Stochastic Order Level Inventory Model with Inventory Returns and Special Salestheijes
This article deals with a single period inventory model with inventory returns and special sales. The demand is assumed to occur in a uniform pattern during a planning period say, tp. Both non-deteriorating items and deteriorating items are considered for the discussion
Application of Business Mathematics in real life (PPT)Emran Hosain
Business Mathematics is mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis.
The reference of this book is from Dominick Salvatore's Managerial Economics. It is in chapter 8 with the following topic: Linear Programming, Production process, Feasible region, Optimal solution, Objective function, Inequality constraints, Nonnegativity constraints, Decision variables, Binding constraints, Slack variable, Simplex method, Primal problem, Dual problem, Shadow price, Duality theorem and Logistic management.
Phương pháp chữa nói lắp toàn diện được Echo Việt nam www.echovietnam.org dịch từ quyển sách Comprehensive Stuttering Therapy và phát hành dưới sự cho phép của tác giả Phillip J. Roberts. Đây là một trong nhiều tài liệu miễn phí hỗ trợ cho người nói lắp Việt Nam. Mọi việc trích dẫn từ sách này phải ghi rõ xuất xứ của quyển sách. Mọi yêu cầu phát hành lại, in lại… phải được sự chấp thuận của Echo Việt Nam, đại diện là người sáng lập Trương Minh Sử Nhiên.
Tài liệu này tuyệt đối không được sử dụng với mục đích thương mại dưới mọi hình thức.
Đại diện, nhóm Echo Việt Nam, tôi xin chúc các bạn sớm thành công trong việc giao tiếp công chúng và đời thường. Thành công sẽ không là xa với nếu ai kiên trì tìm kiếm nó.
Tôi cũng xin gửi lời cảm ơn đến tác giả Phillip J. Roberts, đã cho phép, tôi, tổ chức Echo Việt nam được phép dịch và phát hành để phục vụ rộng rãi cho cộng đồng nói lắp Việt nam.
Sài Gòn, tháng 10 năm 2009
Người sáng lập Echo Việt nam
Trương Minh Sử Nhiên
tmsnhien@gmail.com
Stochastic Order Level Inventory Model with Inventory Returns and Special Salestheijes
This article deals with a single period inventory model with inventory returns and special sales. The demand is assumed to occur in a uniform pattern during a planning period say, tp. Both non-deteriorating items and deteriorating items are considered for the discussion
Application of Business Mathematics in real life (PPT)Emran Hosain
Business Mathematics is mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis.
The reference of this book is from Dominick Salvatore's Managerial Economics. It is in chapter 8 with the following topic: Linear Programming, Production process, Feasible region, Optimal solution, Objective function, Inequality constraints, Nonnegativity constraints, Decision variables, Binding constraints, Slack variable, Simplex method, Primal problem, Dual problem, Shadow price, Duality theorem and Logistic management.
Phương pháp chữa nói lắp toàn diện được Echo Việt nam www.echovietnam.org dịch từ quyển sách Comprehensive Stuttering Therapy và phát hành dưới sự cho phép của tác giả Phillip J. Roberts. Đây là một trong nhiều tài liệu miễn phí hỗ trợ cho người nói lắp Việt Nam. Mọi việc trích dẫn từ sách này phải ghi rõ xuất xứ của quyển sách. Mọi yêu cầu phát hành lại, in lại… phải được sự chấp thuận của Echo Việt Nam, đại diện là người sáng lập Trương Minh Sử Nhiên.
Tài liệu này tuyệt đối không được sử dụng với mục đích thương mại dưới mọi hình thức.
Đại diện, nhóm Echo Việt Nam, tôi xin chúc các bạn sớm thành công trong việc giao tiếp công chúng và đời thường. Thành công sẽ không là xa với nếu ai kiên trì tìm kiếm nó.
Tôi cũng xin gửi lời cảm ơn đến tác giả Phillip J. Roberts, đã cho phép, tôi, tổ chức Echo Việt nam được phép dịch và phát hành để phục vụ rộng rãi cho cộng đồng nói lắp Việt nam.
