Thursday, September 29, 2016

Can a Purely State Based Database Schema Migration Be Trusted? by Robert Lucente

A really good article on the tradeoffs between state based vs migration based schema transformation is titled Critiquing two different approaches to delivering databases: Migrations vs state by Alex Yates on 6/18/2015. The blog Database Schema Migration by S. Lott on 9/27/2016 ends with "It's all procedural migration. I'm not [sure] declarative ("state") tools can be trusted beyond discerning the changes and suggesting a possible migration."

Let me start by examining the statement of the problem: state based vs migration based schema transformation. The problem statement implies that the solution is an either or type of thing. Why not both?

As opposed to speaking in generalities, let me pick a specific problem which is often encountered in real systems which demonstrates the core issue. Also, let me pick a particular tool set to execute on this particular problem.

The specific problem involves
  1. Adding some domain table and its associated data.
    1. Adding a not null / mandatory column to some table that already has data.
      1. Creating a foreign key between the domain table and the new mandatory column.
        Below is a picture for the above words. The "stuff" in color are the tables and columns being added.


        In a migration based schema approach the following steps would have to be performed
        1. SomeTable exists with data.
          1. A new domain table (SomeDomain) gets created.
            1. The new domain table (SomeDomain) gets populated with data.
              1. A new nullable / not mandatory column SomeDomainUuid is added to SomeTable.
                1. Column SomeDomainUuid in SomeTable gets populated with data.
                  1. Column SomeDomainUuid in SomeTable is made not null / mandatory.
                    1. A foreign key is created between the two tables.
                      Notice that the above is very labor intensive and involves 7 steps. Software should be able to figure out all the steps and their sequences except for the following
                      1. The new domain table (SomeDomain) gets populated with data.
                        1. Column SomeDomainUuid in SomeTable gets populated with data.
                          The key thing to notice is that the steps that can't be automated involve data. There is no way for the software to know about the specifics of the data.
                            Now that we have defined a specific problem, let's execute on solving the problem using a specific tool set. I am going to use the Visual Studio SQL Server Database Project concept with SQL Server as the target database. Via a series of clicks, the end state of the database is specified in the "Visual Studio SQL Server Database Project".
                              Next we write a script (Populate_dbo_SomeDomain.sql) to populate SomeDomain table with data.
                              
                              
                              INSERT INTO dbo.SomeDomain
                                  VALUES 
                                  (newid(), 'Fred'), (newid(), 'Barney');
                              
                              
                              
                              The second step is to write a script (Update_dbo_Deal_AdvertiserTypeUuid.sql) to populate SomeDomainUuid column in SomeTable.
                              
                              
                              UPDATE [dbo].[SomeTabe] 
                              SET    [SomeDomainUuid] = (SELECT SomeDomainUuid
                                                        FROM   [dbo].[SomeDomain] 
                                                        WHERE  Name = 'Fred');
                              
                              
                              The last preparation step is to write a script (Script.PostDeployment.sql) to run the above 2 scripts after the state based change has happened.
                              
                              
                              :r ".\Populate_dbo_SomeDomain.sql"
                              go
                              
                              :r ".\Update_dbo_Deal_AdvertiserTypeUuid.sql"
                              go
                              
                              
                              
                              Now that the desired end state has been specified as well as the data manipulation scripts written, it is time to modify a database. The Microsoft terminology for this is "publishing the database project". There will be an issue because the state changes will be made and then the Script.PostDeployment.sql script will be run. In between the state changes and the script being run, there will need to be data in the SomeDomainUuid column in the table SomeTable. This issue is addressed by using the GenerateSmartDefaults option when publishing the database project.

                              Let's summarize what this combination of state based and migration based schema transformation has allowed us to do. We were able to take 7 steps and reduce it down to 2 steps. These 2 steps couldn't be automated anyways because they involved data. These are the pros. The con is that have to be familiar with the framework and select the GenerateSmartDefaults option out of the 60 plus available options.

                              In conclusion, a purely state based approach can't work because of data. There is no way for the software to know how to do data migrations. Only humans know the correct way to do data migrations. In our example, there is no way for the software to know whether or not the new column SomeDomainUuid is to be initially populated with "Fred" or "Barney". This is a long winded and nice way of saying that a purely state based database schema migration can't be trusted. However, the combination of state based and migration based can truly improve productivity.

