OPTIMAL DESIGN OF A MULTITIER REWARD SCHEME. Amir Gandomi *, Saeed Zolfaghari **


 Lorena Walton
 1 years ago
 Views:
Transcription
1 OPTIMAL DESIGN OF A MULTITIER REWARD SCHEME Amir Gandomi *, Saeed Zolfaghari ** Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Ontario * Tel.: x7702, ** Tel.: x7735, Various forms of customer loyalty programs have been designed and adopted in real world markets. A principal element of the loyalty programs design is the reward structure. In this study, an optimization model is developed for a commonlyused yet underexplored type of reward structure known as the multitier reward scheme. Multitier reward schemes offer disproportionately higher rewards to more loyal customers. We study a threelevel tiered scheme. The design elements are breakpoints and the reward value at each tier. We model an asymmetric duopoly market where only one firm adopts the multitier loyalty scheme. Customer choice behavior is modeled using the binarylogit model. The utility components are the price, reward and the distance to a reward. The customers accumulated purchase through different periods turns out to form a Markov chain. The transition probabilities are obtained to formulate the firm s revenue function. The revenue function is maximized in terms of the loyalty program s design elements. The structural properties of the optimal solution yield useful insights into the profitability of multitier loyalty programs. Keywords: Marketing, Optimization, Loyalty Programs, Multitier reward, Stochastic Programming.. Introduction Because of the wellestablished link between customer loyalty and profitability (Reichheld & Teal, 200; Smith & Sparks, 2009), acquiring loyal customers is of growing importance. Loyalty programs are one of the marketing strategies to build and enhance customers' loyalty and thereby increase a firm's longterm profitability (Gandomi & Zolfaghari, 20). Since early 980 s, the contemporary forms of loyalty programs have increasingly grown in popularity and have expanded in various industries including airlines, credit card companies, retail and hotel chains (Kim, Shi, & Srinivasan, 200; Kumar, 2008). On the other end, consumers participation in such programs has considerably evolved during the past few years. The 20 COLLOQUY Loyalty Census reveals that the number of loyalty memberships in the US exceeds 2 billion, netting out to more than 8 memberships per household (COLLOQUY, 20). This indicates a 4.7% increase in memberships in the US since Given the ubiquity of loyalty programs in practice, academics have recently shown interest in the area. The approaches to research on loyalty programs can be classified into two broad categories. While some researchers use empirical methods to assess the effect of loyalty programs on customers buying behavior (Kivetz & Simonson, 2002; B. Sharp & A. Sharp, 997), some other adopt mathematical models to analyze the effects of loyalty programs on a firm s profitability and market conditions (e.g., Kim et al., 200; Singh, Jain, & Krishnan, 2008; Gandomi & Zolfaghari, 20). However, virtually all existing empirical and analytical studies on loyalty program have considered a particular reward structure known as the linear reward. Specifically, multitier reward scheme has remained understudied in the OR/marketing literature. Based on a multitier reward scheme, more loyal customers earn disproportionately higher rewards. That is, multitier schemes offer different rewards to different levels of loyalty. In other words, the reward per dollar spent is not fixed and depends on some measure of customers purchase history. Some examples of such reward systems are Microsoft s Xbox Live Reward in the US, Shopper s Optimum Card in Canada and British Airways Executive Club in the UK. 992
2 The reward structure, as one of the main components of a loyalty program s design (Kumar, 2006, p. 72), is a key driver of the loyalty program s effectiveness. Thus, the lack of research on multitier reward schemes is a significant gap in the loyalty programs literature. In this study, a mathematical model is developed to address part of this gap. Specifically, we develop a model to optimize the profitability of the commonlyseen 3level reward schemes where customers loyalty status is determined based on their accumulated purchase at the end of a selling cycle. The decision variables are the breakpoints and reward values at each tier. We model a duopoly market where only one firm offers loyalty discounts. Customers choose one of the firms and buy one unit of the product in each period. Their choice behavior is modeled using binarylogit model where the utility is a function of the offered price, the reward value and the distance to the reward. By including the distance component in the utility, we address the fact that customers accelerate their purchasing process as they progress toward earning a particular reward (Kivetz, Urminsky, & Zheng, 2006). It will be shown that the customers accumulated purchase evolves as a Markov chain. The transition probabilities of the Markov chain are obtained in terms of the decision variables and are used to formulate the firm s expected revenue function. The revenue function is optimized in terms of the reward scheme s design elements. The optimal solution yields some useful insights into the profitability of multitier reward systems. The rest of the paper is organized as follows: section 2 describes the underlying assumptions and the model formulation. Section 3 presents some sample results derived from the model. We conclude in section 4 with a summary and the future directions. 