Quick response in fashion supply chains with retailers having boundedly rational managers

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1 Intl. Trans. in Op. Res. 24 (2017) DOI: /itor INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH Quick response in fashion supply chains with retailers having boundedly rational managers Tsan-Ming Choi Business Division, Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong [Choi] Received 26 December 2015; received in revised form 19 February 2016; accepted 6 May 2016 Abstract In fashion retailing, inventory decisions are usually made by a human manager who is not necessarily perfectly rational. In this situation, the inventory decisions made may not always be optimal. At the same time, with advances in technology, fashion retailers have access to the latest market information and can implement the quick response (QR) system that is very helpful to systematically deal with market disruptions. In this paper, we explore the value of QR with the consideration of a boundedly rational human manager in the fashion retailing company. We show that for both cases, with and without QR, the human retail manager s level of bounded rationality significantly hurts the expected profits of the retailer and supply chain, but it does not hurt the manufacturer s expected profit. In addition, for both cases, with and without QR, we indicate how a minimum ordering quantity (MOQ) measure can be imposed by the manufacturer on the retailer, so that the manufacturer can benefit (in terms of expected profit) from the retailer s bounded rationality behavior. We further prove that if the manufacturer sets the MOQ to be the same as the retailer s theoretical optimal ordering quantity, the manufacturer will enjoy a higher profit with 50% chance, if the retailer is boundedly rational. Keywords: bounded rationality; quick response system; fashion apparel; inventory planning 1. Introduction Quick response (QR) is an inventory management practice widely adopted in the fashion industry. The origin of QR can be dated back to the 1980s in the American fashion apparel industry. The core idea of QR is to respond quickly to market disruptions and changes, by shortening the lead time. With advances in technology, especially those supporting information sharing among supply chain agents (Chen, 2011; Zhang et al., 2015), QR is becoming increasingly common. It is well known that QR is a useful strategy to enhance supply chain performance even though it may not benefit the seller and buyer equally (see Iyer and Bergen, 1997). Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA.

2 892 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) Consider a make-to-order fashion supply chain system that includes an upstream garment manufacturer and downstream fashion retailer. The retailer initiates the order of a fashion product by providing its required quantity to the manufacturer, and the manufacturer reacts by producing and supplying the required quantity. For the retailer, the inventory decision is made by a human retail manager who is naturally not perfectly rational (i.e., only boundedly rational). In this case, the retail inventory decision made by the human retail manager need not be optimal all the time. Thus, from the retailer s perspective, if it implements the computerized data driven QR system to help with making the perfectly rational inventory decision, what will be the impacts on the retailer, manufacturer, and supply chain? Will the manufacturer benefit from the retailer s boundedly rational behavior? These are some open research questions that we would like to address in this paper. To be specific, motivated by the importance of QR in fashion supply chain management to deal with market changes and disruptions, and the existence of boundedly rational human retail managers, we conduct a theoretical study in this paper. We first construct a formal analytical model under the Bayesian conjugate pair framework. Then, we derive the expected profit and inventory decision under the case without QR and with the boundedly rational retail manager. After that, we investigate the case with QR and with a computerized fully rational retail decision-making system. We also consider a separate case in which the retailer under QR still employs a boundedly rational human decision maker (i.e., the same manager). By comparing between the cases with and without QR, insights regarding how the QR systems (computerized and human-based) affect the supply chain and the supply chain agents can be revealed. In particular, we show that for both cases, with and without QR, the retail manager s level of bounded rationality significantly hurts both the retailer s expected profit and the supply chain s expected profit. However, it does not hurt the manufacturer s expected profit. In addition, for both cases, with and without QR, we prove that by imposing the minimum ordering quantity (MOQ) measure on the retailer, the manufacturer can benefit from the retailer s bounded rationality behavior. If the manufacturer sets the MOQ to be the same as the retailer s theoretical optimal ordering quantity, the manufacturer will enjoy a higher profit with 50% likelihood, if the retailer is boundedly rational. To the best of my knowledge, this paper is the first study that examines the QR system with boundedly rational decision making. Many of the research findings provide new insights to advance our understanding of the commonly seen QR system in supply chain management and the fashion business. The remainder of this paper is organized as follows. First, in Section 2, we conduct a literature review. Then, in Section 3, we develop the Bayesian analytical model. In Section 4, we explore the case with the human retail manager under the scenario without QR. In Section 5, we study the scenario with QR for the cases with the computerized decision support system and human retail manager, respectively. In Section 6, we proceed to investigate the impacts brought by QR on the supply chain system. In Section 7, we present the concluding remarks, with a proposal on future research. All proofs are included in the Appendix. 2. Literature review This paper relates to two scopes of studies, namely, QR fashion supply chain systems and boundedly rational decision making in supply chain management. We review some related studies concisely.

