Proceedings of IEEE CCIS2012

THREE-STAGED CLOUD COMPUTING SERVICE SUPPLY CHAIN COORDINATION BY COMBINED

CONTRACT Lingyun Wei, Shuo ��∗

Department of Logistics Engineering, School of Automation, Beijing University of Posts and Telecommunications, Beijing 100876, China

weilingyun2010@sina.com, qishuo05@sina.com

Abstract: We mainly design a revenue sharing combined buy-back contract to coordinate the three-staged cloud computing service supply chain. This discussed supply chain includes one application service provider (ASP), one platform service provider (APP) and one application infrastructure provider (AIP). AIP supplies the infrastructure and computer capacity to APP; APP supplies the application platform to ASP; ASP sells the value-added application services to the market. We discuss four coordination strategies for the cloud computing service supply chain: namely, centralized control, decentralized control (wholesale price contract), revenue sharing contract and combined contract. We first prove that the wholesale price contract can coordinate the services supply chain, but AIP and APP cannot get a large portion of supply chain’s profits. Moreover, we also prove that the revenue sharing contract cannot coordinate the supply chain. Finally, we design a revenue sharing combined buy-back contract, which can perfectly coordinate the three-staged cloud computing services supply chain.

Keywords: Cloud computing; Supply chain; Revenue sharing contract; Combined contract;

1 Introduction Cloud computing is an emerging ICT framework and business model, which is used to create and deliver public services, such as applications, platforms and infrastructure. When using cloud computing, the ultimate users can easily access the fully functional online software and services via the Internet, with a little or even no cost at all to connect them by using computers or mobile communication devices. Moreover,the cloud’s inherent capability to dynamically scale up or down the infrastructure commitment as demand changes on a pay-as-you-go basis has a positive influence on the service provider’s overhead costs, energy costs, and in reducing its carbon footprint. Because of these advantages, more and more companies focus on the cloud computing services and adopt the model of IaaS (Infrastructure-as-a-Service), PaaS (Plartform-as-a-Service) and SaaS (Software-as-a-Service). On the other hand, a lot of researchers focus on this field. Sean [1] identifies the strengths, weaknesses, opportunities and threats for cloud

computing industry and the various issues that will affect the different stakeholders of cloud computing.Weinhardt [2] places business models at infrastructure, platform or application level and discusses on the business opportunities of cloud computing. Michael [3] points out software needs a pay-for-use licensing model to match needs of cloud computing and he identifies the top 10 obstacles and opportunities of cloud computing.However, only a few researchers qualitatively analyze the coordination strategies in the cloud computing service supply chain. Haluk [4] studies an application services supply chain consisting of one application service provider (ASP) and one application infrastructure provider (AIP). He examines the supply chain’s performance under four different coordination strategies involving risk and information sharing between ASP and AIP. Haluk and Hsing [5] study the coordination strategies in a SaaS supply chain model, which consider the effects of congestion. They point out it is possible to create the right incentives so that the economically efficient outcome is also the Nash equilibrium. Although they study the coordination strategies in a cloud computing service supply chain,but they don’t take the supply chain contract into account. What’ more, Haluk’s model is only limited intwo members, ASP and AIP.

Our paper attempts to research the coordination strategies of a three-staged cloud computing service supply chain which consists of one application service provider (ASP), one platform service provider (APP) and one application infrastructure provider (AIP). In thismodel, AIP provides the services of IaaS, APP provides the services of PaaS and ASP provides the services of SaaS. ASP first purchases computer capacity from APP, and then sells it with value-added services to the market. To maximize its expect profit, ASP needs to make reasonable arrangements by deciding how much capacity to order from APP and how much to charge its services to the market. Meanwhile, APP prefers tooptimize its expected profit by setting an optimal price of the computer capacity and determining how much capacity to order from AIP. At the same time, AIP needs to work out an optimal price of the computer capacity it sells in order to maximize its profits. We examine four different coordination strategies, including centralized control, decentralized control, revenue

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Proceedings of IEEE CCIS2012

sharing contract and combined contract. The combined contract is specially designed to perfectly coordinate the services supply chain. Ilaria [6] points that supply chain contract must allow three main objectives to be achieved: (i) to increase the total supply chain’s profit so as to make it closer to the profit resulting from a centralized control and (ii) to share the risks among the partners of the supply chain. (iii) to synchronously improve the profits of all supply chain actors. So, we design the combined contract for cloud computing services supply chain upon those requirements.

