Retailers selling seasonal products often face the challenge in matching their inventory levels with uncertain market demand which is sensitive to weather conditions, such as the average seasonal temperature. Therefore, how to make the joint ordering and pricing decisions may help retailers to increase their profits. In this paper, we address the joint determination of pricing and ordering decisions in a newsvendor setting, where a retailer (newsvendor) sells the seasonal products and faces demand risk due to weather uncertainty. We show that the maximum expected profit function is continuous and concave, so the optimal solution to the retail price and order quantity exists and it is the one and only solution. In addition, we numerically investigate the impacts of related parameters on the retailer’s expected profit and the optimal pricing and ordering decisions and illustrate some useful management insights into the economic behavior of firms.
Noncatastrophic (examples of catastrophic weather conditions mainly include natural disaster type weathers, such as blizzards, tornados, and cyclonic) weather represents an important determinant of demand for many seasonal products such as weatherproof, soft drinks and ice cream products, coats and sweaters, and heating oil. The U.S. National Research Council has estimated that 46% of U.S. gross domestic product (GDP) is affected by weather [
Weather affects the companies’ economic activities in many business industries. In the retail industry, WalMart Stores, Inc., reported in June 2005 that its inventory levels were higher than normal because belownormal temperatures crimped demand [
In this paper, we try to address the joint decisions of inventory level and retail price in a newsvendor setting, where the newsvendor (retailer) sells a seasonal product and faces inventory risk due to weather uncertainty. (For more details about singleproduct models that deal with joint ordering and pricing issues, the reader is referred to [
How should the retailer determine the optimal retail price and order quantity for seasonal product under weathersensitive demand?
How would the optimal retail price and order quantity change as the model parameters (such as weather index (temperature), inventory holding cost) change?
In order to address the above questions and gain managerial insights into pricing and ordering policies for seasonal products, we need to model the uncertain market demand. Similar to [
The rest of the paper is organized as follows. In the next section, we give a brief literature review, which is followed by the formulation of this problem. In Section
In this paper, our work is closely related to the literature in demand risk (weather risk caused by weather) management and joint ordering and pricing decisions of products. We briefly review the most relevant work to clarify the contribution of the paper.
There are many ways in which retailers can mitigate the impact of the demand uncertainty (caused by weather, price, and other factors) on their overall profit. The most common mechanisms involve operational hedging, which can be achieved via delayed product differentiation [
Our work is more closely related to weather risk management. The weather risk we discussed in this paper is receiving discussion from other literature. Sabir et al. [
In the operations management literature, our work is related to the optimal pricing and ordering decisions of products in a newsvendor setting. There is abundant literature on pricing and ordering strategies of common products. Weng [
Our work is most closely related to Gao et al. [
In this study, our objective is to investigate the joint optimal pricing and ordering decisions of seasonal products. Particularly, we consider a riskneutral retailer that sells a seasonal product with weathersensitive demand. The demand occurs during the regular selling season and is contingent on the seasonal weather status. In this paper, we represent the seasonal weather status with the average seasonal temperature
Next, we proceed to discuss our assumptions. Without loss of generality, we assume that lower values of
At the beginning of the selling season, the retailer only knows the distribution of the average temperature
Similar to [
To rule out the uninteresting or trivial cases, we assume that the following relationships exist among the various model parameters:
We now turn out our attention to the main model and provide a technical analysis of the main problem.
In our analysis, the retailer first determines the optimal order quantity under market demand uncertainty. Then, the retailer determines the optimal selling price
When the temperature is high, that is to say,
Under both the cases, the representative customer makes a purchase if the selling price is lower than her valuation. From (
We illustrate an intuitive understanding of the demand in Figure
Demand corresponding to the two temperature states.
The retailer’s order quantity decision in the selling period is denoted by
The retailer’s profit as a function of his order quantity decision, pricing decisions, and the realized weather state is as follows:
Next, for given
The optimization problem becomes maximizing a piecewise liner function. By analyzing the coefficients of the terms with
For given
If
If
If
If
If
From (
Note that, if
Now, the effort required to compute the optimal pricing policy depends on the shape of
The optimal pricing decisions under the scenario
From (
From (
Similarly, from (
The analogous optimal pricing decisions for the case
The analogous optimal pricing decisions for the case
The analogous optimal pricing decision for the case
For convenience of notation, we define new variables
Thus, we show a simplified expression for the retailer’s optimal pricing decisions as follows:
Therefore, Theorem
For convenience of notation, from (
Similarly, we also show a simplified expression for the demand function corresponding to the case of
The optimal ordering decision under the scenario
From Theorem
In this section, we mainly focus on examining the impact of the parameters on the retailer’s decisions and present numerical analysis of the joint ordering and pricing decisions. It will be valuable to generate further managerial insights about the impact of parameters such as the temperature state and those associated with the costs. For the numerical examples, we select the basic case parameterized in Table
Simulation parameters.
Variable 










Value  0.5  182  200  239  10  −4.2  400  500 
The optimal retail price in the high temperature state,
Effects of weather conditions.








0.400  0.271  0.136  0.271  291.000  364.330  33.978 
0.450  0.267  0.136  0.267  291.000  366.450  32.984 
0.500  0.135  0.135  0.262  291.500  369.000  31.944 
0.550  0.133  0.133  0.261  293.140  369.500  31.029 
0.600  0.131  0.131  0.261  295.340  369.500  30.057 
The optimal order quantity,
Effects of inventory holding cost.






8  0.266  290.000  367.000  33.229 
9  0.264  290.000  368.000  32.687 
10  0.262  290.500  369.000  32.149 
11  0.261  291.500  369.500  31.615 
12  0.258  292.500  369.500  31.086 
The optimal order quantity,
Effects of emergency ordering cost.






229.000  0.261  295.500  364.500  32.010 
234.000  0.266  293.000  367.000  32.000 
239.000  0.270  291.500  369.500  31.872 
244.000  0.273  291.000  370.000  31.745 
249.000  0.273  291.000  370.000  31.881 
The market demand for seasonal products such as cooling/heating appliances (air conditioner), newstyle jacket, and snow equipment is weather sensitive. Naturally, adverse weather conditions that negatively affect the use of these items will reduce the demand. Retailers selling seasonal products have to face a challenge in matching their order quantities with uncertainty market demand during the selling season. Under this scenario, the market demand is shaped by the weather state and customer’s valuations. And then, we present a joint decisions model in a newsvendor setting, where a retailer sells the seasonal products at the weatherdependent prices. We provide a detailed analysis of the problems and characterizations of the optimal decisions when the retailer is riskneutral. We find that the optimal solution to the retail price and order quantity exists and it is the one and only. What is more, some useful insights, which are based on reasonable assumptions, have been generated in our extensive simulation experiments.
Our paper extends the analysis in Gao et al. [
The average seasonal temperature
The probability of a low temperature state
The probability of a high temperature state
The strike average temperature
Retail price per unit in the low temperature state
Retail price per unit in the high temperature state
Purchasing cost per unit
Inventory holding cost per unit
Emergency purchasing cost per unit
Net salvage value per unit
The maximum valuations of the customer in high temperature state
The maximum valuations of the customer in low temperature state
The demand in high temperature state
The demand in low temperature state
Order quantity.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors thank the two anonymous referees for their valuable comments and suggestions, which helped improve this paper. This research was supported by the National Natural Science Foundation of China (Grant nos. 70972056, 11301570) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant no. 20120191110042).