Optimal demand response: problem formulation and deterministic case


 Darren Webster
 1 years ago
 Views:
Transcription
1 Opimal demand response: problem formulaion and deerminisic case Lijun Chen, Na Li, Libin Jiang, and Seven H. Low Absrac We consider a se of users served by a single loadserving eniy (LSE. The LSE procures capaciy a day ahead. When random renewable energy is realized a delivery ime, i manages user load hrough realime demand response and purchases balancing power on he spo marke o mee he aggregae demand. Hence opimal supply procuremen by he LSE and he consumpion decisions by he users mus be coordinaed over wo imescales, a day ahead and in real ime, in he presence of supply uncerainy. Moreover, hey mus be compued joinly by he LSE and he users since he necessary informaion is disribued among hem. In his paper we presen a simple ye versaile user model and formulae he problem as a dynamic program ha maximizes expeced social welfare. When random renewable generaion is absen, opimal demand response reduces o join scheduling of he procuremen and consumpion decisions. In his case, we show ha opimal prices exis ha coordinae individual user decisions o maximize social welfare, and presen a decenralized algorihm o opimally schedule a day in advance he LSE s procuremen and he users consumpions. The case wih uncerain supply is repored in a companion paper. 1 Inroducion 1.1 Moivaion There is a large lieraure on various forms of load side managemen from he classical direc load conrol o he more recen realime pricing [1, 2]. Direc load conrol in paricular has been pracised for a long ime and opimizaion mehods have been Lijun Chen, Na Li, Libin Jiang and Seven H. Low Engineering and Applied Science, California Insiue of Technology, USA {chenlj, nali, libinj, 1
2 2 Lijun Chen, Na Li, Libin Jiang, and Seven H. Low proposed o minimize generaion cos e.g. [3, 4, 5, 6], maximize uiliy s profi e.g. [7], or minimize deviaion from users desired consumpions e.g. [8, 9], someimes inegraed wih uni commimen and economic dispach e.g. [4, 10]. Almos all demand response programs oday arge large indusrial or commercial users, or, in he case of residenial users, a small number of hem, for wo, among oher, imporan reasons. Firs demand side managemen is invoked rarely o mosly cope wih a large correlaed demand spike due o weaher or a supply shorfall due o fauls, e.g., during a few hoes days in summer. Second he lack of ubiquious woway communicaion in he curren infrasrucure prevens he paricipaion of a large number of diverse users wih heerogeneous and imevarying consumpion requiremens. Boh reasons favor a simple and saic mechanism involving a few large users ha is sufficien o deal wih he occasional need for load conrol, bu boh reasons are changing. Renewable sources can flucuae rapidly and by large amouns. As heir peneraion coninues o grow, he need for regulaion services and operaing reserves will increase, e.g., [11, 12]. This can be provided by addiional peaker unis, a a higher cos, or supplemened by realime demand response [13, 14, 15, 12, 16]. We believe ha demand response will no only be invoked o shave peaks and shif load for economic benefis, bu will increasingly be called upon o improve securiy and reduce reserves by adaping elasic loads o inermien and random renewable generaion [17]. Indeed, [12, 18, 19] advocaes he creaion of a disribuion/reail marke o encourage greaer load side paricipaion as an alernaive source for fas reserves. Such applicaion however will require a much faser and more dynamic demand response han pracised oday. This will be enabled in he coming decades by he largescale deploymen of a sensing, conrol, and woway communicaion infrasrucure, including he flexible AC ransmission sysems, he GPSsynchronized phasor measuremen unis, and he advanced meering infrasrucure, ha is currenly underway around he world [20]. Demand response in such conex mus allow he paricipaion of a large number of users, and be dynamic and disribued. Dynamic adapaion by hundreds of millions of end users on a subsecond conrol imescale, each conribuing a iny fracion of he overall raffic, is being pracised everyday on he Inerne in he form of congesion conrol. Even hough boh he grid and he Inerne are massive disribued nonlinear feedback conrol sysems, here are imporan differences in heir engineering, economic, and regulaory srucures. Noneheless he precedence on he Inerne lends hope o a much bigger scale and more dynamic and disribued demand response archiecure and is benefi o grid operaion. Ulimaely i will be cheaper o use phoons han elecrons o deal wih a power shorage. Our goal is o design algorihms for such a sysem.
3 Opimal demand response: problem formulaion and deerminisic case Summary Specifically we consider a se of users ha are served by a single loadserving eniy (LSE. The LSE may represen a regulaed monopoly like mos uiliy companies in he Unied Saes oday, or a nonprofi cooperaive ha serves a communiy of end users. Is purpose is (possibly regulaed o promoe he overall sysem welfare. The LSE purchases elecriciy on he wholesale elecriciy markes (e.g., dayahead, realime balancing, and ancillary services and sells i on he reail marke o end users. I provides wo imporan values: i aggregaes loads so ha he wholesale markes can operae efficienly, and i hides he complexiy and uncerainy from he users, in erms of boh power reliabiliy and prices. Our model capures hree imporan feaures: Uncerainy. Par of he elecriciy supply is from renewable sources such as wind and solar, and hus uncerain. Supply and demand. LSE s supply decisions and he users consumpion decisions mus be joinly opimized. Two imescale. The LSE mus procure capaciy on he dayahead wholesale marke while user consumpions should be adaped in real ime o miigae supply uncerainy. Hence he key is he coordinaion of dayahead procuremen and realime demand response over wo imescales in he presence of supply uncerainy. Moreover, he opimal decisions mus be compued joinly by he LSE and he users as he necessary informaion is disribued among hem. The goal of his paper is o formulae his problem precisely. Due o space limiaion, we can only fully rea he case wihou supply uncerainy. Resuls for he case wih supply uncerainy are summarized here, bu fully developed in a companion paper [21]. Suppose each user has a se of appliances (elecric vehicle, air condiioner, lighing, baery, ec.. She (or her energy managemen sysem is o decide how much power she should consume in each period = 1,...,T of a day. The LSE needs o decide how much capaciy i should procure a day ahead and, when he random renewable energy is realized a real ime, how much balancing power o purchase on he spo marke o mee he aggregae demand. In Secion 2, we presen our user and supply models, and formulae he overall problem as an (1+T period dynamic program o maximize expeced social welfare. The key idea is o regard he LSE s dayahead decision as he conrol in period 0 and he users consumpion decisions as conrols in he subsequen periods = 1,...,T. By unifying several models in he lieraure, our user model incorporaes a large class of appliances. Ye, i is simple, hus analyically racable, where each appliance is characerized by a uiliy funcion and a se of linear consumpion consrains. In Secion 3, we consider he case wihou renewable generaion. In he absence of uncerainy i becomes unnecessary o adap user consumpions in realime and hence supply and consumpions can be opimally scheduled a once insead of over wo days. We show ha opimal prices exis ha coordinae individual users decisions in a disribued manner, i.e., when users selfishly maximize heir own surplus