Sài Gòn, tháng 10 năm 2009
Người sáng lập Echo Việt nam
Trương Minh Sử Nhiên
tmsnhien@gmail.com
Phương pháp tự điều trị cho người nói lắp được Echo Việt nam www.echovietnam.org dịch từ quyển sách Self Therapy for stutterers của tác giả MALCOLM FRASER và phát hành dưới sự cho phép của tổ chức www.stutteringhelps.org. Đây là một trong nhiều tài liệu miễn phí hỗ trợ cho người nói lắp Việt Nam. Mọi việc trích dẫn từ sách này phải ghi rõ xuất xứ của quyển sách. Mọi yêu cầu phát hành lại, in lại… phải được sự chấp thuận của Echo Việt Nam, đại diện là người sáng lập Trương Minh Sử Nhiên.
Tài liệu này tuyệt đối không được sử dụng với mục đích thương mại dưới mọi hình thức.
Đại diện, nhóm Echo Việt Nam, tôi xin chúc các bạn sớm thành công trong việc giao tiếp công chúng và đời thường. Thành công sẽ không là xa với nếu ai kiên trì tìm kiếm nó.
Tôi cũng xin gửi lời cảm ơn đến tổ chức Stuttering Helps, đã cho phép, tôi, tổ chức Echo Việt nam được phép dịch và phát hành để phục vụ rộng rãi cho cộng đồng nói lắp Việt nam.
Sài Gòn, 22 tháng 10 năm 2010
Người sáng lập Echo Việt nam
Trương Minh Sử Nhiên
tmsnhien@gmail.com
Productivity and GDP per capita growth: A long-term perspective, Bergeaud, Ce...Soledad Zignago
Gilbert Cette's slides at the Secular Stagnation and Growth Measurement Conference, Banque de France, January 16, 2017, with Antonin Bergeaud & Remy Lecat https://www.banque-france.fr/stagnation-seculaire-et-mesure-de-la-croissance-conference-organisee-par-la-banque-de-france-et-le
13th Athens Big Data Meetup - 2nd Talk - Training Neural Networks With Enterp...Athens Big Data
Title: Training Neural Networks With Enterprise Relational Data
Speaker: Dr. Christos Malliopoulos (https://linkedin.com/in/cmalliopoulos//)
Date: Thursday, June 21, 2018
Event: https://meetup.com/Athens-Big-Data/events/251411957/
Heptagonal Fuzzy Numbers by Max Min MethodYogeshIJTSRD
In this paper, we propose another methodology for the arrangement of fuzzy transportation problem under a fuzzy environment in which transportation costs are taken as fuzzy Heptagonal numbers. The fuzzy numbers and fuzzy values are predominantly used in various fields. Here, we are converting fuzzy Heptagonal numbers into crisp value by using range technique and then solved by the MAX MIN method for the transportation problem. M. Revathi | K. Nithya "Heptagonal Fuzzy Numbers by Max-Min Method" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-3 , April 2021, URL: https://www.ijtsrd.com/papers/ijtsrd38280.pdf Paper URL: https://www.ijtsrd.com/mathemetics/applied-mathamatics/38280/heptagonal-fuzzy-numbers-by-maxmin-method/m-revathi
A Novel Forecasting Based on Automatic-optimized Fuzzy Time SeriesTELKOMNIKA JOURNAL
In this paper, we propose a new method for forecasting based on automatic-optimized fuzzy time
series to forecast Indonesia Inflation Rate (IIR). First, we propose the forecasting model of two-factor highorder
fuzzy-trend logical relationships groups (THFLGs) for predicting the IIR. Second, we propose the
interval optimization using automatic clustering and particle swarm optimization (ACPSO) to optimize the
interval of main factor IIR and secondary factor SF, where SF = {Customer Price Index (CPI), the Bank of
Indonesia (BI) Rate, Rupiah Indonesia /US Dollar (IDR/USD) Exchange rate, Money Supply}. The
proposed method gets lower root mean square error (RMSE) than previous methods.
