Resource Allocation: Marketing Engineering Technical Note 1


 Leo McDaniel
 2 years ago
 Views:
Transcription
1 Resource Allocaton: Marketng Engneerng Techncal Note 1 Table of contents Introducton Response Functons Specfcaton and Calbraton Optmzng Resource Deployment Call Plannng for a Salesperson Resource Plannng for Sales Force Management Summary Responses Introducton A welldesgned resource allocaton model enables an understandng of the ndvdual and combned effects of marketng resources (or marketng mx elements) such as advertsng, sales effort, or prce, on a response measure of nterest to the company (e.g., sales, proft, customer acquston, ROI), and the capablty to apply ths understandng to dentfy good ways to expend those resources. Resource allocaton across the marketng mx elements ntegrates three modelng concepts: (1) sales response modelng, (2) Estmaton/calbraton of marketng response functons, and (3) optmzng the use of marketng resources to maxmze one or more desrable response measures. For purposes of ths note, we focus on resources that can be contnuously vared (e.g., advertsng expendture, sales effort, web ste nvestment), rather than on resources that can only be vared only n a dscrete manner (e.g., new copy desgn, ntroducton of a new product). Response Functons Specfcaton and Calbraton At the heart of a resource allocaton system are response functons that represent the relatonshps between one or more marketng mx elements and the correspondng outcome measure n each sales entty of nterest. A sales entty s anythng wth whch we can assocate potental sales for the frm customer, 1 Ths techncal note s a supplement to Chapter 7 of Prncples of Marketng Engneerng, by Gary L. Llen, Arvnd Rangaswamy, and Arnaud De Bruyn (2007). (All rghts reserved) Gary L. Llen, Arvnd Rangaswamy, and Arnaud De Bruyn. Not to be reproduced wthout permsson. Vst for addtonal nformaton. 1
2 prospect, market segment, geographc area, product sold by the frm, and so forth. If the frm estmates response functons for each such sales entty, t can use these functons to calculate the levels of effort to allocate to each entty to maxmze profts or to acheve other objectves. The sum of the effort across a set of nonoverlappng enttes s then the level of marketng effort or sales resources the frm needs. The frm can dvde ths total by the average effort (e.g., 750 sales calls per year) to estmate the amount of resources (e.g., salespeople) t needs. Specfcaton and calbraton of response models: There are many types of sales response functons used n marketng (see Response Modelng Marketng Engneerng Techncal Note) to model sales response n each sales entty. Typcally a nonlnear Sshaped response functon, such as the ADBUDG response model, s a good choce for representng marketng response to advertsng and sales effort. Before response models can be used for resource allocaton, they must be calbrated or estmated keepng n mnd the context n whch they are to be used. If, for example, the objectve s to determne the marketng budget for the sales force and the allocaton of the total sales force effort across products, then we need to estmate sales response functons that ndcate the future sales for each product under dfferent levels of effort the frm mght deploy on that product. There are broadly three approaches for estmatng response models: (1) statstcal estmaton usng hstorcal data of response behavor, (2) manageral judgment, and (3) expermentaton (more common among onlne frms). Often, a combnaton of methods (e.g., statstcal estmaton combned wth judgment) works best to account for both the endurng constrants of the marketplace, as well as the opportuntes afforded by the future. EXAMPLE: A common functonal form used n resource allocaton s the ADBUDG response model, whch has the followng functonal form: where c X r ( X ) = b + ( a b ), (1) c d + X =a sales entty, =1, 2, 3,..., I (# of sales enttes); 2
3 X =total effort devoted to sales entty durng a plannng perod measured n number of calls, ndexed so that current effort=1 (for smplcty we treat ths as a contnuously varyng quantty rather than as an nteger); r (X ) =ndexed level of sales at entty f the salesforce devotes X amount of effort to that entty; b a c d =mnmum sales that can be expected wth no sales effort allocated to sales entty ; =maxmum sales that can be expected wth an unlmted amount of sales effort allocated to sales entty ; =parameter that determnes the shape of r (X ) whether t s concave or Sshaped; and =an ndex of compettve effort levels drected toward sales entty (the larger ths value, the smaller the mpact of the frm s own sales effort on sales). On way to calbrate ths model s va nonlnear least squares regresson usng hstorcal data of both X and r(x) n each sales entty. Another approach s to use judgmental methods, whch nvolves askng experenced managers (e.g., from sales, marketng, or marketng research functons) what the response r(x) wll be for varous specfc levels of X. Often such calbraton s done wth reference to a base level of X=1, for whch response r(x) s 1, e.g., at current levels of effort, we expect to observe the current level of sales. Typcally, n judgmental calbraton, t s useful to obtan group consensus estmates for the response functons usng the Delph method (Armstrong 2001). Wth the Delph method, before askng for the judgmental estmates, t s useful to provde all the partcpants wth a summary of the hstorcal data pertanng to the entty for whch the sales response s to be obtaned. //end Example Optmzng Resource Deployment A response functon merely ndcates the response on an outcome measure that the frm s lkely to acheve at varous potental levels of effort deployment. By tself, t provdes no gudance on how much effort should be deployed to a 3