4 4 Lijun Chen, Na Li, Libin Jiang, and Seven H. Low under he opimal prices, heir consumpion decisions urn ou o also maximize he social welfare. We develop an offline disribued algorihm ha joinly schedules he LSE s procuremen decisions and he users consumpion decisions for each period in he following day. The algorihm is decenralized where he LSE only knows he aggregae demand bu no user uiliy funcions or consumpion consrains, and he users do no need o coordinae among hemselves bu only respond o common prices from he LSE. Wih renewable generaion, he uncerainy precludes pure scheduling and calls for realime consumpions decisions ha adap o he realizaion of he random renewable generaion. Moreover, his mus be coordinaed wih procuremen decisions over wo imescales o maximize he expeced welfare. Disribued algorihms for opimal demand response in his case and he impac of uncerainy on he opimal welfare are developed in he companion paper [21] We make wo remarks. Firs he effeciveness of realime pricing for demand response is sill in acive research. On he one hand, empirical sudies have shown consisenly ha price elasiciy is low and heerogeneous; see [22, 23, 24] and references herein. On he oher hand, here are srong economic argumens ha realime reail prices improve he efficiency of he overall sysem by allowing users o dynamically adap heir loads o shorages, wih poenial benefis far exceeding he cos of implemenaion [18]. Moreover, he longrun efficiency gain is likely o be significan even if demand elasiciy is small, bu unforunaely, he popular openloop imeofuse pricing may capure a very small share of he efficiency gain of realime pricing [25]. We neiher argue for nor agains realime pricing. Indeed we do no consider in his paper he economic issues associaed wih such a sysem, such as locaional marginal prices, revenueadequacy, ec. Wha we refer o as prices are simply conrol signals ha provide he necessary informaion for users o adap heir consumpion in a disribued, ye opimal, manner. Wheher his conrol signal should be linked o moneary paymens o provide he righ incenive for demand response is beyond he scope of his paper, i.e., we do no address he imporan issue of how o incenivize users o respond o supply and demand flucuaions. 1 Second, unlike many curren sysems, he kind of largescale disribued demand response sysem envisioned here mus be fully auomaed. Human users se parameers ha specify uiliy funcions and consumpion consrains and may change hem on a slow imescale, bu he algorihms proposed here will execue auomaically and ransparenly o opimize social welfare. The radiional direc load conrol approach assumes ha he conroller (e.g. a uiliy company knows he user consumpion requiremens, in he form of payback characerisics of he deferred load, and can opimally schedule deferred consumpions and heir paybacks cenrally. This is reasonable for he curren sysem where he paricipaing users are few and heir requiremens are relaively saic. We ake he view ha he uiliies and requiremens of user consumpions are diverse and privae. I is no pracical, nor necessary, o have direc access o such informaion in order o opimally coordinae heir consumpions in a large, disribued, and dynamic sysem of he fuure. The algorihm 1 See however [19] for a discussion on some implemenaion issues of realime pricing for reail markes and a proposal for he Ialian marke.
5 Opimal demand response: problem formulaion and deerminisic case 5 presened here is an example ha can achieve opimaliy wihou requiring users o disclose heir privae informaion. 1.3 Oher relaed work A large lieraure exiss on demand response. Besides hose cied above, more recen works include, e.g., [26, 27] on load conrol of hermal mass in buildings, [28, 29, 30] on residenial load conrol hrough coordinaed scheduling of differen appliances, [31, 32, 33] on he scheduling of plugin elecric vehicle charging, and [34] on he opimal allocaion of a supply defici (raioning among users using heir supply funcions. Load side managemen in he presence of uncerain supply has also been considered in [16, 10, 35, 36, 12, 37]. Unlike he convenional approach ha compensaes for he uncerainy o creae reliable power, [16] advocaes selling inerrupible power and designs service conracs, based on [38], ha can achieve greaer efficiency han he convenional approach. In [10] various opimizaion problems are formulaed ha inegrae demand response wih economic dispach wih ramping consrains and forecass of renewable power and load. Boh cenralized dispach using model predicive conrol and decenralized dispach using prices, or supply and demand funcions, are considered. A woperiod sochasic dispach model is sudied in [35] and a selemen scheme is proposed ha is revenueadequae even in he presence of uncerain supply and demand. A queueing model is analyzed in [36] where he queue holds deferrable loads ha arise from random supply and demand processes. Convenional generaion can be purchased o keep he queue small and sraegies are sudied o minimize he imeaverage cos. The models ha are closes o ours, developed independenly, are [12, 37]. All our models include random renewable generaion, consider boh dayahead and realime markes, and allow demand response, bu our objecives and sysem operaions are quie differen. [12] advocaes he esablishmen of a reail marke where users (e.g., PHEVs can buy power from or sell reserves, in he form of demand response capabiliy, o heir LSE. The paper formulaes he LSE s and users problems as dynamic programs ha minimize heir expeced coss over heir bids, which can be eiher simple, uncorrelaed (price, quaniy pairs for each period, or complex, (price, quaniy pairs wih emporal correlaions. The model in [37] includes nonelasic users ha are price nonresponsive, and elasic users ha can eiher leave he sysem or defer heir consumpions when he elecriciy price is high. The goal is o maximize LSE s profi over dayahead procuremen, dayahead prices for nonelasic users, and realime prices for elasic users.
6 6 Lijun Chen, Na Li, Libin Jiang, and Seven H. Low 1.4 Noaions Given quaniies such as demands q ia ( from appliance a of user i in period, q ia := (q ia (, T denoes he vecor of demands a differen imes, q i ( := (q ia (,a A i he vecor of demands of differen appliances, q i := (q ia,a A i he vecor of demands of i s appliances a differen imes, and q := (q i, i he vecor of all demands. Similarly for aggregae demands Q i ( = a Ai q ia (, Q ia := q ia (, Q i, Q, ec. Scrip leers denoe ses, e.g., N,A i,t. Small leers denoe individual quaniies, e.g., q ia (, q ia, q i (, q i, q, ec. Capial leers denoe aggregae quaniies, e.g., Q i (, Q ia, P d (,P r (,P o (,P b (, ec. We use q ia (,q ia,q i (, ec for loads and P d (,P r (, ec for supplies. We someimes wrie i a Ai q ia ( as i,a q ia (. For any real a,b,c, [a] + := max{a,0} and [a] c b := max{b,min{a,c}}. Finally, we wrie a vecor as x = (x i, i wihou specifying wheher i is a column or row vecor so we can ignore he ranspose sign o simplify he noaion; he meaning should be clear from he conex. 2 Model and problem formulaion Consider a se N of N users ha are served by a single loadserving eniy (LSE. We use a discreeime model wih a finie horizon ha models a day. Each day is divided ino T periods of equal duraion, indexed by T := {1,2,,T }. The duraion of a period can be 5, 15, or 60 mins, corresponding o he ime resoluion a which energy dispach or demand response decisions are made. 2.1 User model Each user i N operaes a se A i of appliances such as HVAC (hea, venilaion, air condiioner, refrigeraor, and plugin hybrid elecric vehicle. User i may also possess a baery which provides furher flexibiliy for opimizing is elecriciy consumpion across ime. Appliance model. For each appliance a A i of user i, q ia ( denoes is energy consumpion in period T, and q ia he vecor (q ia (, over he whole day. An appliance a is characerized by: a uiliy funcion U ia (q ia ha quanifies he uiliy user i obains from using appliance a; a K ia T marix A ia and a K ia vecor η ia such ha he vecor of power q ia saisfies he linear inequaliy A ia q ia η ia. (1 In general U ia depends on he vecor q ia. In his paper, however, we consider four ypes of appliances whose uiliy funcions ake one of hree simple forms. These
7 Opimal demand response: problem formulaion and deerminisic case 7 models are summarized in Table 1 and jusified in deail in he Appendix. The uiliy of a ype 1 or ype 2 appliance is addiive in : 2 U ia (q ia := U ia (q ia (,. (2 The uiliy of a ype 3 appliance depends only on he aggregae consumpion: U ia (q ia := U ia ( q ia (. (3 The uiliy of a ype 4 appliance depends on he inernal emperaure and power consumpions in he pas. I is of he form: U iq (q ia := U ia (T ia ( + β (1 α τ q ia (τ (4 where T ia ( is a given sequence of emperaures defined in equaion (29 in he Appendix and α,β are given hermal consans. All uiliy funcions are assumed o be coninuously differeniable and concave funcions for each. For example, some of our simulaions in [39, 21] use he following ime independen and addiive uiliy funcion of form (2: le y ia ( be a desired energy consumpion by appliance a in period ; hen he funcion τ=1 U ia (q ia (, := U ia (q ia ( := (q ia ( y ia ( 2 (5 measures he uiliy of following he desired consumpion profile y ia (. Such uiliy funcions minimize user discomfor as advocaed in [8, 9]. Table 1: Srucure of uiliy funcions and consumpion consrains for appliances. Appliances Uiliy funcion Consumpion consrains Examples Type 1 (2 (6 Lighings Type 2 (2 (6, (7 TV, video game, compuer Type 3 (3 (6, (7 PHEV, washers Type 4 (4 (6, (8 HVAC, refrigeraor Baery D i (r i (6, (7 r i = q ia for baery a The consumpion consrains (1 for hese appliances ake hree paricular forms. Firs, for all appliances, he (real power consumpion mus lie beween a lower and an upper bound, possibly imedependen: q ia ( q ia ( q ia (. (6 2 We abuse noaion o use U ia o denoe boh a funcion of vecor q ia and ha of a scalar q ia (; he meaning should be clear from he conex.