                              Saturday, February 27, 2016

                              Gentle Introduction to Various Math Stuff

                              I recently attended a meetup in Pittsburgh titled Analytics of Social Progress: When Machine Learning meets Human Problems given by Amy Hepner. She did an outstanding job of introducing some math concepts very simply and intuitively. If you are interested in the slides showing how she did this, you can go to her web site by clicking here.

                              This got me thinking about how I could help others with simple and intuitive ways to explain math stuff. I get annoyed when people say "doubly differentiable" as opposed to no gaps and no kinks. What makes this difficult is that everyone is at a different level and so you won't be able to please most people. However, I figure, any help is better than no help at all.

                              As expected, there is already plenty of material on the internet. For statistics, a good place to start is "The Most Comprehensive Review of Comic Books Teaching Statistics by Rasmus Baath." A second good place to look is "A Brief Review of All Comic Books Teaching Statistics by Rasmus Baath and Christian Robert." For links to the book themselves, see the list below.
                              1. The Cartoon ...
                                1. The Cartoon Guide to Statistics by Larry Gonick, Woollcott Smith
                                2. The Cartoon Introduction to Statistics by Grady Kelin, Alan Dabney
                              2. Manga Guide to Statistics by Shin Takahashi
                              3. ... for Dummies
                                1. Biostatistics For Dummies by John Pezzullo
                                2. Business Statistics For Dummies by Alan Anderson
                                3. Predictive Analytics For Dummies by Anasse Bari
                                4. Probability For Dummies by Deborah J. Rumsey
                                5. Psychology Statistics For Dummies by Donncha Hanna
                                6. Statistical Analysis with Excel For Dummies by Joseph Schmuller
                                7. Statistics Essentials For Dummies by Deborah J. Rumsey
                                8. Statistics for Big Data For Dummies by Alan Anderson
                                9. Statistics For Dummies by Deborah J. Rumsey
                                10. Statistics II For Dummies by Deborah J. Rumsey
                                11. Statistics Workbook For Dummies by Deborah J. Rumsey
                                12. Statistics: 1,001 Practice Problems For Dummies (+ Free Online Practice) by Consumer Dummies
                               For other gentle introduction to other math stuff, you can check out the list below. People have complained that the list below is too long. My response is if you are not willing to spend 10 minutes to skim through the list, you are not ready to make the commitment to upgrade your math skills.
                              1. Algebra ...
                                1. Algebra I For Dummies by Mary Jane Sterling
                                2. Algebra I Essentials For Dummies by Mary Jane Sterling
                                3. Algebra I Workbook For Dummies by Mary Jane Sterling
                                4. Algebra II For Dummies by Mary Jane Sterling
                                5. Algebra II Workbook For Dummies by Mary Jane Sterling
                                6. Algebra II: 1,001 Practice Problems For Dummies (+ Free Online Practice) by Mary Jane Sterling
                              2. Basic Math and Pre-Algebra ...
                                1. Basic Math and Pre-Algebra For Dummies by Mark Zegarelli
                                2. Basic Math and Pre-Algebra: 1,001 Practice Problems For Dummies (+ Free Online Practice) by Mark Zegarelli
                              3. Calculus ...
                                1. Calculus For Dummies by Mark Ryan
                                2. Calculus II For Dummies by Mark Zegarelli
                                3. Calculus Essentials For Dummies by Mark Ryan
                                4. Calculus Workbook For Dummies by Mark Ryan
                                5. Calculus: 1,001 Practice Problems For Dummies (+ Free Online Practice) by Patrick Jones
                              4. Complete Idiot's Guide to Algebra Word Problems by Izolda Fotiyeva
                              5. Cartoon Guide ...
                                1. Cartoon Guide to Calculus by Larry Gonick
                                2. Cartoon Guide to Physics by Larry Gonick
                              6. Data ...
                                1. Data Mining For Dummies by Meta S. Brown
                                2. Data Science For Dummies by Lillian Pierson
                                3. Data Smart: Using Data Science to Transform Information into Insight by John W. Foreman
                              7. Differential Equations ...
                                1. Differential Equations For Dummies by Steven Holzner
                                2. Differential Equations Workbook For Dummies by Steven Holzner
                              8. Excel Data Analysis For Dummies by Stephen L. Nelson
                              9. Geometry ...
                                1. Geometry Essentials For Dummies by Mark Ryan
                                2. Geometry For Dummies by Mark Ryan
                                3. Geometry Workbook For Dummies by Mark Ryan
                                4. Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice) by Allen Ma
                              10. How to Solve Word Problems in Algebra by Mildred Johnson
                              11. Linear Algebra For Dummies by Mary Jane Sterling
                              12. Manga Guide to ...
                                1. Manga Guide to Calculus by Hiroyuki Kojima
                                2. Manga Guide to Linear Algebra by Shin Takahashi
                                3. Manga Guide to Physics by Hideo Nitta
                                4. Manga Guide to Regression Analysis Shin Takahashi
                                5. Manga Guide to Relativity by Hideo Nitta
                              13. Math Word Problems ...
                                1. Math Word Problems Demystified by Allan Bluman
                                2. Math Word Problems For Dummies by Mary Jane Sterling
                              14. Optimization Modeling with Spreadsheets by Kenneth R. Baker
                              15. Physics ...
                                1. Physics I For Dummies by Steven Holzner
                                2. Physics I Workbook For Dummies by Steven Holzner
                                3. Physics II For Dummies by Steven Holzner
                              16. Pre-Calculus ...
                                1. Pre-Calculus For Dummies by Yang Kuang
                                2. Pre-Calculus Workbook For Dummies by Yang Kuang
                                3. Pre-Calculus: 1,001 Practice Problems For Dummies (+ Free Online… by Mary Jane Sterling
                              17. Predictive Analytics For Dummies by Anasse Bari
                              18. R For Dummies by Andrie de Vries
                              19. Schaum's ...
                                1. Schaum's Outline of Introduction to Probability and Statistics by Seymour Lipschutz
                                2. Schaum's Outline of Probability by Seymour Lipschutz
                                3. Schaum's Outline of Probability and Statistics: 760 Solved Problems + 20 Videos by John Schiller
                                4. Schaum's Outline of Statistics by Murray Spiegel
                              20. Technical Math For Dummies by Barry Schoenborn
                              21. Trigonometry ...
                                1. Trigonometry For Dummies by Mary Jane Sterling
                                2. Trigonometry Workbook For Dummies by Mary Jane Sterling

