1 / 33

Dynamic Pricing of Products with Heterogeneous Quality

Dynamic Pricing of Products with Heterogeneous Quality. Yalcin Akcay Koc University, Istanbul, Turkey joint work with Fikri Karaesmen and Seray Aydin. Product Quality. Product Quality Spectrum. High. Low. quality decreases. h omogeneous quality. heterogeneous quality.

luella
Download Presentation

Dynamic Pricing of Products with Heterogeneous Quality

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Dynamic Pricing of Products with Heterogeneous Quality Yalcin Akcay Koc University, Istanbul, Turkey joint work with Fikri Karaesmen and Seray Aydin

  2. Product Quality Product Quality Spectrum High Low quality decreases homogeneous quality heterogeneous quality Problem:sellheterogeneous quality products over a finite time horizon facing uncertain demand so as to maximize expected profits

  3. $9 $2 $3 $6 $5 $4 $7 $8 $1 Pricing Policies • Individual pricing – set a different price for each product depending on quality

  4. $9 $5 $2 $5 $3 $5 $6 $5 $5 $5 $4 $5 $5 $7 $8 $5 $5 $1 Pricing Policies • Individual pricing – set a different price for each product depending on quality • Static pricing – set a single price for all products through out the selling season

  5. $5 $9 $7 $7 $2 $5 $3 $5 $7 $5 $6 $7 $5 $7 $5 $7 $4 $5 $7 $5 $7 $7 $5 $8 $7 $1 $5 Pricing Policies • Individual pricing – set a different price for each product depending on quality • Static pricing – set a single price for all products through out the selling season • Dynamic pricing – set a single price for all products at the beginning of the selling season, and update the price during the season

  6. $5 $9 $5 $2 $2 $3 $5 $2 $5 $2 $6 $5 $5 $2 $4 $5 $2 $7 $5 $5 $8 $2 $1 $5 Pricing Policies • Individual pricing – set a different price for each product depending on quality • Static pricing – set a single price for all products through out the selling season • Dynamic pricing – set a single price for all products at the beginning of the selling season, and update the price during the season

  7. Quality Control (alternative perspective) SUPPLIER SELLER CUSTOMERS

  8. Quality Control (alternative perspective) SUPPLIER SELLER CUSTOMERS seller’s quality requirement acceptable unacceptable seller pays premium for high quality products

  9. Quality Control (alternative perspective) SUPPLIER SELLER CUSTOMERS seller’s quality requirement acceptable unacceptable

  10. Quality Control (alternative perspective) SUPPLIER SELLER CUSTOMERS seller’s quality requirement acceptable unacceptable seller pays for inspection seller needs expertise seller needs to deal with scrap

  11. Quality Control (alternative perspective) SUPPLIER SELLER CUSTOMERS

  12. Quality Control (alternative perspective) SUPPLIER SELLER CUSTOMERS

  13. Quality Control (alternative perspective) SUPPLIER SELLER CUSTOMERS customers choose the best first! quality of remaining inventory over time dynamic pricing

  14. Dynamic Pricing Model • Two period model (regular sales & clearance sales periods) • Demand ~ Poisson • Single price for all inventories on hand • Customers are homogenous utility = θq – p • Seller can only observe available inventory (but not the actual demand) • qx > qx-1 > .... > q2 > q1 (general distribution for random demand) update quality distribution at the beginning of period 1 quality distribution at the beginning of period 2 period 2 period 1 end of selling season beginning of selling season random demand in period 2 random demand in period 1 price set at the beginning of period 2 price set at the beginning of period 1

  15. Dynamic Programming Formulation utility of a customer from a product of quality q priced at p a product “qualifies” for sales only if likelihood that a product will be sold at price p likelihood that the highest quality product will be sold at price p order statistics likelihood that the 2nd highest quality product will be sold at price p number of qualifying products at price p joint order statistics

  16. Dynamic Programming Formulation maximum expected revenue probability of selling s1 units of the product in period 1 probability of selling s2 units of the product in period 2 given that s1 units were sold in period 1

  17. Dynamic Programming Formulation demand number of “qualifying” products

  18. Sample Evaluations (Period 1) Suppose there are 10 products at the beginning of period 1

  19. Sample Evaluations (Period 1) Suppose there are 10 products at the beginning of period 1

  20. Sample Evaluations (Period 2) Suppose there are 10 products at the beginning of period 1

  21. Sample Evaluations (Period 2) Suppose there are 10 products at the beginning of period 1

  22. Sample Evaluations (Period 2) Suppose there are 10 products at the beginning of period 1

  23. Sample Evaluations (Period 2) Suppose there are 10 products at the beginning of period 1 several (tricky) steps required to convert these expressions to joint distributions (order statistics) of two variables.

  24. Single Product Case • q ~ U[0,1] • α = customer arrival probability dynamic

  25. Single Product Case dynamic static

  26. Single Product Case dynamic static individual (full info)

  27. Single Product Case dynamic static İndividual (full info)

  28. Numerical Results Base-case scenario: • Total expected demand = 40 (Poisson) • Two same-length sales periods • Quality ~ Uniform[0,10] • θ = 1 (quality sensitivity scalar) • Per unit procurement cost = $2.5 • Initial inventory = 40 units

  29. Effect of variability in quality x=40 x=60 x=20

  30. Effect of improvement in quality

  31. Effect of quality inspection

  32. Effect of the timing of price update in all cases total expected demand is 40

  33. Conclusions • Dynamic pricing is an effective tool for inventory management in the presence of demand uncertainty. • As inventory is depleted, adjusting prices enables the seller to better exploit the current supply-demand mismatch. • In an environment where the best items are sold first, dynamic pricing has the potential to be an even stronger lever. • In this situation, not only the remaining inventory level but also the remaining quality level provides valuable information for the seller • We model the problem as a stochastic dynamic program with quality distribution updates and illustrate the effectiveness of this approach • Dynamic pricing particularly beneficial under adverse operating conditions • the seller has little information about product quality (variable quality) • the seller deals with low quality products • the seller does not have access to effective quality inspection processes

More Related