2. The model formulation The market is served by two firms where only one firm offer loyalty rewards (Firm A). Firms sell the same good/service through the selling cycle which is divided into 4 discrete time periods. The market size is normalized to one and remains constant across periods. Suppose that both Firm A and Firm B offer the same price,, throughout the selling horizon. is incorporated as a parameter in the model. Firm adopts a threetier reward scheme. Customers progress through reward tiers based on their accumulated purchase at Firm. The reward is determined based on a customer s loyalty status at the end of the selling horizon. Customers who make enough purchases to achieve Tier 2 status earn a reward of and those who make it to Tier 3 win a reward of. and are the breakpoints that specify the limits of each loyalty level. Customers whose total purchase exceeds earn the Tier 3 reward. Tier 2 status is granted to accumulated purchases falling in the range,. If the total purchase is less than, no loyalty reward is offered. Note that and are the monetary values of the breakpoints.,, and are incorporated as Firm s decision variables in the model. In each period, customers buy one unit of the product, either at Firm or at Firm. Here, the binarylogit model is employed to model customers choice behavior. First, let,,,,...,4, () be a customer s utility from buying at Firm in period. is the marginal sensitivity of the utility to the price level and, is the random component of the utility which captures the heterogeneity in customers preferences. Similarly, we can formulate customers utility from buying at Firm. As mentioned earlier, we assume that each individual s utility depends on two additional factors: the reward level in the next tier and the 993
3 distance to the next tier. The values of both factors in a period depend on a customer s accumulated purchase up until the previous period. Let represent the reward value in the next loyalty tier. Based on Firm s reward scheme described earlier, it follows that:,,,4, (2), where denotes the total money spent by the customer at Firm up to period. We assume that 0, that is, customers initiate accumulating points at the beginning of the selling horizon. Moreover, let denote the distance to the next loyalty level. can be written as a function of as follows:,,,...,4. (3) 0, Having defined and, we can now formulate the net utility derived from making a purchase at Firm in period,,, as follows:,,,,...,4. (4) In the above equation, and denote the utility sensitivity to the price and to the distance from the next reward, respectively and, is the random disturbance term. In every period, customers choose between Firm and Firm. Intuitively, a customer chooses Firm over Firm in period if,,. Hence, the probability that the customer buys at Firm in period,,, is given by,,,,,,,...,4. (5) Now, we adopt the commonly used assumption that, and,,...,4) are i.i.d random variables and,,,...,4) has a logistic distribution with mean zero and scale parameter (BenAkiva & Lerman, 985, p. 07). Let. denote the CDF of the distribution. From Equation (5), it follows that,,,...,4. (6) Note that and are piecewise functions and depend upon, the customer s accumulated purchase in period. To formulate Firm s expected revenue function, we need to derive the probability distribution of the accumulated purchase at the end of the selling horizon. That is, we must find Pr for any 0,,4. It can be shown that,..,4 satisfies the conditional independence property and hence evolves according to a Markov chain. For notational simplicity, let,, 4 represent a customer s total number of purchases at Firm up to period. Clearly,,..,4 is also a Markov chain with the state space Ω0,,2,3, 4. Let be the transition probability matrix whose, element is, Pr,,,4, and 0,,4. (7) In other words,, is the probability that a customer s total number of purchases at Firm reaches given that he/she has bought units of the product at Firm up to the previous period. Considering the fact that each customer buys exactly one unit of the product in each period either at Firm or at Firm,, in the above equation can be expressed as 994
4 ,,,,, 0, 0,,4, (8) where, can be derived based on equations (2), (3) and (6) as,,,, 0,,4. (9) Now, Pr can be found using the 4step transition probability matrix of,. To simplify the notation, let,,,,5, (0) be a vector containing the elements of the first row of. Thus, the entry of represents the probability that a customer buys products over the entire selling cycle. Having found the total purchase probabilities, now we can formulate Firm s expected revenue function,, as follows:, () where denotes the expected cost of reward that Firm incurs during the selling horizon. Based on Firm A s reward structure, it can be shown that where. (2) :, 0,,4 and :, 0,,4. (3) Thus, the revenue function in Equation () can be rewritten as. (4) The purpose is to study the structural properties of Firm s optimal reward scheme. Thus, one can optimize Firm s revenue function,, in terms of,, and. Note that depends also on the model parameters (i.e.,, and ). So, the optimal solution will depend on parameter values. For analytical convenience, we normalize the price to and change and correspondingly, so that the choice probabilities remain the same. Subsequently, after obtaining the optimal solution, the values of decision variables and revenue functions must be scaled back with the same factor. The optimization model can be written as follows: 995
5 , (5),,, subject to:, (5a) 2, (5b), (5c) 0, (5d) 0, (5e), (5f), (5g),,, 0. (5h) The first two constraints state that at least two purchases are needed to achieve the second tier and minimum three purchases are required to earn the Tier3 loyalty status. Constraint (5c) guarantees that the reward will not exceed the offered price in any period. Constraints (5d) and (5e) ensure that the net utility that loyalty program creates is nonnegative. Constraints (5f) and (5g) refer to the fact that under optimal conditions, the value of the next reward must be less than or equal to the amount of money a customer must pay to gain it. In other words, the distance to the next reward must be less than the reward itself. Otherwise, a customer may basically earn money by making an additional purchase. Thus, without these two constraints, the assumption that customers make only one purchase in each period becomes implausible. 3. Sample results It can be shown that the above model is a nonconvex NLP. One can employ the interiorpoint algorithm proposed by Byrd, Gilbert, & Nocedal (2000) to find the optimal solution. Various analyses can be performed using the developed model. For instance, Figure () presents the effects of and on the optimal breakpoint values. As can be seen, and both increase with and decrease with. That is, as the sensitivity to distance from a reward increases, the firm is better off to set higher requirements for both Tier 2 and Tier 3 loyalty levels. On the other hand, as the customer s sensitivity to price increases, the optimal breakpoints decrease Figure. Optimal values of and under different levels of and 996