8 8 Lijun Chen, Na Li, Libin Jiang, and Seven H. Low An imporan characer of an appliance is is allowable ime of operaion; e.g., an EV can be charged only beween 9pm and 6am, TV may be on only beween 7 9am and 6 12pm. If an appliance operaes only in a subse T ia T of periods, we require ha q ia ( = q ia ( = 0 for T ia and U ia (0 = 0. We herefore do no specify T ia explicily in he descripion of uiliy funcions and always sum over all T. The second kind of consrain specifies he range in which he aggregae consumpion mus lie: Q ia q ia ( Q ia. (7 The las kind of consrain is slighly more general (see derivaion in he Appendix: η ia A ia q ia η ia. (8 Baery model. We denoe by B i he baery capaciy, by b i ( he sae of charge in period, and by r i ( he power (energy per period charged o (when r i ( 0 or discharged from (when r i ( < 0 he baery in period. We use a simplified model of baery ha ignores power leakage and oher inefficiencies, where he sae of charge is given by b i ( = r i (τ + b i (0. (9 τ=1 The baery has an upper bound on charge rae, denoed by r i, and an upper bound on discharge rae, denoed by r i. We hus have he following consrains on b i ( and r i (: 0 b i ( B i, r i r i ( r i. (10 We assume any baery discharge is consumed by oher appliances (zero leakage, and hence i canno be more han wha he appliances need: r i ( a A i q ia (. (11 Finally, we impose a minimum on he energy level a he end of he conrol horizon: b(t γ i B i where γ i [0,1]. The cos of operaing he baery is modeled by a funcion D i (r i ha depends on he vecor of charged/discharged power r i := (r i (,. This cos may correspond o he amorized purchase and mainenance cos of he baery over is lifeime, and depends on how fas/much/ofen i is charged and discharged; see an example D i (r i in [39]. The cos funcion D i is assumed o be a convex funcion of he vecor r i. Noe ha in his model, a baery is equivalen o an appliance: is uiliy funcion is D i (r i and is consumpion consrains (9, (10, and b(t γ i B i are of he same form as (6 (7 wih q ia = r i. Therefore a baery can be specified simply as anoher appliance, in which case he consrain (11 requires ha i s aggregae demand be nonnegaive, a Ai q ia ( + r i ( 0. This is summarized in Table 1. Henceforh,
9 Opimal demand response: problem formulaion and deerminisic case 9 we will ofen use appliances o also include baery and may no refer o baery explicily when his does no cause confusion. 2.2 Supply model We now describe a simple model of he elecriciy markes. The LSE procures power for delivery in each period, in wo seps. Firs i procures dayahead capaciies P d ( for each period a day in advance and pays for he capaciy coss c d (P d (;. The renewable power in each period is a nonnegaive random variable P r ( and i coss c r (P r (;. I is desirable o use as much renewable power as possible; for noaional simpliciy only, we assume c r (P; 0 for all P 0 and all. Then a ime (real ime, he random variable P r ( is realized and used o saisfy demand. The LSE saisfies any excess demand by some or all of he dayahead capaciy P d ( procured in advance and/or by purchasing balancing power on he realime marke. Le P o ( denoe he amoun of he dayahead power ha he LSE acually uses and c o (P o (; is cos. Le P b ( be he realime balancing power and c b (P b (; is cos. These realime decisions (P o (,P b ( are made by he LSE so as o minimize is oal cos, as follows. Given he demand vecor q( := (q ia (,a A i, i, le Q( := i,a q ia ( be he oal demand and (Q( := Q( P r ( he excess demand, in excess of he renewable generaion P r (. Noe ha (Q( is a random variable in and before period 1, bu is realizaion is known o he LSE a ime. Given excess demand (Q( and dayahead capaciy P d (, he LSE chooses (P o (,P b ( ha minimizes is oal realime cos, i.e., i chooses (P o (,P b ( ha solves he problem: c s ( (Q(,P d (; := min { c o(p o (; + c b (P b (; P b ( 0, P o (,P b ( P o ( + P b ( (Q(, P d ( P o ( 0}. (12 Clearly Po ( + Pb ( = (Q( unless (Q( < 0. The oal cos is c(q(,p d (;P r (, := c d (P d (; + c s ( (Q(,P d (;. (13 wih (Q( := Q( P r (. We assume ha, for each, c d ( ;, c o ( ; and c b ( ; are increasing, convex, and coninuously differeniable wih c d (0; = c o (0; = c b (0; = 0. Example: supply cos Suppose c b (0 > c o(p, P 0, i.e., he marginal cos of balancing power is sricly higher han he marginal cos of dayahead power, he LSE will use he balancing power only afer he dayahead power is exhaused, i.e., P b ( > 0 only if (Q( > P d (. The soluion c s ( (Q(,P d (; of (12 in his case is paricularly simple and (13 can be wrien explicily in erms of c b,c o,c b :
10 10 Lijun Chen, Na Li, Libin Jiang, and Seven H. Low c(q(,p d (;P r (, = c d (P d (; + ( c o [ (Q(] P ( d( 0 ; + c b [ (Q( Pd (] + ;. (14 i.e., he oal cos consiss of he capaciy cos c d and he energy cos c o of dayahead power, and he cos c b of he realime balancing power. 2.3 Problem formulaion: welfare maximizaion Recall ha q := (q(, T and Q( := i,a q ia (. The social welfare is he sandard user uiliy minus supply cos: W(q,P d ;P r := U ia (q ia i,a T =1 c(q(,p d (;P r (,. (15 As menioned above he LSE s objecive is no o maximize is profi hrough selling elecriciy, bu raher o maximize he expeced social welfare. Given he dayahead decision P d, he realime procuremen (P o (,P b ( is deermined by he simple opimizaion (13. This is mos ransparen in (14 for he special case: he opimal decision is o use dayahead power P o ( o saisfy any excess demand (Q( up o P d (, and hen purchase realime balancing power P b ( = [ (Q( P d(] + if necessary. Hence he maximizaion of (15 reduces o opimizing over dayahead procuremen P d and realime consumpion q in he presence of random renewable generaion P r (. I is herefore criical ha, in he presence of uncerainy, q( should be decided afer P r ( have been realized a imes. P d however mus be decided a day ahead before P r ( are realized. The radiional dynamic programming model requires ha he objecive funcion be separable in ime. The welfare funcion in (15 is no as he firs erm U ia (q ia depends on he enire conrol sequence q ia = (q ia (,. So does he consumpion consrain (1. We now inroduce an equivalen sae space formulaion of ha will allow us o sae precisely he overall opimizaion problem as an (1 + T period dynamic program. Consider a dynamical sysem over an exended ime horizon = 0, 1,..., T. The conrol inpus are he LSE s dayahead decision P d := (P d (, in period 0 and he user s decisions q( in each subsequen period. Le v( denoe he inpus, i.e., v(0 = P d and v( = q(, = 1,...,T. Noe ha v(0 R T + whereas q( R M where M := N i=1 A i. The sysem sae x( := ( x 1 (,x 2 ia (,x3 (,x 4 ia (, a A i, i has four componens, defined as follows: Wihou loss of generaliy, x(0 sars from he origin. x 1 ( R T keeps rack of he dayahead decisions P d : for each = 1,...,T, x 1 ( = P d = (P d (τ,τ = 1,...,T.