                              Friday, August 7, 2015

                              Sunday, June 7, 2015

                              Quantifying the Efficacy of Machine Learning Algorithms

                              There are many articles and books and talks and so on all making claims about machine learning algorithms. Out of those, how many actually QUANTIFY THE EFFICACY OF THE ALGORITHM?.

                              Below are some references which will hopefully save people some leg work and help others quantify the performance of their algorithms.
                              1. Articles
                              2. Books
                                1. Assessing and Improving Prediction and Classification by Timothy Masters
                                2. Evaluating and Comparing the Performance of Machine Learning Algorithms by Melanie Mitchell
                                3. Evaluating Learning Algorithms: A Classification Perspective by Japkowicz, Shah
                                  1. Amazon
                                    1. Customer Reviews
                                      1. Howard B. Bandy on July 7, 2014
                                        1. ... examples presented are all of stationary data ...
                                    2. Cambridge.Org
                                      1. Looking for an examination copy?
                                        1. If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.
                                      2. Google
                                        1. Has table of contents and you can look at some randomly selected pages
                                        2. MohakShah.Com
                                          1. Email Address: eval@mohakshah.com
                                            1. For electronic editions, ...
                                              1. Computing Resources
                                          2. Evaluation and Analysis of Supervised Learning Algorithms and Classifiers by Niklas Lavesson
                                            1. Machine Learning and Data Mining: 14 Evaluation and Credibility by Pier Luca Lanzi