6 4. Conclusion In this paper, an analytical model was developed to optimize the structure of a 3tier loyalty reward scheme. The decision variables were the breakpoints and reward values of each tier. The purpose was to optimize the total revenue function. The formulation resulted in a nonlinear programming. The optimal solution of the model was found at some arbitrary values of and, the utility sensitivity coefficients. The results can be used to perform various analyses. For example, it is useful to study the effects of and on the optimal values of reward at each tier and each firm s overall profitability. Moreover, we can assume that Firm offers a lower price and then compare the effectiveness of loyalty programs with that of the lower price strategy. In our model, the selling cycle was broken into 4 discrete time periods. One can extend the model to a more general case where the cycle is divided into periods. The model can also be expanded by removing the assumption that the offered price is constant across periods. In fact, this assumption was made to ensure that customers accumulated purchases follow the Markov chain. The stochastic dynamic programming approach can be used to formulate and optimize the revenue function under the variable price assumption. Finally, one can incorporate the offered prices of each firm as decision variables and study the equilibrium conditions using game theoretic models. References BenAkiva, M., & Lerman, S. R. (985). Discrete choice analysis: Theory and application to travel demand (st ed.). The MIT Press. Byrd, R. H., Gilbert, J. C., & Nocedal, J. (2000). A trust region method based on interior point techniques for nonlinear programming. Mathematical Programming, 89(), COLLOQUY. (20, April). The billion member march: The 20 COLLOQUY loyalty census. Retrieved July 5, 20, from Paper.pdf Gandomi, A., & Zolfaghari, S. (20). A stochastic model on the profitability of loyalty programs. Computers & Industrial Engineering, In Press, Corrected Proof. Kim, B., Shi, M., & Srinivasan, K. (200). Reward programs and tacit collusion. Marketing Science, 20(2), Kivetz, R., & Simonson, I. (2002). Earning the right to indulge: Effort as a determinant of customer preferences toward frequency program rewards. Journal of Marketing Research, 39(2), Kivetz, R., Urminsky, O., & Zheng, Y. (2006). The goalgradient hypothesis resurrected: Purchase acceleration, illusionary goal progress, and customer retention. Journal of Marketing Research, 43(), Kumar, V. (2006). Customer relationship management: A database approach. Hoboken, N.J: John Wiley & Sons. Kumar, V. (2008). Managing customers for profit: Strategies to increase profits and build loyalty. Indianapolis, IN: Wharton School Publishing. Reichheld, F. F., & Teal, T. (200). The loyalty effect: the hidden force behind growth, profits, and lasting value. Boston, MA: Harvard Business Press. Sharp, B., & Sharp, A. (997). Loyalty programs and their impact on repeatpurchase loyalty patterns. International Journal of Research in Marketing, 4(5), Singh, S. S., Jain, D. C., & Krishnan, T. V. (2008). Customer loyalty programs: are they profitable? Management Science, 54(6), Smith, A., & Sparks, L. (2009). It s nice to get a wee treat if you ve had a bad week : Consumer motivations in retail loyalty scheme points redemption. Journal of Business Research, 62(5),
Sharing Online Advertising Revenue with Consumers
Sharing Online Advertising Revenue with Consumers Yiling Chen 2,, Arpita Ghosh 1, Preston McAfee 1, and David Pennock 1 1 Yahoo! Research. Email: arpita, mcafee, pennockd@yahooinc.com 2 Harvard University.
More informationA Production Planning Problem
A Production Planning Problem Suppose a production manager is responsible for scheduling the monthly production levels of a certain product for a planning horizon of twelve months. For planning purposes,
More informationSharing Online Advertising Revenue with Consumers
Sharing Online Advertising Revenue with Consumers Yiling Chen 2,, Arpita Ghosh 1, Preston McAfee 1, and David Pennock 1 1 Yahoo! Research. Email: arpita, mcafee, pennockd@yahooinc.com 2 Harvard University.
More informationSoftware Antipiracy and Pricing in a Competitive Environment: a Game Theoretic Analysis
Software Antipiracy and Pricing in a Competitive Environment: a Game Theoretic Analysis We study a problem of two software firms competing on price in a market where consumers can choose between purchasing
More informationOPTIMIZATION AND OPERATIONS RESEARCH Vol. IV  Markov Decision Processes  Ulrich Rieder
MARKOV DECISIO PROCESSES Ulrich Rieder University of Ulm, Germany Keywords: Markov decision problem, stochastic dynamic program, total reward criteria, average reward, optimal policy, optimality equation,
More informationA PREDICTIVE MODEL OF REDEMPTION AND LIABILITY IN LOYALTY REWARD PROGRAMS INDUSTRY
Proceedings of the rd Hawaii International Conference on System Sciences  00 A PREDICTIVE MODEL OF REDEMPTION AND LIABILITY IN LOYALTY REWARD PROGRAMS INDUSTRY Aaron Luntala NSAKANDA Sprott School of
More informationInflation. Chapter 8. 8.1 Money Supply and Demand
Chapter 8 Inflation This chapter examines the causes and consequences of inflation. Sections 8.1 and 8.2 relate inflation to money supply and demand. Although the presentation differs somewhat from that
More informationComputing Near Optimal Strategies for Stochastic Investment Planning Problems
Computing Near Optimal Strategies for Stochastic Investment Planning Problems Milos Hauskrecfat 1, Gopal Pandurangan 1,2 and Eli Upfal 1,2 Computer Science Department, Box 1910 Brown University Providence,
More informationWhy do merchants accept payment cards?