3 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) First, for QR fashion supply chain systems, Iyer and Bergen (1997) pioneer an influential study that adopts the Bayesian conjugate pair under the normal process for formulating the informationupdating process under QR. They analytically prove that QR benefits the retailer but hurts the manufacturer. They also develop measures based on industrial practices from the American fashion industry to help achieve Pareto improvement in the QR fashion supply chain. Donohue (2000) studies the QR supply chain with a fashion apparel product with multiple ordering. Her study is the first to consider supply chain optimization using incentive alignment contracts with multiple ordering decisions. After that, Choi et al. (2003) extend the study by Iyer and Bergen (1997) to the case when there are two inventory-ordering opportunities (one without QR and the other with QR). They focus on exploring the optimal dynamic inventory policy, but do not explore the channel coordination issue. Choi (2006) explores a fashion QR system with a focal point on channel coordination and a more sophisticated information updating process in which both mean and variance of the normal process are unknown variables. Cachon and Swinney (2011) explore the value of fast fashion in the presence of strategic consumers. The authors propose that QR is a critical element of implementing fast fashion and an important measure to effectively deal with forward-looking strategic consumer behaviors. Other related research on QR and/or information updating in supply chain operations management includes many studies (Fisher and Raman, 1996; Fisher et al., 2001; Gallego and Ozer, 2001; Kim, 2003; McCardle et al., 2004; Tang et al., 2004; Sethi et al., 2005; Chen et al., 2006; Shaltayev and Sox, 2010; Chow et al., 2012; Choi, 2013; Liu and Nagurney, 2013; Yang et al., 2015). For more details about the related literature on QR supply chain management, refer to the review paper by Choi and Sethi (2010). Note that similar to many reviewed studies above, such as Iyer and Bergen (1997) and Chow et al. (2012), this paper also uses the normal Bayesian conjugate pair model for conducting the analysis. Different from these studies, this paper considers the presence of a boundedly rational human manager, which has never been examined in any one of the prior studies. Second, for boundedly rational decision making in supply chain management, Schweitzer and Cachon (2000) conduct human subject based behavioral experiments to identify some decision biases in the newsvendor problem. After that, the operations management literature has been rather active in exploring inventory-related problems by behavioral experiments. The most notable related study is Su s (2008) award-winning paper on the newsvendor problem with a boundedly rational decision maker. To be specific, Su (2008) conducts human subject based behavioral studies under the newsvendor setting. With the uniform demand distribution, he proves that human decision makers exhibit a truncated normal form of boundedly rational inventory decision. In recent years, researchers have extended the analysis of boundedly rational decision-making problems from a single-agent (i.e., single echelon) domain to the two-agent multiechelon supply chain system. For example, Wu and Chen (2014) examine the impacts brought by bounded rationality on the supply chain contract design. Chow et al. (2014) study buyback supply contracting with risk-sensitive retailers under information asymmetry. Similar to the above related works, this paper also considers the boundedly rational decision making in the supply chain. However, different from all of them, this paper explores the QR supply chain system with information updating, which has never been examined by prior research in the literature.

