research article emergency coordination model of fresh agricultural products...

Research ArticleEmergency Coordination Model of Fresh Agricultural Products’Three-Level Supply Chain with Asymmetric Information

Juan Yang,1 Haorui Liu,2 Xuedou Yu,3 and Fenghua Xiao1

1School of Economics and Management, Dezhou University, Dezhou 253023, China2School of Automotive Engineering, Dezhou University, Dezhou 253023, China3Science and Technology Department, Dezhou University, Dezhou 253023, China

Correspondence should be addressed to Juan Yang; [email protected]

Received 31 December 2015; Accepted 15 February 2016

Academic Editor: Kishin Sadarangani

Copyright © 2016 Juan Yang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In consideration of influence of loss, freshness, and secret retailer cost of products, how to handle emergency events during three-level supply chain is researched when market need is presumed to be a nonlinear function with retail price in fresh agriculturalproduct market. Centralized and decentralized supply chain coordination models are studied based on asymmetric information.Optimal strategy of supply chain in dealing with retail price perturbation is caused by emergency events. The research revealsrobustness for optimal production planning, wholesale price for distributors, wholesale price for retailers, and retail price of three-level supply chain about fresh agricultural products. The above four factors can keep constant within a certain perturbation ofexpectation costs for retailers because of emergency events; the conclusions are verified by numerical simulation.This paper also canbe used for reference to the other related studies in how to coordinate the supply chain under asymmetric and punctual researchesinformation response to disruptions.

1. Introduction

Nowadays, emergency events about fresh agricultural prod-ucts happen frequently and seriously impact producing,selling, and demand, and faith of consumers on food safetysuch as poisonous beans emerging in Hainan province andswelling ingredients discovered in watermelons.

Supply chain of fresh agriculture products is a complexnet with dynamics and open system consisted of farm-ers, wholesalers, distribution centers, and retailers [1–3].However, emergency events are results of complexity anduncertainty in supply chain. Meanwhile, the special nature offresh agricultural product determines that the supply chainis weaker in resisting risk. Thus, a sudden emergency eventcan partly impact the supply chain or even destroy thewhole chain. In recent years, more andmore researchers havestudied emergency cooperation of fresh agricultural prod-uct. Chen and Dan investigated the emergency cooperationproblem, respectively, based on value and entity loss [4]. Fur-thermore, Zhao and Wu analyzed cooperation of two-level

supply chain with random production and demand basedon benefit-sharing contract [5]. Under the same contract,Lin et al. researched cooperation of three-level supply chain[6]. Based on a punishment and revenue sharing contract,Zhang et al. studied the coordination issues among singlemanufacturer, distributor, and retailer in a three-level supplychain [7]. Liu and Shi took the retail price being endogenousvariables or exogenous variables as the essential characteristicof differentiating unconventional emergencies and conven-tional emergencies and built emergencies contingencymodelwith buy-back contract when unconventional emergenciesoccur [8].

Gurler and Parlar studied two-level supply chain com-posed of two production suppliers generating an objectfunction revealing average expense in a long time and finallyachieving respective optimal order and inventory quantityfor two suppliers relying on the application of optimal strat-egy [9]. Chen and Ding researched supply chain includinga producer, a dominant retailer, and some other weakerretailers and conclude that producer should adjust wholesale

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016, Article ID 2780807, 9 pageshttp://dx.doi.org/10.1155/2016/2780807

2 Mathematical Problems in Engineering

Ord

er q

uant

ity (q

r)

Prod

ucts

(q r)

Supplier

Logistics

Order quantity (qr)

Whole sale price for retailer (p

w2 )

Market demand information (q

r )

Information flow Cash flow

Sales quantity (qr)Sales income

Retailer

Distributor

Order information (qr)

p w1

)

Who

lesale

for d

istrib

utor

(

Cost (p w

1· q

r) Cost (p

w2 · q

r )

Figure 1: Three-supply-chain schematic for fresh agricultural product.

price with wholesale price contract when sudden demandemerges. The higher the market share of dominant retaileris, the lower the wholesale price determined by producer is.Thus, producer will preferentially take liner quantity discountcontract into consideration when demand experiences a bigchange and production cost is quite low [10, 11]. Huo andLiu analyzed supply chain system composed of a producerand a retailer and renew original static production plan andsupply chain coordination strategy when demand suddenlyincreases by applying wholesale quantity discount contractwhich realizes optimal potential profit in supply chains [12].Zhang et al. researched supply chain system composed ofa producer and two retailers, showing that, with suddenincrease of demand, original benefit-sharing contract cannotperfectly coordinate supply chains system but a new one canwhich can be verified by numerical examples [13].

As transfer of leading right in the 21st century, retailersare playing an increasing important role in supply chain[14, 15].Therefore study on coordination of three-level supplychain has practical value under sharp increasing demand.Munson and Rosenblatt launched a research on three-level supply chain composed of a production supplier, aproducer, and a retailer and analyze how quantity discountcontract affects decision of retailers and help increase profitof production suppliers [16].Wang andHu discussed optimalstrategy on emergency events in three-level supply chainunder centralized and decentralized condition by applyingquantity discount contract [17]. Wang and Jiang constructedoptimal strategy of three-level supply chain and model ofoptimal quantity discount which involves production sup-pliers, producers, and retailers under fuzzy random demandcircumstance. Finally, practicality of model is verified byexamples [18].