Why do merchants accept payment cards? Julian Wright National University of Singapore Abstract This note explains why merchants accept expensive payment cards when merchants are Cournot competitors. The
More informationPrice Discrimination: Part 2. Sotiris Georganas
Price Discrimination: Part 2 Sotiris Georganas 1 More pricing techniques We will look at some further pricing techniques... 1. Nonlinear pricing (2nd degree price discrimination) 2. Bundling 2 Nonlinear
More informationMODELING CUSTOMER RELATIONSHIPS AS MARKOV CHAINS. Journal of Interactive Marketing, 14(2), Spring 2000, 4355
MODELING CUSTOMER RELATIONSHIPS AS MARKOV CHAINS Phillip E. Pfeifer and Robert L. Carraway Darden School of Business 100 Darden Boulevard Charlottesville, VA 22903 Journal of Interactive Marketing, 14(2),
More informationPAST PRESENT FUTURE YoU can T TEll where ThEY RE going if YoU don T know where ThEY ve been.
PAST PRESENT FUTURE You can t tell where they re going if you don t know where they ve been. L everage the power of millions of customer transactions to maximize your share of customer travel spend. Vistrio
More informationMathematics of Risk. Introduction. Case Study #1 Personal Auto Insurance Pricing. Mathematical Concepts Illustrated. Background
Mathematics of Risk Introduction There are many mechanisms that individuals and organizations use to protect themselves against the risk of financial loss. Government organizations and public and private
More informationOptimal proportional reinsurance and dividend payout for insurance companies with switching reserves
Optimal proportional reinsurance and dividend payout for insurance companies with switching reserves Abstract: This paper presents a model for an insurance company that controls its risk and dividend
More information1 Interest rates, and riskfree investments
Interest rates, and riskfree investments Copyright c 2005 by Karl Sigman. Interest and compounded interest Suppose that you place x 0 ($) in an account that offers a fixed (never to change over time)
More informationSPARE PARTS INVENTORY SYSTEMS UNDER AN INCREASING FAILURE RATE DEMAND INTERVAL DISTRIBUTION
SPARE PARS INVENORY SYSEMS UNDER AN INCREASING FAILURE RAE DEMAND INERVAL DISRIBUION Safa Saidane 1, M. Zied Babai 2, M. Salah Aguir 3, Ouajdi Korbaa 4 1 National School of Computer Sciences (unisia),
More information1 Portfolio mean and variance
Copyright c 2005 by Karl Sigman Portfolio mean and variance Here we study the performance of a oneperiod investment X 0 > 0 (dollars) shared among several different assets. Our criterion for measuring
More informationBasic Quantitative Analysis for Marketing
Harvard Business School 584149 Rev. September 29, 1986 Basic Quantitative Analysis for Marketing Simple calculations often help in making quality marketing decisions. To do good numbers work, one needs
More informationA simple analysis of the TV game WHO WANTS TO BE A MILLIONAIRE? R
A simple analysis of the TV game WHO WANTS TO BE A MILLIONAIRE? R Federico Perea Justo Puerto MaMaEuSch Management Mathematics for European Schools 94342  CP  12001  DE  COMENIUS  C21 University
More informationA Model of Optimum Tariff in Vehicle Fleet Insurance
A Model of Optimum Tariff in Vehicle Fleet Insurance. Bouhetala and F.Belhia and R.Salmi Statistics and Probability Department Bp, 3, ElAlia, USTHB, BabEzzouar, Alger Algeria. Summary: An approach about
More information5Step Guide To Successful Loyalty Programs. Combining Technology And Service To Bridge The Loyalty Gap
5Step Guide To Successful Loyalty Programs Combining Technology And Service To Bridge The Loyalty Gap % Contents Introduction... 3 Define a Loyalty Customer Base via Data Collection and Analysis.. 5 Create
More informationExam Introduction Mathematical Finance and Insurance
Exam Introduction Mathematical Finance and Insurance Date: January 8, 2013. Duration: 3 hours. This is a closedbook exam. The exam does not use scrap cards. Simple calculators are allowed. The questions
More informationPart Five. Cost Volume Profit Analysis
Part Five Cost Volume Profit Analysis COST VOLUME PROFIT ANALYSIS Study of the effects of changes of costs and volume on a company s profits A critical factor in management decisions Important in profit
More informationFinancial Markets. Itay Goldstein. Wharton School, University of Pennsylvania
Financial Markets Itay Goldstein Wharton School, University of Pennsylvania 1 Trading and Price Formation This line of the literature analyzes the formation of prices in financial markets in a setting
More informationCalculating Term Life Insurance Premiums
Calculating Term Life Insurance Premiums Jacquelyn Mott May 1, 2015 Quinnipiac University MA 490: Math Senior Seminar Professor Nelan The mortality rate for 30yearolds in the United States is 0.001,
More informationCostVolumeProfit Analysis
CostVolumeProfit Analysis Costvolumeprofit (CVP) analysis is used to determine how changes in costs and volume affect a company's operating income and net income. In performing this analysis, there
More informationOn the Interaction and Competition among Internet Service Providers
On the Interaction and Competition among Internet Service Providers Sam C.M. Lee John C.S. Lui + Abstract The current Internet architecture comprises of different privately owned Internet service providers
More informationPrice Dispersion. Ed Hopkins Economics University of Edinburgh Edinburgh EH8 9JY, UK. November, 2006. Abstract
Price Dispersion Ed Hopkins Economics University of Edinburgh Edinburgh EH8 9JY, UK November, 2006 Abstract A brief survey of the economics of price dispersion, written for the New Palgrave Dictionary
More informationMarkov chains and Markov Random Fields (MRFs)
Markov chains and Markov Random Fields (MRFs) 1 Why Markov Models We discuss Markov models now. This is the simplest statistical model in which we don t assume that all variables are independent; we assume
More information3.2 Roulette and Markov Chains
238 CHAPTER 3. DISCRETE DYNAMICAL SYSTEMS WITH MANY VARIABLES 3.2 Roulette and Markov Chains In this section we will be discussing an application of systems of recursion equations called Markov Chains.