4 894 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) The Bayesian analytical model We construct the analytical model in this section. For analytical tractability, we use the newsvendor model for formulating the inventory decision, and the Bayesian normal conjugate pair for modeling the information-updating process under QR. We present the details as follows. First, in this paper, we consider a single upstream manufacturer, single downstream retailer 1 make-to-order fashion supply chain with a fashion product X. The feature of the fashion product X follows the newsvendor model. In particular, we consider the situation when the retailer orders a certain quantity of X from the manufacturer and sells in a single selling season (i.e., it is a single-period problem). The retailer can only order once before the selling season starts (which is a practice commonly observed in many fashion retailers; Iyer and Bergen, 1997). The manufacturer operates in the make-to-order mode in which it does not produce any quantity of X in advance; it only produces after receiving the retailer s order. For the cost revenue structure, the manufacturer produces X at a unit production cost of m, and supplies to the retailer at a unit wholesale price w. The retailer sells X to the market (in the upcoming selling season) at a unit retail selling price r,and any leftover of X will be salvaged at a unit price v. Before the selling season starts, the retailer needs to determine the order quantity of X and places the order to the manufacturer. In this paper, we consider two scenarios, namely without QR and with QR. For the scenario without QR, we state that the retailer needs to order at time point 0 (called Stage 0), which is far from the upcoming selling season. For the scenario with QR, the retailer needs to order at time point 1 (called Stage 1), which is much closer to the upcoming selling season. We consider the case that the manufacturer is reliable and can definitely fulfill the retail order. In addition, if the order is placed at Stage 0, the retailer needs to pay a unit logistics cost of l 0. If the order is placed at Stage 1, the retailer has to pay a higher unit logistics cost of l 1, i.e., l 1 > l 0. Note that this relationship can be visualized by the fact that a shorter lead time (ordering at Stage 1) requires a faster delivery mode, which is, in general, more expensive. Thus, for the retailer, the unit ordering cost at Stage 0 (without QR) is c 0 = w + l 0, and the unit ordering cost at Stage 1 (with QR) is c 1 = w + l 1. Obviously, we have c 1 > c 0. It is well known that QR enhances retail inventory planning and supply chain performance because the retailer can postpone its ordering decision to a time point when better information is available. Here, better information refers to the improved market demand forecast. In this paper, following the literature (e.g., Iyer and Bergen, 1997; Chow et al., 2012), we use the Bayesian conjugate pair to formulate the information-updating process. Denote the predicted demand of X at Stage 0 by x 0, which is a normally distributed random variable with mean θ and variance δ: x 0 N(θ, δ), whereθ is also normally distributed with mean μ 0 and variance d 0 : θ N(μ 0, d 0 ). Thus, at Stage 0, the marginal distribution of x 0 also follows a normal distribution with mean μ 0 and variance (d 0 + δ): x 0 N(μ 0, d 0 + δ). Between Stage 0 (without QR) and Stage 1 (with QR), the retailer can collect market information about x 0, represented by an observation ˆx 0, and use it to update its demand forecast as follows: θ N(μ 1, d 1 ),whereμ 1 = ( d 0 d 0 +δ ) ˆx 0 + ( δ d 0 +δ )μ 0,and d 1 = δ d 0 /(d 0 + δ). Under QR, we define the respective predicted demand of X (at Stage 1) byx 1, and its distribution is x 1 N(μ 1, d 1 + δ),whereμ 1 N(μ 0, d 2 0 /(d 0 + δ)). As a summary, Fig. 1 shows the time sequence of QR and Table 1 shows the game sequence in the QR supply chain. 1 In the QR fashion supply chain model used in this paper, unless otherwise specified, the terms retailer and fashion retailer are used interchangeably.

5 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) Stage 0 Assess the prior demand distribution parameters Conduct market observation Stage 1 Update the prior distribution by using the market observation and determine the optimal ordering quantity under QR Season starts and demand is realizes Fig. 1. The time sequence and information updating under QR. Table 1 The fashion supply chain game sequence (under the basic QR model) 1. At Stage 0: (i) The manufacturer provides the pure wholesale pricing supply contract to the fashion retailer with the unit wholesale price w. (ii) The fashion retailer has its initial demand forecast (the prior demand distribution). 2. Under QR, the fashion retailer makes the market observation between Stages 0 and At Stage 1: (i) The fashion retailer uses the market observation to update its initial forecast and yield the posterior demand distribution. (ii) With the posterior demand distribution, the decision maker (human manager) of the fashion retailer makes the optimal ordering decision. 4. The manufacturer reacts to the order in a make-to-order mode, and fulfills the production and distribution job so that the ordered quantity by the fashion retailer will arrive just before the season starts. The notations are described as follows: (a) For the normal distribution, we define ϕ( ) and ( ) as the standardized normal density function (df) and standardized normal cumulative distribution function (cdf), respectively. We further denote 1 ( ) as the inverse function of the standard normal cdf and (x) = x (y x)ϕ(y)dy. (b) For the analytical expressions, we represent the order quantity, expected profit, and variance of profit by q, EP, andvp, respectively. Moreover, the subscripts 0 and 1 represent Stages 0 and 1, respectively. Similarly, the subscripts R, M, SC denote the retailer, manufacturer, and supply chain, correspondingly. 4. The boundedly rational retail manager Following the industrial practice we observed in the real world, for almost all fashion retailers, the inventory decision is made by human managers. Imagine that there is no QR and the single order has to be placed at Stage 0. Then, following the standard newsvendor model s solution, the optimal ordering quantity, which can maximize the retailer s expected profit, is given as follows: q 0,R = μ 0 + d 0 + δ 1 [(r c 0 )/(r v)]. (1) Now, in this paper, we consider the case when the human manager is not fully rational, but only boundedly rational. In this scenario, the real ordering quantity Q 0,R, which is placed by the human manager, may vary from time to time and we model it by (2): Q 0,R f Normal [Q 0,R (q 0,R,V )], (2) which means that Q 0,R is a normally distributed random variable with mean q 0,R and variance V.