Qi and Yu studied simple supply chain only involving aproduction supplier and a retailer. Firstly, market demand forretailers is supposed to be a liner function with price. Thenwhen demand fluctuates, how to apply whole units quantitydiscount contract should be discussed in handling emergencyevents and keeping supply chain coordinate [19, 20]. Wu etal. began with study of solving emergency events happening

in two-level supply chain composed of a production supplierand two retailers who compete with each other and thenfurther study about coordinate strategy under fluctuationof production cost, market demand, and price sensitivecoefficient. Meanwhile, liner quantity discount is applied torealize supply chain coordinationwith the influence of severalfactors [21–24].

Qin et al. analyzed the condition when market demandof two-level supply chain varies with emergency events instochastic market as well as supply chain coordination afteremergency only with asymmetric demand information [25].Meanwhile, they study synchronous variations of marketdemand and marginal costs of retailers and also investigatecoordination effectiveness of buy-back contract on supplychain after the emergency when marginal costs informationof retailers are asymmetric [26].

In this paper, the study object is a three-level supply chainof fresh agriculture products composed of a production sup-plier𝑀, a distributer 𝐿, and a retailer 𝑅. Meanwhile, retailersplay a leading role in system and distributor predominatesover producers. In single cycle model, retailers make orderof goods at the beginning of sales cycle.

The above three-level supply chain is operated in detail inFigure 1 [15, 27].

In consideration of loss in number and decrease infreshness during transportation of fresh agricultural product,this paper discusses how to achieve optimal system andrealize robustness of the system and maximum profit of allmembers in system. The above study can provide theoryfoundation for decision-makers to draw strategy.

2. Supply Chain Coordination withSymmetric Information

The following prerequisite hypothesis should be met in thisstudy. Firstly, all business deals happen among companiesalong with supply chain and producer cannot directly supplygoods for retailers. Secondly, production suppliers have sym-metric information with retailers. Thirdly, the study object is

Mathematical Problems in Engineering 3

fresh agriculture products which only have short life cycle.Surplus products have no value and there does not exist goodsorder cycle.The research also does not take into considerationthe loss of short supply, inventory, and inventory costs. Allinformation is shared such as costs andmarket demands.Thesupply chain coordination is studied within a sale cycle, andthus influence of fixed facilities costs can be ignored becausethey keep constant. Besides all decision-makers undertakemedium risk and seek the maximum profit for themselves.

All parameters used in the models are listed as follows:

𝑞𝑟—market demand forecasted by retailers or order

quantity of retailers;𝑡—transportation time which can affect quality offresh agricultural product;𝑇—effective life cycle of fresh agricultural productwhich is also valid transportation time constraint forretailers, 0 ≤ 𝑡 ≤ 𝑇;𝑝𝑟—retail price;

𝑝𝑤1—wholesale price for distributors;

𝑝𝑤2—wholesale price for retailers;

𝜆—sensitive coefficient of price, 𝜆 > 0;𝑚—market demand scale (maximum);𝑐𝑠—production cost unit of production supplier;𝑐𝑙—transportation costs unit for distributors;𝑐𝑟—marginal costs for retailers.

Fourthly, the study describes characteristics of fresh agri-cultural products supply chain and defines 𝜙(𝑡) = 1 − 𝑡2/𝑇2,a monotonic continuous reduction function, as freshnessfactor of the products and 𝜙(𝑡) ∈ [0, 1] as parameter of revel-ing composite quality characteristics such as water content,luster degree on the surface, and decay degree. Compositequality characteristic is one of the most important factorswhich affects practical supply quantity and market demand.Freshness degree 𝜙(𝑡) is mainly influenced by preservation,management, moving, and other behaviors during trans-portation. 𝛼(𝑡) is generated to show rate coefficient of entityloss in transportation,meeting the function 𝛼(𝑡) = 𝑒(ln2)/𝑇−1.

If effective rate factor 𝛽(𝑡) = 1−𝛼(𝑡) = 2−𝑒((ln 2)/𝑇)𝑡 exists,𝛽(𝑡) ∈ [0, 1], which is corresponding with transportationtime. Then order made by retailers can be expressed as𝑞𝑟/2 − 𝑒

((ln 2)/𝑇)𝑡 with goal of receiving maximum profit forretailers. It can be seen from the above derivations thatthe transportation time can influence supply and practicaldemand of goods in cooperation across different regions.Theoretically, the shorter the transportation time is thefresher the goods are. Meanwhile, supply rate of goods ishigher and entity loss is less. Thus, the market demand willincrease.

𝑞𝑟is supposed to be a nonlinear function of retail price.

The function is denoted as 𝑞𝑟= (𝑚𝑝

−𝜆

𝑟/ ln 2) ln(2 − 𝑡2/𝑇2);

retailers order a certain amount of products at wholesaleprice and then sell them at the retail price, 𝑝

𝑟= (𝑚 ln(2 −

𝑡2

/𝑇2

)/𝑞𝑟ln 2)1/𝜆.

The simple supply chain is usually dominated by adecision-maker to seek themaximumprofit for thewhole sys-tem, which only involves a production supplier, a distributer,and a retailer:

𝜋 (𝑞𝑟) = 𝑞𝑟(𝑝𝑟−

𝑐𝑟+ 𝑐𝑠+ 𝑐𝑙

2 − 𝑒((ln 2)/𝑇)𝑡)

= 𝑞𝑟((

𝑚 ln (2 − 𝑡2/𝑇2)𝑞𝑟ln 2

)

1/𝜆

−𝑐𝑟+ 𝑐𝑠+ 𝑐𝑙

2 − 𝑒((ln 2)/𝑇)𝑡) .

(1)

The study depends on first-order optimality conditions,𝜕𝜋(𝑞𝑟)/𝜕𝑞𝑟= 0. The supply chain system is supposed to be

able to achieve maximum profit for the whole system andhave an unique optimal point for order, 𝑞∗

𝑟.