More informationChapter 9 Experience rating
0 INTRODUCTION 1 Chapter 9 Experience rating 0 Introduction The rating process is the process of deciding on an appropriate level of premium for a particular class of insurance business. The contents of
More informationCredit Card Market Study Interim Report: Annex 5 Firm business model analysis
MS14/6.2: Annex 5 Market Study business model analysis November 2015 Introduction 1. This annex summarises issuers approach to evaluating profitability, as well as a summary of the role of affinity and
More informationRaising the Bar of Customer Loyalty Programs
Raising the Bar of Customer Loyalty Programs Identifying Your Best Customers and Driving Their Most Profitable Behavior by Carlos Dunlap, Vice President, Strategic Services, Maritz Loyalty Marketing A
More informationManaging Customer Retention
Customer Relationship Management  Managing Customer Retention CRM Seminar SS 04 Professor: Assistent: Handed in by: Dr. Andreas Meier Andreea Iona Eric Fehlmann Av. GénéralGuisan 46 1700 Fribourg eric.fehlmann@unifr.ch
More informationPROFITABLE CUSTOMER ENGAGEMENT Concepts, Metrics & Strategies
PROFITABLE CUSTOMER ENGAGEMENT Concepts, Metrics & Strategies V. Kumar Dr V.Kumar Chapter 4 Valuing customer contributions The future looks green!!! Instructor s Presentation Slides 2 Traditional measures
More informationWe hope you will find this sample a useful supplement to your existing educational materials, and we look forward to receiving your comments.
To Teachers of Mathematics: Thank you for visiting the BeAnActuary.org booth at the annual meeting of the National Council of Teachers of Mathematics. BeAnActuary.org is sponsored by the Joint Career Encouragement
More informationChapter. CostVolumeProfit Relationships
Chapter 6 CostVolumeProfit Relationships 62 LEARNING OBJECTIVES After studying this chapter, you should be able to: 1. Explain how changes in activity affect contribution margin. 2. Compute the contribution
More informationMATHEMATICS OF FINANCE AND INVESTMENT
MATHEMATICS OF FINANCE AND INVESTMENT G. I. FALIN Department of Probability Theory Faculty of Mechanics & Mathematics Moscow State Lomonosov University Moscow 119992 g.falin@mail.ru 2 G.I.Falin. Mathematics
More informationMerchandise Accounts. Chapter 7  Unit 14
Merchandise Accounts Chapter 7  Unit 14 Merchandising... Merchandising... There are many types of companies out there Merchandising... There are many types of companies out there Service company  sells
More informationWhy is Insurance Good? An Example Jon Bakija, Williams College (Revised October 2013)
Why is Insurance Good? An Example Jon Bakija, Williams College (Revised October 2013) Introduction The United States government is, to a rough approximation, an insurance company with an army. 1 That is
More informationEquilibrium: Illustrations
Draft chapter from An introduction to game theory by Martin J. Osborne. Version: 2002/7/23. Martin.Osborne@utoronto.ca http://www.economics.utoronto.ca/osborne Copyright 1995 2002 by Martin J. Osborne.
