Buy one get one with discount Promotional Strategy Kyong-Kuk Kim, Chi-Ghun Lee and Sunggyun Park ISysE Department, FEG 002079
Contents Introduction Literature Review Model Solution Further research 2 ISysE Department, FEG 002080
Introduction Promotion 3 ISysE Department, FEG 002081
Introduction Buy one Get one Discount For Specific Product, For Specific time and Inventory What is the Optimal Price? What is the Optimal Discount rate? 4 ISysE Department, FEG 002082
Literature Review Dynamic Pricing for one Product Gallego, G., G. J. Van Ryzin. 1994. Optimal dynamic pricing of inventories with stochastic demand over finite horizons Zhao, W., Y.S. Zheng. 2000. Optimal dynamic pricing for perishable assets with nonhomogeneous demand. Dynamic Pricing for Multiple Product Gallego, G., G. van Ryzin. 1997. A multiproduct dynamic pricing problem and its applications to network yield management. Maglaras, C., Meissner, J. 2006. Dynamic pricing strategies for Multiproduct revenue Management Problems 5 ISysE Department, FEG 002083
Literature Review Bundling Bitran, R., Ferrer, J,C., 2000. On Pricing and Composition of Bundles. Bulut, Z., Gurler, U., Spen, A. 2009. Bundle pricing of inventories with stochastic demand. Marketing Literature Sinha, I., Smith, M, F. 2000. Consumer s perceptions of promotional framing of price. Li, S., Sun, Y., Wang, Y. 50% off or Buy one get one free? Frame preferences as a Function of consumable nature in Dairy products 6 ISysE Department, FEG 002084
Model Assumption Single Product, Monopoly Market Customer Poisson Process arrival One customer purchases one unit of a product or two units of a product or nothing 7 ISysE Department, FEG 002085
Model Customer Reservation Price If the price is lower than a customer reservation price, the customer purchases the product Reservation price can be explained by X,Y two random Variable X,Y correlation structure copulas,, Parameters explain the product character 2 8 ISysE Department, FEG 002086
Model Purchase Probability A retailor sets Price p and discount rate q - one unit price = p - two units price = p+pq Probability of Purchase one unit of product at t,,, Probability of Purchase two unit of product at t,, 2, 9 ISysE Department, FEG 002087
Model Purchase Probability Probability of Purchase nothing at t,, 1 y x 10 ISysE Department, FEG 002088
Model Purchase Probability 2 y x Probability with copula structure,,,,, 1 2, 11 ISysE Department, FEG 002089
Model Expected Revenue with inventory s and time t Define, as supremum of expected revenue from any admissible policy over 0, with Given a pricing policy, an initial stock S>0, and a sales horizon T>0, where, 0 0 0, 0 12 ISysE Department, FEG 002090
Model Jacobi- Bellman equation, sup,, 1, 2,,, sup,,, λ,,, 1, λ,,, 2, Jacobi Bellman Equation, sup,, λ,, λ,,, 1,, 2, 13 ISysE Department, FEG 002091
Solution Solution from Numerical Test Price set is Discrete Discount rate set is Discrete Discrete Approximation of the continuous time model - Discretizing the time horizon [ T,0 ] into N time intervals of length,, sup,, λ,,, 1, λ,,, 2, Normalize to 1 and choose 14 ISysE Department, FEG 002092
Solution Basic Parameters - λ10, 20-1, 1, 0.99, - X has normal distribution with mean 5, σ 4 - Y has normal distribution with mean 5, σ 4 - ρ0.9,normal Copulas Product에 따른성질 - Change parameters,, Customer 의 분포에 따른 성질 -Change parameters λ, and copulas(normal, Clayton, Gumbel) 15 ISysE Department, FEG 002093
Solution 50% off or but one get one free? 16 ISysE Department, FEG 002094
Solution 50% off or but one get one free? Stock-up characteristic Consumption level Stock-up Non-stock-up High α β γ α β γ (Powdered milk) (fresh milk) Low α β γ α β γ (Powdered cheese) (yogurt) Stock-up characteristic Consumption level Stock-up Non-stock-up High Low α=2 β=4 γ=1 α=0.25 β=0.75 γ=0.85 (Powdered milk) (fresh milk) α=2.5 β=0.5 γ=1 α=1.5 β=0.5 γ=0.85 (Powdered cheese) (yogurt) 17 ISysE Department, FEG 002095
Solution Weight - 1-1 2 3, 3, - Normal Copula - As w increases, Consumption Level increases - 50% off 1+1 promotion, Difference decrease 18 ISysE Department, FEG 002096
Solution Constant c - - 3, 3 - Normal Copula - As c increases, Consumption Level increases - 50% off 1+1 promotion, Difference decrease 19 ISysE Department, FEG 002097
Further research Induce the structure property of our model Verify our model from empirical test Decouple the assumptions Extend to other promotional strategies 20 ISysE Department, FEG 002098