4 partcular entty. Typcally, a frm has many enttes competng for the same resource, and t has to evaluate alternatve ways of deployng the same resource across dfferent enttes. To do ths systematcally, we specfy an optmzaton model, whch allocates a resource across enttes to optmze a specfc objectve (e.g., shortterm proft, customer retenton). There are many dfferent types of optmzaton models used n marketng (e.g., lnear programs, nonlnear optmzaton, nteger programs, stochastc optmzaton, mult objectve optmzaton), each approprate n dfferent contexts. We llustrate resource optmzaton n the context of sales force effort allocaton n two dfferent contexts: (1) A sngle salesperson makng decsons about how much effort s/he should devote to each account (customer). (2) Company management decdng how bg a sales force t should have, and how t should deploy that total effort across products and markets. Call Plannng for a Salesperson CALLPLAN (Lodsh 1971, 1974) s an nteractve callplannng system that helps salespeople to determne how many calls to make to each clent and prospect (equvalently, to each category of clents and prospects) n a gven tme perod to maxmze the returns from ther calls. The system determnes call frequences wth respect to an effort perod, whch s the plannng perod used by the salesperson (e.g., one quarter). The model s based on the assumpton that the expected sales to each clent and prospect over a response perod, whch s the plannng perod of the frm (e.g., a year), s a functon of the average number of calls per effort perod durng that response perod. The response perod selected should be long enough to accommodate potental carryover effects from each effort perod. Specfyng the response functons: We wll use a smple verson of CALLPLAN based on the ADBUDG response functon to llustrate the central ssues. CALLPLAN tres to develop an effectve way for the salesperson to allocate effort across the dfferent accounts. The model assumes that the salespeople seek to maxmze contrbuton (profts) from ther sellng efforts; however, they have lmted tme and therefore they wsh to use ths resource as effectvely as possble. A sales terrtory s assumed to be dvded nto mutually exclusve geographc areas (e.g., zp codes). The salesperson makes trps to some or all areas n the terrtory n each effort perod. In each trp to an area the salesperson ncurs varable costs for expense tems such as travel and lodgng. 4
5 In a trp to an area, the salesperson calls on any gven account at most once. Before we descrbe the formal model, we defne ts parameters: n j = number of trps per effort perod to area j, where j=1, 2, 3,..., J. Because the salesperson calls on an account at most once durng a trp, n j s also equal to the maxmum number of calls made to any account n terrtory j; c j = varable costs ncurred when makng a trp to area j; t = tme that the salesperson spends wth the customer when makng a call to account (t may be set to be the same for all customers); U j = tme t takes to get to area j; e = number of effort perods n a response perod (f the effort perod s a month and the response perod s a year, then e=12); T = total work tme avalable to a salesperson n an effort perod, whch ncludes both sellng and nonsellng tmes; a = a customerspecfc proftadjustment factor that reflects the proft contrbuton of sales to that customer. r (X )= ADBUDG response model for each account (other concave or S shaped functons can also be used). The optmzaton model maxmzes profts (Z) for a sngle sales terrtory takng nto account both the costs of vstng the accounts and the expected contrbuton from all the accounts and prospects: Fnd the set of X to maxmze total proft contrbuton margn Z = a r ( X ) e n jc j, (2) subject to t + n ju j X T, (3) j n j = max( X n geographc area j), (4) LB X UB (5) j Constrant (3) ensures that the total tme (call tme plus travel tme) used n 5