11 Opimal demand response: problem formulaion and deerminisic case 11 xia 2 ( Rk ia of appropriae dimension k ia for each (i,a pair keeps rack of he consumpion consrain (1. The sae definiion and is ransiion are problem specific; see a concree example in Secion 2.4. x 3 ( R + keeps rack of he random renewable power x 3 (0 = 0, x 3 ( = P r (, = 1,...,T. The purpose of his sae definiion is merely noaional, so ha he conrol policy can depend on he realizaion of he random renewable power P r ( hrough is dependence on sae x 3 (. xia 4 ( RT 1 for each (i,a pair racks he user decisions v ia ( 1 = q ia ( 1 in he previous period: xia 4 (1 = 0 T 1, he T 1 dimensional zero vecor; for each = 2,...,T, he ( 1h componen [xia 4 (] 1 of xia 4 ( is se o be he inpu v ia ( 1 and all he oher componens [xia 4 (] τ of xia 4 ( remain he same as hose of xia 4 ( 1, so ha he final sae x4 ia (T is he vecor (q ia(, = 1,...,T 1 of inpus up o period T 1. The firs erm in (15 is hen a funcion of he sae and inpu in period T, U ia (q ia = U ia (xia 4 (T,v ia(t. This allows us o rewrie he welfare funcion in (15 in a form ha is separable in ; see below. The above discussion is summarized by a imevarying sae ransiion funcion f : x( + 1 = f (x(,v(,p r ( + 1, = 0,...,T i.e., he new sae x( + 1 depends on he curren sae x(, he inpu v(, and he new random variable P r (, and is herefore random. The consumpion consrains (1, which may include he baery consrains, generally ranslae ino consrains on he sae x 2 ( and inpu v( and we represen his by x( X ( and v( V ( R M, M := N i=1 A i. Someimes hese consrains also give rise o a erminal reward ha we denoe by W T +1 (x(t + 1. Consider he class of feedback conrol laws v( = φ (x(, where φ 0 : X (0 R T + specifies he dayahead decision P d and φ : X ( V ( specifies he user decisions q( for each period = 1,...,T. Hence he conrol v( depends only on he curren sae x(. Under he conrol law φ := (φ, = 0,...,T, he sae evolves (sochasically according o x( + 1 = f (x(,φ (x(,p r ( + 1. (16 We emphasize ha x( is obained under policy φ even hough his may no be explici in he noaion. To make he welfare funcion in (15 separable in, use (13 o define he welfare in each period, under he conrol law φ, as a funcion of he curren sae x( and he curren inpu v( = φ (x(: W φ := W φ (x(,v( T τ=1 ( c d ([v(0] τ ;τ, = 0 := c s (Q φ (,[x 1 (] ;, 1 < T i,a U ia ((xia 4 (T,v ( ia(t c s (Q φ (T,[x 1 (T ] T ;T, = T (17
12 12 Lijun Chen, Na Li, Libin Jiang, and Seven H. Low where Q φ ( = i,a [v(] ia is he aggregae demand in period under φ, and v ia (T = q ia (T are he realime consumpion decisions in he las conrol period T. Then he welfare funcion in (15 is equivalen o J φ := T =0 W φ (x(,v( +W φ T +1 (x(t + 1 where he definiion of he erminal reward W φ T +1 (x(t + 1 is problem specific. We can now sae precisely our objecive as he consrained maximizaion of he expeced welfare over he conrol law φ: max φ E J φ = E ( T W φ +W φ T +1 =0 where he expecaion is aken over P r (, = 1,...,T. s.. x φ ( X (. (18 Remark. An imporan assumpion in his formulaion is ha he consumpion consrains (1 can be modeled by an appropriae definiion of saes xia 2 (, heir ransiions f, he consrain ses X (,V (, and possibly a erminal reward W T +1 (x(t + 1. We now illusrae he problem formulaion using a concree example. 2.4 Example To simplify he noaion we make wo assumpions ha do no cause any loss of generaliy. Firs we use he oal cos funcion c in (14 in he definiion of he welfare funcion (15. Second we assume each user i has a single ype2 appliance and no baery (so we drop he subscrip a. From Table 1, user uiliy funcions are addiive in ime, U i (q i = U i (q i (; and he consumpion consrains are q i ( q i ( q i (, i (19 Q i T =1 q i(. (20 Since he uiliy funcions are separable in, we do no need o define x 4 (. We now describe he (1 + T period dynamic program by specifying he definiion of x 2 (, he sae ransiion funcion f, and he consrain ses X (,V (. The sysem sae x( := (x 1 (,x 2 (,x 3 ( consiss of hree componens of appropriae dimensions wih x( = (P d,x 2 (,P r (, = 1,...,T where x 2 ( is deermined by he consrain (20. Define x 2 i ( o be he remaining demand of user i a he beginning of each period : x 2 i (1 = Q i, and for each =
13 Opimal demand response: problem formulaion and deerminisic case 13 1,...,T, xi 2( +1 = x2 i ( v i( where v i ( = q i (. To enforce ha x 2 (T +1 0, we define he erminal cos c T +1 (x(t + 1 = 0 if x 2 (T N and c T +1 (x(t + 1 = oherwise, where 0 n is he ndimensional zero vecor. Le he iniial sae be x(0 = 0 T +N+1. Denoe Q := (Q i, i. The sysem dynamics is hen linear imevarying: ( 0 I T x(1 = x(0 + T v(0 + Q 0 (N+1 T P r (1 ( IT x( + 1 = +N 0 T +N x( 0 T N ( 0T I 0 T +N 0 N v( + +N P 1 r ( + 1, 1 T 0 where I n is he n n idenify marix, 0 m n he m n zero marix, and P r (T +1 := 0. The welfare in each period, under inpu sequence v, is (using (14 and for = 1,...,T, W v 0 (x(0,v(0 := T τ=1c d (P d (τ;τ = W v (x(,v( ( := U i (q i (; c o [Q( P r (] P d( 0 ; i ( [1v( = U i (v i (; c o x 3 ( ] [x 1 (] ; 0 i T τ=1 c d ([v(0] τ ;τ c b ( [Q( Pr ( P d (] + ; c b ( [1v( x 3 ( [x 1 (] ] + ; where 1 is he (row vecor of 1 s. The consrain (19 yields he inpu consrain ses V (0 := R T + and, for = 1,...,T, V ( := {q( R N q( q( q(}. There is no consrain on he sae, i.e., X ( = R T +N+1. Le φ := {φ 0 : R T +N+1 R T +, φ : R T +N+1 V (, = 1,...,T } be he conrol policy so ha v( = φ (x(, 0 T. Then he welfare maximizaion problem (18 is ( max φ E W φ T 0 (x(0,v(0 + W φ (x(,v( c T +1 (x(t + 1 =1 where he sae x( and he inpu v( are obained under policy φ. In [21] we sudy he problem (21 in deail. We propose a disribued heurisic algorihm o solve he (1 + T period dynamic program. We prove ha he algorihm is opimal when he welfare is quadraic and he LSEs procuremen decisions are sricly posiive. Oherwise, we bound he gap beween he welfare achieved by he heurisic algorihm and he maximum. Simulaion resuls sugges ha he performance of he heurisic algorihm is very close o opimal. As we scale up he size of a renewable generaion plan, boh is mean producion and is variance will likely (21
14 14 Lijun Chen, Na Li, Libin Jiang, and Seven H. Low increase. As expeced, he maximum welfare increases wih he mean producion, when he variance is fixed, and decreases wih he variance, when he mean is fixed. More ineresing, we prove ha as we scale he size of he plan up, he maximum welfare increases. 3 Opimal scheduling wihou supply uncerainy In his paper we only fully rea he case where here is no supply uncerainy, i.e., P r ( 0. Our goal is o opimally coordinae supply and demand o maximize social welfare. In he absence of uncerainy (our model also ignores demand uncerainy, i becomes unnecessary o adap user consumpions in realime and hence supply and consumpions can be opimally scheduled a once insead of over wo days. Welfare maximizaion (18 hen akes a simpler form and we develop an offline disribued algorihm ha joinly opimizes he LSE s procuremens and he users consumpions for each period in he following day. 3.1 Opimal procuremens and consumpions We firs consider LSE s procuremen decisions. Recall ha Q i ( := a Ai q ia ( and i Q i ( is he aggregae demand in period. Wih supply uncerainy, while P d is decided a day ahead, he opimizaion (12 mus be carried ou in real ime afer P r ( has been realized o obain opimal P o (,P b (. Here, on he oher hand, all hree decisions (P d (,P o (,P b ( can be compued in advance in he absence of uncerainy. Hence, given an aggregae demand i Q i (, he LSE solves (insead of (12 (13: ( c Q i (; i := min P d (,P o (,P b ( c d(p d (; + c o (P o (; + c b (P b (; (22 s.. P o ( + P b ( Q i (, P d ( P o ( 0, P b ( 0 i o obain he oal cos. The soluion of (22 specifies he opimal decisions (P d (,P o (,P b ( o saisfy he aggregae demand i Q i ( for each period in he following day. I is no difficul o show ha c(, is an nondecreasing, convex, and coninuously differeniable funcion for each, so he problem (22 is convex. Since c d (P; > 0, he KKT condiion implies ha P d ( = P o ( a opimaliy, i.e., i is opimal o exhaus all he dayahead capaciy. This is always possible because all procuremen decisions are compued joinly wihou uncerainy. If we furher assume ha he marginal cos of he balancing power is higher han ha of he dayahead power, i.e., c b (0; > c d (P; + c o(p; for all P 0, hen KKT implies ha
15 Opimal demand response: problem formulaion and deerminisic case 15 i will never pay o use balancing power, i.e., Pb ( = 0 a opimaliy. In his case, Pd ( = P o ( = i Q i (. Hence welfare maximizaion reduces o he compuaion of he user consumpions q ia (; he corresponding procuremen decisions are hen given by (22. The opimizaion of he social welfare in (15 hen becomes: ( max U ia (q ia c Q i (; (23 q i,a i s.. A ia q ia η ia, a A i, i, (24 0 Q i ( Q i, i (25 The inequaliies in (24 are he consumpion consrains (1 of user i s appliances and baery. The lower inequaliy in (25 is he same as (11; see he discussion a he end of Secion 2.1 on baery consrains. The upper inequaliy in (25 imposes a bound on he oal power drawn by user i. By assumpion, he objecive funcion is concave and he feasible se is convex. Hence an opimal poin can in principle be compued offline cenrally by he LSE. This however will require ha he LSE know all he users uiliy and baery cos funcions and all he consrains, which is impracical for echnical or privacy reasons. The objecive funcion in (23 and he consrains (24 (25 can be decomposed ino subproblems ha are solvable in a decenralized manner where he LSE only needs o know he aggregae demand bu no he individual privae informaion. The key idea is for he LSE o se prices π := (π(, o induce he users o individually choose socially opimal consumpions q i := (q ia (, in response. Indeed, given prices π, we assume ha each user i chooses is own demand q i so as o maximize is ne benefi, her oal uiliy minus he elecriciy cos, i.e., each user i solves: max q i U ia (q ia a A i π(q i ( s.. (24 (25. (26 Given prices π, we denoe an opimal soluion of (26 and he corresponding aggregae demand by ( q i (π := (q ia (;π,, a A i, Q i (π := (Q i (;π, := q i,a (;π,. a A i Recall q(π := (q i (π, i. I is a remarkable fac in economics ha here exis prices π ha align he users objecives and he LSE s objecive of maximizing welfare, i.e., here are prices π such ha if q i (π opimize i s objecives for all users i hen hey also opimize he social welfare. Definiion 1. A consumpion vecor q is called opimal if i solves (23 (25. A price vecor π is called opimal if q(π is opimal, i.e., any soluion q(π of (26 also solves (23 (25.