Optimal sale quantity,

𝑞∗

𝑟=

𝑚 ln (2 − 𝑡2/𝑇2)𝑞𝑟ln 2

⋅ (

(𝜆 − 1) (2 − 𝑒((ln 2)/𝑇)𝑡

)

𝜆 (𝑐𝑟+ 𝑐𝑠+ 𝑐𝑙)

)

𝜆

. (2)

Corresponding optimal retail price,

𝑝∗

𝑟=


(𝜆 − 1) (2 − 𝑒((ln 2)/𝑇)𝑡)

. (3)

Maximum profit for the whole three-level supply chainsystem,

𝜋 (𝑞∗

𝑟) =

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

⋅1

𝜆𝜆

⋅ (

(𝜆 − 1) (2 − 𝑒((ln 2)/𝑇)𝑡

)


)

𝜆−1

.

(4)

3. Supply Chain Coordination withAsymmetric Information

In practical life, condition of only having asymmetric infor-mation wildly exists in three-level supply chain systemof fresh agricultural products. The following prerequisitehypothesis should be met in this research.

Firstly, information is asymmetric among productionsuppliers, distributors, and retailers. However, 𝑐

𝑟are known

by retailers and distributors but not by production supplierswho can only infer the following information from functions𝑐𝑟∈ [𝑐𝑟

−

, 𝑐𝑟

+

]. Distribution function, probability densityfunction, and expectation are, respectively,𝐹(𝑐

𝑟),𝑓(𝑐𝑟), and𝜇,

with the range of 0 ≤ 𝑐𝑟

−

≤ 𝑐𝑟

+

< ∞. 𝐹(𝑐𝑟) is a differentiable

and strictly increasing function and 𝐹(0) = 0, 𝐹(𝑐𝑟) = 1 −

𝐹(𝑐𝑟).Secondly, production suppliers, distributors, and retailers

all undertake medium risk and seek for the maximum profitfor themselves.

Thirdly, other parameters are open information for retail-ers, distributors, and production suppliers.

Under decentralized control, retailers decide order quan-tity 𝑞𝑟according to random market demand 𝑚. Distributers


must provide order quantity 𝑞𝑟made by retailers in order to

get maximum profit. Thus distributers will buy 𝑞𝑟unit goods

at the wholesale price 𝑝𝑤1

and then sell them to retailersat a reasonable wholesale price 𝑝

𝑤2to receive maximum

profits. For production suppliers, they should first providegoods in order quantity of 𝑞

𝑟and at the same time make sure

how to decide wholesale price 𝑝𝑤1

to distributers to receivemaximum profits. Form the above descriptions, it can beconcluded that profit of retailers, distributors, and productionsuppliers is, respectively, as follows.

For production suppliers, maximizing their profit is theone that should be optimized. The optimizing problem andobject function can be, respectively, shown as

max𝑝𝜔1

𝐸 [𝜋𝑠(𝑝𝜔1)] = max

𝑝𝜔1

∫

𝑐𝑟

+

𝑐𝑟

−

𝜋𝑆

𝑠(𝑝𝜔1) 𝑓 (𝑐𝑟) 𝑑𝑐𝑟

s.t. IC : 𝑞𝑟= argmax

𝑞𝑟

𝜋𝑁

𝑟(𝑝𝑟) .

(5)

Function (1) shows IC constraints in incentive compati-bility of retailers. Retailers determine order quantity to be 𝑞

𝑟

to maximize their profits; expectation profits of productionsuppliers depend on order quantity 𝑞

𝑟made by retailers

who make their decision relying on incentive compatibilityconstraints.

(1) Optimizing Problem of Retailers. Expectation profit func-tion of retailers can be described as

𝜋𝑟(𝑝𝑟) = 𝑞𝑟(𝑝𝑟−

𝑐𝑟+ 𝑝𝜔2

2 − 𝑒((ln 2)/𝑇)𝑡)

=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

𝑝−𝜆

𝑟(𝑝𝑟−

𝑐𝑟+ 𝑝𝜔2

2 − 𝑒((ln 2)/𝑇)𝑡) .

(6)

Based on first-order optimality conditions, 𝜕𝑟𝜋(𝑝𝑟)/𝜕𝑝𝑟=

0, optimal retail price can be determined:

𝑝𝑟(𝑝𝜔2) =

𝜆 (𝑐𝑟+ 𝑝𝜔2)

(𝜆 − 1) (2 − 𝑒((ln 2)/𝑇)𝑡)

. (7)

The corresponding optimal sales quantity,

𝑞𝑟(𝑝𝜔2)

=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(

(𝜆 − 1) (2 − 𝑒((ln 2)/𝑇)𝑡

)

𝜆 (𝑐𝑟+ 𝑝𝜔2)

)

𝜆

.

(8)

(2) Optimizing Problem of Distributers. Expectation profitfunction of distributers can be denoted:

max𝑝𝜔2

𝐸 [𝜋𝑠(𝑝𝜔2)]

= 𝐸[𝑞𝑟(𝑝𝜔2)

2 − 𝑒((ln 2)/𝑇)𝑡(𝑝𝜔2− 𝑐𝑠− 𝑐𝑙)] .

(9)

We can deduce Theorem 1 based on first-order optimalityconditions, 𝜕𝐸[𝜋

𝑠(𝑝𝜔2)]/𝜕𝑝𝜔2= 0.

