,from Cp2>0, we know that dG1/G1/dp0/p0=dG2/G2/dp0/p0<0, suggesting that the fluctuation of supply price caused by emergencies reduces the downstream profits G1 and G2, and both have the same profit change rate.


## 4.2. Decrease of Supply Quantity

Under this circumstance, Stackelberg’s decision-making sequence is as follows: firstly, functional logistics service providers make decisions ofp1 based on the subcontractor supply function and profit maximization; secondly, logistics service integrators determine the optimal price p2 according to logistics customers, providers p1 and profit maximization. In this case, the expected profit function of logistics service integrator is(8)maxG2=p2−p1×Cp2.SubstituteC=ad−bdp2 into equation (8), let dEG2/dp2=0 and obtain p2=ad+bdp1/2bd. Provider profit function is(9)maxG1=p1−p0×C.The results of solving parameters are as follows:(10)p1=ad−2asbd+2adbsbd4bs+bd,p2=12bdad+ad−2asbd+2adbs4bs+bd,C=adbs+asbd4bs+bd,p0=ad−4as4bs+bd,G1=2adbs+asbd2bd4bs+bd2,G2=G12=adbs+asbd2bd4bs+bd2.For the analysis of the sudden decrease in the supply capacity of logistics service subcontractors caused by urgencies, hereby we study a typical case in which bothas and bs decreases. The change of supply curve is shown in Figure 4:Figure 4
Sudden decrease in supply capacity.The sudden reduction of supply capacity can be decomposed into two basic processes: Process 1 refers to that the intercept of logistics subcontractor’s supply capacityS=as+bsp0 drops, as turns to as′, which makes the curve S become S′; Process 2 is a change in the price elasticity of S=as+bsp0 that causes the slope to go down and the supply to go from S′ to S″. This research examines how these two scenarios influence downstream of the LSSC, thus influencing the demand and pricing of it.Process 1:as decreases Δas bs does not change. When supply becomes S′=as−Δas+bsp0, the coefficient of demand elasticity is(11)dC/Cdas/as=asbdadbs+asbd<1.Demand and supply change in the same direction, and the degree of change in demand is less than the degree of change in supply. The results of calculated parameters are as follows:(12)ΔC=Δasbd4bs+bd,Δp0=4Δas4bs+bd,Δp1=2Δas4bs+bd,Δp2=Δas4bs+bd,ΔG1=−2Δasbd2adbs+2asbd−Δasbdbd4bs+bd2,ΔG2=−Δasbd2adbs+2asbd−Δasbdbd4bs+bd2,whereΔC<0,ΔC<Δas, that is, in Process 1, the continuous decrease of supply causes the decrease of demand, Δp0>Δp1>Δp2>0 indicates that the continuous decrease of supply causes the price increase of the downstream in this case, and the lower increase rate of price along the LSSC. The supply chain node plays a buffer role in the price risk transmission.Process 2:bs decreases Δbs, as does not change. That is, the supply capacity is S=as+bs−Δbsp0, and we obtain(13)ΔC=Δbsbd4as−ad4bs−4Δbs+bd4bs+bd.FromΔbs>0 and bs>Δbs, we have 4bs−4Δbs+bd4bs+bd>0. The value of ΔC is determined by 4as−ad, that is when 4as>ad, ΔC>0, whereas when 4as<ad, ΔC<0. The results of parameters are:(14)Δp0=4Δbsad−4as4bs−4Δbs+bd4bs+bd,Δp1=2Δbsad−4as4bs−4Δbs+bd4bs+bd,Δp2=Δbsad−4as4bs−4Δbs+bd4bs+bd,ΔG1=2Δbsad−4asadbdΔbs−2bs+4asbdΔbs−2bs+8adbsΔbs−bs−2bd2as4bs−4Δbs+bd24bs+bd2,ΔG2=Δbsad−4asadbdΔbs−2bs+4asbdΔbs−2bs+8adbsΔbs−bs−2bd2as4bs−4Δbs+bd24bs+bd2.