6 an effort perod does not exceed the tme avalable to the salesperson; constrant (4) equates the number of trps to terrtory j to the maxmum number of calls made to any specfc account n that terrtory, thus ensurng that n any trp to terrtory j the salesperson does not call on any account more than once; constrant (5) allows the salesperson to ncorporate judgmentbased lower and upper bounds on the number of calls made to any account n an effort perod. Model usage: It s useful to frst run the model wth no upper bounds n constrant (5) and wth a lower bound of 0 for all. Then the model s lkely to suggest that the salesperson never call on some accounts and call on some accounts too often. The salesperson may feel that such an allocaton s not reasonable and can then specfy mnmum and maxmum constrants for each account to modfy these results. These judgments account for the effects of factors not explctly ncluded n the model. (For example, some accounts may be betatest stes that help wth testng a new product before release. However, sales effort on those accounts may not necessarly lead to ncreased sales.) A salesperson should nclude both accounts and prospects n a callng portfolo. However, prospects typcally respond weakly to sales efforts as compared wth exstng accounts; therefore the model wll tend to exclude them from the callng plans t develops. One way to gve adequate treatment to both s to run the model separately for accounts and for prospects: Run the analyss for prospects by settng asde tme equal to T P <T n constrant (3) to be allocated to prospects. Do the same for accounts by settng asde tme equal to T A for exstng accounts such that T A +T P =T, the total tme avalable to the salesperson. A comparson of the results wth and wthout tme set asde for prospects shows how much of the current proft the salesperson s wllng to forgo to cultvate longterm prospects. EXAMPLE To understand the ncremental analyss the CALLPLAN model uses to determne the optmal allocaton of effort, consder a smple example wth four accounts, summarzed n Exhbt 1. Suppose that the salesperson s currently devotng 15 calls to these accounts as shown, brngng n total sales of $11,985. If the cost of a sngle sales call s $200, the net contrbuton s then $8,985. 6
7 EXHIBIT 1 Example of optmzaton procedure n CALLPLAN. The table at the top s a numercal representaton of salesresponse functons n four accounts. The bar charts at the bottom show the current and modelrecommended allocaton of effort to the four accounts when the salesperson makes a total of 15 calls. An optmzaton procedure would allocate the frst call to account 3, whch has the hghest margnal contrbuton ($3,600). It wll also allocate the second call to ths account, whch has the next hghest margnal contrbuton ($1,800). The thrd to the ffth calls wll be allocated to account 2 wth a total contrbuton of $3,350, the sxth call to account 3, the seventh and eghth calls to account 2 wth a total contrbuton of $1,140, the nnth to twelfth calls to account 1 wth a total contrbuton of $1,400, the thrteenth to account 2, the fourteenth to account 1, and the ffteenth call to account 2. Ths allocaton procedure 7
8 results n total contrbutons of $13,000 wth a net contrbuton (after payng for the sales calls) of $10,000, whch represents a 11.3 percent mprovement over the current net contrbuton of these 15 calls. Note that the model recommends makng no calls on account 4. The frm could use less costly methods such as telemarketng to contact such accounts. Note also that t would not pay to make any call whose margnal contrbuton would be less than $200, the cost of a call. Let us explore what would happen f the salesperson were able to make more than 15 calls. Then the eghteenth call wll be to account 4, wth a margnal contrbuton of $180. Thus the maxmum number of calls the salesperson makes to ths set of accounts should be 17. (If the salesperson makes only 15 calls to these accounts, the opportunty loss of not makng the sxteenth and seventeenth calls s equal to $25, the net contrbuton of makng the two addtonal calls. The sxteenth call would be to account 1, and the seventeenth to account 3.) Resource Plannng for Sales Force Management The salesforce management problem allocates the effort of the entre salesforce to sales enttes to maxmze frm profts over a plannng horzon, subject to several constrants. We call to the model below ReAllocator to focus attenton on the combnaton and szng and allocaton of effort. Each run of the model requres a constrant specfyng a proposed salesforce sze. Ths constrant ensures that the model allocates effort n the best way possble for a gven salesforce sze. The base model follows: Fnd the set of X s to I maxmze Z = r ( X ) S a CF(profts), (6) subject to = 1 I = 1 X e = F( salesforce sze constrant), (7) where S = forecasted sales for entty accordng to the strategc plan; 8
9 a = contrbuton margn per ncremental dollar of sales for sales entty ; C = full costs (salary, benefts, etc.) of a sngle salesperson; F = planned salesforce sze (number of salespeople); and e = planned deployment of sales effort to entty accordng to the strategc plan. r (X )= ADBUDG response model for each account (other concave or S shaped functons can also be used). The base model gves the optmal allocaton of effort for any gven salesforce sze F. Ths model s then solved repeatedly for varous levels of F, and the frm should keep addng salespersons as long as the ncremental proft assocated wth each person s postve. At the optmal level of salesforce sze, the margnal proft of an addtonal salesperson s 0 (Exhbt 2). EXHIBIT 2 Ths graph shows how the results from ReAllocator can be organzed to ndcate (1) the opportunty cost (the shaded area) of mantanng the salesforce at the current level and (2) the requred change to the current salesforce sze to maxmze profts. 9