(3) Optimizing Problem of Production Suppliers. Expectationprofit function of production suppliers can be displayed as

max𝑝𝜔1

𝐸 [𝜋𝑠(𝑝𝜔1)] = 𝐸[

𝑞𝑟(𝑝𝜔1)

2 − 𝑒((ln 2)/𝑇)𝑡(𝑝𝜔1− 𝑐𝑠)] . (10)

We can deduce Theorem 1 based on first-order optimalityconditions, 𝜕𝐸[𝜋

𝑠(𝑝𝜔1)]/𝜕𝑝𝜔1= 0.

Theorem 1. Under decentralized control coordination contractof three-level supply chain is without emergency and symmetricinformation.

Optimal wholesale price for distributors is

𝑝𝑁

𝜔1=𝜆𝑐𝑠+ 𝜇

𝜆 − 1; (11)

optimal wholesale price for retailers is

𝑝𝑁

𝜔2=𝜆 (𝑐𝑠+ 𝑐𝑙) + 𝜇

𝜆 − 1; (12)

optimal retail price is

𝑝𝑁

𝑟= (

𝜆

𝜆 − 1)

3

(𝑐𝑠+ 𝑐𝑙+ 𝜇

2 − 𝑒((ln 2)/𝑇)𝑡) ; (13)

optimal sales quantity for retailers is

𝑞𝑁

𝑟

=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(𝜆 − 1

𝜆)

2𝜆

(2 − 𝑒((ln 2)/𝑇)𝑡

𝑐𝑠+ 𝑐𝑙+ 𝜇

)

𝜆

.

(14)

Corresponding expectation profit of retailers is

𝜋𝑁

𝑟=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(𝜆 − 1

𝜆)

2𝜆−3

⋅ (2 − 𝑒((ln 2)/𝑇)𝑡


)

𝜆−1

.

(15)

Expectation profit of distributors is

𝜋𝑁

𝜔2= (𝜆 (𝑐

𝑠+ 𝑐𝑙) + 𝜇)

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

⋅(𝜆 − 1)

2𝜆−1

𝜆2𝜆(2 − 𝑒((ln 2)/𝑇)𝑡


)

𝜆

.

(16)

Expectation profit of production suppliers is

𝜋𝑁

𝜔1=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

⋅(𝜆 − 1)

2𝜆−1

[𝜆𝑐𝑠+ 𝜇]

𝜆2𝜆(2 − 𝑒((ln 2)/𝑇)𝑡


)

𝜆

.

(17)


4. Supply Chain CoordinationMechanism under Emergency andAsymmetric Information

When selling season is approaching, retailers make optimalorder quantity and then distributers and production suppliersarrange distribution plan and producing strategy with theorder quantity. If emergency affects retailer cost distributionfunction but without having any effect on other parameters,then 𝐹(𝑐

𝑟) and density function 𝑌(𝑐

𝑟) will be, respectively,

substituted by 𝑓(𝑐𝑟) and 𝑦(𝑐

𝑟). 𝑌(𝑐𝑟) is also differentiable and

strictly increasing like 𝐹(𝑐𝑟), with 𝑌(0) = 0, 𝑌(𝑐

𝑟) = 1 − 𝑌(𝑐

𝑟),

and expected to be 𝜇𝑌.

Optimal order quantity made by retailers, 𝑞𝐷𝑟/(2 −

𝑒((ln 2)/𝑇)𝑡

), is also changed after emergency events; thus𝑞𝐷

𝑟/(2 − 𝑒

((ln 2)/𝑇)𝑡) > 𝑞

𝑁

𝑟/(2 − 𝑒

((ln 2)/𝑇)𝑡), and optimal order

quantity has to be renewed.However, original producing planis also broken. Then new producing cost 𝜌

1is generated for

productions which is added in order plan after emergencyevents, (𝑞𝐷

𝑟− 𝑞𝑁

𝑟)/(2 − 𝑒

((ln 2)/𝑇)𝑡). Otherwise, when order

quantity 𝑞𝑁𝑟/(2−𝑒

((ln 2)/𝑇)𝑡) is less than original one, then extra

distribution payment 𝜌2will be generated because of surplus

products (𝑞𝑁𝑟−𝑞𝐷

𝑟)/(2−𝑒

((ln 2)/𝑇)𝑡). Moreover, if order quantity

by retailer 𝑞𝑁𝑟/(2 − 𝑒

((ln 2)/𝑇)𝑡) is less than that by distributers,

additional disposal cost 𝜌3, (𝑘)+ = max(0, 𝑘), is yielded

because of these surplus products (𝑞𝑁𝑟− 𝑞𝐷

𝑟)/(2 − 𝑒

((ln 2)/𝑇)𝑡).

Emergency is supposed to cause increase of retailer costs.With 𝑌(𝑐

𝑟) ≥ 𝐹(𝑐

𝑟), 𝑞𝐷𝑟≥ 𝑞𝑁

𝑟exists for arbitrary 𝑐

𝑟≥ 0.

Expectation profits function is

��𝑠(𝑝𝜔1)

=1

2 − 𝑒((ln 2)/𝑇)𝑡[𝑞𝑟(𝑝𝜔1− 𝑐𝑠) − 𝜌1(𝑞𝐷

𝑟− 𝑞𝑁

𝑟)] .

(18)

Optimal problem of producing supplier is

max𝑝𝜔1

𝐸 [��𝑠(𝑝𝜔1)] = max

𝑝𝜔1

∫

𝑐𝑟

+

𝑐𝑟

−

��𝑠(𝑝𝜔1) 𝑦 (𝑐𝑟) 𝑑𝑐𝑟


𝑞𝑟

��𝑟(𝑝𝑟) ,

��𝑟(𝑝𝑟) = 𝑞𝑟(𝑝𝑟−𝑐𝑙+ 𝑐𝑟+ 𝑝𝜔1

2 − 𝑒((ln 2)/𝑇)𝑡)

=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

𝑝−𝜆

𝑟(𝑝𝑟−𝑐𝑙+ 𝑐𝑟+ 𝑝𝜔1

2 − 𝑒((ln 2)/𝑇)𝑡) .

