1. INTRODUCTION
For recent years, a share in product sales under an ecommerce environment has been increasing worldwide. However, online sales tend to have a higher returns ratio than brickandmortar sales (Vlachos and Dekker, 2003; Chen and Bell, 2009; Chen and Bell, 2011; Chen, 2011; Liu et al., 2014; Saito and Kusukawa, 2015). The product demand and customer returns may be uncertain for the unit price of products and the refund ratio of customer returns (Liu and He, 2013). Also, it is important issue for retailers and manufacturers to handle the unsold products and customers returns in a market (Lee, 2001; Vlachos and Dekker, 2003; Choi et al., 2004; Lee, 2007; Kusukawa et al., 2009). When manufacturers and retailers make buyback contract for unsold products and customer returns, it is necessary for manufacturers to buy back unsold products and customer returns considering the difference between their qualities. Moreover, when product demand and customer returns are uncertain, it is necessary for retailers, manufacturers and the whole system to consider the effect of variance of the individual profit in eSC on the optimal operation in an eSC. As one of helpful tools to solve this issue, the meanvariance analysis (Choi et al., 2008; Xu et al., 2013; Liu and He, 2013) is applied into the operation in a SC/an eSC.
In a supply chain management, it is necessary to determine the optimal operations to establish a SC to obtain its profitability. In a decentralized SC, all members in the SC determine the optimal operations so as to maximize their profits. As one of the optimal decisionmaking approaches under a decentralized SC, the Stackelberg game is adopted (Cachon and Netessine, 2004; Cai et al., 2009; Berr, 2011; Hu et al., 2011; Aust and Buscher, 2012). In the Stackelberg game, there is a single leader of the decision making and a single (multiple) follower(s) of the decisionmaking of the leader. The leader of the decisionmaking determines the optimal strategy so as to maximize the leader’s (expected) profit. The follower(s) of the decision making determine(s) the optimal strategy so as to maximize the follower(s)’s (expected) profit under the optimal strategy determined by the leader of the decisionmaking.
Also, in a supply chain management, the optimal decisions under an integrated supply chain maximizing the whole supply chain’s expected profit can bring the more expected profit to the whole supply chain than those under a decentralized supply chain maximizing the expected profit of each member in a supply chain. So, from the aspect of the total optimization in supply chain management, it is preferable for all members in supply chain to shift the optimal decisions under the integrated supply chain. In this case, it is the absolute requirement for all members under the integrated supply chain to obtain the more expected profits than those under the decentralized supply chain. In order to achieve the increases in profits of all members under the integrated supply chain, a variety of supply chain coordination approaches between all members have been discussed by Cachon and Netessine (2004), Chauhan and Proth (2005), Nagarajan and Sosic (2008) and Du et al. (2011).
The motivation of this paper is to (i) incorporate meanvariance analysis regarding the uncertainties in product demand for the unit retail price and customer returns for the refund ratio into decisionmaking for the optimal operation under the decentralized eSC and the integrated eSC as to risk attitude of eSC members regarding the uncertainties, and (ii) discuss supply chain coordination to adjust the unit wholesale price and the unit buyback prices of the unsold products and the unresold customer returns between members under ISC in order to promote the shift to the optimal operation under the integrated eSC. Concretely, this paper discusses risk analysis and supply chain coordination for the optimal operation in an eSC with the uncertainties in product demand and customer returns. An eSC consists of a retailer and a manufacturer. The return handlings are discussed on customer returns and unsold products. A retailer receives customer returns from a market once and resells the resalable returns in the same market. A manufacturer buys back the unsold products and the unresold customer returns from the retailer, considering the difference of quality between those products. Here, the product demand is sensitive on the unit retail price and refund ratio of the customer returns for the unit retail price, and the customer returns ratio is sensitive on refund ratio. This study discusses three types of risk attitude regarding the uncertainties in products demand and customer returns: riskneutral attitude (attitude N) to maximize the decision maker’s expected profit in eSC without consideration of variance of the relevant profit in eSC, riskaverse attitude (attitude A) with negative consideration of the variance, and riskprone attitude (attitude P) with positive consideration of the variance (Choi et al., 2008). Using the meanvariance analysis for each risk attitude, the optimal decisions for the product order quantity, the unit retail price and the refund ratio of customer returns under the decentralized eSC (DSC) and the integrated e SC (ISC) are determined. DSC optimizes the retailer’s utility function as to risk attitude. As with case of DSC, ISC optimizes the utility function of the whole system as to risk attitude. The analysis numerically verifies how three types of risk attitude, attitude N, attitude A and attitude P, on product demand and customer returns affect the optimal operations under DSC and ISC. In order to promote the shift to the optimal operation under ISC, supply chain coordination (SCC) is discussed by adjusting the unit wholesale price and the unit buyback prices of the unsold products and the unresold customer returns between eSC members under ISC as Nash bargaining solutions (Nagarajan and Sosic, 2008; Du et al., 2011; Saito and Kusukawa, 2015).
The rest of this paper is organized as follows. In Section 2, a review of the literature regarding this paper is presented. Section 3 provides model descriptions regarding notation of mathematical expressions used in this paper, operational flows of an eSC and model assumptions. Section 4 formulates expectation and variance of a retailer, a manufacturer and the whole system in the eSC. Section 5 discusses meanvariance analysis of the individual profit in the eSC for uncertainties in product demand and customer returns. In Section 6, the optimal operations under DSC as to risk attitude are proposed. In Section 7, the optimal operations under ISC as to risk attitude are proposed. Section 8 discusses supply chain coordination in ISC to promote the shift to the optimal operation under ISC from that under DSC. Section 9 shows results of numerical analyses and describes managerial insights. Finally, Section 10 summarizes conclusions and future researches for this paper.
2. LITERATURE REVIEW
As issues related to this paper, the following two topics are often discussed: the optimal operation in an e SC with buyback contract and customer returns and risk analysis using meanvariance theory.
There are rich literature related to the optimal operation in an eSC with buy back contract. For example, Chen and Bell (2011) investigated a decentralized supply chain that consisted of a manufacturer and a retailer where the retailer simultaneously determined the unit retail price and the product order quantity while experiencing customer returns and price dependent stochastic demand. As supply chain coordination, an agreement between the manufacturer and the retailer that included buyback prices for unsold inventory and customer returns was proposed. Here, the information of customer returns was shared between members, and unsold products and customer returns were bought back at the same price. Chen (2011) discussed a situation where the information of customer returns was not shared between members, and investigated how information sharing of customer returns impacted the optimal operation with buyback policy of the unsold products and customer returns from a market and the expected profits of eSC members. However, unsold products and customer returns are bought back at the same price. Saito and Kusukawa (2015) incorporated a buyback policy with different prices between unsold products and unresold customer returns into the optimal operation in an eSC. They verified how information sharing regarding customer returns ratio affected the optimal operation including resale of product returns as to a manufacturer’s buyback policy in the eSC. Liu et al. (2014) examined a supply chain consisting of a single manufacturer and a single retailer, who faced with demand uncertainty. They investigated how customer returns influenced the retailer's ordering decision as well as the profits of the manufacturer and the retailer. When the refund amount was either exogenous or a decision variable, they investigated which situation on the refund amount could coordinate the supply chain by the buyback contract. However, the above previous papers determined the optimal operation in an eSC so as to maximize the expected profits of members and the whole system in an e SC.
There are some literature related to the optimal operation in a SC/an eSC using risk analysis using the meanvariance (Choi et al., 2008; Wu et al., 2009; Xu et al., 2013; Liu and He, 2013). Risk analysis using the meanvariance analysis (Markowitz, 1959) is first incorporated into inventory control problem especially newsvendor problem (Lau, 1980). Lau (1980) applied first the meanvariance analysis into optimal decision for order quantity of a single type of products in a single period. Instead of maximizing the expected profit, this previous paper proposed an alternative objective which aimed at maximizing an objective function of the expected profit and the variance/the standard deviation of profit. Next, noticing the importance of agents’ risk preference on the supply chain decisions including supply chain coordination, studies on not only risk averse agents, but also risk prone agents become increasingly popular in recent years (Choi et al., 2008). Choi et al. (2008) discussed supply chain agents, a retailer and a manufacturer, with the three risk attitudes (risk neutral, risk averse and risk prone). They verified the impacts on the optimal order quantity of a single type of a product in a single period and setting the supply chain coordinating contract regarding a wholesale pricing policy when the supply chain agents have different risk attitudes under an meanvariance objective which consists of both the expected profit and the variance of profit of supply chain agents. Xu et al.(2013) discussed the optimal operation coordinating buyback contracts with riskaverse retailer on the uncertainty in product demand in a SC. The pricesensitivity on product demand was discussed, but customer returns were not discussed. Liu and He (2013) discussed the optimal operation with coordinating buybackrefund contracts with riskaverse retailer under the uncertainties in product demand and customer returns. The pricesensitivity on refund was discussed, but that on product demand did not discussed.
As mentioned above, little research has discussed the optimal operation in an eSC simultaneously considering risk attitude of eSC members for the uncertainties in product demand and customer returns and supply chain coordination to shift to the optimal operation under the integrated eSC (ISC) from that under the decentralized e SC (DSC) by adjusting the unit buyback price as to quality of the unsold products and customer returns. This paper attempts to incorporate above issues into optimal operation for an eSC. The outcomes obtained from the theoretical analyses and the numerical analyses for an eSC will answer the following questions for practitioners, academic researchers and realworld policymakers, regarding operations in an eSC: (i) how different risk attitudes: riskneutral attitude, riskaverse attitude and riskprone attitude will affect the optimal operations in an eSC, (ii) how SCC on wholesale price and buyback prices as to quality of the unsold products and customer returns will be conducted so as to shift to the optimal operation under ISC from DSC.
3. MODEL DESCRIPTIONS
3.1. Notation