2 The model of cloud computing service supply chain Our paper considers a three-stage cloud computing service supply chain, which consists of risk neutral AIP, APP and ASP. To provide application services for its customers, ASP acquires computer capacity Q� from APP who charges w� per unit of capacity. Meanwhile, APP acquires computer capacity Q� from AIP who charges w� per unit of capacity. Therefore, Q� and Q� could be differ. In order to optimize its expected profit, however, once ASP has set Q�, APP will set Q� = Q� =Q as well. The uniform distribution is chosen in our model for analysis. ASP sells its value-added service at price p per unit of capacity, and confronts a random market demand which is sensitive to selling price for its service at a large extent, x is the linear demand function of price p, and is described by x(p)������ = d − ap, where d, a > 0, and d/a ≥ p ≥ 0. It gives us a picture of the standard linear demand curve with the maximum market potential of d and price sensitivity parameter of a. The price-sensitive random demand follows a uniform distribution over the range x(p)������ − b, x(p)������ +b. Let f( x ∣∣ p ) be the probability density function of x, and F( x ∣∣ p ) be the distribution function of x, we can see that F( x ∣∣ p ) is differentiable, strictly increasing, and F(0) = 0, F( x ∣∣ p )����������� = 1 − F( x ∣∣ p ), μ = E( x ∣∣ p ). Because of the uncertainty of market demands, unit opportunity costs k of lost sales exists due to insufficient capacity. We assume that the opportunity costs only exist in the ASP. The unit infrastructure producing cost of AIP is described by c�, the unit platform building cost of APP is described by c� and the unit application service cost of ASP is described by c� , c = c� + c� + c� , c is the unit cost of the whole supply chain. The diseconomy of scale cost parameter related to the AIP’s management of infrastructure is described by e. This diseconomy of scale in infrastructure management results from increasing costs of managing capacity and user access and rising complexity of the supply chain. At the end of the sales time, let parameter v represents the salvage value of unused capacity, and v <p.

Assuming the expected sales quantity of ASP isS(Q, p), and it can be described in Eq.(1):

S(Q, p) = ∫ Qf( x ∣∣ p )dx + ∫ xf( x ∣∣ p )dx =��

��

Q − ∫ F( x ∣∣ p )dx�� (1)

Under the uniform distribution, the expected sales quantity S(Q, p) can be described in Eq.(2):

S(Q, p) = − Q�4b + (d − ap + b)Q

2b − (d − ap − b)�4b (2)

Let I(Q, p)be the expected left over quantity, it can be described in Eq. (3):

I(Q, p) = ∫ (Q − x)f( x ∣∣ p )dx = Q − S(Q, p)�� (3)

Let L(Q, p)be the expected lost sales quantity, it can be described in Eq.(4):

L(Q, p) = ∫ (x − Q)f( x ∣∣ p )dx∞�

= μ − S(Q, p) (4)

Let μ be the average demand, it can be described in Eq. (5):

μ = d − ap (5)

3 The coordination strategies of cloud computing service supply chain 1) Strategy one: centralized control

In this strategy, a single firm plays an integrated role of AIP, APP and ASP. The cloud computing service supply chain can be perfectly coordinated under this situation. The whole supply chain’s expected profit consists of five parts, including sales income, salvage income, opportunity costs, variation costs and infrastructure management costs. Assuming SP�(p, Q) is the profit of the whole supply chain, the function of supply chain’s profit can be described in Eq.(6):

SP�(p, Q) = (p − v + k)S(Q, p)

+ (v − c)Q − kμ − eQ� (6)

To find the optimal supply chain’s expected profit, first order conditions require����(�,�)

�� = 0 and ����(�,�)�� = 0 as

follows.

dSP�(p, Q)dQ = (p − v + k) �− Q

2b + (d − ap + b)2b �

+v − c − 2eQ = 0 (7)

Q��� = (�����)(������)���(���)��������! (8)

����(�,�)�� = − �"

�� + (������)��� − (������)"

�� +

�(�����)(��������)�� + ak = 0 (9)

W h e n �"���(�,�)��" < 0, �"���(�,�)

��" < 0, △�= �"���(�,�)��" ∗

�"���(�,�)��" − �"���(�,�)

���� ∗ �"���(�,�)���� > 0, Eq. (6) has a maxi

mum value. The optimal solution(p∗, Q∗)can be obtained from the Eq. (7) and Eq. (9) when p > v and b <

Proceedings of IEEE CCIS2012

a(ae + 1)(p − v) + ak(ae + 1).