More informationChapter 7. Sealedbid Auctions
Chapter 7 Sealedbid Auctions An auction is a procedure used for selling and buying items by offering them up for bid. Auctions are often used to sell objects that have a variable price (for example oil)
More informationSinglePeriod Balancing of Pay PerClick and PayPerView Online Display Advertisements
SinglePeriod Balancing of Pay PerClick and PayPerView Online Display Advertisements Changhyun Kwon Department of Industrial and Systems Engineering University at Buffalo, the State University of New
More information1. (First passage/hitting times/gambler s ruin problem:) Suppose that X has a discrete state space and let i be a fixed state. Let
Copyright c 2009 by Karl Sigman 1 Stopping Times 1.1 Stopping Times: Definition Given a stochastic process X = {X n : n 0}, a random time τ is a discrete random variable on the same probability space as
More informationFinancial Reporting Update
Financial Reporting Update December 2007 Issue 38 KPMG IN HONG KONG HK(IFRIC) Interpretation 13, Customer loyalty programmes In this issue: Background and IFRIC's consensus 1 Application of HK(IFRIC) 13
More informationIntroduction to time series analysis
Introduction to time series analysis Margherita Gerolimetto November 3, 2010 1 What is a time series? A time series is a collection of observations ordered following a parameter that for us is time. Examples
More informationA Markov Chain Model Analysis of GSM Network Service Providers Marketing Mix
International Journal of Engineering & Technology IJETIJENS Vol: 11 No: 04 38 A Markov Chain Model Analysis of GSM Network Service Providers Marketing Mix Datong, G. Monday, School of Arts and Sciences,
More informationAnalysis of a Production/Inventory System with Multiple Retailers
Analysis of a Production/Inventory System with Multiple Retailers Ann M. Noblesse 1, Robert N. Boute 1,2, Marc R. Lambrecht 1, Benny Van Houdt 3 1 Research Center for Operations Management, University
More informationMoral Hazard. Itay Goldstein. Wharton School, University of Pennsylvania
Moral Hazard Itay Goldstein Wharton School, University of Pennsylvania 1 PrincipalAgent Problem Basic problem in corporate finance: separation of ownership and control: o The owners of the firm are typically
More informationAn Empirical Investigation of Customer Defection & Acquisition Rates for Declining and Growing Pharmaceutical Brands
An Empirical Investigation of Customer Defection & Acquisition Rates for Declining and Growing Pharmaceutical Brands Erica Riebe and Byron Sharp, University of South Australia Phil Stern, University of
More informationChapter 11 Pricing Strategies for Firms with Market Power
Managerial Economics & Business Strategy Chapter 11 Pricing Strategies for Firms with Market Power McGrawHill/Irwin Copyright 2010 by the McGrawHill Companies, Inc. All rights reserved. Overview I. Basic
More informationApplying CRM in Information Product Pricing
Applying CRM in Information Product Pricing Wenjing Shang, Hong Wu and Zhimin Ji School of Economics and Management, Beijing University of Posts and Telecommunications, Beijing100876, P.R. China shang_wj83@yahoo.com.cn
More informationA Case Study of ValueAdded Tax Issues on Customer Loyalty Programs in Korea
International Journal of Economics and Finance; Vol. 6, No. 6; 2014 ISSN 1916971X EISSN 19169728 Published by Canadian Center of Science and Education A Case Study of ValueAdded Tax Issues on Customer
More information17.6.1 Introduction to Auction Design
CS787: Advanced Algorithms Topic: Sponsored Search Auction Design Presenter(s): Nilay, Srikrishna, Taedong 17.6.1 Introduction to Auction Design The Internet, which started of as a research project in
More informationMONEY, INTEREST, REAL GDP, AND THE PRICE LEVEL*
Chapter 11 MONEY, INTEREST, REAL GDP, AND THE PRICE LEVEL* Key Concepts The Demand for Money Four factors influence the demand for money: The price level An increase in the price level increases the nominal
More informationMarket Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole
Market Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole Luís M. B. Cabral New York University and CEPR November 2005 1 Introduction Beginning with their seminal 2002 paper,
More informationBargaining Solutions in a Social Network
Bargaining Solutions in a Social Network Tanmoy Chakraborty and Michael Kearns Department of Computer and Information Science University of Pennsylvania Abstract. We study the concept of bargaining solutions,
More informationWhite Paper 7 Questions You Should Be Asking About Your Channel Sales Incentive/Loyalty Program, & The Platform & Services That Power It
7 Questions You Should Be Asking Sales Incentive/Loyalty A Compelling Case For Optimizing Your Solution Now A Compelling Case For Optimizing Your Solution Now Your current sales incentive and loyalty program
More informationTHIS IS NOT A REQUIRED READING. Chapter 11B. Nonlinear Pricing. 11B.2 Perfect price discrimination, revisited
THIS IS NOT A REQUIRED READING. Chapter 11B Nonlinear Pricing 11B.1 Motivation and objectives In Chapter 11 we looked at sophisticated pricing strategies that implicitly differentiate among customers.
More information2 Applications to Business and Economics
2 Applications to Business and Economics APPLYING THE DEFINITE INTEGRAL 442 Chapter 6 Further Topics in Integration In Section 6.1, you saw that area can be expressed as the limit of a sum, then evaluated
More informationTwoState Option Pricing
Rendleman and Bartter [1] present a simple twostate model of option pricing. The states of the world evolve like the branches of a tree. Given the current state, there are two possible states next period.