Testing the Numerical Precisions Required to Execute Real World Programs ijseajournal
The IEEE 754 Standard for floating point number formats is over 30 years old. Computational
requirements have changed dramatically during these 30 years. This paper describes methods by which,
for a given program required to yield results of a given accuracy, one may determine:
1) whether the choices of numerical precision are adequate;
2) the minimum numerical precisions actually required;
3) the statements most vulnerable to loss of precision.
Precision is specified as an exact number of mantissa bits for each real kind.
The method is applied to two small Fortran simulation programs with surprising results. The implications
are that considerable savings could be made in computer hardware by computing with reduced precision,
and that speed improvements may be made on existing systems by packing data for inter-processor
communication, removing those parts of the bit patterns which are not needed.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
Grouping and Displaying Data to Convey Meaning: Tables & Graphs chapter_2 _fr...Prashant Borkar
This presentation is about Grouping and Displaying Data to Convey Meaning: Tables and Graphs
Contents were taken from Statistics for Management by Levin & Rubin.
Presentation includes,
How can we Arrange Data?
Raw Data
Arranging Data using Data Array & Frequency Distribution
Constructing a Frequency Distribution
Graphing Frequency Distributions
It also covers some solved examples of it.
Effects of dividends on common stock prices the nepalese evidencePankajKunwar3
presentation on effects of dividends on common stock prices in the nepelese evidence paper was was published by prof. rade shyam pradhan in the the excellence
Fin 351Project 2Derivation of the Efficient Frontier Part .docxmydrynan
Fin 351
Project 2
Derivation of the Efficient Frontier
Part 1
1. Log into WRDS (Wharton) database, using the following information:
Userid: sseechar
Pwd: Plza.123
a. Choose CRSP (Center for the Research of Security Prices) database
b. Choose North America
c. Choose Equities
d. Choose Monthly data files
2. Download data on monthly returns (choose Holding Period Return variable) for the most recent 5-year period on four companies (or mutual funds, ETFs, etc.) from CRSP database into the Excel file. Choose companies from unrelated industries. Use your common sense here. For example, computer hardware and software industries are closely related, but computer hardware and food industries are not. Make sure that your dates are consistent across all four stocks, i.e. you select returns for the same 5-year period.
You can download similar data from Bloomberg
3. Using commands in the Excel Functions menu (click on fx button), calculate expected monthly returns on all three stocks (use AVERAGE function), their variances (VAR function), standard deviations (STDEV function), arrange them into variance-covariance matrix.
The more efficient way to calculate the variance-covariance matrix is using cov-matrix.xlam application, posted on BB. You need to download this application onto your computer and then open it within your Excel program. Don’t forget to enable macros.
In this example, Variance-Covariance is a 4 by 4 table. Suppose that it is located in cells (C98:F101), that is rows 98 through 101, columns C through F. On the diagonal of this matrix are variance estimates, on off-diagonal are covariance terms (we will use these addresses later in mmult command).
4. Now find the correlation coefficient between each pair of companies (CORREL function). Arrange them into the 4 by 4
· Correlation matrix
5. Annualize expected returns, variances and covariances. It means you have to multiply monthly expected returns, variances and covariances by 12. We can do this because we assume markets to be efficient at least in a weak form. Market efficiency means that monthly returns are independent of each other; that is the correlation coefficient between returns in one month and returns in any other month is 0. The annual standard deviation is just the square root of the annual variance. The annual correlation coefficient is the same as the monthly correlation coefficient.
You can multiply the entire variance-covariance matrix by 12. Below is the link to the excellent tutorial on matrix manipulations in excel:
http://facweb.cs.depaul.edu/mobasher/classes/csc575/assignments/MatrixOperations-Excel2007.pdf
6. Report monthly and annual statistics, calculated in (3) -- (5). Present annualized variances and covariances in the variance-covariance.
Part 2
7. In the next four columns specify weights of the four stocks in your portfolio. Remember, that the weight of the forth stock in the portfolio can be expressed as w4 = 1- w1 – w2– w3. Alternatively, ...