## 4.3. Changes in Logistics Demand

Similar to the change of supply capacity, it is necessary to analyze the scenario that both parametersad and bd change in the demand function when LSSC logistics demand changes due to urgencies. Since the increase and decrease of demand are completely reverse processes in the function, this research only needs to study the continuous increase of demand. The change in demand increase is shown in Figure 5.Figure 5
Continuous increase in demand capacity.It can be divided into two basic processes: Process 1 is the change fromad to ad′ in the logistics customer demand C=ad−bdp2, which leads to the change of curve from C to C′; Process 2 is the change in elasticity of C=ad−bdp2 that causes a change in the slope, which moves from C′ to C″. This research studies how these two risks spread to the upstream of LSSC, and then affect the supply and pricing.Process 1:ad changes Δad,bd does not change. That is, when the demand function is C=ad+Δad−bdp2, we have(15)ΔC=Δadbs4bs+bd,Δp0=Δad4bs+bd,Δp1=Δadbd+2bsbd4bs+bd,Δp2=Δad×3bs+bdbd4bs+bd,ΔG1=2Δadbs2adbs+asbd+Δadbsbd4bs+bd2,ΔG2=Δadbs2adbs+asbd+Δadbsbd4bs+bd2,whereΔC>0 and ΔC<Δad/4. In Process 1, the increase in demand causes the increase in upstream orders, but the increase is less than the change in demand. Δp2>Δp1>Δp0>0 shows that the continuous increase of demand in this case causes the upstream price of LSSC to rise, and the further away from the demand increase point, the smaller the price changes. The supply chain node also plays a buffer role.Process 2:bd decreases by Δbd, ad does not change. When the demand function is C=ad−bd−Δbdp2, we obtain(16)ΔC=Δbdbsad−4as4bs+bd4bs+bd−Δbd.Frombd>Δbd, we know 4bs+bd−Δbd>0, the sign of ΔC therefore depends on ad−4as, that is, when ad>4as, ΔC>0; otherwise, ΔC<0. The results of parameters are(17)Δp0=Δbdad−4as4bs+bd4bs+bd−Δbd,Δp1=Δp02+Δbdad2bdbd−Δbd,Δp2=Δp04−Δbdad4bdbd−Δbd,ΔG1=2Δbdbsad−4as4bs+bdadbs+asbd−Δbd+4bs+bd−Δbdadbs+asbdbd−Δbd4bs+bd24bs+bd−Δbd2+2Δbdbdadbs+asbd2bd−Δbd4bs+bd2,ΔG2=Δbdbsad−4as4bs+bdadbs+asbd−Δbd+4bs+bd−Δbdadbs+asbdbd−Δbd4bs+bd24bs+bd−Δbd2+Δbdbdadbs+asbd2bd−Δbd4bs+bd2.