6 896 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) Observe that V captures the level of bounded rationality of the human manager and a larger V implies a higher level of bounded rationality. When V goes to infinity, the human manager is irrational; when V goes to zero, the human manager is perfectly rational. As a remark, the use of a normal distribution (with the mean equal to the theoretical optimal solution) helps capture the bounded rationality behavior of the retailer s ordering decision in which the ordering quantity is more likely to be around the theoretical optimal decision than others, and the ordering quantity farther away from the theoretical optimal decision has a lower likelihood to be adopted by the decision maker. Of course, this model is an approximation of the more precise models reported in the literature (see, e.g., Su, 2008), while it helps to derive more analytically tractable closed-form results. This is why we model the boundedly rational inventory decision using (2) in this paper. Define V = s 2. With (2), for a given Q 0,R, the expected profit of the retailer is derived to be: EP 0,R Q 0,R = (r v)μ 0 (c 0 v)q 0,R (r v) ( ) Q0,R μ 0 d 0 + δ. (3) d0 + δ The unconditional expected profit is hence derived to be as follows: where EP 0,R = E [EP 0,R Q 0,R ] Q0,R ( = (r v)μ 0 (c 0 v)q 0,R (r v) d 0 + δ = (r v)μ 0 (c 0 v)q o,r (r v) d 0 + δ ( = (r c 0 )μ 0 d 0 + δ [(c o v)z 0 + (r v) 0 (V )], 0 (V ) = ( ( ( ) )) Vz r d0 + δ + c0 1 ϕ(z)dz. r v ( Q0,R μ 0 d0 + δ ( Q0,R μ 0 d0 + δ )) f Normal (Q 0,R )dq 0,R )) f Normal (Q 0,R )dq 0,R When the manager is perfectly rational, the retailer s optimal expected profit at Stage 0 can be derived as follows: EP 0,R where = EP 0,R q 0,R = (r c 0 )μ 0 d 0 + δ [(c o v)z 0 + (r v) (Z 0 )], (4) Z 0 = 1 ( r c0 r v ).

7 Note that by definition: T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) EP 0,R = EP 0,R when V = 0, and 2. EP 0,R EP 0,R, Q 0,R (as EP 0,R is the retailer s maximum achievable expected profit among all order quantities). (5) At Stage 0, the expected loss owing to the human manager s bounded rationality (ELBR) is expressed as follows: ELBR 0,R = EP 0,R EP 0,R = (r v) d 0 + δ [ 0 (V ) (Z 0 ) ]. (6) From (6), we have Proposition 1. Proposition 1. (a)elbr 0,R 0 and it is increasing in V. (b) ELBR 0,R = 0 when V = 0. Proof of Proposition 1. All proofs can be found in the Appendix. Proposition 1 is intuitive. First of all, a positive ELBR 0,R implies that the retailer s expected profit with the boundedly rational decision is less than the profit under the perfectly rational optimal decision. Second, ELBR 0,R is increasing in V, which actually means that the retailer s expected profit with the human manager is decreasing in the level of his bounded rationality. Thus, for the retailer, a higher level of bounded rationality of the human manager leads to a lower expected profitability. 5. The QR system Now, suppose that the retailer plans to improve its inventory planning by implementing a QR system. To be specific, under this QR system, the retailer incorporates market information between Stages 0 and 1 into the decision framework and plans the inventory at Stage Computerized decisions In this section, we consider the case in which this QR system is computerized and is fully data driven. As a result, its recommendation is fully rational. It is easy to find that if the retailer orders inventory at Stage 1 under the QR system, the optimal ordering quantity is given as follows (see Iyer and Bergen, 1997): q 1,R = μ 1 + d 1 + δ 1 [(r c 1 )/(r v)], (7) EP 1,R (q 1,R ) μ 1 = (r v)μ 1 (c 1 v)q 1,R (r v) ( ) q1,r μ 1 d 1 + δ, (8) d1 + δ EP 1,R (q 1,R ) μ 1 = (r c 1 )μ 1 d 1 + δ[(c 1 v)z 1 + (r v) (Z 1 )], (9) where ( ) r Z 1 = 1 c1. r v