Moment Preserving Approximation of Independent Components for the Reconstruct...rahulmonikasharma
The application of Independent Component Analysis (ICA) has found considerable success in problems where sets of observed time series may be considered as results of linearly mixed instantaneous source signals. The Independent Components (IC’s) or features can be used in the reconstruction of observed multivariate time seriesfollowing an optimal ordering process. For trend discovery and forecasting, the generated IC’s can be approximated for the purpose of noise removal and for the lossy compression of the signals.We propose a moment-preserving (MP) methodology for approximating IC’s for the reconstruction of multivariate time series.The methodologyis based on deriving the approximation in the signal domain while preserving a finite number of geometric moments in its Fourier domain.Experimental results are presented onthe approximation of both artificial time series and actual time series of currency exchange rates. Our results show that the moment-preserving (MP) approximations of time series are superior to other usual interpolation approximation methods, particularly when the signals contain significant noise components. The results also indicate that the present MP approximations have significantly higher reconstruction accuracy and can be used successfully for signal denoising while achieving in the same time high packing ratios. Moreover, we find that quite acceptable reconstructions of observed multivariate time series can be obtained with only the first few MP approximated IC’s.
Cracking the Workplace Discipline Code Main.pptxWorkforce Group
Cultivating and maintaining discipline within teams is a critical differentiator for successful organisations.
Forward-thinking leaders and business managers understand the impact that discipline has on organisational success. A disciplined workforce operates with clarity, focus, and a shared understanding of expectations, ultimately driving better results, optimising productivity, and facilitating seamless collaboration.
Although discipline is not a one-size-fits-all approach, it can help create a work environment that encourages personal growth and accountability rather than solely relying on punitive measures.
In this deck, you will learn the significance of workplace discipline for organisational success. You’ll also learn
• Four (4) workplace discipline methods you should consider
• The best and most practical approach to implementing workplace discipline.
• Three (3) key tips to maintain a disciplined workplace.
Attending a job Interview for B1 and B2 Englsih learnersErika906060
It is a sample of an interview for a business english class for pre-intermediate and intermediate english students with emphasis on the speking ability.
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What is the TDS Return Filing Due Date for FY 2024-25.pdfseoforlegalpillers
It is crucial for the taxpayers to understand about the TDS Return Filing Due Date, so that they can fulfill your TDS obligations efficiently. Taxpayers can avoid penalties by sticking to the deadlines and by accurate filing of TDS. Timely filing of TDS will make sure about the availability of tax credits. You can also seek the professional guidance of experts like Legal Pillers for timely filing of the TDS Return.
Improving profitability for small businessBen Wann
In this comprehensive presentation, we will explore strategies and practical tips for enhancing profitability in small businesses. Tailored to meet the unique challenges faced by small enterprises, this session covers various aspects that directly impact the bottom line. Attendees will learn how to optimize operational efficiency, manage expenses, and increase revenue through innovative marketing and customer engagement techniques.
3.0 Project 2_ Developing My Brand Identity Kit.pptxtanyjahb
A personal brand exploration presentation summarizes an individual's unique qualities and goals, covering strengths, values, passions, and target audience. It helps individuals understand what makes them stand out, their desired image, and how they aim to achieve it.
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
The world of search engine optimization (SEO) is buzzing with discussions after Google confirmed that around 2,500 leaked internal documents related to its Search feature are indeed authentic. The revelation has sparked significant concerns within the SEO community. The leaked documents were initially reported by SEO experts Rand Fishkin and Mike King, igniting widespread analysis and discourse. For More Info:- https://news.arihantwebtech.com/search-disrupted-googles-leaked-documents-rock-the-seo-world/
Memorandum Of Association Constitution of Company.pptseri bangash
www.seribangash.com
A Memorandum of Association (MOA) is a legal document that outlines the fundamental principles and objectives upon which a company operates. It serves as the company's charter or constitution and defines the scope of its activities. Here's a detailed note on the MOA:
Contents of Memorandum of Association:
Name Clause: This clause states the name of the company, which should end with words like "Limited" or "Ltd." for a public limited company and "Private Limited" or "Pvt. Ltd." for a private limited company.
https://seribangash.com/article-of-association-is-legal-doc-of-company/
Registered Office Clause: It specifies the location where the company's registered office is situated. This office is where all official communications and notices are sent.