(19)

It can be concluded fromfirst-order optimality conditions𝜕��𝑟(𝑝𝑟)/𝜕𝑝𝑟= 0 that optimal retail price

𝑝𝑟(𝑝𝜔1) =

𝜆 (𝑐𝑙+ 𝑐𝑟+ 𝑝𝜔1)

(𝜆 − 1) (2 − 𝑒((ln 2)/𝑇)𝑡)

. (20)

Corresponding optimal sale quantity is

𝑞𝑟(𝑝𝜔1)

=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(

(𝜆 − 1) (2 − 𝑒((ln 2)/𝑇)𝑡

)

𝜆 (𝑐𝑙+ 𝑐𝑟+ 𝑝𝜔1)

)

𝜆

.

(21)

Relying on first-order optimality conditions 𝜕𝐸[��𝑠(𝑝𝜔1)]/

𝜕𝑝𝜔1= 0, optimal wholesale price for distributers is

𝑝𝐷

𝜔1=𝜆 (𝑐𝑠+ 𝜌1) + 𝜇𝑌

(𝜆 − 1). (22)

Optimal wholesale price for retailers is

𝑝𝐷

𝜔2=𝜆 (𝑐𝑠+ 𝑐𝑙+ 𝜌1+ 𝜌2) + 𝜇𝑌

(𝜆 − 1). (23)

Corresponding optimal sale quantity is

𝑞𝐷

𝑟=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(𝜆 − 1

𝜆)

3𝜆

⋅ (2 − 𝑒((ln 2)/𝑇)𝑡

𝑐𝑠+ 𝑐𝑙+ 𝜌1+ 𝜌2+ 𝜇𝑌

)

𝜆

< 𝑞𝑁

𝑟

=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(𝜆 − 1

𝜆)

3𝜆

(2 − 𝑒((ln 2)/𝑇)𝑡


)

𝜆

.

(24)

However, the conclusion is in contradiction with hypoth-esis. Therefore, for arbitrary 𝑐

𝑟≥ 0, 𝑞𝐷

𝑟≤ 𝑞𝑁

𝑟exists when

emergency events cause increase of retailer costs, 𝑌(𝑐𝑟) ≥

𝐹(𝑐𝑟). As is applied with same theory, 𝑞𝐷

𝑟≥ 𝑞𝑁

𝑟exists when

emergency events cause decrease of retailer costs, 𝑌(𝑐𝑟) ≤

𝐹(𝑐𝑟).In the following part, coordination mechanism of the

above two conditions is discussed.For arbitrary 𝑐

𝑟≥ 0, Situation 1 𝑞𝐷

𝑟≤ 𝑞𝑁

𝑟exists when

emergency events cause increase of retailer costs, 𝑌(𝑐𝑟) ≤

𝐹(𝑐𝑟); Situation 2 𝑞𝐷

𝑟≤ 𝑞𝑁

𝑟exists when emergency events

cause decrease of retailer costs with 𝑌(𝑐𝑟) ≥ 𝐹(𝑐

𝑟).

Profit function of production supplier is

��𝑠1(𝑝𝜔1) =

1

2 − 𝑒((ln 2)/𝑇)𝑡[𝑞𝑟(𝑝𝜔1− 𝑐𝑠)

− 𝜌1(𝑞𝐷

𝑟− 𝑞𝑁

𝑟)] ,

��𝑠2(𝑝𝜔1) =

1

2 − 𝑒((ln 2)/𝑇)𝑡[𝑞𝑟(𝑝𝜔1− 𝑐𝑠)

− (𝜌2+ 𝜌3) (𝑞𝑁

𝑟− 𝑞𝐷

𝑟)] .

(25)

Optimizing problem of production supplier is

max𝑝𝜔1

𝐸 [��𝑠1(𝑝𝜔1)] = max

𝑝𝜔1

∫

𝑐𝑟

+

𝑐𝑟

−

��𝑠1(𝑝𝜔1) 𝑦 (𝑐𝑟) 𝑑𝑐𝑟

max𝑝𝜔1

𝐸 [��𝑠2(𝑝𝜔1)] = max

𝑝𝜔1

∫

𝑐𝑟

+

𝑐𝑟

−



𝑞𝑟

��𝑟(𝑝𝑟) .

(26)


Profit function of distributers is

��𝑠1(𝑝𝜔2) =

1

2 − 𝑒((ln 2)/𝑇)𝑡[𝑞𝑟(𝑝𝜔2− 𝑐𝑠− 𝑐𝑙)

− (𝜌1+ 𝜌2) (𝑞𝐷

𝑟− 𝑞𝑁

𝑟)] ,

��𝑠2(𝑝𝜔2) =

1

2 − 𝑒((ln 2)/𝑇)𝑡[𝑞𝑟(𝑝𝜔2− 𝑐𝑠− 𝑐𝑙)

− 𝜌3(𝑞𝑁

𝑟− 𝑞𝐷

𝑟)] .

(27)

Optimizing problem of distributers is

max𝑝𝜔2

𝐸 [��𝑠1(𝑝𝜔2)] = max

𝑝𝜔2

∫

𝑐𝑟

+

𝑐𝑟

−


max𝑝𝜔2

𝐸 [��𝑠2(𝑝𝜔2)] = max

𝑝𝜔2

∫

𝑐𝑟

+

𝑐𝑟

−



𝑞𝑟

��𝑟(𝑝𝑟) .