8 898 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) Thus, from (9), the unconditional expected profit of the retailer (under the computerized perfectly rational decision-making scenario, which is similar to Iyer and Bergen, 1997) at Stage 1 with QR is as follows: EP 1,R = E μ1 [EP 1,R (q 1,R ) μ 1 ] = (r c 1 )μ 0 d 1 + δ[(c 1 v)z 1 + (r v) (Z 1 )]. (10) Obviously, this computerized QR system helps in two perspectives: 1. It provides the latest market information to allow the retailer to order more precisely with a better demand forecast. 2. It does not involve the decision bias owing to the bounded rationality of the human manager. Thus, the truly optimal inventory decision can be made Human decisions In this section, we consider the situation in which the company that adopts QR would still ask the same human retail manager to make the real ordering decision. In this case, the real ordering quantity depends on the human manager s level of bounded rationality. Similar to Section 3, we have the following model: Q 1,R f Normal [Q 1,R (q 1,R,V )], (11) which means that Q 1,R is a normally distributed random variable with mean q 1,R and variance V. Note that since we consider the presence of the same human manager in making inventory decision in this section, his level of bounded rationality is the same as the one in Section 3, which is V. With (11), for given Q 1,R and μ 1, the expected profit of the retailer is given as follows: EP 1,R Q 1,R,μ 1 = (r v)μ 1 (c 1 v)q 1,R (r v) ( ) Q1,R μ 1 d 1 + δ. (12) d1 + δ Unconditioning with respect to Q 1,R, the expected profit is hence derived to be: EP 1,R μ 1 = E Q1,R [EP 1,R Q 1,R,μ 1 ] = (r v)μ 1 (c 0 v)q 1,R (r v) d 1 + δ ( ( )) Vz d1 + δ + Z 1 ϕ(z)dz. (13)

9 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) From (13), we can obtain the unconditional expected profit as follows: EP 1,R = E μ1 [EP 1,R μ 1 ] = (r v)μ 0 (c 1 v)(μ 0 + ( ) r d 1 + δ 1 c1 ) (r v) d r v 1 + δ 1 (V ), (14) where ( ( ( ) )) Vz r 1 (V ) = d1 + δ + c1 1 ϕ(z)dz. r v After simplification, we can rewrite (14) as (15): EP 1,R = (r c 1 )μ 0 d 1 + δ[(c 1 v)z 1 + (r v) 1 (V )]. (15) Observe that EP 1,R = EP 1,R when V = 0. Similar to the case without QR, at Stage 1, the ELBR is ELBR 1,R = EP 1,R EP 1,R = (r v) d 1 + δ [ 1 (V ) (Z 1 ) ]. (16) In addition, we define the following: The retailer s expected gain using the human-based QR program (EGH R )is EGH R = EP 1,R EP 0,R. (17) The retailer s expected gain using the computer-based QR program (EGC R )is EGC R = EP 1,R EP 0,R. (18) Define c H,1 = arg[egh R = 0], (19) c 1 c C,1 = arg[egc R = 0]. (20) c 1 We have Proposition 2. Proposition 2. (a) ELBR 1,R is positive and increasing in V. (b) EGH R is strictly positive when c 1 < c H,1.(c)EGC R is strictly positive when c 1 < c C,1. (d) EGC R is increasing in V. (e) EGH R can be increasing or decreasing in V depending on c 0,c 1,d 0 and d 1. Proposition 2a is similar to Proposition 1a, which shows that bounded rationality of the human retail manager lowers the expected profit of the retailer. Proposition 2b and Proposition 2c uncover that the expected gains by using QR depend on the unit ordering cost at Stage 1 (with QR). If the unit ordering cost at Stage 1 is below the respective threshold (c 1 < c H,1 for the case with human boundedly rational decision making under QR; c 1 < c C,1 for the case with computerized perfectly rational decision making), the expected gain from using QR is strictly positive. This result is intuitive as the benefit of QR relies on the unit ordering cost at Stage 1; if it is too high (compared to the