Objective Clause: This clause delineates the main objectives for which the company is formed. It's important to define these objectives clearly, as the company cannot undertake activities beyond those mentioned in this clause.
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Liability Clause: It outlines the extent of liability of the company's members. In the case of companies limited by shares, the liability of members is limited to the amount unpaid on their shares. For companies limited by guarantee, members' liability is limited to the amount they undertake to contribute if the company is wound up.
https://seribangash.com/promotors-is-person-conceived-formation-company/
Capital Clause: This clause specifies the authorized capital of the company, i.e., the maximum amount of share capital the company is authorized to issue. It also mentions the division of this capital into shares and their respective nominal value.
Association Clause: It simply states that the subscribers wish to form a company and agree to become members of it, in accordance with the terms of the MOA.
Importance of Memorandum of Association:
Legal Requirement: The MOA is a legal requirement for the formation of a company. It must be filed with the Registrar of Companies during the incorporation process.
Constitutional Document: It serves as the company's constitutional document, defining its scope, powers, and limitations.
Protection of Members: It protects the interests of the company's members by clearly defining the objectives and limiting their liability.
External Communication: It provides clarity to external parties, such as investors, creditors, and regulatory authorities, regarding the company's objectives and powers.
https://seribangash.com/difference-public-and-private-company-law/
Binding Authority: The company and its members are bound by the provisions of the MOA. Any action taken beyond its scope may be considered ultra vires (beyond the powers) of the company and therefore void.
Amendment of MOA:
While the MOA lays down the company's fundamental principles, it is not entirely immutable. It can be amended, but only under specific circumstances and in compliance with legal procedures. Amendments typically require shareholder
Enterprise Excellence is Inclusive Excellence.pdfKaiNexus
Enterprise excellence and inclusive excellence are closely linked, and real-world challenges have shown that both are essential to the success of any organization. To achieve enterprise excellence, organizations must focus on improving their operations and processes while creating an inclusive environment that engages everyone. In this interactive session, the facilitator will highlight commonly established business practices and how they limit our ability to engage everyone every day. More importantly, though, participants will likely gain increased awareness of what we can do differently to maximize enterprise excellence through deliberate inclusion.
What is Enterprise Excellence?
Enterprise Excellence is a holistic approach that's aimed at achieving world-class performance across all aspects of the organization.
What might I learn?
A way to engage all in creating Inclusive Excellence. Lessons from the US military and their parallels to the story of Harry Potter. How belt systems and CI teams can destroy inclusive practices. How leadership language invites people to the party. There are three things leaders can do to engage everyone every day: maximizing psychological safety to create environments where folks learn, contribute, and challenge the status quo.
Who might benefit? Anyone and everyone leading folks from the shop floor to top floor.
Dr. William Harvey is a seasoned Operations Leader with extensive experience in chemical processing, manufacturing, and operations management. At Michelman, he currently oversees multiple sites, leading teams in strategic planning and coaching/practicing continuous improvement. William is set to start his eighth year of teaching at the University of Cincinnati where he teaches marketing, finance, and management. William holds various certifications in change management, quality, leadership, operational excellence, team building, and DiSC, among others.
RMD24 | Retail media: hoe zet je dit in als je geen AH of Unilever bent? Heid...BBPMedia1
Grote partijen zijn al een tijdje onderweg met retail media. Ondertussen worden in dit domein ook de kansen zichtbaar voor andere spelers in de markt. Maar met die kansen ontstaan ook vragen: Zelf retail media worden of erop adverteren? In welke fase van de funnel past het en hoe integreer je het in een mediaplan? Wat is nu precies het verschil met marketplaces en Programmatic ads? In dit half uur beslechten we de dilemma's en krijg je antwoorden op wanneer het voor jou tijd is om de volgende stap te zetten.
