Research Reads - Markdown pricing

Paper #1 - Markdowns in E-Commerce Fresh Retail: A Counterfactual Prediction and Multi-Period Optimization Approach

Key Notes

• Due to the limited shelf life of perishable products and the limited opportunity of price changes, it is difficult to predict
• sales of a product at a counterfactual price, and therefore it is hard to determine the optimal discount price to control inventory and to maximize future revenue.
• Sequential pricing strategy by Markov decision process, and design a two-stage algorithm to solve it
• Many perishable products, such as vegetables, meat, milk, eggs, bread, have a limited shelf life promotional markdown is a common approach for e-commerce fresh retails
• The normal channel, where goods are sold by no-discount retail price
• Markdown channel, where customers can buy goods by discount under the condition that their total purchase has reached a certain amount

Key Questions

• First, can goods be sold out with the retail price before its expiry date?
• Second, if not, what is the optimal discount price for promotional markdown to ensure the goods being sold out while maximizing the profit?
• The first problem is about sales forecasting 
• Second problem is about price-demand curve fitting
• We observe the sales of a product with price A and B, we aim to predict the sales of a product with price C, which is counterfactual

• To avoid price discrimination, the discounts of the same product in different stores within the same region should be all equal
• To optimize the discount price, we need to take all stores in a region into consideration
• We collect a set of observable covariate features 𝒙𝑖 ∈ R, including categories, holidays, event information, inherent properties and historical sales of products and shops
• The key of pricing decision making is to accurately predict the demand of products at different discount prices
• We aggregate data of all products by using the category information and learn the causal effect of each product jointly
• The price elasticity is daily updated once the new transaction data is collected

Paper #2 - Markdown Pricing Under Unknown Demand

• Unimodal Multi-Armed Bandit problem where the goal is to find the optimal price under an unknown unimodal reward function
• “optimal” solutions exist under numerous variations on (a) the set of demand functions allowed, on (b) how inventory is treated, and on (c) the frequency at which prices are allowed to change, just to name a few. 
• A Markdown Policy and Performance Guarantee: We introduce a policy which satisfies the markdown constraint
• Optimality via a Minimax Lower Bound: We prove that our policy is in fact orderoptimal by showing

Paper #3 - Markdown Pricing Under Unknown Parametric Demand Models

• Markdown Policies with Theoretical Guarantees
• Tight Minimax Lower Bound
• Impact of Smoothness
• In the Discrete Multi-armed Bandit problem, the player is o↵ered a finite set of arms, with each arm providing a random revenue from an unknown probability distribution specific to that arm. The objective of the player is to maximize the total revenue earned by pulling a sequence of arms 

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