2) Strategy two: decentralized control (wholesale price contract)

In this strategy, ASP acquires computer capacity Q from APP who charges w� per unit of the capacity. Meanwhile, APP acquires equivalent computer capacity Q from AIP who charges w� per unit of the capacity. ASP determines the price to the market and the capacity to purchase from the APP and bears the risk of over-and under-capacity costs of the supply chain; AIP bears the cost of infrastructure management. All of the three parts have the unit variation cost. At the end of the sales time, ASP has the salvage value of unused capacity.

Assuming HP�(Q), PP�(Q), AP�(p, Q) is the profit of AIP, APP and ASP, it can be described in Eq.(10), Eq.(11) and Eq.(12):

HP�(Q) = w�Q − c�Q − eQ� (10)

PP�(Q) = w�Q − c�Q − w�Q (11) AP�(p, Q) = (p − v + k)S(Q, p) +

(v − c� − w�)Q − kμ (12)

To find the optimal ASP’s expected profit, first order conditions require �$�"(�,�)

�� = 0 and �$�"(�,�)�� = 0 as

follows. dAP�(p, Q)

dQ = − (p − v + k)Q2b + (p − v + k)(d − ap + b)

2b

+v − c� − w� = 0 (13)

dAP�(p, Q)dp = − Q�

4b + (d − ap + b)Q2b − (d − ap − b)�

4b

+ �(�����)(��������)�� + ak = 0 (14)

When �"$�"(�,�)��" < 0, �"$�"(�,�)

��" < 0, △�= �"$�"(�,�)��" ∗

�"$�"(�,�)��" − �"$�"(�,�)

���� ∗ �"$�"(�,�)���� > 0 , Eq.(12) has a

maximum value. The optimal solution can be obtained from Eq.(13) and Eq.(14) when p > v and b < a(p −v) + ak.

We can see the wholesale price contract can coordinate the supply chain when �$�"(�,�)

�� = ����(�,�)�� = 0 and

�$�"(�,�)�� = ����(�,�)

�� = 0. Easily to confirm the wholesale price contract would coordinate the channel only if w� = c − c� + 2eQ∗. However, AIP and APP can’t get a large portion of profits under this contract, so they prefer a higher wholesale price. As a result, the wholesale price contract is not considered a coordinating contract.

3) Strategy three: revenue sharing contract

In this strategy, APP gives a lower unit rent price w� to ASP and ASP gives APP a percentage of his revenue. Assume all revenue is shared between APP and ASP, including sales income and salvage revenue. Let φ� is the fraction ASP earns and (1 − φ�)is the fraction APP

earns. Meanwhile, AIP gives a lower unit rent price w� to APP and APP gives AIP a percentage of his revenue (this revenue include the shared revenue from ASP and the rent income from ASP). Let φ� is the fraction which APP earns and (1 − φ�) is the fraction ASP earns. Assuming HP&(p, Q), PP&(p, Q), AP&(p, Q) is the profit of AIP, APP and ASP, it can be described in Eq.(15), Eq.(16) and Eq.(17):

HP&(p, Q) = (1 − φ�)(1 − φ�)(p − v)S(Q, p) − eQ�

+[(1 − φ�)(1 − φ�)v + (1 − φ�)w�+w� − c�]Q (15)

PP&(p, Q) = φ�1 − φ�(p − v)S(Q, p) +

'φ�1 − φ�v + φ�w� − w� − c�*Q (16)

AP&(p, Q) = [φ�(p − v) + k]S(Q, p)

+(φ�v − w� − c�)Q − kμ (17)

To find the optimal ASP’s expected profit, first order conditions require �$�-(�,�)

�� = 0 and �$�-(�,�)�� = 0 as

follows.

�$�-(�,�)�� = 'φ�(p − v) + k* 5− �

�� + (������)

�� 7 + φ�v − w� − c� = 0 (18)

Q&$� = d − ap + b − ��(89�:9���9):9(���)�� (19)

�$�-(�,�)

�� = φ� 5− �"�� + (������)�

�� (������)"�� 7 +

�[:9(���)��](��������)�� + ak = 0 (20)

When �"$�-(�,�)��" < 0, �"$�-(�,�)

��" < 0, △&= �"$�-(�,�)��" ∗

�"$�-(�,�)��" − �"$�-(�,�)

���� ∗ �"$�-(�,�)���� > 0 , Eq.(17) has a

maximum value. The optimal solution can be obtained from the Eq.(18) and Eq.(20) when p > v and b <a(p − v) + ��

φ9.