10 Constrant (7) can nclude more enttylevel constrants. For example, the constrants mght nclude mnmum and maxmum levels of effort allocated to any partcular entty. The modfed constrant set can be specfed as follows: I = 1 X e F, (8) LB X e UB. (9) LB and UB are the lower and upper bounds on effort devoted to any partcular sales entty. For example, the frm mght specfy that total effort devoted to product A should not exceed the equvalent of 100 salespersons (UB) and be at least 50 (LB). Model usage: ReAllocator can be used both for determnng the sze of the sales force (F) as well as the allocaton of that total effort across products, markets, or other sales enttes. Indeed, the strength of the model s ts ablty to help management to determne both the total effort, as well as, the approprate ways to allocate that effort. The model can also be used to assess the overall value of the salesforce. It doesn t make sense to ncrease the sales force sze, f those salespeople are not utlzed for the maxmum beneft for the frm. In today s compettve envronment, frms must justfy ther nvestments n terms of ther opportunty costs. One way to meanngfully estmate opportunty cost n the context of salesforce nvestment s by computng the dfference between profts calculated for effort levels correspondng to the selected salesforce sze and the profts the frm would earn by expendng zero sales effort on all sales enttes (all upper bounds set to 0). In some stuatons, there wll be nteractons between the enttes of nterest, whch broadly fall n two categores: complementary effects (postve synerges) or substtuton effects (negatve synerges). For example, sales force effort on two complementary products wll lkely beneft both, whereas sales force effort on two substtutable products sold by the frm s lkely to cannbalze sales of both products. As another example, n the pharmaceutcal ndustry, the postve or negatve experence that specalsts have wth new drugs affects the prescrbng behavor of the muchlarger populaton of general practtoners. Recognzng that phenomenon, many pharmaceutcal companes target key 10
11 specalsts wth promotons, hopng for postve spllover effects to the more general physcan populaton. One way to extend the Syntex resource allocaton model to account for nteractons s by ntroducng coeffcents, {b k }, nto the response model, where b k = effect that an ncremental dollar of spendng on sales entty k has on sales entty relatve to the drect effect of spendng n entty (1 > b k > 1). The restrcton on b k ensures that the absolute magntude of the complementarty or substtutablty effect s less than the drect effect. Then, ReAllocator s modfed as follows (parallelng equatons (6 9): Let X be the (ndexed) level of marketng resource (number of salespeople, $000 of ad spendng, etc.). The problem s then: Fnd the set of X s to MaxmzeZ = I r X + bk X k Sa d X e (10) = 1 k where b k s defned as above d s the cost per unt of X and the other terms are as defned earler. Agan, constrants of the form: I = 1 X e F (total resource constrant), and (11) LB X e UB (sales entty constrant) (12) can be mposed. Even wth these enhancements, ReAllocator has several lmtatons. It s best suted for repettve buyng stuatons where the number of calls made to accounts s an mportant determnant of sales. In repettve buyng stuatons 11
12 the purchase cycle s short, customers buy from an assortment of products, and the salesperson provdes a much more sophstcated verson of remnder advertsng than one gets from other meda such as TV. Here the regular contacts wth customers help cement relatonshps and allow the salesperson to recognze potental problems n advance and deal wth them. Some common examples of sales calls n repettve buyng stuatons are pharmaceutcal reps callng on physcans, packaged goods salespeople callng on grocery stores, agrcultural product reps callng on stores and farmers, and ndustral parts reps callng on dstrbutors. Summary In ths techncal note we descrbed the use of response models n resource allocaton, and llustrated ther applcaton n the context of sales effort allocaton. The approach descrbed here can be used for allocatng the overall marketng budget, or for allocatng a marketng mx element (e.g., meda spend) to dfferent products, markets, or other sales enttes. The basc concepts of market response modelng, calbraton/estmaton, and optmzaton of one or more objectves, can be used n addressng more complex problems n resource allocaton. There are many areas of marketng where resource allocaton models are becomng crtcal, ncludng shelfspace management, campagn plannng and management, meda plannng, and lead management, to name a few. References Armstrong, J. Scott, ed., 2001a, Prncples of Forecastng, Kluwer, Boston, Massachusetts. Lodsh, Leonard M., 1971, CALLPLAN: An nteractve salesman s call plannng system, Management Scence, Vol. 18, No. 4, Part 2 (December), pp Lodsh, Leonard M., 1974, `Vaguely rght approach to sales force allocatons, Harvard Busness Revew, Vol. 52, No. 1 (January February), pp