DSC: index to indicate the decentralized supply chain

ISC: index to indicate the integrated supply chain

i : index to indicate the type of decision making in an eSC

D: index to indicate the optimal decision (optimal operation) under DSC

C: index to indicate the optimal decision (optimal operation) under ISC

R: retailer

M: manufacturer

S: the whole system

member: index to indicate members in an eSC

${\Pi}_{member}^{}(\cdot )$: the profit of $member\hspace{0.17em}(\in \{R,\hspace{0.17em}M,\hspace{0.17em}S\})$

$E[{\Pi}_{member}^{}(\cdot )]$: the expected profit of $member\hspace{0.17em}(\in \{R,\hspace{0.17em}M,\hspace{0.17em}S\})$

$V[{\Pi}_{member}^{}(\cdot )]$: the variance of the profit of $member\hspace{0.17em}(\in \{R,\hspace{0.17em}M,\hspace{0.17em}S\})$

N: riskneutral attitude

A: riskaverse attitude

P: riskprone attitude

j : index to indicate the type of attitude

$U[{\Pi}_{member}^{j}(\cdot )]$: the utility function of the profit of $member\hspace{0.17em}(\in \{R,\hspace{0.17em}M,\hspace{0.17em}S\})$ with attitude
$j(\in \{N,\hspace{0.17em}A,\hspace{0.17em}P\})$

u: degree of risk influence.
• Decision variables

Q : order quantity of a single type of products (product order quantity)

p : the unit retail price of the products

r : refund ratio of customer returns (0 ≤ r ≤ 1)

${Q}_{i}^{j}$: the product order quantity under $i(\in \{DSC,\hspace{0.17em}ISC\})$ as to attitude $j(\in \{N,\hspace{0.17em}A,\hspace{0.17em}P\})$