We can see the revenue sharing contract can coordinate the supply chain when �$�-(�,�)

�� = ���-(�,�)�� = ����(�,�)

�� =0( Q&�� = Q&$� = Q���) and �$�-(�,�)

�� = ���-(�,�)�� = 0 . To

find the optimal APP’s expected profit, first order conditions require ���-(�,�)

�� = 0 as follows.

���-(�,�)�� = φ� ;(1 − φ�) 5(���)(��������)

�� + v7 + w�? − (c� + w�) = 0 (21)

Q&�� = d − ap + b − ��[8@�:@89��@�:@(��:9)�]:@(��:9)(���) (22)

According to Eq. (8), Eq. (19) and Eq. (22), let Q&$� =Q���, we can obtain the expression of w� in Eq. (23). Then, let Q&�� = Q&$�, we can obtain the expression of w� in Eq. (24).

w� = [�!(������)����][:9(���)��]��������! + φ�v − c� (23)

Proceedings of IEEE CCIS2012

w� = :@[�!(������)����](��:9)(���)��������! +φ�w� −

c� + φ�(1 − φ�) (24)

According to Eq.(9), Eq.(20) and �$�-(�,�)�� = ����(�,�)

�� =0 , we can see that the revenue sharing contract can coordinate the discussed supply chain only if k=0 or k ≠ 0, φ� = 1. However, there are opportunity costs in the cloud computing service supply chain because of the loss of goodwill. Meanwhile, the revenue sharing contract is equivalent to the wholesale price contract when φ� = 1 . As a result, because of the change of price strategy, the revenue sharing contract can’t coordinate the supply chain [7]. But we can also increase the profit of the supply chain. That is letting w�, w� as Eq. (23) and Eq. (24). The unit price p is decided in Eq. (18) and Eq. (20). In addition, we should change the fraction parameter φ� and φ� ( 0 < φ� <1,0 < φ� < 1), in order to ensure the profits of AIP, APP and ASP are not lower than the ones that they don’t adopt the revenue sharing contract.

4) Strategy four: combined contract

In this strategy, we design a revenue sharing combined buy-back contract to coordinate the supply chain. Because the change of price strategy only appears in ASP, we use the combined contract between APP and ASP and also use revenue sharing contract between AIP and APP. APP gives a lower unit rent price w� to ASP and ASP gives APP a percentage of his revenue. This revenue only includes sales income. Let φ� is the fraction ASP earns and (1 − φ�) is the fraction APP earns. Meanwhile, AIP gives a lower unit rent price w� to APP and APP gives AIP a percentage of his revenue, including the shared revenue and the rent income from ASP. Let φ� is the fraction APP earns and (1 − φ�)is the fraction ASP earns. Moreover, APP pays the ASP m per unit unused capacity and the salvage value of unused capacity is hold by APP. Assuming HP�(p, Q), PP�(p, Q), AP�(p, Q) is the profit of AIP, APP and ASP, it can be described in Eq.(25), Eq.(26) and Eq.(27):

HP�(p, Q) = 1 − φ�1 − φ�pS(Q, p) + '1 − φ�w�+w� − c�*Q − eQ� (25)

PP�(p, Q) = [φ�1 − φ�p + m − v]S(Q, p) + v − m + φ�w� − w� − c�Q (26) AP�(p, Q) = (φ�p + k − m)S(Q, p) + (m − w� − c�)Q − kμ (27)

To find the optimal ASP’s expected profit, first order conditions require �$�C(�,�)

�� = 0 and �$�C(�,�)�� = 0 as

follows.

�$�C(�,�)�� = (:9����D)(��������)

�� + (m − w� − c�) = 0 (28) Q�$� = d − ap + b − ��(89��9�D)

:9����D (29)

�$�C(�,�)�� = φ� 5− �"

�� + (������)��� − (������)"

�� 7 + �(φ9����D)(��������)

�� + ak = 0 (30)

When �"$�C(�,�)��" < 0, �"$�C(�,�)

��" < 0, △�= �"$�C(�,�)��" ∗

�"$�C(�,�)��" − �"$�C(�,�)

���� ∗ �"$�C(�,�)���� > 0 , Eq.(27) has a

maximum value. The optimal solution can be obtained from Eq.(28) and Eq.(30) when k > m and b < ap +�(��D)

φ9 .

We can see that the combined contract can coordinate the supply chain when �$�C(�,�)

�� = ���C(�,�)�� = ����(�,�)

�� =0 ( Q��� = Q�$� = Q���) and �$�C(�,�)

�� = ����(�,�)�� = 0 . To

find the optimal APP’s expected profit, first order conditions require ���C(�,�)

�� = 0 as follows.