16 16 Lijun Chen, Na Li, Libin Jiang, and Seven H. Low The following resul follows from he welfare heorem in economics. I implies ha seing he prices o he marginal coss of power is opimal. Theorem 1. The prices ha saisfy π ( := c ( i Q i (;π ; 0 are opimal. Proof. Wrie he welfare maximizaion problem as ( max U ia (q ia q i Q i,y i c Y i (; i i,a s.. Y i ( = a A i q ia (, i, where he feasible se Q i is defined by he consrains (24 (25. Clearly, an opimal soluion q exiss. Moreover, here exis Lagrange mulipliers πi (, i,, such ha (aking derivaive wih respec o Y i ( πi ( = c ( Yi (; = c ( q ia(; 0. i i a A i Since he righhand side is independen of i, he LSE can se he prices as π ( := πi ( 0 for all i. One can check ha he KKT condiion for he welfare maximizaion problem are idenical o he KKT condiions for he collecion of users problems. Since all hese problems are convex, he KKT condiions are boh necessary and sufficien for opimaliy. This proves he heorem. 3.2 Offline disribued scheduling algorihm Theorem 1 moivaes a disribued algorihm o compue he opimal prices π and user decisions q(π. The LSE ses prices o be he marginal coss of power and each user solves is own maximizaion problem (26 in response. The model is ha a he beginning of each day he LSE and (he energy managemen sysems of he users ieraively compue he elecriciy prices π( and consumpions q i ( for each period of he following day. These decisions are hen carried ou for ha day. This is an offline algorihm since all decisions are made a once before he day sars. I is decenralized where he LSE only knows he aggregae demand bu no user uiliy funcions or consumpion consrains and he users do no need o coordinae among hemselves bu only respond o common prices. Algorihm 1: Opimal scheduling wihou supply uncerainy For each ieraion k = 1,2,..., afer iniializaion: 1. The LSE collecs aggregae demand forecass, denoed by (Q k i (,, from all users i over a communicaion nework. I updaes he prices o he marginal coss π k+1 ( := c ( i Q k i (; and broadcass (π k+1 (, o all users. 2. Each user i updaes is demands q k+1 i afer receiving π k+1 according o
17 Opimal demand response: problem formulaion and deerminisic case 17 [ ( ( ] Uia q k i q k+1 ia ( = q k ia( + γ q k ia ( πk+1 ( where γ > 0 is a consan sepsize, and [ ] Qi denoes he projecion ono he feasible se Q i specified by consrains (24 (25. User i s aggregae demand forecas in period is updaed o Qi k+1 ( = a Ai q k+1 ia (. 3. Incremen ieraion index o k + 1 and goo Sep 1. Algorihm 1 converges asympoically o opimal prices π and opimal consumpions q(π, provided he sepsize γ > 0 is small enough. Theorem 2. Suppose he uiliy funcions U ia (q ia are sricly concave for all i,a. Suppose he Hessian marices 2 U ia and he second derivaive c ( ; are boh uniformly bounded. Then he sequence (π k,q k generaed by Algorihm 1 converges o he opimal price and consumpion vecor (π,q(π, provided γ > 0 is sufficienly small. Proof. Le he welfare funcion be h(q := i,a U ia (q ia c ( Q i (; i Then h(q is sricly concave since U ia (q ia are sricly concave. The gradien h(q has componens ( [ h(q] ia ( = U ia (q i q ia ( c Q i (; i Hence Algorihm 1 is a gradien projecion algorihm where in each ieraion k, he variable q k is updaed o q k+1 according o: [ ] q k+1 = q k + γ h(q k where Q := Q 1 Q N. Moreover he assumpion in he heorem on 2 U ia and c implies ha h(q is Lipschiz. Then, provided γ > 0 is small enough, any accumulaion poin q of he sequence q k generaed by Algorihm 1 is opimal, i.e., maximizes welfare h(q [40, p. 214]. The consrains (24 (25 imply ha he sequence q k lies in a compac se and hence mus have a convergen subsequence. Bu sric concaviy of h implies ha he opimal q is unique. Therefore all convergen subsequences, hence he original sequence q k, mus converge o q. By coninuiy of c, π k ( = c ( i Q k i (; converges o he unique price c ( i Q i (; which, by Theorem 1, is opimal. We simulae his algorihm in [39] wih realisic sysem parameers. The simulaion resuls show ha, as expeced, he prices are capable of coordinaing he Q Q i
18 18 Lijun Chen, Na Li, Libin Jiang, and Seven H. Low decisions of differen appliances in a decenralized manner, o reduce peak aggregae demand and flaen is profile, grealy increasing he load facor. Furhermore, baery amplifies he benefis of demand response. Appendix: Deailed appliance models We describe deailed models of common elecric appliances summarized in Secion 2.1. Type 1. This caegory of appliances includes lighing ha mus be on for a cerain period of ime. The consumpion consrain is (6, wih he undersanding ha q ia ( = q ia ( = 0 for periods ha are ouside is ime of operaion. User i aains a uiliy U ia (q ia (, from consuming power q ia ( independen of is consumpion in oher periods, and he overall uiliy (2 is herefore separable in. Type 2. This caegory includes TV, video games, and compuers. For hese appliances, a user s uiliy depends on her consumpion in each period she wishes o use i as well as he oal amoun of consumpion in a day. Hence he consumpion consrains are (6 and (7. For example, a user may have a favorie TV program ha she wishes o wach everyday. Wih DVR, she can wach he program a any ime. However he oal power demand of TV should a leas cover he program. Type 2 appliances have he same kind of uiliy funcions (2 as Type 1 appliances. The ime dependen uiliy funcion models he fac ha a user may ge differen benefis from consuming he same amoun of power a differen imes, e.g., she may enjoy a TV program o differen levels a differen imes. Type 3. This caegory includes PHEV, dish washer, clohes washer. For hese appliances, a user only cares abou wheher he ask is compleed by a cerain ime. This means ha he aggregae power consumpion by such an appliance mus exceed a hreshold wihin is ime of operaion [28, 29, 33]. Hence he consumpion consrains are (6 and (7. The uiliy depends only on he oal power consumed, hence (3. Type 4. This caegory includes HVAC (heaing, venilaion, air condiioning and refrigeraor ha conrol he emperaure of a user s environmen. Le Tia in ( and Tia ou ( denoe he emperaures a ime inside and ouside he place ha appliance (i,a is in charge of, and T ia denoes he se of imes when user i cares abou he emperaure. For insance, for air condiioner, Tia in ( is he emperaure inside he house, Tia ou( is he emperaure ouside he house, and T ia is he se of imes when she is a home. The inside emperaure evolves according o he following linear dynamics [27, 9, 26]: T in ia ( = T in ia ( 1 + α(tia ou ( T in ia ( 1 + βq ia ( (27
19 Opimal demand response: problem formulaion and deerminisic case 19 where α and β are parameers ha specify hermal characerisics of he appliance and he environmen in which i operaes. The second erm in equaion (27 models hea ransfer. The hird erm models he hermal efficiency of he sysem; β > 0 if appliance a is a heaer and β < 0 if i is a cooler. Here, we define Tia in (0 as he emperaure Tia in(t from he previous day. Le [T ia, T ia ] be a range of preferred emperaure, leading o he consrain: T ia T in ia ( T ia, T ia. (28 Using Equaion (27, we can wrie T in ia ( in erms of (q ia(τ,τ = 1,...,: Tia in ( = (1 α Tia in (0 + Define Then τ=1 T ia ( := (1 α Tia in (0 + T in ia ( = T ia ( + β (1 α τ αt ou (τ + β τ=1 τ=1 ia τ=1 (1 α τ q ia (τ. (1 α τ αtia ou (τ. (29 (1 α τ q ia (τ. (30 Wih (30, he consrain (28 becomes a linear consrain on he load vecor q ia : for any T ia, T ia T ia ( + β τ=1 (1 α τ q ia (τ T ia. This is he consrain (8, in addiion o (6. Assume user i aains a uiliy U ia (Tia in( when he emperaure is Ti,a in (. Then (30 gives he uiliy funcion (4. References 1. C. W. Gellings and J. H. Chamberlin. DemandSide Managemen: Conceps and Mehods. The Fairmon Press, M. H. Albadi and E. F. ElSaadany. Demand response in elecriciy markes: An overview. In Proceedings of he IEEE Power Engineering Sociey General Meeing, June A. I. Cohen and C. C. Wang. An opimizaion mehod for load managemen scheduling. IEEE Transacions on Power Sysems, 3(2: , May Y. Y. Hsu and C. C. Su. Dispach of direc load conrol using dynamic programming. IEEE Transacions on Power Sysems, 6(3: , Augus D. C. Wei and N. Chen. Air condiioner direc load conrol by mulipass dynamic programming. IEEE Transacions on Power Sysems, 10(1: , February J. Chen, F. N. Lee, A. M. Breipohl, and R. Adapa. Scheduling direc load conrol o minimize sysem operaion cos. IEEE Transacions on Power Sysems, 10(4: , November 1995.