                                          Sunday, May 24, 2015

                                          Python Books / Videos on Algorithms and Math

                                          Below is a list of references on Python that are related to algorithms or mathematics. The hope is to save others some leg work. For a complete list of Python books and videos, click here.
                                          1. Algorithms & Data Structures in Python by S Jagannathan, N Sinenian
                                          2. Annotated Algorithms in Python by M Di Pierro
                                          3. Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference by C Davidson-Pilon
                                          4. Building Machine Learning Systems with Python by W Richert, L Pedro Coelho
                                          5. Building Probabilistic Graphical Models with Python by K R Karkera
                                          6. Computational Physics by M Newman
                                          7. Data Structure and Algorithmic Thinking with Python by N Karumanchi
                                          8. Data Structures and Algorithms Using Python by R D Necaise
                                          9. Data Structures and Algorithms: Using Python and C++ by D M Reed, J Zelle
                                          10. Data Structures and Algorithms in Python by M T Goodrich, R Tamassia, ...
                                          11. Data Structures and Algorithms with Python by K D Lee, S Hubbard
                                          12. Doing Math with Python by Amit Saha
                                          13. Equilibrium Statistical Physics: with Computer simulations in Python by Leonard M. Sander
                                          14. Image Processing and Acquisition using Python by R Chityala, S Pudipeddi
                                          15. Introduction to Machine Learning with Python by S Guido
                                          16. Introduction to Numerical Programming: A Practical Guide for Scientists and Engineers Using Python and C/C++ by T A Beu
                                          17. Learning scikit-learn: Machine Learning in Python by R Garreta, G Moncecchi
                                          18. Machine Learning in Python: Essential Techniques for Predictive Analysis by M Bowles
                                          19. Marketing Data Science: Modeling Techniques in Predictive Analytics with R and Python by T W Miller
                                          20. Mathematics and Python Programming by J C Bautista
                                          21. Mathematics for the Digital Age and Programming in Python by M Litvin, G Litvin
                                          22. Modeling Techniques in Predictive Analytics with Python and R by T W Miller
                                          23. Numerical Methods in Engineering with Python by J Kiusalaas
                                          24. OpenCV Computer Vision with Python by J Howse
                                          25. Parallel Programming with Python by J Palach
                                          26. Primer on Scientific Programming with Python by H P Langtangen
                                          27. Problem Solving with Algorithms and Data Structures Using Python by B N Miller, D L Ranum
                                            1. Edition: 2
                                          28. Programming and Mathematical Thinking: A Gentle Introduction to Discrete Math Featuring Python by A M Stavely
                                          29. Programming Computer Vision with Python: Tools and algorithms for analyzing images by J E Solem
                                          30. Python Algorithms: Mastering Basic Algorithms in the Python Language by M L Hetland
                                          31. Python for Signal Processing: Featuring IPython Notebooks by J Unpingco
                                          32. Python for Scientists by John M. Stewart
                                          33. Python Scripting for Computational Science by H P Langtangen
                                          34. Scientific Computation: Python Hacking for for Math Junkies by B E Shapiro
                                          35. Statistics, Data Mining, and Machine Learning in Astronomy by Z Ivezic, A Connolly, ...
                                          36. Think DSP - Digital Signal Processing in Python by A B Downey

                                          Saturday, May 16, 2015

                                          Regular Expressions

                                          Below is a list of references related to regular expressions. The hope is to save others some leg work.
                                          1. Books
                                            1. Automate the Boring Stuff with Python - Practical Programming for Total Beginners by Albert Sweigart
                                              1. O'Reilly
                                                1. Part II. Automating Tasks
                                                  1. Chapter 6: Pattern Matching with Regular Expressions
                                              2. Beginning Regular Expressions by Andrew Watt
                                              3. Introducing Regular Expressions - Unraveling regular expressions, step - by - step by Michael Fitzgerald
                                              4. Mastering Python Regular Expressions by Felix Lopez, Victor Romero
                                              5. Mastering Regular Expressions - Understand Your Data and Be More Productive by Jeffrey E.F. Friedl
                                                1. Edition: 3
                                              6. Oracle Regular Expressions Pocket Reference by Jonathan Gennick, Peter Linsley
                                              7. Regular Expression Pocket Reference - Regular Expressions for Perl, Ruby, PHP, Python, C, Java and .NET by Tony Stubblebine
                                                1. Edition: 2
                                              8. Regular Expressions Cookbook - Detailed Solutions in Eight Programming Languages by Jan Goyvaerts, Steven Levithan
                                                1. Edition: 1
                                                2. Edition: 2
                                            2. Videos
                                              1. Learning Regular Expressions by Mike McMillan
                                            3. RegExr.Com (GitHub.Com): An online, real-time regular expression sandbox tool that lets you visually tweak, undo, redo, save, and share directly in the browser by Grant Skinner (Twitter.Com).

