DYNAMIC PRICING AT K-FASHION
IIMT3636
K-Fashion is a boutique store for women’s fashion apparel located in a big shopping mall at the Causeway Bay. The store is targeting young female white-collar who care less about brand but more about fashion and price.
For the next season (12 weeks), K-Fashion has ordered 200 different stock keeping units1 (SKUs) from a foreign supplier. Due to the long production and order lead time, K-Fashion can place the order only once. Given the large store traffic at Causeway Bay, the store ordered 10 pieces for each SKU.
Your job is to focus on the pricing of the three SKUs—A, B, and C—of a particular style. The sale of this style is independent of other styles. To simplify the analysis, we also assume that the demand for each SKU is independent. For example, customers that suit size L will never buy size M. In other words, if a customer who intends to buy size L finds that size L is not available,
1 An SKU is defined by the style, color, and size of a product. For example, a blue, size-M shirt of a unique style.
the s/he will walk away without buying other sizes. The goal is to maximize the total revenue, given the fixed amount of inventory over the next 12 weeks. Any unsold inventory after the 12th week will be discarded with zero salvage value. The constraint is that you must set the same price for all the three SKUs as they differ only in color or size. The price can be adjusted every Monday.
Customers arrive randomly. Historical data suggests that the traffic is smaller in the first two months or 8 weeks and larger in the last 4 weeks. For the first 8 weeks, the weekly total number of visits to the store approximately follows normal distribution with a mean of 800 and a standard deviation of 200; for the last 4 weeks, the weekly total visits also follows normal distribution with a mean of 1,600 and a standard deviation of 400. The number of visits will be an integer.
According to past experience, about one out of fifty (1/50) customers on average will show interests in the focal style (i.e., ask about the price and/or try it on). These interested customers will like an SKU with an equal probability (i.e., 1/3), but they will never like two or more SKUs of the same style. Hence, the chance that a customer entering the store will like SKU A is (1/50)*(1/3). Nevertheless, showing interests does not mean necessarily buying the product. A customer will buy a product only when his/her willingness-to-pay is higher than or equal to the price. A customer’s willingness-to-pay for the focal style is random and will be uniformly drawn from the interval [0, 1000 – 4*(t – 1)^2], where t is the index of the week. For example, in week t=1, the maximum acceptable price is $1,000.
Please collaborate with your teammates to find out a scientific way of setting the price of each week in order to maximize the total revenue. Monte Carlo simulation is recommended.
Your strategy will be tested in class on April 12. On that day, you will make decisions on the fly, and your performance (total revenue) will be compared against other teams. The team that achieves the highest total revenue will receive an award. The score of each team will be determined according to a comparison against the highest possible total revenue. The team that does not show up or participate in the competition will receive a score of zero.
Figure: The Timeline
Table: The Scoring Scheme
Your total revenue / The highest possible revenue
Your Score
0.9 or above
10/10
0.7 or above
9/10
0.5 or above
7/10
Below 0.5
5/10