20 20 Lijun Chen, Na Li, Libin Jiang, and Seven H. Low 7. K. H. Ng and G. B. Sheble. Direc load conrol a profibased load managemen using linear programming. IEEE Transacions on Power Sysems, 13(2: , May W.C. Chu, B.K. Chen, and C.K. Fu. Scheduling of direc load conrol o minimize load reducion for a uiliy suffering from generaion shorage. IEEE Transacions on Power Sysems, 8(4: , November B. Ramanahan and V. Vial. A framework for evaluaion of advanced direc load conrol wih minimum disrupion. IEEE Transacions on Power Sysems, 23(4: , November M. D. Ilic, L. Xie, and J.Y. Joo. Efficien coordinaion of wind power and priceresponsive demand par I: Theoreical foundaions; par II: Case sudies. IEEE Transacions on Power Sysems, 99, Y. V. Makarov, C. Louan, J. Ma, and P. de Mello. Operaional impacs of wind generaion on California power sysems. IEEE Transacions on Power Sysems, 24(2: , May M. C. Caramanis and J. M. Foser. Coupling of day ahead and realime power markes for energy and reserves incorporaing local disribuion nework coss and congesion. In Proceedings of he 48h Annual Alleron Conference, Sepember Ocober D. Kirschen. Demandside view of elecriciy marke. IEEE Transacions on Power Sysems, 18(2: , May J. C. Smih, M. R. Milligan, E. A. DeMeo, and B. Parsons. Uiliy wind inegraion and operaing impac: Sae of he ar. IEEE Transacions on Power Sysems, 22(3: , Augus N. Ruiz, I. Cobelo, and J. Oyarzabal. A direc load conrol model for virual power plan managemen. IEEE Transacions on Power Sysems, 24(2: , May P. P. Varaiya, F. F. Wu, and J. W. Bialek. Smar operaion of smar grid: Risklimiing dispach. Proceedings of he IEEE, 99(1:40 57, January Deparmen of Energy. Benefis of demand response in elecriciy markes and recommendaions for achieving hem. Technical repor, February S. Borensein. Timevarying reail elecriciy prices: Theory and pracice. In Griffin and Puller, ediors, Elecriciy Deregulaion: Choices and Challenges. Universiy of Chicago Press, C. Triki and A. Violi. Dynamic pricing of elecriciy in reail markes. Quarerly Journal of Operaions Research, 7(1:21 36, March M. D. Ilic. Dynamic monioring and decision sysems for enabling susainable energy services. Proceedings of he IEEE, 99(1:58 79, January L. Jiang and S. H. Low. Opimal demand response: wih uncerain supply. In Technical Repor, P. M. Schwarz, T. N. Taylor, M. Birmingham, and S. L. Dardan. Indusrial response o elecriciy realime prices: Shor run and long run. Economic Inquiry, 40(4: , C. Goldman, N. Hopper, R. Bharvirkar, B. Neenan, R. Boisver, P. Cappers, D. Pra, and K. Bukins. Cusomer sraegies for responding o dayahead marke hourly elecriciy pricing. Technical repor, Lawrence Berkeley Naional Lab, LBNL57128, Augus Repor for CA Energy Commission. 24. T. N. Taylor, P. M. Schwarz, and J. E. Cochell hourly response o realime pricing wih up o eigh summers of experience. Journal of Regulaory Economics, 27(3: , January S. Borensein. The longrun efficiency of realime elecriciy pricing. The Energy Journal, 26(3:93 116, Febuary J.E. Braun. Load conrol using building hermal mass. Journal of solar energy engineering, 125(3: , Augus P. Xu, P. Haves, M. A. Piee, and L. Zagreus. Demand shifing wih hermal mass in large commercial buildings: Field ess, simulaion and audis. Technical repor, Lawrence Berkeley Naional Lab, LBNL58815, A. MohsenianRad and A. LeonGarcia. Opimal residenial load conrol wih price predicion in realime elecriciy pricing environmens. IEEE Transacions on Smar Grid, 1(2: , Sepember 2010.
PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More informationTask is a schedulable entity, i.e., a thread
RealTime Scheduling Sysem Model Task is a schedulable eniy, i.e., a hread Time consrains of periodic ask T:  s: saring poin  e: processing ime of T  d: deadline of T  p: period of T Periodic ask T
More informationThe Application of Multi Shifts and Break Windows in Employees Scheduling
The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance
More informationStochastic Optimal Control Problem for Life Insurance
Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian
More informationResearch on Inventory Sharing and Pricing Strategy of Multichannel Retailer with Channel Preference in Internet Environment
Vol. 7, No. 6 (04), pp. 365374 hp://dx.doi.org/0.457/ijhi.04.7.6.3 Research on Invenory Sharing and Pricing Sraegy of Mulichannel Reailer wih Channel Preference in Inerne Environmen Hanzong Li College
More informationDETERMINISTIC INVENTORY MODEL FOR ITEMS WITH TIME VARYING DEMAND, WEIBULL DISTRIBUTION DETERIORATION AND SHORTAGES KUNSHAN WU
Yugoslav Journal of Operaions Research 2 (22), Number, 67 DEERMINISIC INVENORY MODEL FOR IEMS WIH IME VARYING DEMAND, WEIBULL DISRIBUION DEERIORAION AND SHORAGES KUNSHAN WU Deparmen of Bussines Adminisraion
More informationANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS
ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,
More informationMODEL AND ALGORITHMS FOR THE REAL TIME MANAGEMENT OF RESIDENTIAL ELECTRICITY DEMAND. A. Barbato, G. Carpentieri
MODEL AND ALGORITHMS FOR THE REAL TIME MANAGEMENT OF RESIDENTIAL ELECTRICITY DEMAND A. Barbao, G. Carpenieri Poliecnico di Milano, Diparimeno di Eleronica e Informazione, Email: barbao@ele.polimi.i, giuseppe.carpenieri@mail.polimi.i
More informationIndividual Health Insurance April 30, 2008 Pages 167170
Individual Healh Insurance April 30, 2008 Pages 167170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
More informationSinglemachine Scheduling with Periodic Maintenance and both Preemptive and. Nonpreemptive jobs in Remanufacturing System 1
Absrac number: 050407 Singlemachine Scheduling wih Periodic Mainenance and boh Preempive and Nonpreempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy
More informationOption PutCall Parity Relations When the Underlying Security Pays Dividends
Inernaional Journal of Business and conomics, 26, Vol. 5, No. 3, 22523 Opion Puall Pariy Relaions When he Underlying Securiy Pays Dividends Weiyu Guo Deparmen of Finance, Universiy of Nebraska Omaha,
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More informationAs widely accepted performance measures in supply chain management practice, frequencybased service
MANUFACTURING & SERVICE OPERATIONS MANAGEMENT Vol. 6, No., Winer 2004, pp. 53 72 issn 523464 eissn 5265498 04 060 0053 informs doi 0.287/msom.030.0029 2004 INFORMS On Measuring Supplier Performance Under
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationAnalysis of Pricing and Efficiency Control Strategy between Internet Retailer and Conventional Retailer
Recen Advances in Business Managemen and Markeing Analysis of Pricing and Efficiency Conrol Sraegy beween Inerne Reailer and Convenional Reailer HYUG RAE CHO 1, SUG MOO BAE and JOG HU PARK 3 Deparmen of
More informationDistributing Human Resources among Software Development Projects 1
Disribuing Human Resources among Sofware Developmen Proecs Macario Polo, María Dolores Maeos, Mario Piaini and rancisco Ruiz Summary This paper presens a mehod for esimaing he disribuion of human resources
More informationDuration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.
Graduae School of Business Adminisraion Universiy of Virginia UVAF38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised
More informationMorningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion
More informationNiche Market or Mass Market?