                                            Saturday, May 9, 2015

                                            Newsvendor Problem / Newsboy Problem

                                            Below is a list of references related to newsvendor problem / newsboy problem. The hope is to save others some leg work.
                                            1. Books
                                              1. Building Intuition - Insights From Basic Operations Management Models and Principles Editors: Dilip Chhajed, Timothy J. Lowe (2008)
                                                1. Chapter 7: The Newsvendor Problem by Evan L. Porteus
                                                  1. Springer.Com
                                                  2. Handbook of Newsvendor Problems - Models, Extensions and Applications - Editors: Choi, Tsan-Ming (Jason) (Ed.) (2012)
                                                  3. Perishable Inventory Systems - Authors: Nahmias, Steven (2011)
                                                    1. The book’s ten chapters first cover the preliminaries of periodic review versus continuous review and look at a one-period newsvendor perishable inventory model.
                                                      1. Springer.Com
                                                      2. Inventory Management and Production Planning and Scheduling (1998)
                                                      3. Management Science: An Introduction to the Use of Decision Models by Kenneth R. Baker, Dean H. Kropp (1985)
                                                      4. Principles of Sequencing and Scheduling by Kenneth R. Baker, Dan Trietsch
                                                    2. Videos
                                                      1. Newsvendor Problem 1 by Piyush Shah (2014)
                                                    3. Articles
                                                      1. Analysis of the multi-product newsboy problem with a budget constraint by Layek L. Abdel-Malek, Roberto Montanari (2005)
                                                      2. Benchmark solution for the risk-averse newsvendor problem by Baruch Keren, Joseph S. Pliskin - European Journal of Operational Research (2006)
                                                      3. Binary solution method for the multi-product newsboy problem with budget constraint by Bin Zhang, Xiaoyan Xu, Zhongsheng Hua (2009)
                                                      4. Capacitated newsboy problem with random yield: The Gardener Problem by Layek Abdel-Malek, Roberto Montanari, Diego Meneghetti (2008)
                                                      5. Channel coordination in supply chains with agents having mean-variance objectives by Tsan-Ming Choi, Duan Li, Houmin Yan, Chun-Hung Chiu (2008)
                                                      6. Competitive multiple-product newsboy problem with partial product substitution by Di Huang, Hong Zhou, Qiu-Hong Zhao (2011)
                                                      7. Comprehensive Analysis of the Newsvendor - Model with Unreliable Supply by Yacine Rekik, Evren Sahin, Yves Dallery (2009)
                                                      8. Distribution-free newsboy problem with resalable returns by Julien Mostard, René de Koster, Ruud Teunterc (2005)
                                                      9. Distribution-free newsboy problem: Extensions to the shortage penalty case by Hesham K. Alfares, Hassan H. Elmorra (2005)
                                                      10. Encyclopedia of Operations Research and Management Science
                                                      11. Exact, approximate, and generic iterative models for the multi-product Newsboy problem with budget constraint by Layek Abdel-Malek, Roberto Montanari, Libia Cristina Morales (2004)
                                                      12. Extended newsboy problem with shortage-level constraints by M.S. Chen, C. C. Chuang (2000)
                                                      13. Fuzzy models for the newsboy problem by Dobrila Petrović, Radivoj Petrović, b, Mirko Vujošević (1996)
                                                      14. Fuzzy multi-product constraint newsboy problem by Zhen Shao, Xiaoyu Ji (2006)
                                                      15. Fuzzy newsvendor approach to supply chain coordination by Kwangyeol Ryu, Enver Yücesan (2010)
                                                      16. IE324 Simulation course - Newsvendor Problem by Kagan Gokbayrak
                                                        1. To go to the newsvendor spreadsheet, click here
                                                        2. Impact of loss aversion on the newsvendor game with product substitution by Wei Liu, Shiji Song, Cheng Wu (2013)
                                                        3. Loss-averse newsvendor game by Charles X. Wang - International Journal of Production Economics (2010)
                                                        4. Loss-averse newsvendor problem by Charles X. Wang, Scott Webster (2009)
                                                        5. Mean-Variance Newsvendor Model with a Background Risk by Jiang-feng Li, Qiong Wu (2015)
                                                          1. Springer.Com
                                                            1. This paper examines the effects of an additive background risk on the optimal order quantity of a risk-averse newsvendor with Mean-Variance utility.
                                                          2. Mean–variance analysis of the newsvendor model with stockout cost by Jun Wu, Jian Li, Shouyang Wang, T.C.E. Cheng (2009)
                                                          3. Model and algorithm for bilevel newsboy problem with fuzzy demands and discounts by Xiaoyu Ji, Zhen Shao (2006)