Institute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING
ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 6105194390,
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes causeandeffect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationMedia Mix Modeling vs. ANCOVA. An Analytical Debate
Meda M Modelng vs. ANCOVA An Analytcal Debate What s the best way to measure ncremental sales, or lft, generated from marketng nvestment dollars? 2 Measurng ROI From Promotonal Spend Where possble to mplement,
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationOn the Optimal Control of a Cascade of HydroElectric Power Stations
On the Optmal Control of a Cascade of HydroElectrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationTHE TITANIC SHIPWRECK: WHO WAS
THE TITANIC SHIPWRECK: WHO WAS MOST LIKELY TO SURVIVE? A STATISTICAL ANALYSIS Ths paper examnes the probablty of survvng the Ttanc shpwreck usng lmted dependent varable regresson analyss. Ths appled analyss
More informationCredit Limit Optimization (CLO) for Credit Cards
Credt Lmt Optmzaton (CLO) for Credt Cards Vay S. Desa CSCC IX, Ednburgh September 8, 2005 Copyrght 2003, SAS Insttute Inc. All rghts reserved. SAS Propretary Agenda Background Tradtonal approaches to credt
More information9.1 The Cumulative Sum Control Chart
Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s
More informationCapital asset pricing model, arbitrage pricing theory and portfolio management
Captal asset prcng model, arbtrage prcng theory and portfolo management Vnod Kothar The captal asset prcng model (CAPM) s great n terms of ts understandng of rsk decomposton of rsk nto securtyspecfc rsk
More informationOptimal Customized Pricing in Competitive Settings
Optmal Customzed Prcng n Compettve Settngs Vshal Agrawal Industral & Systems Engneerng, Georga Insttute of Technology, Atlanta, Georga 30332 vshalagrawal@gatech.edu Mark Ferguson College of Management,
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationPROFIT RATIO AND MARKET STRUCTURE
POFIT ATIO AND MAKET STUCTUE By Yong Yun Introducton: Industral economsts followng from Mason and Ban have run nnumerable tests of the relaton between varous market structural varables and varous dmensons
More informationRobust Design of Public Storage Warehouses. Yeming (Yale) Gong EMLYON Business School
Robust Desgn of Publc Storage Warehouses Yemng (Yale) Gong EMLYON Busness School Rene de Koster Rotterdam school of management, Erasmus Unversty Abstract We apply robust optmzaton and revenue management
More informationPowerofTwo Policies for Single Warehouse MultiRetailer Inventory Systems with Order Frequency Discounts
Powerofwo Polces for Sngle Warehouse MultRetaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)
More informationThe Greedy Method. Introduction. 0/1 Knapsack Problem
The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton
More informationProblem Set 3. a) We are asked how people will react, if the interest rate i on bonds is negative.
Queston roblem Set 3 a) We are asked how people wll react, f the nterest rate on bonds s negatve. When
More informationOptimal Bidding Strategies for Generation Companies in a DayAhead Electricity Market with Risk Management Taken into Account
Amercan J. of Engneerng and Appled Scences (): 86, 009 ISSN 94700 009 Scence Publcatons Optmal Bddng Strateges for Generaton Companes n a DayAhead Electrcty Market wth Rsk Management Taken nto Account
More informationThe covariance is the two variable analog to the variance. The formula for the covariance between two variables is
Regresson Lectures So far we have talked only about statstcs that descrbe one varable. What we are gong to be dscussng for much of the remander of the course s relatonshps between two or more varables.
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationAn Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services
An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces Charles V. Trappey a,1, Hsnyng Wu b a Professor (Management Scence), Natonal Chao
More informationReturn decomposing of absoluteperformance multiasset class portfolios. Working Paper  Nummer: 16
Return decomposng of absoluteperformance multasset class portfolos Workng Paper  Nummer: 16 2007 by Dr. Stefan J. Illmer und Wolfgang Marty; n: Fnancal Markets and Portfolo Management; March 2007; Volume
More informationStaff Paper. Farm Savings Accounts: Examining Income Variability, Eligibility, and Benefits. Brent Gloy, Eddy LaDue, and Charles Cuykendall
SP 200502 August 2005 Staff Paper Department of Appled Economcs and Management Cornell Unversty, Ithaca, New York 148537801 USA Farm Savngs Accounts: Examnng Income Varablty, Elgblty, and Benefts Brent
More informationMarginal Benefit Incidence Analysis Using a Single Crosssection of Data. Mohamed Ihsan Ajwad and Quentin Wodon 1. World Bank.