Explore our most comprehensive guide on lookback analysis at SafePaaS, covering access governance and how it can transform modern ERP audits. Browse now!
Premium MEAN Stack Development Solutions for Modern BusinessesSynapseIndia
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Personal Brand Statement:
As an Army veteran dedicated to lifelong learning, I bring a disciplined, strategic mindset to my pursuits. I am constantly expanding my knowledge to innovate and lead effectively. My journey is driven by a commitment to excellence, and to make a meaningful impact in the world.
Unveiling the Secrets How Does Generative AI Work.pdfSam H
At its core, generative artificial intelligence relies on the concept of generative models, which serve as engines that churn out entirely new data resembling their training data. It is like a sculptor who has studied so many forms found in nature and then uses this knowledge to create sculptures from his imagination that have never been seen before anywhere else. If taken to cyberspace, gans work almost the same way.
3. Outline Transitivity in multilateral comparisons Measuring TFP change using index numbers Conclusions 3 ECON377/477 Topic 5.3
4. Transitivity in multilateral comparisons The problem of deriving price and quantity index numbers over space at a given point of time arises when making output, input and productivity comparisons across a number of countries, regions, firms, plants, etc. We are typically interested in all pairs of comparisons, such as comparisons across all pairs of firms To derive an index, Iij, for a pair of firms (i,j) using a formula of our choice, we consider all pairs (i,j) with i,j = 1,2,...,I where I represents the total number of firms ECON377/477 Topic 5.3 4
5. Transitivity in multilateral comparisons Then we have a matrix of comparisons between all pairs of firms: This matrix represents all multilateral comparisons involving I firms that we would like to be internally consistent, i.e., to satisfy the property of transitivity ECON377/477 Topic 5.3 5
6. Transitivity in multilateral comparisons Internal consistency requires that a direct comparison between any two firms i and j, should be the same as a possible indirect comparison between i and j through a third firm k Thus, we require, for any i, j and k, For example, if a matrix of index numbers shows that firm i produces 10 per cent more than firm k and firm k produces 20 per cent more than firm j, then we should always find that firm i produces 32 per cent (1.1 1.2 = 1.32) more than firm j ECON377/477 Topic 5.3 6
7. Transitivity in multilateral comparisons None of the index number formulae satisfies the transitivity property, but the Fisher and Törnqvist indices do satisfy the time-reversal test: Ist = 1/Its A simple solution to obtain consistent multilateral comparisons between firms is to generate transitive indices from a set of non-transitive multilateral comparisons using the EKS method The EKS method is to derive multilateral Törnqvist indices that are transitive ECON377/477 Topic 5.3 7
8. Transitivity in multilateral comparisons We start with Törnqvist indices for all pairs i,j Then, for all firms i and j, we use the EKS method to convert the Törnqvist indices into multilateral (CCD) indices by calculating: These indices satisfy four properties: , for i,j = 1,2,...,I, are transitive The new indices deviate least from the original Törnqvist indices in a least-squares sense After Caves, Christensen and Diewert ECON377/477 Topic 5.3 8
9. Transitivity in multilateral comparisons If we focus on quantity indices based on the Törnqvist formula, the CCD index in log-change form can be shown to be equal to: where and ECON377/477 Topic 5.3 9
10. Transitivity in multilateral comparisons The formula on the previous slide has an intuitive interpretation: a comparison between two firms is obtained by first comparing each firm with the average firm and then comparing the differences in firm levels relative to the average firm ECON377/477 Topic 5.3 10
11. Transitivity in multilateral comparisons We now examine the main logic behind the CCD index Although equation (4.33) in CROB is the most popular form for a multilateral Törnqvist index, it is desirable to use the form in equation (4.32) as the root of the multilateral index Equation (4.32) provides an approach that can be applied to binary indices without detailed price and quantity data Suppose we have a matrix of binary Fisher or Törnqvist price and quantity indices ECON377/477 Topic 5.3 11