                                                          4. Multi-period newsboy problem by Keisuke Matsuyama - European Journal of Operational Research (2006)
                                                          5. Multi-product budget-constrained acquisition and pricing with uncertain demand and supplier quantity discounts by Jianmai Shi, Guoqing Zhang (2010)
                                                            1. ScienceDirect.Com
                                                              1. We consider the joint acquisition and pricing problem where the retailer sells multiple products with uncertain demands and the suppliers provide all unit quantity discounts. The problem is to determine the optimal acquisition quantities and selling prices so as to maximize the retailer’s expected profit, subject to a budget constraint. This is the first extension to consider supplier discounts in the constrained multi-product newsvendor pricing problem. We establish a mixed integer nonlinear programming (MINLP) model to formulate the problem, and develop a Lagrangian-based solution approach. Computational results for the test problems involving up to thousand products are reported, which show that the proposed approach can obtain high quality solutions in a very short time.
                                                            2. Multi-product constrained newsboy problem with progressive multiple discounts by Moutaz Khouja, Abraham Mehrez (1996)
                                                            3. Multi-product multi-constraint newsboy problem: Applications, formulation and solution by Hon-Shiang Lau, Amy Hing-Ling Lau (1995)
                                                            4. Multi-product newsboy problem with limited capacity and outsourcing by Bin Zhang, Shaofu Du (2010)
                                                            5. Multi-product newsboy problem with supplier quantity discounts and a budget constraint by Guoqing Zhang (2010)
                                                            6. Multi-product newsboy problem with two constraints by Layek L. Abdel-Malek, Roberto Montanari (2005)
                                                            7. Multi-stage newsboy problem: A dynamic model - Konstantin Kogan, Sheldon Lou (2003)
                                                            8. Multiple-item budget-constraint newsboy problem with a reservation policy by Liang-Hsuan Chen, Ying-Che Chen (2010)
                                                            9. Newsboy problem under progressive multiple discounts by Moutaz Khouja - European Journal of Operational Research (1995)
                                                            10. Newsboy problem with a simple reservation arrangement by Liang-Hsuan Chen, Ying-Che Chen (2009)
                                                            11. Newsboy problem with reactive production by Chia-Shin Chung, James Flynn (2001)
                                                            12. Newsboy problem with resalable returns: A single period model and case study by Julien Mostard, Ruud Teunter (2006)
                                                            13. Newsstand problem: A capacitated multiple-product single-period inventory problem by Hon-Shiang Lau, Amy Hing-Ling Lau (1996)
                                                            14. Newsvendor problem: Review and directions for future research by Yan Qin, Ruoxuan Wang, Asoo J. Vakharia, Yuwen Chen, Michelle M.H. Seref (2011)
                                                            15. Newsvendor Problems by Hayriye Ayhan, Jim Dai, Joe Wu (2003)
                                                            16. Newsvendor solutions via conditional value-at-risk minimization by Jun-ya Gotoh, , Yuichi Takano (2007)
                                                            17. Optimal feeding buffers for projects or batch supply chains by an exact generalization of the newsvendor model by Trietsch, Dan (2006)
                                                            18. Portfolio approach to multi-product newsboy problem with budget constraint by Bin Zhang, Zhongsheng Hua (2010)
                                                            19. Quadratic programming approach to the multi-product newsvendor problem with side constraints by Layek L. Abdel-Malek, Nathapol Areeratchakul (2007)
                                                            20. Reordering strategies for a newsboy - type product by Hon-Shiang Lau, Amy Hing-Ling Lau (1997)
                                                            21. Robust multi-item newsboy models with a budget constraint by George L Vairaktarakis (2000)
                                                            22. Simple formulas for the expected costs in the newsboy problem: An educational note by Hon-Shiang Lau (1997)
                                                            23. Single-item newsboy problem with dual performance measures and quantity discounts by Chen-Sin Lin, Dennis E. Kroll (1997)
                                                            24. Single-period (news-vendor) problem: literature review and suggestions for future research by Moutaz Khouja (1999)
                                                            25. Supply chain coordination with manufacturer's limited reserve capacity: An extended newsboy problem by Jianli Li, Liwen Liu (2008)
                                                            26. Two-item newsboy problem with substitutability by Moutaz Khouja, Abraham Mehrez, Gad Rabinowitz (1996)
                                                            27. Using separable programming to solve the multi-product multiple ex-ante constraint newsvendor problem and extensions by Julie A. Niederhoff (2007)
                                                            28. Wikipedia: Newsvendor model
                                                              1. Would a risk-averse newsvendor order less at a higher selling price? by Charles X. Wang, Scott Webster, Nallan C. Suresha (2009)