${p}_{D}^{j}$: the unit retail price under i as to attitude j

${r}_{D}^{j}$: the refund ratio under i as to attitude j
• System parameters

c : the unit production cost of the products

w : the unit wholesale price the products

g : shortage penalty cost per unsatisfied demand of the products

ℓ_{r} : the retailer’s unit handling cost of customer returns from a market

ℓ_{m} : the manufacturer’s unit handling cost of the unsold products and customer returns bought back from a retailer

x : demand of a single type of products in a market (product demand)

D(p,r) : the expected product demand for the unit retail price p and the refund ratio r

ε_{d} : random variable from the expected product demand

μ_{d}: mean of ε_{d}

${\sigma}_{d}^{2}$: variance of ε_{d}

${f}_{d}\left({\epsilon}_{d}\right)$: the probability density function of ε_{d}

${F}_{d}({\epsilon}_{d})$: the cumulative distribution function of ε_{d}

α : returns ratio of customer returns from a market (0 ≤α ≤1)

A(r) : the expected customer returns ratio for refund ratio r (0 ≤ A(r) ≤ 1)

ε_{α} : random variable from the expected customer returns ratio

μ_{α} : mean of ε_{α}

${\sigma}_{\alpha}^{2}$: variance of ε_{α}

${f}_{\alpha}\left({\epsilon}_{\alpha}\right)$: the probability density function of ε_{α}

${F}_{\alpha}({\epsilon}_{\alpha})$: the cumulative distribution function of ε_{α}

k : resalable ratio of customer returns in a market (0 ≤ k ≤ 1)

b : the unit buyback price of the unsold products

b_{r} : the unit buyback price of the unresold customer returns

s : the unit salvage price of the unsold products bought back by a manufacturer

sr : the unit salvage price of the unresold customer returns bought back by a manufacturer
• System parameters adjusted as supply chain coordination

${w}_{N}^{j}$ : wholesale price per product adjusted under risk attitude j(∈{N, A, P})

${b}_{N}^{j}$ : buyback price per unsold product adjusted under risk attitude
$j(\in \{N,\hspace{0.17em}A,\hspace{0.17em}P\})$

${b}_{r}{}_{N}^{j}$ : buyback price per returned and unresold product adjusted under risk attitude j(∈{N, A, P})
3.2. Operational Flows of an eSC
This paper considers an eSC which consists of a retailer and a manufacturer. The operational flows of the e SC is shown as follows:

(1) A retailer places an order for an order quantity Q of a single type of products (product order quantity) with a manufacturer under the uncertainties in product demand and customer returns in a market.

(2) A manufacturer produces the product order quantity Q at the unit cost c and sells it to a retailer at the unit wholesale price w.

(3) The retailer sells the products in a market during a single period at the unit retail price p.

(4) While the products are sold in the market within the selling period, the retailer receives customer returns from a market at a specific return rate α (0 ≤ α ≤ 1). The retailer refunds a part of the unit retail price p as to the refund ratio r (0 ≤ r ≤ 1) to the customers in the market. The unit payback price of the customer returns is calculated as r_{p}.

(5) The retailer inspects customer returns. After the restoration, a certain ratio k (0 ≤ k ≤ 1) of the reusable customer returns can be resold in the same market at the unit retail price p. The retailer incurs the unit handling cost l_{r} of customer returns.

(6) When the product order quantity Q does not satisfy the product demand x, the retailer incurs the unit shortage penalty cost g for the unsatisfied product.

(7) After the single sales period, the manufacturer buys back the unsold products at the unit price b and does the unresold customer returns at the unit price b_{r}, considering difference of quality between those products from the retailer.

(8) The manufacturer sells the unsold products at the unit salvage price s and does the unresold customer returns at the salvage price s_{r} in a disposal market, considering difference of quality between those products bought back. In this case, the manufacturer incurs the unit handling cost l_{m} of all products bought back.
3.3. Model Assumptions

(1) A single type of product such as apparel products and consumer electronics (mobile phone, personal computer) is produced and is sold in a market during a single sales period.

(2) The product demand x(>0) in a market is uncertain for the unit retail price p and the refund ratio r of the customer returns for the unit retail price p. The expected product demand D(p, r) (> 0) is a function of p and r. D(p, r) decrease as to p and increases as to r. The product demand x is modeled as $x=D(p,\hspace{0.17em}r)+{\epsilon}_{d}$, using the expected product demand D(p, r) and an additive random variable ε_{d}. Here, ε_{d} follows the normal distribution with mean ${\mu}_{{\epsilon}_{d}}=0$ and variance ${\sigma}_{{\epsilon}_{d}}^{2}$. The probability density function is ${f}_{{\epsilon}_{d}}({\epsilon}_{d})$ and the cumulative distribution function is ${F}_{{\epsilon}_{d}}({\epsilon}_{d}).$.

(3) It is allowed that the customer retunes for the same product is acceptable once only to the retailer.

(4) The customer returns α (0<α ≤1) is uncertain in terms of the refund ratio r of the customer returns for the unit retail price p. The expected customer returns A(r) is a function of r. A(r) increases as to r. The customer returns α is modeled as $\alpha =A(r)+{\epsilon}_{\alpha}$, using A(r) and an additive random variable ε_{α}. Here, ε_{α} follows the normal distribution with mean ${\mu}_{{\epsilon}_{\alpha}}=0$ and variance ${\sigma}_{{\epsilon}_{\alpha}}^{2}.$ The probability density function is ${f}_{{\epsilon}_{\alpha}}({\epsilon}_{\alpha})$ and the cumulative distribution function is ${F}_{{\epsilon}_{\alpha}}({\epsilon}_{\alpha}).$

(5) ε_{d} and ε_{α} are independent of each other.