12. Transitivity in multilateral comparisons Even if data are not available, it is feasible to apply equation (4.32) to derive multilateral comparisons that are transitive But it is not obvious from equation (4.32) how this procedure can be applied if the preferred index formula is different from the Törnqvist index Suppose, we are working with Fisher index numbers for output index numbers between firms ECON377/477 Topic 5.3 12
13. Transitivity in multilateral comparisons Let QijFrepresent the Fisher index for firm i with firm j as base Obviously, the QijFs for i,j = 1,2,...,I do not satisfy transitivity But the EKS procedure in equation (4.32) can be applied to yield consistent indices as: The resulting quantity index numbers, QstF-EKS, satisfy the transitivity property ECON377/477 Topic 5.3 13
14. Transitivity in multilateral comparisons The condition of transitivity is an operational constraint preserving internal consistency The imposition of the transitivity condition implies that a quantity (or price) comparison between two firms, s and t, is influenced by price and quantity data for not just these two firms but all the other firms in the analysis Hence, the addition of an extra firm to the sample necessitates the recalculation of all indices ECON377/477 Topic 5.3 14
15.
16. a multilateral situation, where the TFP index is computed for several cross-sectional unitsECON377/477 Topic 5.3 15
17. TFP change measurement using index numbers: binary comparisons Consider first the Hicks-Moorsteen (HM) TFP index for two time periods (or enterprises), s and t The HM TFP index in its logarithmic form is We need to use one of the index number formulae to compute numerical values of this measure of TFP change ECON377/477 Topic 5.3 16
18. TFP change measurement using index numbers: binary comparisons The most obvious choice is to use the Fisher index or the Törnqvist index to compute the input and output indices from the observed price and quantity data on outputs and inputs Let qsand xs represent output and input quantities, and rsand ss represent the revenue shares of outputs and cost shares for inputs, respectively The Törnqvist index formula is commonly used to calculate output and input indices ECON377/477 Topic 5.3 17
19. TFP change measurement using index numbers: binary comparisons The Törnqvist TFP index is defined, in its logarithmic form, as where the first part of the right-hand side is the logarithmic form of the Törnqvist index applied to output data, and the second part is the input index, calculated using input quantities and the corresponding cost shares ECON377/477 Topic 5.3 18
20. TFP change measurement using index numbers: binary comparisons In many respects, the Fisher index is more intuitive than the Törnqvist index and, more importantly, it decomposes the value index exactly into price and quantity components The fact that it is in an additive format also makes the Fisher index more easily understood The Fisher TFP index is given by ECON377/477 Topic 5.3 19
21. TFP change measurement using index numbers: binary comparisons The Fisher and Törnqvist index numbers provide reasonable approximations to the true output and input quantity indices in most practical applications involving time-series data They yield very similar numerical values for the TFP index ECON377/477 Topic 5.3 20
22. TFP change measurement using index numbers: binary comparisons The Malmquist TFP index can be approximated, under a set of conditions, by the ratio of an output quantity index to an input quantity index, where both indices are computed using the Törnqvist formula Assume the Malmquist output distance functions for periods s and t have a translog functional form with identical second-order terms, and assume technical and allocative efficiency of the firm in the two periods ECON377/477 Topic 5.3 21
23. TFP change measurement using index numbers: binary comparisons The geometric average of the two output-based Malmquist TFP productivity indices is given by where ; t and s are the local returns-to-scale values at the observed input and output levels; and sns and snt are the shares of n-th input in total input cost ECON377/477 Topic 5.3 22
24. TFP change measurement using index numbers: binary comparisons Even when the exact nature of the output distance functions is unknown, we can define an exact measure of the geometric average of the Malmquist output-orientated productivity indices, based on the technologies of periods s and t If constant returns to scale prevail in both periods (t = s = 1), then ECON377/477 Topic 5.3 23
25. TFP change measurement using index numbers: binary comparisons Under decreasing returns to scale, using duality results and a profit-maximisation assumption, the returns-to-scale parameters can be measured using the observed price and quantity data as: In the case of increasing returns to scale, observed costs and revenues cannot be used to compute returns–to-scale parameters ECON377/477 Topic 5.3 24
