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Estimation of Retail Demand Under Partially-Observed Out-of-Stocks
Agenda ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Motivation: iPhone How would the analyst with  Apple store data know whether when you went to buy the  product the store was OOS?
Big Picture: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Managerial Issues:
…Motivation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Contribution: What’s new? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Modeling the impact of OOS: ,[object Object],[object Object],[object Object],[object Object],[object Object],Mktg Variables OOS dummy variable
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Example: no yes 2 0 O N=20 no yes 2 0 O 19 no yes 3 0 B 18 no yes 3 0 O 17 no yes 3 0 O 16 no yes 4 0 B 15 no yes 4 0 O 14 no no 4 1 A 13 no no 4 2 A 12 no no 4 3 A 11 no no 4 3 O 10 no no 4 4 A 9 no no 4 5 A 8 no no 4 6 A 7 no no 4 6 O 6 no no 4 7 A 5 no no 5 7 B 4 no no 5 8 A 3 no no 5 9 A 2 no no 5 10 A 1 oos B oos A beg inv B beg inv A choice consumer
Example: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],no no 2 1 A N=20 no no 2 1 O 19 no no 3 1 B 18 no no 3 1 O 17 no no 3 1 O 16 no no 4 1 B 15 no no 4 1 O 14 no no 4 1 O 13 no no 4 2 A 12 no no 4 3 A 11 no no 4 3 O 10 no no 4 4 A 9 no no 4 5 A 8 no no 4 6 A 7 no no 4 6 O 6 no no 4 7 A 5 no no 5 7 B 4 no no 5 8 A 3 no no 5 9 A 2 no no 5 10 A 1 oos B oos A beg inv B beg inv A choice consumer
Demand Model: ,[object Object],consumer product period choice availability indicator marketing variables market demand shock
Demand Model: ,[object Object],[object Object],demographics consumer product period choice availability indicator marketing variables market demand shock
Estimation: ,[object Object],[object Object],[object Object],[object Object],[object Object]
Simulating Sequence of Choices ,[object Object],choice indicator Choices Inventory Product Availability initial inventory sales inventory faced by customer i product availability indicator Constraints
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Out-of-Stocks (OOS) no yes 2 0 O N=20 no yes 2 0 O 19 no yes 3 0 B 18 no yes 3 0 O 17 no yes 3 0 O 16 no yes 4 0 B 15 no yes 4 0 O 14 no no 4 1 A 13 no no 4 2 A 12 no no 4 3 A 11 no no 4 3 O 10 no no 4 4 A 9 no no 4 5 A 8 no no 4 6 A 7 no no 4 6 O 6 no no 4 7 A 5 no no 5 7 B 4 no no 5 8 A 3 no no 5 9 A 2 no no 5 10 A 1 1-a iB 1-a iA beg inv B beg inv A choice consumer
Out-of-Stocks (OOS) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],no yes 2 0 O N=20 no yes 2 0 O 19 no yes 3 0 B 18 no yes 3 0 O 17 no yes 3 0 O 16 no no 4 1 A 15 no no 4 1 O 14 no no 4 2 A 13 no no 4 3 A 12 no no 4 4 A 11 no no 4 4 O 10 no no 4 5 A 9 no no 4 6 A 8 no no 4 6 B 7 no no 4 6 O 6 no no 4 7 A 5 no no 5 7 B 4 no no 5 8 A 3 no no 5 9 A 2 no no 5 10 A 1 1-a iB 1-a iA beg inv B beg inv A choice consumer
Estimation ,[object Object],[object Object],choices in new sequence product availability based on new sequence
Estimation: Initial Values:  Sequence of Choices, Availability  and  Demand Parameters Individual Choices &  Availability Individual  Parameters Hyper  Parameters Gibbs Sampler: MCMC Simulation Demand Shocks
Simulation Study: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
…Simulation Study ,[object Object],[object Object],[object Object]
First Case: OOS=35% mean of pref. coefficients interaction with z 2 heterogeneity var(  )
Second Case: OOS=1.4% mean of pref. coefficients interaction with z 2 heterogeneity var(  )
Results: ,[object Object],true true estimated estimated est(%) = 1-0.5*(S 1tm +N tm )/N tm est(%) : simulated from posterior R = 0.70
Estimating Lost Sales: ,[object Object],[object Object],[object Object]
Estimating Lost Sales: ,[object Object],MCMC draws
Real Data Set: ,[object Object],[object Object],[object Object],[object Object],[object Object]
Summary Statistics
Empirical Results:
Estimating Lost Purchases: Market 1 Market 2 Market 3 Market 4 Market 5 Market 6
% Lost Sales vs. OOS incidence Number of OOS products % Lost Sales
Dynamic Pricing: Sales Improvement Missing products in Day 5 & Market 5:  4 (Timotei), 9 (Other), 10-13 (Pantene), 14 (Other), 18-19 (H&S), 23 (Cabello Sano)
Dynamic Pricing: Profit Improvement Item implied by Lost Revenue  ≠ Lost Profit ≠ Most Frequent OOS
Extensions / Next Steps ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Behavioral Issues: ,[object Object],[object Object],[object Object],Proxy for Complexity outside good
Backorder Effects: ,[object Object],[object Object],[object Object],Previous OOS outside good Previous  no purchase
Quantity Decisions ,[object Object],choices ,[object Object],[object Object],[object Object],[object Object],5 4 5 Total A BBB A ? 4 AAA BB ? 2 A B AA 3 A BBB AA N=5 3 6 3 Total B 0 AAA B 1 3 2 1 Consumer Period
Price Endogeneity: ,[object Object],[object Object],[object Object],[object Object]
Sampling Choices in groups of k components. ,[object Object],choices ,[object Object],[object Object],[object Object],[object Object],B A ? 4 A B ? 2 A B ? 3 A B A N=5 4 2 3 Total A A A B 1 3 2 1 Consumer Period
Sampling Choices in groups of k components. ,[object Object],Note: number of terms in the denominator may increase at k! rate (e.g., ABC, ACA, BAC, BCA, CAB, CBA). choices ,[object Object],[object Object],[object Object],[object Object],B A ? 4 A B ? 2 A B ? 3 A B A N=5 4 2 3 Total A A A B 1 3 2 1 Consumer Period
In-Store Shopping Behavior ,[object Object],[object Object],[object Object]
In-Store Shopping Behavior A B C D q A  =10 q B  =5 q C  =7 q D  =10 q AB  =5 q BC  =4 q BD  =1 q AC  =3 q AD  =2 q CD  =7
Conclusions: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Thank You