(6) p > w > c > s ≥ s_{r} ≥ g > l_{r} ≥ l_{m}, w > b > b_{r}, w > c, $(s{\ell}_{m})<b,\hspace{0.17em}({s}_{r}{\ell}_{m})<{b}_{r},$ and 0 ≤ k ≤1
4. EXPECTATION AND VARIANCE OF INDIVISUAL PROFIT IN AN ESC
Based on section 2, the profits of a retailer, a manufacturer and the whole system in an eSC are formulated. The expectation and variance of the individual profit in the eSC are derived.
The profit of a retailer consists of both the sale and the resale of the products in a market, the buyback incomes of the unsold products and the unresold customer returns from a manufacturer, the procurement cost of the products, the refund cost of the customer returns from a market, the handling cost of the customer returns and the shortage penalty cost for unsatisfied demand of the products. From the magnitude relation between the product order quantity Q and product demand x, the retailer’s profit for the product order quantity Q, the unit retail price p and the refund ratio r, ${\Pi}_{R}(Q,\hspace{0.17em}p,\hspace{0.17em}r)$ is formulated as
Eq. (1) can be rewritten as
The elicitation process of Eq. (2) is derived in Appendix A [A1]. Taking expectations of x and α in Eq. (2), the expected profit of the retailer for Q, p and r is obtained as(5)
The elicitation processes in Eqs. (4)(6) are derived in Appendix A [A2][A4].
Taking variance (Frishman, 1975) of x and α in Eq. (2), the variance of the retailer’s profit for Q, p and r is obtained as
The elicitation process in Eq. (7) is derived in Appendix A [A5].(9)
The elicitation processes in Eqs. (8)(10) are derived in Appendix A [A6][A8].
The profit of a manufacturer consists of the product wholesales, the sales of the unsold products and the unresold customer returns in a disposal market, the production cost of the products, the buyback cost and the handling costs of unsold products and customer returns bought back from a retailer. From the magnitude relation between Q and x, the manufacturer’s profit for Q, p and r, ${\Pi}_{M}^{}\left(Q,\hspace{0.17em}p,\hspace{0.17em}r\right)$ is formulated as
Eq. (11) can be rewritten as
The elicitation process in Eq. (12) is derived in Appendix B [B1].
Taking expectations of x and α in Eq. (12), the expectation of the manufacturer’s profit for Q, p and r in Eq. (12) is obtained as
Taking variance (Frishman, 1975) of x and α in Eq. (12), the variance of the manufacturer’s profit for Q, p and r in Eq. (12) is obtained as
The elicitation process in Eq. (14) is derived in Appendix B [B2].
The profit of the whole system is calculated from sum of the profits of a retailer and a manufacturer. From Eqs. (1) and (11), The profit of the whole system ${\pi}_{S}\left(Q,\hspace{0.17em}t,\hspace{0.17em}u\right)$ for Q, p and r is calculated as
Eq. (15) can be rewritten as
The elicitation process in Eq. (16) is derived in Appendix C [C1]. The expected profit of the whole system is calculated from sum of the expected profits of a retailer and a manufacturer in Eqs. (3) and (12), The expected profit of the whole system ${\pi}_{S}\left(Q,\hspace{0.17em}t,\hspace{0.17em}u\right)$ for Q, p and r is calculated as
The variance (Frishman, 1975) of the whole system’s profit for Q, p and r in Eq. (16) is obtained as
The elicitation process in Eq. (18) is derived in Appendix C [C2].
5. MEANVARIANCE ANALYSIS OF INDIVIDUAL PROFIT IN AN ESC FOR UNCERTAINTIES IN PRODUCT DEMAND AND CUSTOER RETURNS
Using the meanvariance analysis of each profit in an eSC, the risk analysis is conducted for the uncertainties in the product demand and the customer returns. The meanvariance analysis uses utility functions of a retailer, a manufacturer, and the whole system based on three types of risk attitude: riskneutral attitude (attitude N), riskaverse attitude (attitude A), and riskprone attitude (attitude P) (Choi et al., 2008) regarding the uncertainties in the product demand and the customer returns. Attitude N considers to maximize the decision maker’s expected profit in an eSC. Attitudes A and P consider to maximize the decision maker’s utility function based on expectation and variance of the relevant profit of in an eSC. Using Eqs. (3), (7), (13), (14), (17), (18), utility functions of a retailer, a manufacturer and the whole system in an eSC are obtained as(20)
Here, u denotes a degree of risk attitude. u = 0 indicates attitude N (j = N). u < 0 indicates attitude A (j = A). u > 0 indicates attitude P (j = P). The larger u, the higher either attitude A or P is.
6. OPTIMAL OPERATIONS UNDER DSC
DSC adopts the optimal decision approach for the Stackelberg game (Cachon and Netessine, 2004; Nagarajan and Sosic, 2008; Cai et al., 2009; Aust and Buscher, 2012; Berr, 2011; Hu et al., 2011). This paper regards a retailer and a manufacturer as the leader and the follower of the decisionmaking in DSC. A retailer makes the optimal decisions for product order quantity ${Q}_{D}^{j}$ , the unit retail price $p{\hspace{0.17em}}_{D}^{j}$ and the refund ratio ${r}_{D}^{j}$ as to attitude j(∈{N, A, P}) so as to maximize the retailer’s utility function in Eq. (19) under degree u of risk attitude. A manufacturer follows the optimal operation in DSC as to degree u. The optimal decisions for Q, p and r under DSC as to attitude j(∈{N, A, P}) are made as following procedures.
• Case of Attitude N
The optimal decisions for product order quantity Q, the unit retail price p and refund ratio r under ISC with attitude N is determined so as to maximize the whole system’s expected profit in Eq. (17), corresponding to Eq. (21) when u = 0.
Step 1: Determine the provisional product order quantity ${Q}_{D}^{N}\left(p,\hspace{0.17em}r\right)$ under p and r in ISC with attitude N. Here, the firstorder and the secondorder derivatives of the whole system’s expected profit in Eq. (17) in terms of Q under p, and r are obtained as
The elicitation processes in Eqs. (22) and (23) are derived in Appendix D. When the following condition:
$\{p+A(r)kp+A(r)(1k){b}_{r}A(r)rpA(r){l}_{r}+gb\}>0$
is satisfied the retailer’s expected profit with attitude N in Eq. (3) is the concave function in terms of Q under p and r. Therefore, the provisional product order quantity ${Q}_{D}^{N}\left(p,\hspace{0.17em}r\right)$ under p and r can be determined as the following solution of the firstorder condition $\frac{dE\left[{\pi}_{R}\left(Qp,r\right)\right]}{dQ}=0:$