26. TFP change measurement using index numbers: binary comparisons If the input use has not changed over the two periods, then returns-to-scale issues do not arise in productivity change calculations There is an economic-theoretic justification for using the standard measure of TFP, defined as a ratio of Törnqvist indices of output and inputs Such a justification holds when the underlying technologies exhibit constant returns to scale ECON377/477 Topic 5.3 25
27. TFP change measurement using index numbers: binary comparisons A final comment is needed to serve as a warning Where our data suggest that either the prices are not market prices or the behaviour of the firms is not optimal, use of the index number approach to TFP measurement may not be measuring the Malmquist TFP index Hence, no real economic-theoretic interpretation can be accorded to the input and output quantity index numbers ECON377/477 Topic 5.3 26
28. TFP change measurement using index numbers: multilateral comparisons In the case of productivity comparisons across a number of firms, it is necessary to impose the transitivity condition on the index numbers used In such cases, the TFP indices in the previous section should be computed using transitive EKS-type index numbers for measuring differences in the levels of inputs and outputs across firms ECON377/477 Topic 5.3 27
29. TFP change measurement using index numbers: multilateral comparisons If the Hicks-Moorsteen approach is used, it is necessary first to generate transitive output and input quantity index numbers, based on the Fisher or Törnqvist indices, and then a ratio of the transitive indices be used to measure TFP change A similar approach needs to be adopted in the case of the Malmquist TFP index Routine application of the Törnqvist formulae to multilateral comparisons leads to the problem of transitivity ECON377/477 Topic 5.3 28
30. TFP change measurement using index numbers: multilateral comparisons The following index is derived by applying the EKS approach to obtain a transitive index (ln TFPst*) that is a multilateral generalisation of the Törnqvist index: ECON377/477 Topic 5.3 29
31. TFP change measurement using index numbers: multilateral comparisons In this index: is the arithmetic mean of the output shares is the arithmetic mean of the input shares = = All averages are taken over I enterprises or time periods or a combination of both ECON377/477 Topic 5.3 30
32. TFP change measurement using index numbers: multilateral comparisons We can define alternative TFP formulae by using transitive output and input indices in the general multilateral TFP index given by: It is feasible to use any output and input index numbers A suitable choice is the multilateral generalisation of the Fisher index derived using the EKS procedure ECON377/477 Topic 5.3 31
33. TFP change measurement using index numbers: numerical examples Refer to the Bus Company example in CROB (pages 124-127) and the empirical application to Australian National Railways (CROB, pages 128-131) These examples demonstrate that we can easily obtain Törnqvist and Fisher TFP indices These calculations could be performed using TFPIP Version 1.0, SHAZAM or spreadsheet software ECON377/477 Topic 5.3 32
34. Conclusions This topic covers the use of index number methods to compute various TFP change indices Using very limited data, we can compute various measures of TFP change and assess the underlying assumptions that make it possible Proper care should be taken in interpreting the resulting TFP measures If the assumptions do not hold, we can still compute the TFP index as a measure of TFP change but the interpretation is not straightforward ECON377/477 Topic 5.3 33
35. Conclusions In such cases, we need to find a way of computing all the distances involved in defining either the Malmquist TFP index or component-based measures of TFP change In both of these cases, we need data on a reasonable number of firms or cross-sections for the two periods under consideration, to use the techniques such as DEA or SFA The index number, DEA and SFA methods for measuring TFP change are compared in a later topic ECON377/477 Topic 5.3 34
36. Conclusions We have focused only on multiplicative index numbers, mainly due to the fact that all the efficiency and productivity measures are multiplicative In the recent years, there have been some applications of additive index numbers Additive index numbers have very interesting applications to the economic approach to decomposing profit change ECON377/477 Topic 5.3 35