## 5. Numerical Analysis

In order to investigate the specific changes of Process 2 in Section4.2 and Process 2 in Section 4.3, the following numerical example is used for further analysis. When verifying the model to analyze the evolutionary effect of emergency risk, and in order to avoid influence of special cases on the reliability of the model, this paper sets the basic parameters randomly within the model parameter constraints in Section 3.1, assuming as=5,bs=5,ad=10 or 25, bd=6,Δbs∈0,4. When 4as>ad, ad=10, when 4as<ad, ad=25. We first investigated Process 2 in Section 4.2, and the parameter changes are shown in Figures 6–9.Figure 6
Changes in price parameters when4as>ad.Figure 7
Changes in profit parameters when4as>ad.Figure 8
Changes in price parameters when4as<ad.Figure 9
Changes in profit parameters when4as<ad.Comparing the trend of price change of each node in the supply chain of the logistics service with the price elasticity and profit of the logistics subcontractor when4as>ad and 4as<ad, it is found that the price and profit change of each node in the logistics service supply chain are related to the basic supply capacity of logistics subcontractors as and the regular demand of logistics customers ad. From Figure 6, we know that when 4as>ad, the value of price change of each node is smaller than 0, and with the increase of the value change of elasticity, the reduction rate of each node becomes more drastic. In this case, the values of profit change for both functional logistics suppliers G1 and logistics service integrators G2 are greater than 0 (Figure 7), and the greater the degree of supply price change is, the greater the increase rates of G1 and G2 are. It might be that the decrease of supply prices p0, p1, and p2 leads to the increase of market customer demand, and compared with demand ad, the basic capacity of the subcontractor of logistics service as is relatively sufficient, so the profits of the functional logistics supplier G1 and of the logistics service integrator G2 in LSSC shows an upward trend. However, From Figure 8, we know that when 4as<ad, due to the lack of basic capacity of logistics service subcontractors as, the price of each node shows an upward trend with the increase of the decreasing range of elasticity. At this time, the increase of logistics procurement price causes the negative profit change of the functional logistics suppliers G1 and of the logistics service integrators G2 (Figure 9). Meanwhile, according to equation (14), the fluctuation of supply price elasticity will be transmitted along the LSSC, and the nodes’ buffer strength of price is 50%. It can be seen that for members of the logistics service supply chain, a stable purchasing price environment is a necessary condition for achieving ideal cooperation performance.Similarly, the demand change Process 2 is further investigated, the basic parameters are set randomly; assumingas=5, bs=5, ad=10 or 25, bd=6, Δbd∈0,4. When 4as>ad, ad=10, when 4as<ad, ad=25, the parameter changes are shown in Figures 10–13. From Figures 10 and 12, we know that when the demand elasticity of logistics customers caused by urgencies increase continuously within a short time frame. In this case, in order to attract more customers, logistics service integrators adopt the sales strategy of price reduction, so when 4as>ad and 4as<ad, the price changes of logistics services p2 are negative and changes of the functional logistics service providers p1 are positive. Although the price of logistics service falls and the purchase price rises, the profit of logistics service integrators G2 increases due to the increase of market demand and orders. At the same time, From Figures 11 and 13, we know that considering the increase of sales price p1 and demand intensity of functional logistics providers, the increase scale of profit G1 is larger than that of profit G2. From the perspective of supply chain operation, demand for sufficient capacity is the driving force of the entire logistics service supply chain. Uncertainty of logistics demand caused by urgencies will directly affect logistics service members’ decision at all levels. The logistics service supply chain can formulate effective risk response strategies for demand urgencies by vertical coordination of the supply chain.Figure 10
Change in price parameters when4as>ad.Figure 11
Changes in profit parameters when4as>ad.Figure 12
Changes in price parameters when4as<ad.Figure 13
Changes in profit parameters when4as<ad.