More informationSpreadsheets have become the principal software application for teaching decision models in most business
Vol. 8, No. 2, January 2008, pp. 89 95 issn 15320545 08 0802 0089 informs I N F O R M S Transactions on Education Teaching Note Some Practical Issues with Excel Solver: Lessons for Students and Instructors
More informationAccounting Building Business Skills. Learning Objectives: Learning Objectives: Paul D. Kimmel. Chapter Fourteen: Costvolumeprofit Relationships
Accounting Building Business Skills Paul D. Kimmel Chapter Fourteen: Costvolumeprofit Relationships PowerPoint presentation by Kate WynnWilliams University of Otago, Dunedin 2003 John Wiley & Sons Australia,
More informationORACLE LOYALTY ANALYTICS
ORACLE LOYALTY ANALYTICS KEY FEATURES & BENEFITS FOR BUSINESS USERS Increase customer retention and purchase frequency Determine key factors that drive loyalty and use that insight to increase overall
More informationResearch  Unley Business Loyalty Card Program. Author: Chris Williams Business & Economic Development July 2009
Research  Unley Business Loyalty Card Program Author: Chris Williams Business & Economic Development July 2009 Unley Loyalty Card Program Introduction 1 The Loyalty Concept 1 Rise of Loyalty Programs
More informationHedging. An Undergraduate Introduction to Financial Mathematics. J. Robert Buchanan. J. Robert Buchanan Hedging
Hedging An Undergraduate Introduction to Financial Mathematics J. Robert Buchanan 2010 Introduction Definition Hedging is the practice of making a portfolio of investments less sensitive to changes in
More informationA ProfitMaximizing Production Lot sizing Decision Model with Stochastic Demand
A ProfitMaximizing Production Lot sizing Decision Model with Stochastic Demand Kizito Paul Mubiru Department of Mechanical and Production Engineering Kyambogo University, Uganda Abstract  Demand uncertainty
More informationChapter 15 Introduction to Linear Programming
Chapter 15 Introduction to Linear Programming An Introduction to Optimization Spring, 2014 WeiTa Chu 1 Brief History of Linear Programming The goal of linear programming is to determine the values of
More informationExcess Volatility and ClosedEnd Fund Discounts
Excess Volatility and ClosedEnd Fund Discounts Michael Bleaney School of Economics University of Nottingham Nottingham NG7 RD, U.K. Tel. (+44) 115 951 5464 Fax (+44) 115 951 4159 email: michael.bleaney@nottingham.ac.uk
More informationFinancial ratio analysis
Financial ratio analysis A reading prepared by Pamela Peterson Drake O U T L I N E 1. Introduction 2. Liquidity ratios 3. Profitability ratios and activity ratios 4. Financial leverage ratios 5. Shareholder
More informationMODELING CUSTOMER RELATIONSHIPS AS MARKOV CHAINS
AS MARKOV CHAINS Phillip E. Pfeifer Robert L. Carraway f PHILLIP E. PFEIFER AND ROBERT L. CARRAWAY are with the Darden School of Business, Charlottesville, Virginia. INTRODUCTION The lifetime value of
More informationMarkov Chains, part I
Markov Chains, part I December 8, 2010 1 Introduction A Markov Chain is a sequence of random variables X 0, X 1,, where each X i S, such that P(X i+1 = s i+1 X i = s i, X i 1 = s i 1,, X 0 = s 0 ) = P(X
More informationReused Product Pricing and Stocking Decisions in ClosedLoop Supply Chain
Reused Product Pricing and Stocking Decisions in ClosedLoop Supply Chain Yuanjie He * California State Polytechnic University, Pomona, USA Abolhassan Halati California State Polytechnic University, Pomona,
More informationSimple Interest. and Simple Discount
CHAPTER 1 Simple Interest and Simple Discount Learning Objectives Money is invested or borrowed in thousands of transactions every day. When an investment is cashed in or when borrowed money is repaid,
More informationIJCHM 17,5. Anna S. Mattila Pennsylvania State University, University Park, Pennsylvania, USA
The Emerald Research Register for this journal is available at www.emeraldinsight.com/researchregister The current issue and full text archive of this journal is available at www.emeraldinsight.com/09596119.htm
More informationA System Dynamics Approach to Study the Sales Forecasting of Perishable Products in a Retail Supply Chain
A System Dynamics Approach to Study the Sales Forecasting of Perishable Products in a Retail Supply Chain Lewlyn L.R. Rodrigues 1, Tanuj Gupta 2, Zameel Akhtar K. 3, Sunith Hebbar 4 1,4 Department of Humanities
More informationP2 Performance Management
Performance Pillar P2 Performance Management Examiner s Answers SECTION A Answer to Question One (a) The optimum selling price occurs where marginal cost = marginal revenue. Marginal cost is assumed to
More informationThe Use of Matrix Algebra in the Simplification of Accounting Transactions Based on the Principle of Double Entry
Abstract The Use of Matrix Algebra in the Simplification of Accounting Transactions Based on the Principle of Double Entry Ajogbeje, Oke James Department of Mathematics, College of Education, Ikere Ekiti,
More informationBronze, Silver and Gold: Effective Membership Design in Customer Rewards Programs
Bronze, Silver and Gold: Effective Membership Design in Customer Rewards Programs Anders Hederstierna and Henrik Sällberg Blekinge Institute of Technology, Ronneby, Sweden anders.hederstierna@bth.se henrik.sallberg@bth.se
More informationCHAPTER 17. Linear Programming: Simplex Method
CHAPTER 17 Linear Programming: Simplex Method CONTENTS 17.1 AN ALGEBRAIC OVERVIEW OF THE SIMPLEX METHOD Algebraic Properties of the Simplex Method Determining a Basic Solution Basic Feasible Solution 17.2
More informationKEELE UNIVERSITY MIDTERM TEST, 2007 BA BUSINESS ECONOMICS BA FINANCE AND ECONOMICS BA MANAGEMENT SCIENCE ECO 20015 MANAGERIAL ECONOMICS II
KEELE UNIVERSITY MIDTERM TEST, 2007 Thursday 22nd NOVEMBER, 12.0512.55 BA BUSINESS ECONOMICS BA FINANCE AND ECONOMICS BA MANAGEMENT SCIENCE ECO 20015 MANAGERIAL ECONOMICS II Candidates should attempt
More informationMath 7 Elementary Linear Algebra MARKOV CHAINS. Definition of Experiment An experiment is an activity with a definite, observable outcome.