(28)

Based on first-order optimality conditions, 𝜕𝐸[��𝑠(𝑝𝜔1)]/

𝜕𝑝𝜔1= 0, 𝜕𝐸[��

𝑠(𝑝𝜔2)]/𝜕𝑝𝜔2= 0, optimal wholesale price for

distributers is

𝑝𝐷

𝜔1−1=𝜆 (𝑐𝑠+ 𝜌1) + 𝜇𝑌

(𝜆 − 1),

𝑝𝐷

𝜔1−2=𝜆 (𝑐𝑠− 𝜌2− 𝜌3) + 𝜇𝑌

(𝜆 − 1).

(29)

Optimal wholesale price for retailers is

𝑝𝐷

𝜔2−1=𝜆 (𝑐𝑠+ 𝑐𝑙+ 𝜌1+ 𝜌2) + 𝜇𝑌

(𝜆 − 1),

𝑝𝐷

𝜔2−2=𝜆 (𝑐𝑠+ 𝑐𝑙− 𝜌3) + 𝜇𝑌

(𝜆 − 1).

(30)

Optimal retail price and sales quantity are, respectively,

𝑝𝐷

𝑟1= (

𝜆

𝜆 − 1)

3

(𝑐𝑠+ 𝑐𝑙+ 𝜌1+ 𝜌2+ 𝜇𝑌)

(2 − 𝑒((ln 2)/𝑇)𝑡),

𝑝𝐷

𝑟2= (

𝜆

𝜆 − 1)

3

(𝑐𝑠+ 𝑐𝑙− 𝜌3+ 𝜇𝑌)

(2 − 𝑒((ln 2)/𝑇)𝑡),

𝑞𝐷

𝑟1=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(𝜆 − 1

𝜆)

3𝜆

⋅ (2 − 𝑒((ln 2)/𝑇)𝑡


)

𝜆

,

𝑞𝐷

𝑟2=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(𝜆 − 1

𝜆)

3𝜆

⋅ (2 − 𝑒((ln 2)/𝑇)𝑡

𝑐𝑠+ 𝑐𝑙− 𝜌3+ 𝜇𝑌

)

𝜆

.

(31)

Expectation profit for retailers is

��𝐷

𝑟1=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(𝜆 − 1

𝜆)

3𝜆−3

⋅ (2 − 𝑒((ln 2)/𝑇)𝑡


)

𝜆−1

,

��𝐷

𝑟2=

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(𝜆 − 1

𝜆)

3𝜆−3

⋅ (2 − 𝑒((ln 2)/𝑇)𝑡


)

𝜆−1

.

(32)

Expectation profit for distributers is

��𝐷

𝜔1−1=𝜆 (𝑐𝑠+ 𝜌1) + 𝜇𝑌

(𝜆 − 1)

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(𝜆 − 1

𝜆)

3𝜆

⋅ (2 − 𝑒((ln 2)/𝑇)𝑡


)

𝜆

+ 𝜌1𝑞𝑁

𝑟,

��𝐷

𝜔1−2=𝜆 (𝑐𝑠− 𝜌2) + 𝜇𝑌

(𝜆 − 1)

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(𝜆 − 1

𝜆)

3𝜆

⋅ (2 − 𝑒((ln 2)/𝑇)𝑡


)

𝜆

− (𝜌2+ 𝜌3) 𝑞𝑁

𝑟.

(33)

Expectation profit for production supplier is

��𝐷

𝜔2−1=𝜆 (𝑐𝑠+ 𝑐𝑙+ 𝜌1+ 𝜌2) + 𝜇𝑌

(𝜆 − 1)

⋅

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(𝜆 − 1

𝜆)

3𝜆

⋅ (2 − 𝑒((ln 2)/𝑇)𝑡


)

𝜆

+ (𝜌1+ 𝜌2) 𝑞𝑁

𝑟,

��𝐷

𝜔2−2=𝜆 (𝑐𝑠+ 𝑐𝑙− 𝜌3) + 𝜇𝑌

(𝜆 − 1)

⋅

𝑚 ln (2 − 𝑡2/𝑇2)ln 2

(𝜆 − 1

𝜆)

3𝜆

⋅ (2 − 𝑒((ln 2)/𝑇)𝑡


)

𝜆

− 𝜌3𝑞𝑁

𝑟.

(34)

5. Example Analysis

Specific example is analyzed to verify the models constructedin the paper. Suppose 𝑚 = 6000, 𝜆 = 2, 𝑐

𝑠= 10, 𝑡 = 3,

𝑇 = 18, 𝜌1= 3, 𝜌

2= 1, and 𝜌

3= 2; cost function of

retailers 𝐹(𝑐𝑟) is in even distribution with 𝜇 = 12. Disturbing

scope of retail cost expectation is presumed to be [1, 20]. Inthe following part, influence of retail cost variation will bediscussed, respectively, on wholesale price of distributors and


1 5 10 15 204

5

6

7

8

9

Opt

imal

sale

s

Retailer cost disruptions

Figure 2: Relationship of 𝜇𝑌with the optimal sales.

1 5 10 15 20

180

200

220

240

260


Opt

imal

reta

iler p

rice

Figure 3: Relationship of 𝜇𝑌with the optimal sales price.

retailers, sale quantity, retail price, and expectation profit ofproduction suppliers, distributors, retailers, and the wholethree-level supply chain system.