Step 2: Calculate the retailer’s expected profit substituting ${Q}_{D}^{N}\left(p,r\right)$ into Eqs. (3)(6) by varying p and r within their feasible ranges: $D\left(p,r\right)>0$ and $0\le r\le 1$ by numerical computing.
Step 3: Find the optimal combination (${Q}_{D}^{N}\left(p,\hspace{0.17em}r\right)$, p, r) which maximizes the retailer’s expected profit calculated in [Step 2]$E\left[{\Pi}_{R}^{}({Q}_{D}^{N}\left(p,\hspace{0.17em}r\right),\hspace{0.17em}p,\hspace{0.17em}r)\right]$, using numerical search. Determine this optimal combination as the optimal operation (${Q}_{D}^{N},\hspace{0.17em}{p}_{D}^{N},{r}_{D}^{N}$) with attitude N under DSC.
․ Case of Attitudes A and P
The optimal decisions for Q, p and r under DSC with attitudes A and P are determined so as to maximize the retailer’s utility function in Eq. (19) when u < 0 in attitude A and u > 0 in attitude P. In attitudes A and P, it is hard to prove that Eq. (19) is the concave function in terms of Q under p and r. This paper makes the optimal decisions for Q, p and r under DSC with attitudes A and P as follows.
Step 1: Calculate the retailer’s utility function in Eq. (19) with attitude $j\in \text{{}A,\hspace{0.17em}P\text{}}$ as degree u of risk attitude by varying Q, p and r within their feasible ranges: $Q\ge 0,\hspace{0.17em}D\left(p,\hspace{0.17em}r\right)>0$, and $0\le r\le 1$ by numerical computing.
Step 2: Find the optimal combination (Q, p, r) which maximizes the retailer’s utility function with attitude $j\in \text{{}A,\hspace{0.17em}P\text{}}$ calculated in [Step 1], ${U}_{R}^{j}\left(Q,\hspace{0.17em}p,\hspace{0.17em}r\right)\hspace{0.17em}\text{(}\hspace{0.17em}j\in \text{{}A,\hspace{0.17em}P\text{})}$ using numerical search. Determine this optimal combination as the optimal operation (${Q}_{D}^{j},\hspace{0.17em}{p}_{D}^{j},\hspace{0.17em}{r}_{D}^{j}$) with attitude $j\in \text{{}A,P\text{}}$ under DSC.
7. OPTIMAL OPERATIONS UNDER ISC
Under ISC, the optimal product order quantity ${Q}_{C}^{j}$, the optimal unit retail price ${p}_{C}^{j}$ and the refund ratio of the customer returns with the refund ratio ${r}_{C}^{j}$ as to attitude $j\in \text{{}N,\hspace{0.17em}A,\hspace{0.17em}P\text{}}$ are determined so as to maximize the whole system’s utility function in Eq. (21) under degree u of risk attitude. A retailer and a manufacturer follow the optimal operation under ISC. The optimal decisions for Q, p and r under ISC as to attitude $j(\in \{N,\hspace{0.17em}A,\hspace{0.17em}P\})$ are made as following procedures.
․ Case of Attitude N
The optimal decisions for product order quantity Q, the unit retail price p and refund ratio r under ISC with attitude N is determined so as to maximize the whole system’s expected profit in Eq. (17), corresponding to Eq. (21) when u = 0.
Step 1: Determine the provisional product order quantity ${Q}_{C}^{N}\left(p,\hspace{0.17em}r\right)$ under p and r in ISC with attitude N. Here, the firstorder and the secondorder derivatives of the whole system’s expected profit in Eq. (17) in terms of Q under p, and r are obtained as
The elicitation processes in Eq. (25) and (26) are derived in Appendix E. When the following condition:
$\begin{array}{l}\{p+A(r)kpA(r)rpA(r){l}_{r}+A(r)(1k)({s}_{r}{l}_{m})\\ (s{l}_{m})+g)\}>0\end{array}$
is satisfied, the whole system’s expected profit with attitude N in Eq. (17) is the concave function in terms of Q under p and r. Therefore, the provisional product order quantity ${Q}_{D}^{N}\left(p,\hspace{0.17em}r\right)$ under p and r can be determined as the following solution of the firstorder condition $\frac{dE\left[{\pi}_{R}\left(Qp,r\right)\right]}{dQ}=0:$
Step 2: Calculate the whole system’s expected profit substituting ${Q}_{D}^{N}\left(p,r\right)$ into Eqs. (17) by varying p and r within their feasible ranges: D(p, r) > 0 and 0 ≤ r ≤ 1 by numerical computing.
Step 3: Find the optimal combination (${Q}_{D}^{N}\left(p,\hspace{0.17em}r\right)$, p, r) which maximizes the retailers’s expected profit calculated in [Step 2]$E\left[{\Pi}_{R}^{}({Q}_{D}^{N}\left(p,\hspace{0.17em}r\right),\hspace{0.17em}p,\hspace{0.17em}r)\right]$, using numerical search. Determine this optimal combination as the optimal operation (${Q}_{D}^{N},\hspace{0.17em}{p}_{D}^{N},\hspace{0.17em}{r}_{D}^{N}$) with attitude N under ISC.
• Case of Attitudes A and P
The optimal decisions for Q, p and r under ISC with attitudes A and P are determined so as to maximize the whole system’s utility function in Eq. (21) when u < 0 in attitude A and u > 0 in attitude P. In attitudes A and P, it is hard to prove that Eq. (21) is the concave function in terms of Q under p and r. As with case under DSC, the optimal decisions for Q, p and r under ISC with attitudes A and P are made as follows.
Step 1: Calculate the whole system’s utility function in Eq. (21) with attitude j∈{A, P} as degree u of risk attitude by varying Q, p and r within their feasible ranges: $Q\ge 0,\hspace{0.17em}D\left(p,\hspace{0.17em}r\right)>0$ and 0 ≤ r ≤ 1 by numerical computing．
Step 2: Find the optimal combination (Q, p, r) which maximizes the whole system’s utility function with attitude j∈{A, P} in [Step 1]${U}_{S}^{j}\left(Q,\hspace{0.17em}p,\hspace{0.17em}r\right)\text{(}\hspace{0.17em}j\in \text{{}A,\hspace{0.17em}P\text{}})$, using numerical search. Determine this optimal combination as the optimal operation ($\left({Q}_{C}^{j},\hspace{0.17em}{p}_{C}^{j},\hspace{0.17em}{r}_{C}^{j}\right)\hspace{0.17em}{p}_{C}^{j},\hspace{0.17em}{r}_{C}^{j}$) with attitude j∈{A, P} under ISC.
8. SUPPLY CHAIN COORDINATION IN ISC
This paper discusses supply chain coordination to promote the shift to the optimal operation under ISC from that under DSC. Here, the unit wholesale price w, buyback prices, b for the unsold products and b_{r} for the unresold retuned products are adjusted between a retailer and a manufacturer under the optimal operation of ISC as to attitude j (∈{N, A, P}). Concretely, w, b and b_{r} are coordinated between both members as the Nash bargaining solutions (Nagarajan and Sosic, 2008; Du et al., 2011; Saito and Kusukawa, 2015) as to attitude j. The coordinated prices ($({w}^{{N}_{j}},\hspace{0.17em}{b}^{Nj},\hspace{0.17em}{b}_{r}^{Nj})$) under ISC as to attitude j are determined so as to maximize Eq. (28) satisfying the constrained conditions in Eqs. (29) and (30):