Margnal Beneft Incdence Analyss Usng a Sngle Crosssecton of Data Mohamed Ihsan Ajwad and uentn Wodon World Bank August 200 Abstract In a recent paper, Lanjouw and Ravallon proposed an attractve and smple
More informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationA DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATIONBASED OPTIMIZATION. Michael E. Kuhl Radhamés A. TolentinoPeña
Proceedngs of the 2008 Wnter Smulaton Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATIONBASED OPTIMIZATION
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationLIFETIME INCOME OPTIONS
LIFETIME INCOME OPTIONS May 2011 by: Marca S. Wagner, Esq. The Wagner Law Group A Professonal Corporaton 99 Summer Street, 13 th Floor Boston, MA 02110 Tel: (617) 3575200 Fax: (617) 3575250 www.ersalawyers.com
More informationA hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):18841889 Research Artcle ISSN : 09757384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationAn Empirical Study of Search Engine Advertising Effectiveness
An Emprcal Study of Search Engne Advertsng Effectveness Sanjog Msra, Smon School of Busness Unversty of Rochester Edeal Pnker, Smon School of Busness Unversty of Rochester Alan RmmKaufman, RmmKaufman
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationOverview of monitoring and evaluation
540 Toolkt to Combat Traffckng n Persons Tool 10.1 Overvew of montorng and evaluaton Overvew Ths tool brefly descrbes both montorng and evaluaton, and the dstncton between the two. What s montorng? Montorng
More informationStudy on CET4 Marks in China s Graded English Teaching
Study on CET4 Marks n Chna s Graded Englsh Teachng CHE We College of Foregn Studes, Shandong Insttute of Busness and Technology, P.R.Chna, 264005 Abstract: Ths paper deploys Logt model, and decomposes
More informationAnalysis of Covariance
Chapter 551 Analyss of Covarance Introducton A common tas n research s to compare the averages of two or more populatons (groups). We mght want to compare the ncome level of two regons, the ntrogen content
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationiavenue iavenue i i i iavenue iavenue iavenue
Saratoga Systems' enterprsewde Avenue CRM system s a comprehensve webenabled software soluton. Ths next generaton system enables you to effectvely manage and enhance your customer relatonshps n both
More informationInternet Media Planning: An Optimization Model
Internet Meda Plannng: An Optmzaton Model Janghyuk Lee 1 and Laoucne Kerbache 2 HEC School of Management, Pars 1 rue de la Lbératon 78351 JouyenJosas, France 1 Assstant Professor of Marketng emal: lee@hec.fr
More informationFinite Math Chapter 10: Study Guide and Solution to Problems
Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationFeature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College
Feature selecton for ntruson detecton Slobodan Petrovć NISlab, Gjøvk Unversty College Contents The feature selecton problem Intruson detecton Traffc features relevant for IDS The CFS measure The mrmr measure
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationCourse outline. Financial Time Series Analysis. Overview. Data analysis. Predictive signal. Trading strategy
Fnancal Tme Seres Analyss Patrck McSharry patrck@mcsharry.net www.mcsharry.net Trnty Term 2014 Mathematcal Insttute Unversty of Oxford Course outlne 1. Data analyss, probablty, correlatons, vsualsaton
More informationChoice Modeling: Marketing Engineering Technical Note 1
Choce Modelng: Maretng Engneerng Techncal Note 1 Table of Contents Introducton Descrpton of the Multnomal Logt (MNL) Model Propertes of the MNL Model Sshaped response functon Inverted U Margnal response
More informationA MULTIOBJECTIVE OPTIMIZATION APPROACH USING THE RFM MODEL IN DIRECT MARKETING
A MULTIOBJECTIVE OPTIMIZATION APPROACH USING THE RFM MODEL IN DIRECT MARKETING By Arben Asllan, Ph.D. Marvn E. Whte Professor of Busness Analytcs Department of Management, #6056 Benasllan@utc.edu (423)
More informationAn MILP model for planning of batch plants operating in a campaignmode
An MILP model for plannng of batch plants operatng n a campagnmode Yanna Fumero Insttuto de Desarrollo y Dseño CONICET UTN yfumero@santafeconcet.gov.ar Gabrela Corsano Insttuto de Desarrollo y Dseño
More informationPRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIGIOUS AFFILIATION AND PARTICIPATION
PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIIOUS AFFILIATION AND PARTICIPATION Danny CohenZada Department of Economcs, Benuron Unversty, BeerSheva 84105, Israel Wllam Sander Department of Economcs, DePaul
More informationIMPACT ANALYSIS OF A CELLULAR PHONE
4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng
More informationProject Networks With MixedTime Constraints
Project Networs Wth MxedTme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa
More information2008/8. An integrated model for warehouse and inventory planning. Géraldine Strack and Yves Pochet
2008/8 An ntegrated model for warehouse and nventory plannng Géraldne Strack and Yves Pochet CORE Voe du Roman Pays 34 B1348 LouvanlaNeuve, Belgum. Tel (32 10) 47 43 04 Fax (32 10) 47 43 01 Emal: corestatlbrary@uclouvan.be
More informationQuestions that we may have about the variables
Antono Olmos, 01 Multple Regresson Problem: we want to determne the effect of Desre for control, Famly support, Number of frends, and Score on the BDI test on Perceved Support of Latno women. Dependent
More informationSIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA
SIX WAYS TO SOLVE A SIMPLE PROBLEM: FITTING A STRAIGHT LINE TO MEASUREMENT DATA E. LAGENDIJK Department of Appled Physcs, Delft Unversty of Technology Lorentzweg 1, 68 CJ, The Netherlands Emal: e.lagendjk@tnw.tudelft.nl
More informationFault tolerance in cloud technologies presented as a service
Internatonal Scentfc Conference Computer Scence 2015 Pavel Dzhunev, PhD student Fault tolerance n cloud technologes presented as a servce INTRODUCTION Improvements n technques for vrtualzaton and performance
More informationForecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract  Stock market s one of the most complcated systems
More informationH 1 : at least one is not zero
Chapter 6 More Multple Regresson Model The Ftest Jont Hypothess Tests Consder the lnear regresson equaton: () y = β + βx + βx + β4x4 + e for =,,..., N The tstatstc gve a test of sgnfcance of an ndvdual
More informationThe Personalization Services Firm: What to Sell, Whom to Sell to and For How Much? *
The Personalzaton Servces Frm: What to Sell, Whom to Sell to and For How Much? * oseph Pancras Unversty of Connectcut School of Busness Marketng Department 00 Hllsde Road, Unt 04 Storrs, CT 06690 joseph.pancras@busness.uconn.edu
More informationNasdaq Iceland Bond Indices 01 April 2015
Nasdaq Iceland Bond Indces 01 Aprl 2015 Fxed duraton Indces Introducton Nasdaq Iceland (the Exchange) began calculatng ts current bond ndces n the begnnng of 2005. They were a response to recent changes
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? ChuShu L Department of Internatonal Busness, Asa Unversty, Tawan ShengChang
More informationChapter 4 Financial Markets
Chapter 4 Fnancal Markets ECON2123 (Sprng 2012) 14 & 15.3.2012 (Tutoral 5) The demand for money Assumptons: There are only two assets n the fnancal market: money and bonds Prce s fxed and s gven, that
More informationInstructions for Analyzing Data from CAHPS Surveys:
Instructons for Analyzng Data from CAHPS Surveys: Usng the CAHPS Analyss Program Verson 4.1 Purpose of ths Document...1 The CAHPS Analyss Program...1 Computng Requrements...1 PreAnalyss Decsons...2 What
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More information1 Approximation Algorithms
CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons
More informationState function: eigenfunctions of hermitian operators> normalization, orthogonality completeness
Schroednger equaton Basc postulates of quantum mechancs. Operators: Hermtan operators, commutators State functon: egenfunctons of hermtan operators> normalzaton, orthogonalty completeness egenvalues and
More informationOmega 39 (2011) 313 322. Contents lists available at ScienceDirect. Omega. journal homepage: www.elsevier.com/locate/omega
Omega 39 (2011) 313 322 Contents lsts avalable at ScenceDrect Omega journal homepage: www.elsever.com/locate/omega Supply chan confguraton for dffuson of new products: An ntegrated optmzaton approach Mehd
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationValuing Customer Portfolios under RiskReturnAspects: A Modelbased Approach and its Application in the Financial Services Industry
Buhl and Henrch / Valung Customer Portfolos Valung Customer Portfolos under RskReturnAspects: A Modelbased Approach and ts Applcaton n the Fnancal Servces Industry Hans Ulrch Buhl Unversty of Augsburg,
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationCS 2750 Machine Learning. Lecture 3. Density estimation. CS 2750 Machine Learning. Announcements
Lecture 3 Densty estmaton Mlos Hauskrecht mlos@cs.ptt.edu 5329 Sennott Square Next lecture: Matlab tutoral Announcements Rules for attendng the class: Regstered for credt Regstered for audt (only f there
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationChapter 7: Answers to Questions and Problems
19. Based on the nformaton contaned n Table 73 of the text, the food and apparel ndustres are most compettve and therefore probably represent the best match for the expertse of these managers. Chapter
More informationSIMPLE LINEAR CORRELATION
SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.