10 900 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) unit ordering cost at Stage 0), it is not beneficial to order at Stage 1 (i.e., under QR). Furthermore, Propositions 2a and 2d report the impacts brought by the human retail manager s level of bounded rationality V. To be specific, when the human retail manager is less rational (i.e., more boundedly rational with a larger V): (a) Proposition 2a reveals that the retailer suffers a bigger expected loss; (b) Proposition 2d further shows that the expected gain by using QR with the perfectly rational computerized decision making is bigger, too. However, the situation is tricky for the case with QR and the human boundedly rational decision maker as the expected gain can be larger or smaller, depending on the unit ordering costs as well as the demand uncertainty parameters as shown in Proposition 2e. All the above findings are very important, as they analytically uncover the relationship between the significance of QR and the level of bounded rationality of the human retail manager under different cases. 6. The QR fashion supply chain system In the above sections, we find that the retailer can be benefited using the QR program, and the respective benefit is higher under the computer-based QR program than the human-based QR program. In this section, we further explore how the QR program affects the performances of the manufacturer and whole supply chain system. First, the manufacturer s expected profits for the case without QR (i.e., the retailer orders at Stage 0) and the case with QR (i.e., the retailer orders at Stage 1) are expressed as follows: EP 0,M Q 0,R = (w m)q 0,R, (21) EP 1,M Q 1,R,μ 1 = (w m)q 1,R. (22) Unconditioning (21) yields the following manufacturer s unconditional expected profit: EP 0,M = E Q0,R [EP 0,M Q 0,R ] = (w m)q 0,R = (w m)(μ 0 + d 0 + δz 0. (23) Similarly, unconditioning (22) with respect to Q 1,R yields the following: EP 1,M μ 1 = E Q1,R [EP 1,M Q 1,R,μ 1 ] = (w m)q 1,R = (w m)(μ 1 + d 1 + δ 1 [(r c 1 )/(r v)]). (24) To obtain the unconditional manufacturer s expected profit, we further uncondition (24) with respect to μ 1 : EP 1,M = E μ1 [EP 1,M μ 1 ] = (w m)(μ 0 + d 1 + δz 1 ). (25)

11 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) By definition, the supply chain system s expected profits for the case without QR and the case with QR are given as follows: EP 0,SC = EP 0,R + EP 0,M, EP 1,SC = EP 1,R + EP 1,M. Theorem 3 gives the critical results that highlight the impacts brought by QR on the fashion supply chain system and its agents. Theorem 3. For both cases, with and without QR, the retailer s bounded rationality hurts the retailer s expected profit, and the supply chain system s expected profit. However, it does not affect the manufacturer s expected profit. Theorem 3 concisely summarizes the key findings of the impacts brought by the human retail manager s bounded rationality on the supply chain system. It is rather expected to find that the human retail manager s level of bounded rationality has no impact on the manufacturer s expected profit. Yet, this finding implies that under the pure wholesale pricing contracting scheme, the manufacturer has little interests in the level of bounded rationality of the human retailer as it does not affect its own expected profit. Observe that even though the level of bounded rationality of the retailer s human manager does not affect the manufacturer s expected profit, can the manufacturer impose some measures so that it can take advantage of and obtain some benefits from the retailer s bounded rationality? Theorem 4 illustrates the use of a commonly seen industrial measure called the MOQ which can enhance the manufacturer s expected profit in the presence of the retailer s bounded rationality behavior. Theorem 4. For both cases, with and without QR: (a) If the manufacturer imposes a positive MOQ on the retailer s ordering, the manufacturer s expected profit will be higher when the human retail manager is boundedly rational (compared to the case when the retailer is perfectly rational). (b) If the manufacturer sets the MOQ to be the same as the theoretical optimal retail ordering quantity: (i) the manufacturer s profit when the retailer is boundedly rational is always higher than or equal to the profit when the retailer is perfectly rational; (ii) the manufacturer s profit will have 50% chance of being strictly higher than the profit when the human retail manager is boundedly rational (compared to the case when the retailer is perfectly rational). Theorem 4 indicates that the use of MOQ can increase the manufacturer s expected profit when the human retail manager is boundedly rational for both cases with and without QR. Thus, the volatile ordering quantity by the human retail manager who is boundedly rational will lead to random order quantities that are always larger than or equal to the retailer s theoretical optimal quantity. This benefits the manufacturer. It is amazing to observe from Theorem 4b that the MOQ can even (a) guarantee the manufacturer s profit (note: it is the realized profit every time, not the expected average profit) and (b) lift the manufacturer s profit with a very high chance (50% probability), if the MOQ is set to be the same as the retailer s theoretical ordering quantity. Observe that the MOQ measure is in line with the quantity commitment idea (Iyer and Bergen, 1997) and is widely observed and applied in practice together with QR (e.g., see Chow et al., 2012). Theorem 4 thus provides evidence from a new perspective to interpret the strength of MOQ in improving the manufacturer s profit. This also explains the popularity of MOQ implementation in the fashion industry together with QR.