Eqs. (29) and (30) are the constraint conditions to guarantee that the expected profit of each member under the optimal operation of ISC with supply chain coordination is higher than those under that of DSC.
Thus, supply chain coordination regarding w, b and b_{r} using Nash bargaining solutions obtained in Eqs. (28) (30) can conduct profit sharing between a retailer and a manufacturer under ISC so as to take balance between the expected profits of both members under ISC after adjusting w, b and b_{r}, guaranteeing the increments of the expected profits of both members when the optimal operation shifts to ISC from DSC.
9. NUMERICAL ANALYSIS
The analysis numerically verifies how three types of risk attitude, attitude N, attitude A and attitude P, regarding the product demand and customer returns affect the optimal operations under DSC and ISC. Concretely, the optimal decisions for the product order quantity Q, the unit retail price p and the refund ratio r and the expected profits of a retailer, a manufacturer and the whole system under DSC are compared with those under ISC by changing the degree u of risk attitude in attitude j (∈{N, A, P}). Also, it is clarified how supply chain coordination can guarantee the increments of the expected profits of a retailer and a manufacturer when the optimal operation shifts to ISC from DSC. Here, the unit wholesale price w, the unit buyback price b of the unsold products and the unit buyback price br of the unresold retuned products are coordinated as Nash bargaining solutions between both members under the optimal operation of ISC.
Data sources of the numerical examples are provided as follows: k = 0.6, c = 10, w = 20, b = 10, b_{r} = 5, s = 5, s_{r} = 3, g = 3, l_{r} = 1, l_{m} = 1. The degree u of risk attitude is varied from 0.0 to 0.1 at a step size 0.01. The expected product demand D(p, r) for the unit retail price p and the refund ratio r is provided as D(p, r) = 40 − p + 10r, where D(p, r) for r(0 ≤ r ≤ 1) and p has the following properties: $dD\left(rp\right)/dr>0,\hspace{0.17em}dD\left(pr\right)/dr<0$ and D(p, r) > 0 show in model assumption (2) of Subsection 3.3. In this case, the product demand x is modeled as $x=D(p,\hspace{0.17em}r)+{\epsilon}_{d}=40p+10r+{\epsilon}_{d}$, using the additive random variable ε_{d}. Here, ε_{d} follows the normal distribution with mean ${\mu}_{{\epsilon}_{d}}=0$ and variance ${\sigma}_{{\epsilon}_{d}}^{2}=3.$. The expected customer returns ratio A(r) for refund ratio r is provided as A(r) = 0.03 + r^{2}, where A(r) for r(0 ≤ r ≤ 1) has the following properties: $dA(r)/dr>0$ and $A(r)(0<A(r)<1$) show in model assumption (4) of Subsection 3.3. In this case, customer returns ratio α (0 ≤ α ≤ 1) is modeled as $\alpha =A(r)+{\epsilon}_{\alpha}\hspace{0.17em}=0.03+{r}^{2}+{\epsilon}_{\alpha}$, using the additive random variable ε_{α}. Here, ε_{α} follows the normal distribution with mean ${\mu}_{{\epsilon}_{\alpha}}=0$ and variance ${\sigma}_{{\epsilon}_{\alpha}}^{2}=0.03$.
A computer programing was developed by using Visual Studio C# in Visual Studio Express 2013 for Windows Desktop in order to conduct the numerical computing and the numerical search and obtain the results of the optimal operations and the expected profits under DSC and ISC. In the development of the computer programming and implementation of the numerical experiment, the following computer : the Dell computer, Vostro 260s model, CPU: Intel(R) Core(TR) i52400, 3.10 GHz: Memory: 4 GB, OS: Windows 7 Professional 32bit was used in this paper.
9.1. Effect of Degree of Risk Attitude on Optimal Operations under DSC and ISC
• Effect on Optimal Product Order Ratio
In order to verify how degree u of risk attitude affects on the optimal product order quantity as to attitude j (∈{N, A, P}), this paper defines the optimal product order ratio (POR). POR is calculated as the following ratio: $POR{\hspace{0.17em}}_{i}^{j}={Q}_{i}^{j}/D\left({p}_{i}^{j},\hspace{0.17em}{r}_{i}^{j}\right)\hspace{0.17em}\left(i\in \left\{D,C\right\};\hspace{0.17em}j\in \left\{N,A,P\right\}\right)$. The molecule is the optimal product order quantity under either DSC or ISC. The denominator is the expected product demand under the optimal decisions for the unit retail price and the refund ratio under either DSC or ISC. The higher $POR{\hspace{0.17em}}_{i}^{j}$ is, the more the product order quantity for the expected product demand is, and vice versa.
Table 1 shows the effect of degree u of risk attitude on $POR{\hspace{0.17em}}_{i}^{j}\hspace{0.17em}\left(i\in \left\{D,C\right\};\hspace{0.17em}j\in \left\{N,\hspace{0.17em}A,\hspace{0.17em}P\right\}\right)$ $\left(i\in \left\{D,C\right\};\hspace{0.17em}j\in \left\{N,A,P\right\}\right)$ under DSC and ISC as to attitude j. From Table 1, the following results can be seen: Under DSC and ISC, $POR{\hspace{0.17em}}_{D}^{A}$ and $POR{\hspace{0.17em}}_{C}^{A}$ with attitude A are lower than ND POR and N C POR with attitude N. P D POR and PC POR with attitude P are higher than ND POR and N C POR with attitude N. The larger the degree u of risk attitude is, the stronger tendencies of the above results are. Under DSC and ISC, as the degree u of risk attitude becomes larger, AD POR and A C POR tend to be lower, meanwhile P D POR and PC POR tend to be higher. Under DSC and ISC, attitude P is more sensitive to the degree u of risk attitude than attitude A. The tendency of the result is stronger under DSC.
• Effect on Optimal Unit Retail Price
Table 2 shows the effect of degree u of risk attitude on the optimal unit retail price j i p (i∈{D, C}; j∈{N, A, P}) under DSC and ISC as to attitude j. From Table 2, the following results can be seen: For any degree u under DSC, AD p with attitude A tends to be lower than ND p with attitude N, meanwhile $p{\hspace{0.17em}}_{D}^{P}$ with attitude P are higher than $p{\hspace{0.17em}}_{D}^{N}$ with attitude N. Under DSC and ISC, attitude P is more sensitive to the degree u of risk attitude than attitude A. The tendency of the result is stronger under ISC.
• Effect on Optimal Refund Ratio