## 6. Conclusion

Based on Stackelberg game, the risk diffusion effect of different types of urgencies in the logistics supply chain has been studied. First, by constructing the urgency scenario framework that fits the structure of logistics service supply chain, the scenarios have been categorized into supply, operation, and demand urgency. Second, based on Stackelberg game model, the decision-making parameters of logistics service subcontractor (S), functional logistics service provider (A), logistics service integrator (I), and logistics customer (C) in a risk-free three-level logistics service supply chain have been solved. Third, a Stackelberg game model has been established for logistics service supply chain with urgencies and the impacts of different urgencies on pricing, profit, and demand intensity of the logistics service supply chain have been discussed. Fourth, based on numerical analysis, specific changes of parameters have been analyzed. The results indicate that the impacts and intensities of different logistics supply chain emergencies may differ. The fluctuation of supply price will cause the profit of the functional logistics service provider G1 and the logistics service integrator G2 to decrease with the same intensity. The decrease of supply will lead to the increase of downstream price of logistics service supply chain, and Δp0>Δp1>Δp2>0, which indicates that the nodes function as buffers of price risk transmission. The sudden increase (decrease) of demand will lead to the increase (decrease) of upstream order quantities, but the increase (decrease) intensity is less than the change intensity of customer demand. To sum up, this study has analyzed the urgent situations in the evolution of logistics service supply chain and the mechanism of main actors on a micro level. It finds that different types of urgencies have different effects on each node of the logistics service supply chain. Therefore, the main “players” should formulate different preventive measures according to their own business environment to reduce the impact and loss of risk events, and effectively improve the operation security and efficiency. First, when faced with the risk of supply urgencies in the logistics service supply chain affecting its supply capacity or supply channels, the multisource capability procurement model of the logistics service integrators can effectively reduce the decline of supply capacity and reduce the dependence of single supplier. Standing-by suppliers as reserved supply resource of integrators are only deployed when the main suppliers are at risk. It is of great significance to introduce standing-by suppliers to deal with the risk of supply capacity urgencies in the logistics service supply chain. Secondly, facing the price risk, the logistics service supply chain can first use the option contract procurement model that pays option premium to suppliers in advance during the sales period, and obtain the right to purchase the agreed quantity of products at the end of the period with the agreed price. The logistics service supply chain can also immediately purchase the required logistics service products in spot market. Finally, from the perspective of supply chain operation, demand for sufficient capacity is the driving force of the entire logistics service supply chain. Uncertainty of logistics demand caused by urgencies will directly affect logistics service members’ decision at all levels. The logistics service supply chain can formulate effective risk response strategies for demand urgencies by vertical coordination of the supply chain. When there is a sudden increase of demand risk, the logistics service supply chain must build a logistics service time-effect model according to the priorities of customer to achieve optimal allocation of sudden demand capacity. While when there is a sudden decrease in demand, in order to maintain overall stability of the system, demand risk subsidies can be used to provide temporary income support to the members, which can effectively stabilize the original cost-profit balance of the logistics service supply chain system.This study focuses on the “risk diffusion mechanism of logistics service supply chain in response to urgencies” and has obtained expected research results, but there still are some issues that need to be further studied and addressed. First, research on the elastic mechanism of logistics service supply chain considering the risk of urgencies is needed. Elasticity refers to the ability of the impacted operation system to quickly bounce back to the normal operation state [22]. The idea is to objectively involve the vulnerability of the supply chain and then embed the resilience into the supply chain design and balance the operation cost and risk event loss, so as to achieve the purpose of constant response to changes [23]. The supply chain with inlaid elastic mechanism demands better preparation, more flexible response, and faster recovery ability than competitors. Therefore, if the existence of urgency risk can be involved in the design and operation mechanism of logistics service supply chain, it will have critical theoretical value and practical significance for the capability to minimize the delivery failure of the service capacity after the occurrence of failure event and quickly restore to the normal operation state to improve customer satisfaction. Second, the risk simulation model of logistics service supply chain based on system dynamics can be introduced. The existing research on the risk system of logistics service supply chain is usually static and qualitative, and it is difficult to fully understand the complexity and dynamics of the strategy as a whole [1]. System dynamics studies the interdependence between the internal mechanism and behavior of the system through mathematical models and gradually discovers the causality based on morphological changes in the process of establishment and operation, which is suitable for the study of system coordination [24]. Vensim software can be applied to simulate and analyze basic data of the mechanism of logistics service supply chain risk, where the determination of factors such as individual members, cooperation structure, the proportion of the whole system, and cost control can be studied. The dynamic characteristics of a risk situation and its impact on the change of performance goals of the logistics service supply chain can be further discussed. Meanwhile, system parameters can be adjusted in order to optimize the LSSC operation performance. Structure of the LSSC under different risk circumstances can be analyzed to adjust the sensitivity of the optimal scheme and to provide feasible suggestions to cope with the challenges.



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*Source: 5906901-2020-02-29.xml*