���C(�,�)�� = [:@(��:9)��D��](��������)

�� + (v − m + φ�w� − w� − c�) = 0 (31) Q��� = d − ap + b − ��(D���:@89�8@��@)

:@(��:9)��D�� (32)

According to Eq.(8), Eq.(29) and Eq.(32), let Q�$� =Q��� , we can obtain the expression of w� in Eq(33). Then, let Q��� = Q�$� we can obtain the expression of w� in Eq. (34). According to Eq.(9) and Eq.(30), set �$�C(�,�)

�� = ����(�,�)�� , we can obtain the expression of

m in Eq. (35). w� = [�!(������)����](:9����D)

��������! + m − c� (33)

w� = (89��9�D)[:@(��:9)��D��]:9����D

−m + v + φ�w� − c� (34)

m = (:9��)'��"��(������)��(������)"*��(��������)

−(1 − φ�)p + v (35)

As a conclusion, the combined contract can coordinate the supply chain when w�, w�, m satisfy Eq.(33), Eq.(34) and Eq.(35). The unit price p and computer capacity Q are decided in Eq.(7) and Eq.(9). In addition, we should change the fraction parameter φ� and φ� ( 0 < J� <1,0 < φ� < 1), in order to ensure the profits of AIP, APP, and ASP are not lower than the ones that they don’t adopt the combined contract..

4 Numerical exploration Based on the optimal conditions of four profit functions in Eq.(6), Eq.(12), Eq.(17) and Eq.(27), we can know that the four profit functions have the optimal solutions when p > K > v > M, N ≤ RK. But it is only a sufficient condition. We select a set of parameters (see Table I) that do not satisfy the constraints and we can also obtain the optimal solutions.

Proceedings of IEEE CCIS2012

Table I Parameters for numerical explorations

Parameter value Parameter value Parameter value d 100.0 v 5.0 c� 0.5 a 2.0 k 8.0 c� 1.0 b 20.0 w� 12.0 c� 1.5 e 0.1 w� 20.0 c 3.0

Now, we discuss the selection of φ� and φ� in the revenue sharing contact. We calculate that in the decentralized control, the profits of AIP, ASP, and APP are 218.37, 230.61 and 270.33. So, we must ensure the Eq. (36), Eq. (37), Eq. (38) satisfied when using the revenue sharing contract. All of the three formulas have been represented in Figure 1. The dashed part in Figure 1 consider the feasible domains for φ� and φ� . It identifies a win–win area, in which the revenue sharing contract can not only increase the profits of the supply chain, but also be accepted by different decision makers.

HP&(p, Q) ≥ 218.37 (36)

PP&(p, Q) ≥ 230.61 (37)

AP&(p, Q) ≥ 270.33 (38)

Figure 1 the fraction parameter φ� and φ�under the revenue sharing contact

Moreover, we must ensure the Eq.(39), Eq.(40), Eq.(41) established when using the combined contract. All of the three formulas have been represented in Figure 2. The dashed part in Figure 2 consider the feasible domains for φ� and φ�. It identifies a win–win area, in which the combined contract can not only increase the profits of the supply chain, but also be accepted by different decision makers.

HP�(p, Q) ≥ 214.156 (39)

PP�(p, Q) ≥ 297.1111 (40)

AP�(p, Q) ≥ 188.827 (41)

Figure 2 The fraction parameter φ� and φ�under the combined contact

5 Conclusions

As a conclusion, we discuss four coordination strategies in the cloud computing service supply chain. We prove that the wholesale price contract can coordinate the supply chain when w� = c − c� + 2eQ∗. However, AIP and APP cannot get a large profit under this contract, so they prefer a higher wholesale price. On the other hand, the revenue sharing contract cannot coordinate the supply chain, but we can also increase the profits of the supply chain. Finally, we designed a revenue sharing combined buy-back contract to coordinate the supply chain. After numerical exploration, we identify a win–win area in which we cannot only increase the profits of the supply chain, but also be accepted by different decision makers.

Acknowledgements This work was supported by National Science Foundation of China (Grant No. 61174167). It was also supported by "the Fundamental Research Funds for the Central Universities" in China.

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[7] Gérard P. Cachon, Martin A. Lariviere. Supply Chain Coordination with Revenue-Sharing Contracts: Strengths and Limitations. Management Science. January 2005: 30–44.