Table 3 shows the effect of the degree u of risk attitude on the optimal refund ratio $r{\hspace{0.17em}}_{i}^{j}\left(i\in \left\{D,C\right\};\hspace{0.17em}j\in \left\{N,A,P\right\}\right)$ under DSC and ISC as to attitude j of a retailer and a manufacturer. From Table 3, the following results can be seen: under DSC and ISC, ${r}_{D}^{A}$ and ${r}_{C}^{A}$ with attitude A tend to be higher than ${r}_{D}^{N}$ and ${r}_{C}^{N}$ with attitude N for any degree u. Under DSC and ISC, ${r}_{D}^{P}$ and ${r}_{C}^{P}$ with attitude P tend to be lower than ${r}_{D}^{N}$ and ${r}_{C}^{N}$ with attitude N for any degree u.
9.2. Comparison of Optimal Operations under DSC and ISC as to Degree of Risk Attitude
• Comparison of Optimal Product Order Quantity
As to degree of risk in attitude j(∈{N, A, P}), the optimal product order quantity jD Q under DSC is compared with the optimal product order quantity jCQ under ISC. Table 4 shows the effect of the effect of degree u of risk attitude on the optimal product order quantity $Q{\hspace{0.17em}}_{i}^{j}$ under DSC and ISC as to attitude j. From Table 4, the following results can be seen: Regardless of attitude j, $Q{\hspace{0.17em}}_{C}^{j}$ is larger than $Q{\hspace{0.17em}}_{D}^{j}$under DSC for any degree u. The reason of the above result is considered as follows: From Eqs. (3) and (24), $Q{\hspace{0.17em}}_{D}^{j}$ is affected by the unit wholesale price w and the unit buyback prices (b, b_{r}) of the unsold products and the unresold product. From Eqs. (17) and (27), $Q{\hspace{0.17em}}_{C}^{j}$ is affected by the unit production cost c, $(s{\ell}_{m})$ and $({s}_{r}{\ell}_{m})$ . Here, the conditions, $w>c,b>(s{\ell}_{m})$ and ${b}_{r}>({s}_{r}{\ell}_{m})$ , are hold from model assumption (6) in Subsection 3.3.
• Comparison of Optimal Unit Retail Price
As to degree of risk in attitude j(∈{N, A, P}), the optimal unit retail price $p{\hspace{0.17em}}_{D}^{j}$ under DSC is compared with the optimal unit retail price $p{\hspace{0.17em}}_{C}^{j}$ under ISC. From Table 2, regardless of attitude j, $p{\hspace{0.17em}}_{C}^{j}$ under ISC is lower than that under DSC for any degree u. Under DSC and ISC, attitude P is more sensitive to the degree u of risk attitude than attitude A.
• Comparison of Optimal Refund Ratio
As to degree of risk in attitude j(∈{N, A, P}), the optimal refund ratio $r{\hspace{0.17em}}_{D}^{j}$ under DSC is compared with the optimal refund ratio $r{\hspace{0.17em}}_{C}^{j}$ under ISC. From Table 3, the following results can be seen: In attitude A, $r{\hspace{0.17em}}_{C}^{A}$ under ISC tends to be lower than $r{\hspace{0.17em}}_{D}^{A}$ under DSC. In attitude P, $r{\hspace{0.17em}}_{C}^{P}$ under ISC tends to be higher than $r{\hspace{0.17em}}_{D}^{P}$ under DSC when degree u is small (u < 0.06), $r{\hspace{0.17em}}_{C}^{P}$ under ISC tends to be lower than $r{\hspace{0.17em}}_{D}^{P}$ under DSC when degree u is large (u > 0.06).
9.3. Effect of Supply Chain Coordination (SCC)
As to degree of risk in attitude j(∈{N, A, P}), the expected profits under DSC are compared with those under ISC. Table 5 shows the effect of SCC on the expected profits under ISC as to attitude j.
From Table 5, the following results can be seen: The expected profits of the whole system and a manufacturer in attitude j under ISC without SCC are higher than those under DSC. The expected profit of a retailer under ISC without SCC in attitude P is higher than that under DSC. Meanwhile, in attitude N and attitude A, the expected profit of the retailer under ISC without SCC is lower than that under DSC. Under the situation, it is impossible for the retailer to shift the optimal decision (optimal operation) under ISC from that under DSC. It is necessary to guarantee always the more expected profit to both members when the optimal operation shifts from DSC to ISC as to attitude j. SCC is adopted to the optimal decision under ISC. The unit wholesale price w and the buyback prices, b and b_{r}, are coordinated under ISC as Nash bargaining solutions between both members. The expected profits under ISC with SCC are compared with those under DSC. It is verified that SCC adjusting w, b and b_{r} under ISC can bring the more expected profits to both members under ISC.
Thus, SCC under ISC enables to guarantee the profit improvement for both members under ISC and can encourage the shift to the optimal operation under ISC from that under DSC.
10. CONCLUSIONS
This paper discussed risk analysis and supply chain coordination for the optimal operation in an eSC under the uncertainties in product demand and customer returns. An eSC consisted of a retailer and a manufacturer. The return handlings on customer returns and unsold products were considered. A manufacturer bought back the unsold products and the unresold customer returns from a retailer, considering the difference of quality between those products. The uncertain product demand was sensitive on the unit retail price and the refund ratio of the customer returns for the unit retail price. The uncertain customer returns ratio was sensitive on the refund ratio. Using the meanvariance analysis, three types of risk attitude on the uncertainties in products demand and customer returns were considered: riskneutral attitude (attitude N), riskaverse attitude (attitude A) and riskprone attitude (attitude P). As to attitude, the optimal decisions for the product order quantity, the unit retail price and the refund ratio of customer returns under the decentralized SC(DSC) and the integrated SC(ISC) were determined. The optimal decisions under DSC maximized the retailer’s expected profit in attitude N, and maximized the retailer’s utility function in attitudes A and P. Similarly, the optimal decisions under ISC maximized the whole system’s expected profit in attitude N, and maximized the whole system’s utility function in attitudes A and P. The analysis numerically verified how each risk attitude on product demand and customer returns affected the optimal operations under DSC and ISC. In order to promote the shift to the optimal operation under ISC, supply chain coordination (SCC) was discussed by adjusting the unit wholesale price and the unit buyback prices of the unsold products and the unresold customer returns between members under ISC as Nash bargaining solutions.
Results of theoretical analysis and numerical analysis in this paper verified the following managerial insights:

