Holiday merchandise has unique demand characteristics, unofficial start data, and a limited life cycle. In an intensely competitive market, individual merchants are able to get more sales opportunities if they display their products earlier. In this study, a time-variant variance and time-variant expected market demand model are introduced to investigate the order strategies that are used by risk-averse holiday merchants. Our results show that risk preference, market uncertainty, and market power have a significant effect on the merchant’s market strategies. Risk-averse merchants prefer to enhance forecast accuracy rather than using an early-display advantage. They can even give up their early-display advantage if they are faced with increased market uncertainty and small market power. Compared with the fixed purchase cost, the time-sensitive purchase cost can stimulate the merchant to purchase in advance, but this can decrease the merchant’s profit. Consequently, risk-averse merchants always display their merchandise later, decrease the order quantity, and, finally, miss the market opportunity.
As a special type of seasonal goods, holiday merchandise has unique demand characteristics, such as an unofficial start date and a finite selling horizon [
The early display not only comes at the expense of reduced sales of other merchandise (e.g., because the shelves used for displaying the Christmas decorations cannot be used for displaying other merchandise, which in turn means reduced sales of the other merchandise and smaller profits for the merchants [
This study aims to investigate the merchant’s challenge of optimizing the display time and inventory management of holiday merchandise in a competitive retail market that is characterized by uncertainty, low-salvage values, and high stock-out costs. The merchant’s risk preference is introduced to consider how these market strategies vary in an uncertain market environment [
The rest of this paper is organized as follows. Section
Our models are largely inspired by the holiday merchandise problem and by previous studies of traditional newsvendor models that examine a demand uncertainty environment and a quick response system. In this section, we will briefly review each stream of the literature related to our study.
The first research stream of interest is demand uncertainty. The demand uncertainty of holiday products has been widely recognized as an important issue in the operations management literature. Milner and Rosenblatt tried to reduce the negative effect of uncertain demand using a quantity flexible contract [
The second research stream of interest is the time-variant market demand model in a quick response system. This research assumes that the merchant can enhance forecast accuracy in an uncertain market by collecting market information. For example, some literature has assumed that lead-time reduction can help enhance the forecast accuracy in an uncertain demand market [
Consider a merchant who sells a kind of holiday merchandise to the retail market, such as an artificial Christmas tree or Spring Festival merchandise. Although this holiday merchandise does not have an official start date to the market, year-round displays of this holiday merchandise do not occur in practice. Consequently, there must exist a critical time point
Consider the following scenario faced by a merchant:
This section will characterize the risk of the merchant’s marketing strategies. Here, we first use a risk-neutral model as a benchmark. The unity for the risk-neutral merchant is the expected profit, as follows:
For any display time
For any time
For a risk-neutral merchant, the order quantity can be expressed by the purchase time as
(1) Solve the equation
(2) Let
(3) Compute the values of (
From Lemma
By substituting
(1) Differentiate the expected function
(2) Let
(3) Obtain the valid extreme values set by excluding the invalid extreme as
(4) Compute the possible optimal values for the expected function
The previous literature has shown that decision-makers will tend to be risk-averse because they are faced with an uncertain environment [
The merchant’s objective is to maximize the following utility function according to the general definition of CVaR [
For a risk-averse merchant, the order quantity can be expressed by the purchase time as
(1) Solve the equation
(2) Let
(3) Compute the values of formula (
From the definition of CVaR, substitute
(1) For any given
if
if
Combine Case 1 and Case 3; the optimal solutions for given
(i) If
(ii) If
(2) By substituting
By substituting
(1) Take the first and second partial derivatives of
(2) Let
(3) Exclude the invalid extreme points and obtain the valid extreme points set as
(4) Substitute these valid extreme points into
It is difficult to obtain the analytical solutions for nonlinear decision equations. Thus, we will conduct a numerical analysis to better understand the impact of these parameters on the risk reference of the merchants’ market strategies. We will then make some recommendations for holiday merchants. Our focus is on investigating how the risk-averse merchant makes the strategies, display time, and order quantity reflect the various influential parameters. To illustrate the impacts of these important parameters, we assume that
In the theoretical analysis, we represent the degree of risk aversion with
The effects of degree of risk aversion
Figure
The effects of uncertainty of market demand
Here,
The effects of coefficient of elasticity of competitive
As described previously, the aim of the price discount provided by the supplier is to stimulate the merchant to purchase earlier. When
The effects of uncertainty of market demand
The power of merchant represented by
The effects of retailer’s power
Holiday merchandise exhibits typical market characteristics due to its unofficial start date and limited life cycle. In this study, we have been able to capture the unique characteristics of holiday merchandise in the retail market by introducing the time-variant variance and time-variant expected market sales model. In particular, this study has investigated the market strategies that are used by merchants with different risk preferences to optimize the display time and inventory management of holiday merchandise in a competitive retail market. This work has enhanced the understanding of the phenomena of holiday goods, and it has provided management insight by conducting a numerical analysis. Our results suggest that the interactions of risk preference and the time-sensitive purchase cost have a significant effect on the merchant’s market strategies. A risk-averse merchant will delay the holiday merchandise display time, decrease the order quantity, and finally miss the market opportunity. Meanwhile, the time-sensitive purchase cost can stimulate the merchant to purchase in advance, but this will also increase the merchant’s order cost and will finally decrease the merchant’s profit. The considerable uncertainty of the holiday market will cause the merchant to wait to avoid opportunity cost, and this pause allows them to enhance their forecast accuracy. A more risk-averse merchant may consider giving up the early-display advantage. All of the merchants, regardless of their risk preference, would prefer to enhance their forecast accuracy rather than capturing the early-display advantage if less of the market will be taken by the competition due to late display. A large market power merchant is not afraid to lose loyal customers due to late display. Generally, a merchant with larger market power will display their merchandise later and will make more profits. In comparison with the fixed purchase cost, a risk-averse merchant has to make a tradeoff between the challenge of making matched market strategies with the purchase cost, the advantage of early display, and the forecast error. While this study uses an extended newsvendor model, it goes further and investigates the display time and the traditional order quantity decision with time-sensitive purchase cost. This helps to offer a more detailed understanding of the interaction among these important parameters through numerical analysis.
It should be pointed out that the main limitation in the current study is that the optimal market strategies cannot be analytically derived from the decision-making equations. Therefore, we have numerically analyzed the impacts of these parameters on the risk reference merchants’ market strategies. Several aspects of the present study warrant further research. For example, the scenarios that were used in this model can be extended to a supply chain context to consider the effects of the behavior of other players on the merchant’s market strategies.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This research was supported by the National Natural Science Foundation of China (71301054), the Fundamental Research Funds for the Central Universities (2015QNXM13, 2017X2D14), Provincial Natural Science Foundation of Guangdong (2015A030310271, 2015A030313679, and 2015A030313681), and Zhongshan City Science and Technology Bureau Project (no. 2017B1015).