T. Henson I. Basic Concepts from Probability Examples of experiments: Math 7 Elementary Linear Algebra MARKOV CHAINS Definition of Experiment An experiment is an activity with a definite, observable outcome.
More informationRFM Analysis: The Key to Understanding Customer Buying Behavior
RFM Analysis: The Key to Understanding Customer Buying Behavior Can you identify your best customers? Do you know who your worst customers are? Do you know which customers you just lost, and which ones
More informationSIMULATING CANCELLATIONS AND OVERBOOKING IN YIELD MANAGEMENT
CHAPTER 8 SIMULATING CANCELLATIONS AND OVERBOOKING IN YIELD MANAGEMENT In YM, one of the major problems in maximizing revenue is the number of cancellations. In industries implementing YM this is very
More informationCost Accounting ACCT 362/562. Basic Cost Behavior. Why knowing about cost behavior is important
Cost Accounting ACCT 362/562 Basic Cost Behavior Cost behavior is a very important topic in cost and managerial accounting. What we are talking about is the amount spent in relation to some measure of
More informationPrinciples of demand management Airline yield management Determining the booking limits. » A simple problem» Stochastic gradients for general problems
Demand Management Principles of demand management Airline yield management Determining the booking limits» A simple problem» Stochastic gradients for general problems Principles of demand management Issues:»
More information1 (a) Calculation of net present value (NPV) Year 1 2 3 4 5 6 $000 $000 $000 $000 $000 $000 Sales revenue 1,600 1,600 1,600 1,600 1,600
Answers Fundamentals Level Skills Module, Paper F9 Financial Management December 2011 Answers 1 (a) Calculation of net present value (NPV) Year 1 2 3 4 5 6 $000 $000 $000 $000 $000 $000 Sales revenue 1,600
More informationFIN40008 FINANCIAL INSTRUMENTS SPRING 2008
FIN40008 FINANCIAL INSTRUMENTS SPRING 2008 Options These notes consider the way put and call options and the underlying can be combined to create hedges, spreads and combinations. We will consider the
More informationSteering Consumer Payment Choice
Steering Consumer Payment Choice Tamás Briglevics Federal Reserve Bank Boston and Boston College Oz Shy Federal Reserve Bank Boston May 16, 2012 Abstract Recent legislation and court settlements in the
More informationForeclosure, Entry, and Competition in Platform Markets with Cloud
Foreclosure, Entry, and Competition in Platform Markets with Cloud Mark J. Tremblay Department of Economics Michigan State University Email: trembl22@msu.edu August 27, 2015 Abstract Platforms in twosided
More informationBreakeven, Leverage, and Elasticity
Breakeven, Leverage, and Elasticity Dallas Brozik, Marshall University Breakeven Analysis Breakeven analysis is what management is all about. The idea is to compare where you are now to where you might
More informationRetirement Financial Planning: A State/Preference Approach. William F. Sharpe 1 February, 2006
Retirement Financial Planning: A State/Preference Approach William F. Sharpe 1 February, 2006 Introduction This paper provides a framework for analyzing a prototypical set of decisions concerning spending,
More informationLearning Objectives. Essential Concepts
Learning Objectives After reading Chapter 3 and working the problems for Chapter 3 in the textbook and in this Workbook, you should be able to: Employ marginal analysis to find the optimal levels of activities
More informationECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE
ECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE YUAN TIAN This synopsis is designed merely for keep a record of the materials covered in lectures. Please refer to your own lecture notes for all proofs.
More informationBINOMIAL OPTIONS PRICING MODEL. Mark Ioffe. Abstract
BINOMIAL OPTIONS PRICING MODEL Mark Ioffe Abstract Binomial option pricing model is a widespread numerical method of calculating price of American options. In terms of applied mathematics this is simple
More information1 Introduction. Linear Programming. Questions. A general optimization problem is of the form: choose x to. max f(x) subject to x S. where.
Introduction Linear Programming Neil Laws TT 00 A general optimization problem is of the form: choose x to maximise f(x) subject to x S where x = (x,..., x n ) T, f : R n R is the objective function, S
More informationWarranty Designs and Brand Reputation Analysis in a Duopoly
Warranty Designs and Brand Reputation Analysis in a Duopoly Kunpeng Li * Sam Houston State University, Huntsville, TX, U.S.A. Qin Geng Kutztown University of Pennsylvania, Kutztown, PA, U.S.A. Bin Shao
More informationCHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression
Opening Example CHAPTER 13 SIMPLE LINEAR REGREION SIMPLE LINEAR REGREION! Simple Regression! Linear Regression Simple Regression Definition A regression model is a mathematical equation that descries the
More informationSufficient Conditions for Monotone Value Functions in Multidimensional Markov Decision Processes: The Multiproduct Batch Dispatch Problem
Sufficient Conditions for Monotone Value Functions in Multidimensional Markov Decision Processes: The Multiproduct Batch Dispatch Problem Katerina Papadaki Warren B. Powell October 7, 2005 Abstract Structural
More informationA Simple Model of Price Dispersion *
Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute Working Paper No. 112 http://www.dallasfed.org/assets/documents/institute/wpapers/2012/0112.pdf A Simple Model of Price Dispersion
More information