Under DSC and ISC, the optimal product order ratio with attitude A tends to be lower than that with attitude N, meanwhile that with attitude P tends to be higher than that with attitude N.

Under DSC and ISC, the optimal unit retail price with attitude A tends to be lower than that with attitude N, meanwhile that with attitude P tends to be higher than that with attitude N.

Under DSC and ISC, the optimal refund ratio with attitude A tends to be higher than that with attitude N. Under DSC and ISC, the optimal refund ratio with attitude P tends to be lower than that with attitude N.

SCC adjusting the unit wholesale price and the unit buyback prices of the unsold products and the unresold customer returns under the optimal operation of ISC as to risk attitude could bring the more expected profits to both members under ISC, and encourage the shift to the optimal operation under ISC from that under DSC.
Thus, this paper provides the following contribution for practitioners, academic researchers, and realworld policymakers, regarding operations in an eSC: (i) the optimal operations in an eSC should be determined as to risk attitudes: riskneutral attitude which maximizes the decision maker’s expected profit in an eSC, riskaverse attitude with negative consideration of variance of the relevant profit, riskprone attitude with positive consideration of the variance, (ii) SCC on wholesale price and buyback prices as to quality of the unsold products should be conducted by taking balance between the expected profits of a retailer and a manufacturer using Nash bargaining solution.
This paper considered the situation where members in an eSC had same risk attitudes, but it is necessary to consider the situation where they have different risk attitudes. Also, this paper assumed that the distribution information on product demand and customer returns were known completely regarding their distribution profiles, their values of mean and variance, but it is necessary to consider that the distribution information on product demand and customer returns are limited/unknown. And then, this paper did not consider the situation where supply disruptions occurred in the processes of production and delivery of products in an eSC, but it is necessary to consider above situation in an eSC. Moreover, this paper did not consider the situation where an eSC faced products with product life cycle, but it is necessary to consider the above situation. Incorporation of above topics into the eSC model in this paper will be discussed as future researches.