The following conclusions can be achieved from Figures2–5 when there are emergency events. Under emergency andasymmetric information, three-level supply chain coordina-tion mechanism shows optimal sales quantity 𝑞𝐷

𝑟, optimal

retail price 𝑝𝐷𝑟, optimal wholesale price for retailers 𝑝𝐷

𝜔2, and

optimal wholesale price for distributers 𝑝𝐷𝜔1.

From Tables 1 and 2, the following conclusions can bedrawn.

Firstly, original producing plan has quite strong robust-ness under emergency events. Thus in a certain range ofretailers cost change, the original coordination mechanismcan be effective to coordinate three-level supply chain.

Secondly, when the change is out that range, then originalcoordination mechanism should be renewed to achieve newcoordination.

1 5 10 15 20

20

24

28

32

36

40

44

48

52

Opt

imal

who

lesa

le p

rice


RetailerDistributor

Figure 4: Relationship between 𝜇𝑌and the optimal sales price of

retailer and distributor.

1 5 10 15 20

150

200

250

300

350

400

450Ex

pect

atio

n pr

ofit


RetailerDistributor

Supplier

Figure 5: Relationship between 𝜇𝑌

and expectation profit forretailers, distributers, and supplier.

6. Conclusions

This paper discusses three-level supply chain coordinationmechanism with asymmetric information and under emer-gency and draws the following conclusions.

(1) When emergency has little influence on retail price,then original optimal strategy can be coordinated byits robustness.That is to say that all plans can keep thesame but all members of supply chain system can stillachieve the optimal profits.

(2) When retail price is seriously influenced by emer-gency, then original optimal strategy should beadjusted to coordinate the supply chain system. That


Table 1: Expectation profit for retailers, distributers, supplier, and three-level supply chain system.

Conditions Optimal sales quantity 𝑞𝐷𝑟

Optimal retail 𝑝𝐷𝑟

Retailers 𝑝𝐷𝜔2

Distributers 𝑝𝐷𝜔1

𝜇𝑌< 𝜇 − 𝜌

1− 𝜌2

𝑞𝐷

𝑟1(> 𝑞𝑁𝑟) 𝑝

𝐷

𝑟1(< 𝑝𝑁𝑟) 𝑝

𝐷

𝜔2−1(< 𝑝𝑁𝜔2) 𝑝

𝐷

𝜔1−1(< 𝑝𝑁𝜔1)

𝜇 − 𝜌1− 𝜌2≤ 𝜇𝑌≤ 𝜇 + 𝜌

3𝑞𝑁

𝑟𝑝𝑁

𝑟𝑝𝑁

𝜔2𝑝𝑁

𝜔1

𝜇𝑌> 𝜇 + 𝜌

3𝑞𝐷

𝑟2(< 𝑞𝑁𝑟) 𝑝

𝐷

𝑟2(> 𝑝𝑁𝑟) 𝑝

𝐷

𝜔2−2(> 𝑝𝑁𝜔2) 𝑝

𝐷

𝜔1−2(> 𝑝𝑁𝜔1)

Table 2: Expectation profit for retailers, distributers, and supplier.

Conditions Retailers ��𝐷𝑟

Distributers ��𝐷𝜔1

Supplier ��𝐷𝜔2

𝜇𝑌< 𝜇 − 𝜌

1− 𝜌2

��𝐷

𝑟1(> ��𝑁𝑟) ��

𝐷

𝜔1−1(> ��𝑁𝜔1) ��

𝐷

𝜔2−1(> ��𝑁𝜔2)

𝜇 − 𝜌1− 𝜌2≤ 𝜇𝑌≤ 𝜇 + 𝜌

3��𝑁

𝑟��𝑁

𝜔1��𝑁

𝜔2

𝜇𝑌> 𝜇 + 𝜌

3��𝐷

𝑟2(< ��𝑁𝑟) ��

𝐷

𝜔1−2(< ��𝑁𝜔1) ��

𝐷

𝜔2−2(< ��𝑁𝜔2)

is to say that all plans should have correspondingadjustment to solve emergency events and achieve theoptimal profits for members of supply chain system.These plans include that of original producing plan,wholesale price for distributers and retailers, andretail price.

In practical life, condition of only having asymmetricinformation wildly exists in three-level supply chain systemof fresh agricultural products. Asymmetric information runsthrough processes of producing, supplying, and distribution,which causes a serious loss in fresh agricultural products andalso a big difficulty for supply chainmanagers. It is a directionfor further research to study emergency cooperation of supplychain with consideration of asymmetric information and riskpreference of supply chain. Therefore, this paper providesa novel thought for emergency cooperation of three-levelsupply chain for fresh agricultural product with asymmetricinformation. A fundamental train of thought and a framefor coordinating the fresh agricultural product supply chainunder asymmetric information response to disruptions areprovided in this study.

Competing Interests

The authors declare that they have no competing interests.

Acknowledgments

This research was supported in part by the Basic ResearchProgram of Dezhou University (Grant no. 2015skrc03), Shan-dong Province Crucial R&D Plan Project (2015GGX105008),Shandong Province Natural Science Fund (ZR2013GL001),and Shandong Humanities and Social Science-Food Econ-omy Management Research Base.

References

[1] H. Zhou, Q. Ding, and J. Otto, “The reality and prospect offresh agricultural product supply chains inChina,” InternationalJournal of Applied Management Science, vol. 5, no. 3, pp. 251–264, 2013.

[2] Q. H. Pang, Y. Chen, and Y. L. Hu, “Three-level supply chaincoordination under disruptions based on revenue-sharing con-tract with price dependent demand,” Discrete Dynamics inNature and Society, vol. 2014, Article ID 464612, 11 pages, 2014.