12 902 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) Concluding remarks In this paper, we have examined a two-echelon make-to-order QR fashion supply chain with a retailer having a boundedly rational human manager as the decision maker. By constructing a formal Bayesian analytical model with a newsvendor type of fashion product, we have first derived the analytical expected profit functions for the fashion supply chain and its agents under the cases with and without QR. By examining these expected profit functions, we have derived the ELBR to the retailer, and also the expected gains from adopting QR. Several important managerial insights have been generated: (a) QR can bring a positive gain to the retailer only when the unit ordering cost under QR is not too high (compared to the case without QR); (b) for both cases, with and without QR, the human retail manager s level of bounded rationality lowers the expected profits of the retailer and the supply chain, but surprisingly it does not affect the manufacturer s expected profit; (c) for both cases, with and without QR, the manufacturer can be benefited from the retailer s bounded rationality behavior if it imposes the commonly adopted MOQ measure on the retailer; (d) when the manufacturer specifically sets the MOQ to be the same as the retailer s theoretical optimal ordering quantity, the manufacturer will have 50% likelihood of enjoying a strictly higher profit (and 50% likelihood of having the same profit) if the retailer is boundedly rational (compared to the case when the retailer is perfectly rational). For future research, one can consider extending the supply chain analysis to include the use of incentive alignment contracts such as the returns policy (Chen, 2011). It is also promising to extend the analysis to the situation when there is product substitution from multiple suppliers (Xia, 2011). Another interesting extension is to explore the supply chain when there is information asymmetry (Mukhopadhyay et al., 2008) between the seller and the buyer. Acknowledgments The author sincerely thanks the general editor, associate editor, and anonymous reviewers for their constructive comments that led to major improvements of this paper. This paper is supported by Research Grants Council of Hong Kong under the General Research Fund with the account code of PolyU H. References Cachon, G., Swinney, R., The value of fast fashion: quick response, enhanced design, and strategic consumer behavior. Management Science 57, 4, Chen, H., Chen, J., Chen, Y., A coordination mechanism for a supply chain with demand information updating. International Journal of Production Economics 103, Chen, J., The impact of sharing the customer returns information in a supply chain with and without a buyback policy. European Journal of Operational Research 213, 3, Choi, T.M., Quick response in fashion supply chains with dual information updating. Journal of Industrial and Management Optimization 2, Choi, T.M., Local sourcing and fashion quick response system: the impacts of carbon footprint tax. Transportation Research Part E 55,

13 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) Choi, T.M., Li, D., Yan, H., Optimal two-stage ordering policy with Bayesian information updating. Journal of the Operational Research Society 54, Choi, T.M., Sethi, S., Innovative quick response programs: a review. International Journal of Production Economics 127, Chow, P.S., Choi, T.M., Cheng, T.C.E., Impacts of minimum order quantity on a quick response supply chain. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 42, Chow, P.S., Choi, T.M., Shen, B., Zheng, J., Supply contracting with risk-sensitive retailers under information asymmetry: an exploratory behavioral study. Systems Research and Behavioral Science 31, 4, Donohue, K.L., Efficient supply contract for fashion goods with forecast updating and two production modes. Management Science 46, Fisher, M., Rajaram, K., Raman, A., Optimizing inventory replenishment of retail fashion products. Manufacturing and Service Operations Management 3, Fisher, M., Raman, A., Reducing the cost of demand uncertainty through accurate response to early sales. Operations Research 44, Gallego, G., Ozer, O., Integrating replenishment decisions with advance demand information. Management Science 47, Iyer, A.V., Bergen, M.E., Quick response in manufacturer-retailer channels. Management Science 43, Kim, H.S., A Bayesian analysis on the effect of multiple supply options in a quick response environment. Naval Research Logistics 50, Liu, Z., Nagurney, A., Supply chain networks with global outsourcing and quick-response production under demand and cost uncertainty. Annals of Operations Research 208, 1, McCardle, K., Rajaram, K., Tang, C.S., Advance booking discount programs under retail competition. Management Science 50, Mukhopadhyay, S.K., Zhu, X., Yue, X., Optimal contract design for mixed channels under information asymmetry. Production and Operations Management 17, Schweitzer, M.E., Cachon, G.P., Decision bias in the newsvendor problem with a known demand distribution. Management Science 46, 3, Sethi, S.P., Yan, H., Zhang, H., Zhou, J., Information updated supply chain with service-level constraints. Journal of Industrial and Management Optimization 1, Shaltayev, D.S., Sox, C.R., The impact of market state information on inventory performance. International Journal of Inventory Research 1, Su, X., Bounded rationality in newsvendor models. Manufacturing and Service Operations Management 10, 4, Tang, C.S., Rajaram, K., Alptekinoglu, A., Ou, J., The benefits of advanced booking discount programs: model and analysis. Management Science 50, Wu, D.Y., Chen, K.Y., Supply chain contract design: impact of bounded rationality and individual heterogeneity. Production and Operations Management 23, 2, Xia, Y., Competitive strategies and market segmentation for suppliers with substitutable products. European Journal of Operational Research 210, 2, Yang, D., Qi, E., Li, Y., Quick response and supply chain structure with strategic consumers. Omega 52, Zhang, T., Zhu, X., Zhou, C., Liu, M., Pricing and advertising the relief goods under various information sharing scenarios. International Transactions in Operational Research, doi: /itor