More informationTechnical Memorandum Number 815. Bigger Slice or Larger Pie? Optimal Marketing Strategies for New Firms. John Angelis Moren Lévesque
Techncal Memorandum Number 815 Bgger Slce or Larger Pe? Optmal Marketng Strateges for New Frms by John Angels Moren Lévesque June 26 Department of Operatons Weatherhead School of Management Case Western
More informationx f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60
BIVARIATE DISTRIBUTIONS Let be a varable that assumes the values { 1,,..., n }. Then, a functon that epresses the relatve frequenc of these values s called a unvarate frequenc functon. It must be true
More informationA Computer Technique for Solving LP Problems with Bounded Variables
Dhaka Unv. J. Sc. 60(2): 163168, 2012 (July) A Computer Technque for Solvng LP Problems wth Bounded Varables S. M. Atqur Rahman Chowdhury * and Sanwar Uddn Ahmad Department of Mathematcs; Unversty of
More informationMultiplePeriod Attribution: Residuals and Compounding
MultplePerod Attrbuton: Resduals and Compoundng Our revewer gave these authors full marks for dealng wth an ssue that performance measurers and vendors often regard as propretary nformaton. In 1994, Dens
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationErrorPropagation.nb 1. Error Propagation
ErrorPropagaton.nb Error Propagaton Suppose that we make observatons of a quantty x that s subject to random fluctuatons or measurement errors. Our best estmate of the true value for ths quantty s then
More informationMarginal RevenueBased Capacity Management Models and Benchmark 1
Margnal RevenueBased Capacty Management Models and Benchmark 1 Qwen Wang 2 Guanghua School of Management, Pekng Unversty Sherry Xaoyun Sun 3 Ctgroup ABSTRACT To effcently meet customer requrements, a
More informationStatistical Methods to Develop Rating Models
Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and
More informationMeasuring Ad Effectiveness Using Geo Experiments
Measurng Ad Effectveness Usng Geo Experments Jon Vaver, Jm Koehler Google Inc Abstract Advertsers have a fundamental need to quantfy the effectveness of ther advertsng For search ad spend, ths nformaton
More informationStudy on Model of Risks Assessment of Standard Operation in Rural Power Network
Study on Model of Rsks Assessment of Standard Operaton n Rural Power Network Qngj L 1, Tao Yang 2 1 Qngj L, College of Informaton and Electrcal Engneerng, Shenyang Agrculture Unversty, Shenyang 110866,
More informationToday s class. Chapter 13. Sources of uncertainty. Decision making with uncertainty
Today s class Probablty theory Bayesan nference From the ont dstrbuton Usng ndependence/factorng From sources of evdence Chapter 13 1 2 Sources of uncertanty Uncertan nputs Mssng data Nosy data Uncertan
More informationFORCED CONVECTION HEAT TRANSFER IN A DOUBLE PIPE HEAT EXCHANGER
FORCED CONVECION HEA RANSFER IN A DOUBLE PIPE HEA EXCHANGER Dr. J. Mchael Doster Department of Nuclear Engneerng Box 7909 North Carolna State Unversty Ralegh, NC 276957909 Introducton he convectve heat
More informationI. SCOPE, APPLICABILITY AND PARAMETERS Scope
D Executve Board Annex 9 Page A/R ethodologcal Tool alculaton of the number of sample plots for measurements wthn A/R D project actvtes (Verson 0) I. SOPE, PIABIITY AD PARAETERS Scope. Ths tool s applcable
More informationTrafficlight a stress test for life insurance provisions
MEMORANDUM Date 006097 Authors Bengt von Bahr, Göran Ronge Traffclght a stress test for lfe nsurance provsons Fnansnspetonen P.O. Box 6750 SE113 85 Stocholm [Sveavägen 167] Tel +46 8 787 80 00 Fax
More informationQuality Adjustment of Secondhand Motor Vehicle Application of Hedonic Approach in Hong Kong s Consumer Price Index
Qualty Adustment of Secondhand Motor Vehcle Applcaton of Hedonc Approach n Hong Kong s Consumer Prce Index Prepared for the 14 th Meetng of the Ottawa Group on Prce Indces 20 22 May 2015, Tokyo, Japan
More informationTime Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6  The Time Value of Money. The Time Value of Money
Ch. 6  The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21 Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 /  Communcaton Networks II (Görg) SS20  www.comnets.unbremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More informationCHULMLEIGH ACADEMY TRUST INDUCTION AND DEVELOPMENT OF DIRECTORS POLICY
CHULMLEIGH ACADEMY TRUST INDUCTION AND DEVELOPMENT OF DIRECTORS POLICY Adopted by BoD:30 May 2012 Polcy Statement The Drectors of Chulmlegh Academy Trust beleve all Drectors brng an equally valued range
More informationCHAPTER 18 INFLATION, UNEMPLOYMENT AND AGGREGATE SUPPLY. Themes of the chapter. Nominal rigidities, expectational errors and employment fluctuations
CHAPTER 18 INFLATION, UNEMPLOYMENT AND AGGREGATE SUPPLY Themes of the chapter Nomnal rgdtes, expectatonal errors and employment fluctuatons The shortrun tradeoff between nflaton and unemployment The
More informationResearch Article A Time Scheduling Model of Logistics Service Supply Chain with Mass Customized Logistics Service
Hndaw Publshng Corporaton Dscrete Dynamcs n Nature and Socety Volume 01, Artcle ID 48978, 18 pages do:10.1155/01/48978 Research Artcle A Tme Schedulng Model of Logstcs Servce Supply Chan wth Mass Customzed
More informationNONLINEAR OPTIMIZATION FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY
NONLINEAR OPTIMIZATION FOR PROJECT SCHEDULING AND RESOURCE ALLOCATION UNDER UNCERTAINTY A Dssertaton Presented to the Faculty of the Graduate School of Cornell Unversty In Partal Fulfllment of the Requrements
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More information