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Stockout

Editor's Notes

  1. OOS are quite common…a recent notable example… May 12 th , 2008: Apple Inc. said iPhone is out of stock online, but added that brick-and-mortar stores run by Apple and iPhone carriers including AT&T Inc. might still have units available. CNN:http://www.cnn.com/2008/TECH/ptech/05/12/iphone.sold.out.ap iPhone sold out online Story Highlights Apple: U.S. and UK online stores are sold out of the popular smart phone Apple retail stores and AT&T may have units left, according to Apple Analysts say this may indicate upcoming launch of next-gen iPhone SAN FRANCISCO, California (AP) -- Apple Inc. said Monday its online stores in the U.S. and UK are sold out of the iPhone, a sign supplies are being winnowed ahead of the launch of the device's next generation featuring faster Internet surfing speeds.The Cupertino-based company confirmed that the iPhone is out of stock online, but added that brick-and-mortar stores run by Apple and iPhone carriers including AT&T Inc. might still have units available.Apple spokeswoman Natalie Kerris declined to comment on reasons for the shortage and on Apple's plans for an update to the device, which is widely expected to be unveiled in June at Apple's Worldwide Developers Conference in San Francisco.The paucity of iPhones for sale in some markets comes as Apple is hustling to meet its goal of selling 10 million of the hybrid iPod-cell phone-Internet surfing gadgets by the end of 2008. So far, Apple has sold 5.4 million iPhones, according to the latest data as of the end of March. Watch how new iPhones will compete with a new BlackBerry model » One way Apple is expanding the iPhone's reach is by inking deals with wireless carriers around the world, even breaking with its pattern of requiring exclusivity to sell in a certain country. On Monday, four mobile providers in the Asia-Pacific region announced partnerships with Apple to bring the iPhone to their regions later this year. SingTel will sell the gadget in Singapore, Bharti Airtel Ltd. in India, Globe Telecom Inc. in the Philippines and Optus in Australia, the companies said in a brief joint statement, without giving details. SingTel owns Optus and holds a 30.5 percent stake in Bharti and 44.5 percent in Globe. SingTel has about 2.3 million mobile subscribers in Singapore and around 7 million in Australia, according to data as of December 31, 2007. Bharti currently has about 64 million subscribers, while Globe reported a 21.3 million mobile subscriber base for the quarter ended March 31. Last week, the top mobile phone operator in Latin America, America Movil SAB, also announced plans to deliver the iPhone to its region. America Movil has 159.2 million subscribers in 16 countries, including Argentina, Brazil, Chile, Colombia and Mexico. In recent weeks Apple has also signed deals with Rogers Communications Inc. to sell the device in Canada; Milan-based Telecom Italia SpA to sell the iPhone in Italy; and Vodafone Group PLC, the world's biggest mobile company by sales, to sell it in a total of 10 countries, including Australia, India, Italy and Turkey. Until the spate of the latest deals, Apple adhered to its policy of exclusivity with one carrier in each country. The exclusive deals for the iPhone were with AT&T Inc. in the United States, O2 in Britain, T-Mobile in Germany and France Telecom's Orange wireless arm in France. Industry observers say some people may be holding off on buying an iPhone until the much-rumored next-generation of the device is launched, and the phone is officially rolled out in more countries. It takes some technical gymnastics, but it's still possible to get the phone in some markets where Apple doesn't have arrangements with wireless carriers. Many of the phones sold so far have been bought legitimately in one country, modified to work on any cellular network, and resold in countries where Apple doesn't have agreements to sell the iPhone. The trend expands the iPhone's reach but deprives Apple of some of the subscriber fees that Apple splits with its carrier partners. Apple is also planning a software update for this summer that makes the iPhone work better with corporate e-mail, a necessary upgrade to help the iPhone compete with Research in Motion Ltd.'s BlackBerry and Palm Inc.'s Treo smart phones. Copyright 2008 The Associated Press . All rights reserved.This material may not be published, broadcast, rewritten, or redistributed. All About Apple iPhone All About Apple Inc.       Find this article at: http://www.cnn.com/2008/TECH/ptech/05/12/iphone.sold.out.ap
  2. Full model: Correlation between true and estimated: 0.76093 Simple model: Correlation between true and estimated: 0.40463 This is important because it’s needed to compute lost sales.
  3. Market #OOS products 1 4.5 2 3.6 3 2.5 4 2.1 5 8.0 6 7.3
  4. 6.6% to 24%
  5. One could also include the log-sum (V missing products)