[3] H. Zhang, Y. Liu, and J. S. Huang, “Supply chain coordina-tion contracts under double sided disruptions simultaneously,”Mathematical Problems in Engineering, vol. 2015, Article ID812043, 9 pages, 2015.

[4] J. Chen and B. Dan, “Fresh agricultural product supplychain coordination under the physical loss-controlling,” SystemEngineering—Theory & Practice, vol. 29, no. 3, pp. 54–62, 2009.

[5] X. Zhao and F. W. Wu, “Coordination of agri-food chain withrevenue-sharing contract under stochastic output and demand,”Chinese Journal of Management Science, vol. 17, no. 5, pp. 88–95,2009.

[6] L. Lin, S. P. Yang, and B. Dan, “Three-level supply chaincoordination of fresh and live agricultural products by revenue-sharing contracts,” Journal of System Engineering, vol. 25, no. 4,pp. 484–491, 2010.

[7] W. K. Zhang, L. H. Guo, and F. L. Guo, “Research on coordina-tion policy in a three-level supply chain based on a punishmentand revenue sharing contract,” Forecasting, vol. 34, no. 2, pp. 76–80, 2015.

[8] L. Liu and Y. Shi, “Coordination of three-stage supply chainwith unconventional disruptions through buy-back contract,”Journal of Systems & Management, vol. 24, no. 2, pp. 296–303,2015.

[9] U. Gurler and M. Parlar, “An inventory problem with tworandomly available suppliers,” Operations Research, vol. 45, no.6, pp. 904–918, 1997.

[10] K. Chen and T. Xiao, “Demand disruption and coordination ofthe supply chain with a dominant retailer,” European Journal ofOperational Research, vol. 197, no. 1, pp. 225–234, 2009.

[11] D. Ding and J. Chen, “Coordinating a three level supply chainwith flexible return policies,”Omega, vol. 36, no. 5, pp. 865–876,2008.

[12] Y.-F. Huo and Z.-S. Liu, “Coordination analysis on retailer-dominant three-level supply chain under disruption demand,”Computer Integrated Manufacturing Systems, vol. 20, no. 4, pp.955–962, 2014.

[13] W. G. Zhang, J. H. Fu, and H. Y. Li, “Coordination ofsupply chain with a revenue-sharing contract under demanddisruptions when retailers compete,” International Journal ofProduction Economics, vol. 138, no. 1, pp. 68–75, 2012.


[14] J. Wang and X. Chen, “Fresh produce retailer’s optimal optionscontracts procurement decisions research with circulationwastage,” System Engineering Theory and Practice, vol. 32, no.7, pp. 1408–1414, 2012.

[15] Q. H. Pang, Y. E. Chen, and Y. L. Hu, “Coordinating three-level supply chain by revenue-sharing contract with sales effortdependent demand,” Discrete Dynamics in Nature and Society,vol. 2014, Article ID 561081, 10 pages, 2014.

[16] C. L. Munson and M. J. Rosenblatt, “Coordinating a three-levelsupply chain with quantity discounts,” IIE Transactions, vol. 33,no. 5, pp. 371–384, 2001.

[17] H. Wang and J. S. Hu, “Coordination mechanism analysis ofthree-level supply chain under disruption,” Journal of QingdaoUniversity (Natural Science Edition), vol. 19, no. 3, pp. 72–76,2006.

[18] C.-X. Wang and L.-K. Jiang, “Quantity discount strategy forcoordinating a three level supply chain with fuzzy randomdemand,” Journal of Shanghai Jiaotong University, vol. 44, no.12, pp. 1672–1677, 2010.

[19] X. T. Qi, J. F. Bard, and G. Yu, “Supply chain coordination withdemand disruptions,” Omega, vol. 32, no. 4, pp. 301–312, 2004.

[20] H. Yu and J. Chen, “Supply chain coordination under disrup-tions with buy-back contract,” Systems Engineering—Theory &Practice, vol. 25, no. 8, pp. 38–43, 2005.

[21] Z. H. Wu, H. Chen, and Q. Zhao, “Supply chain coordinationwith demand and purchase cost of retailers disruptions,” Chi-nese Journal of Management Science, vol. 20, no. 6, pp. 110–117,2012.

[22] Z. H. Wu, H. Chen, and C. L. Liang, “Supply chain disruptionscoordination model of fresh agricultural products under time,”Chinese Journal of Management Science, vol. 23, no. 6, pp. 126–134, 2015.

[23] H. R. Liu, F. Y. Yi, and H. L. Yang, “Adaptive grouping cloudmodel shuffled frog leaping algorithm for solving continuousoptimization problems,” Computational Intelligence and Neuro-science, vol. 2016, Article ID 5675349, 8 pages, 2016.

[24] X. X. Chen, Y. Wang, and H. L. Yu, “Three-level supplychain model for deteriorating items with time-varying demandbased on the third-party logistics provider,” Chinese Journal ofManagement Science, vol. 22, no. 1, pp. 65–73, 2014.

[25] Y. H. Qin, X. Y. Cao, and L. J. Song, “Supply chain coordina-tion with asymmetric demand information under disruption,”Operations Research and Management Science, vol. 21, no. 4, pp.60–64, 2012.

[26] X. Y. Cao and Y. H. Qin, “Buy back contracts in supply chainunder emergence and asymmetric information,” IndustrialEngineering Journal, vol. 15, no. 5, pp. 99–104, 2012.

[27] Y. Feng, Y. L. Yu, and Y. Z. Zhang, “Coordination in a three-echelon supply chain of fresh agri-products with TPLSP’sparticipation in decision-making,” Journal of Industrial Engi-neering/Engineering Management, vol. 29, no. 4, pp. 213–221,2015.

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