14 904 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) Appendix: All proofs Proof of Proposition 1 1. Since EP 0,R EP 0,R Q 0,R, ELBR 0,R = EP 0,R EP 0,R When V increases, 0 (V ) = ( ( Vz d0 +δ 1 ( r c 0 )))ϕ(z)dz increases. Thus, r v [ 0 (V ) (Z 0 )] increases. As ELBR 0,R = (r v) d 0 + δ[ 0 (V ) (Z 0 )], an increasing V will yield a larger ELBR 0,R 3. ELBR 0,R = 0whenV = 0. Proof of Proposition 2 1. It follows the proof of Proposition First, checking the first-order derivative of EGH R with respect to c 1 reveals that EGH R is a decreasing function of c 1.Asc 1 is larger than c 0, checking the limit shows that lim EGH R > 0 c 1 c 0 and lim EGH R < 0. Thus, c H,1 = arg[egh R = 0] uniquely exists between c 0 and r. We thus have c1 r c 1 EGH R ( >=< ) 0 if c 1 ( <=> ) c H,1. 3. The logic and approach are the same as in part (2). 4. Checking the first-order derivative of EGC R with respect to V shows that it is an increasing function of V. 5. Checking the first-order derivative of EGH R with respect to V gives the following: EGH R V ( ) ( ( r v ) ( )) Vz Vz = 2 V d0 + δ + Z 0 d1 + δ + Z 1 zϕ(z)dz, which can be positive or negative depending on the values of c 0, c 1, d 0,andd 1. Proof of Theorem 3 From (23) and (25), we can see that the manufacturer s expected profits for the cases with and without QR are independent of V. Thus, the retailer s bounded rationality does not hurt the manufacturer s expected profit. From Propositions 1 and 2, we know that the retailer s bounded rationality hurts the retailer (as the expected loss is positive). Since the supply chain s expected profit is the sum of the retailer s expected profit and the manufacturer s expected profit, the retailer s bounded rationality also hurts the supply chain s expected profit.

15 Proof of Theorem 4 T.-M. Choi / Intl. Trans. in Op. Res. 24 (2017) (a) From the analytical model, since Q 0,R f Normal [Q 0,R (q 0,R,V )]. If the manufacturer offers a positive MOQ on the retailer s ordering, for the case without QR, the retailer s ordering quantity will become either of the following two cases: Case (1): The retail ordering quantity equals the MOQ, if the retailer s preferred quantity Q 0,R (which is random under the retailer s boundedly rational decision-making process) is equal to or lower than the MOQ. Case (2): The retail ordering quantity is greater than the MOQ, if the retailer s preferred quantity Q 0,R (which is random under the retailer s boundedly rational decision-making process) is larger than the MOQ. Thus, in the presence of MOQ, the expected retail ordering quantity will be larger than E[Q 0,R ] q 0,R which means the manufacturer s expected profit will also be higher. The same argument applies for the case with QR. (b) Consider the case without QR. If MOQ equals the theoretical retail optimal ordering quantity q 0,R, then the retail ordering quantity is larger than or equal to q 0,R. Since the retailer s bounded rationality will lead to the preferred ordering quantity of Q 0,R f Normal [Q 0,R (q 0,R,V )], there will be 50% chance in which the ordering quantity is q 0,R (when Q 0,R MOQ = q 0,R ) and 50% chance the ordering quantity is above q 0,R. Thus, the manufacturer s profit when the retailer is boundedly rational is always larger than or equal to the one when the retailer is perfectly rational. In addition, there is 50% chance that the manufacturer s profit is higher when the retailer is boundedly rational (compared to the case when the retailer is perfectly rational). Using the similar logic, we can prove the case with QR.