Niche Marke or Mass Marke? Maxim Ivanov y McMaser Universiy July 2009 Absrac The de niion of a niche or a mass marke is based on he ranking of wo variables: he monopoly price and he produc mean value.
More informationChapter 1.6 Financial Management
Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1
More informationMultiprocessor SystemsonChips
Par of: Muliprocessor SysemsonChips Edied by: Ahmed Amine Jerraya and Wayne Wolf Morgan Kaufmann Publishers, 2005 2 Modeling Shared Resources Conex swiching implies overhead. On a processing elemen,
More informationOptimal Investment and Consumption Decision of Family with Life Insurance
Opimal Invesmen and Consumpion Decision of Family wih Life Insurance Minsuk Kwak 1 2 Yong Hyun Shin 3 U Jin Choi 4 6h World Congress of he Bachelier Finance Sociey Torono, Canada June 25, 2010 1 Speaker
More informationWorking Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits
Working Paper No. 482 Ne Inergeneraional Transfers from an Increase in Social Securiy Benefis By Li Gan Texas A&M and NBER Guan Gong Shanghai Universiy of Finance and Economics Michael Hurd RAND Corporaion
More informationA Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
More informationLongevity 11 Lyon 79 September 2015
Longeviy 11 Lyon 79 Sepember 2015 RISK SHARING IN LIFE INSURANCE AND PENSIONS wihin and across generaions Ragnar Norberg ISFA Universié Lyon 1/London School of Economics Email: ragnar.norberg@univlyon1.fr
More informationDYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS
DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper
More informationThe Grantor Retained Annuity Trust (GRAT)
WEALTH ADVISORY Esae Planning Sraegies for closelyheld, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business
More informationINTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES
INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchangeraded ineres rae fuures and heir opions are described. The fuure opions include hose paying
More informationPATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM
PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM WILLIAM L. COOPER Deparmen of Mechanical Engineering, Universiy of Minnesoa, 111 Church Sree S.E., Minneapolis, MN 55455 billcoop@me.umn.edu
More informationMACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR
MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR The firs experimenal publicaion, which summarised pas and expeced fuure developmen of basic economic indicaors, was published by he Minisry
More informationTEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS
TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.
More informationGraduate Macro Theory II: Notes on Neoclassical Growth Model
Graduae Macro Theory II: Noes on Neoclassical Growh Model Eric Sims Universiy of Nore Dame Spring 2011 1 Basic Neoclassical Growh Model The economy is populaed by a large number of infiniely lived agens.
More informationA RealTime Pricing Model for Electricity Consumption
A RealTime Pricing Model Elecriciy Consumpion Ranjan Pal Universiy o Souhern Calinia Email: rpal@usc.edu Absrac The Calinia elecric company, i.e., PG&E (Paciic Gas and Elecric Co.,), has recenly announced
More information11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic DS dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuingedge
More informationMarket Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand
36 Invesmen Managemen and Financial Innovaions, 4/4 Marke Liquidiy and he Impacs of he Compuerized Trading Sysem: Evidence from he Sock Exchange of Thailand Sorasar Sukcharoensin 1, Pariyada Srisopisawa,
More informationInternational Journal of Supply and Operations Management
Inernaional Journal of Supply and Operaions Managemen IJSOM May 05, Volume, Issue, pp 5547 ISSNPrin: 859 ISSNOnline: 855 wwwijsomcom An EPQ Model wih Increasing Demand and Demand Dependen Producion
More informationAnalogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar
Analogue and Digial Signal Processing Firs Term Third Year CS Engineering By Dr Mukhiar Ali Unar Recommended Books Haykin S. and Van Veen B.; Signals and Sysems, John Wiley& Sons Inc. ISBN: 073807 Ifeachor
More informationDEMAND FORECASTING MODELS
DEMAND FORECASTING MODELS Conens E2. ELECTRIC BILLED SALES AND CUSTOMER COUNTS Sysemlevel Model Counylevel Model Easside King Counylevel Model E6. ELECTRIC PEAK HOUR LOAD FORECASTING Sysemlevel Forecas
More informationDependent Interest and Transition Rates in Life Insurance
Dependen Ineres and ransiion Raes in Life Insurance Krisian Buchard Universiy of Copenhagen and PFA Pension January 28, 2013 Absrac In order o find marke consisen bes esimaes of life insurance liabiliies
More informationWhy Did the Demand for Cash Decrease Recently in Korea?
Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in
More informationChapter 5. Aggregate Planning
Chaper 5 Aggregae Planning Supply Chain Planning Marix procuremen producion disribuion sales longerm Sraegic Nework Planning miderm shorerm Maerial Requiremens Planning Maser Planning Producion Planning
More informationARCH 2013.1 Proceedings
Aricle from: ARCH 213.1 Proceedings Augus 14, 212 Ghislain Leveille, Emmanuel Hamel A renewal model for medical malpracice Ghislain Léveillé École d acuaria Universié Laval, Québec, Canada 47h ARC Conference
More informationAppendix D Flexibility Factor/Margin of Choice Desktop Research
Appendix D Flexibiliy Facor/Margin of Choice Deskop Research Cheshire Eas Council Cheshire Eas Employmen Land Review Conens D1 Flexibiliy Facor/Margin of Choice Deskop Research 2 Final Ocober 2012 \\GLOBAL.ARUP.COM\EUROPE\MANCHESTER\JOBS\200000\22348900\4
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationImpact of scripless trading on business practices of Subbrokers.
Impac of scripless rading on business pracices of Subbrokers. For furher deails, please conac: Mr. T. Koshy Vice Presiden Naional Securiies Deposiory Ld. Tradeworld, 5 h Floor, Kamala Mills Compound,
More informationStrategic Optimization of a Transportation Distribution Network
Sraegic Opimizaion of a Transporaion Disribuion Nework K. John Sophabmixay, Sco J. Mason, Manuel D. Rossei Deparmen of Indusrial Engineering Universiy of Arkansas 4207 Bell Engineering Cener Fayeeville,
More informationA OneSector Neoclassical Growth Model with Endogenous Retirement. By Kiminori Matsuyama. Final Manuscript. Abstract
A OneSecor Neoclassical Growh Model wih Endogenous Reiremen By Kiminori Masuyama Final Manuscrip Absrac This paper exends Diamond s OG model by allowing he agens o make he reiremen decision. Earning a
More informationSmooth Priorities for MultiProduct Inventory Control
Smooh rioriies for Muliroduc Invenory Conrol Francisco José.A.V. Mendonça*. Carlos F. Bispo** *Insiuo Superior Técnico  Universidade Técnica de Lisboa (email:favm@mega.is.ul.p) ** Insiuo de Sisemas e
More informationChapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
More informationBALANCE OF PAYMENTS. First quarter 2008. Balance of payments
BALANCE OF PAYMENTS DATE: 20080530 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College  Physics 2426  Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationAnalysis of Tailored BaseSurge Policies in Dual Sourcing Inventory Systems
Analysis of Tailored BaseSurge Policies in Dual Sourcing Invenory Sysems Ganesh Janakiraman, 1 Sridhar Seshadri, 2, Anshul Sheopuri. 3 Absrac We sudy a model of a firm managing is invenory of a single
More informationEfficient Risk Sharing with Limited Commitment and Hidden Storage
Efficien Risk Sharing wih Limied Commimen and Hidden Sorage Árpád Ábrahám and Sarola Laczó March 30, 2012 Absrac We exend he model of risk sharing wih limied commimen e.g. Kocherlakoa, 1996) by inroducing
More informationOptimal Stock Selling/Buying Strategy with reference to the Ultimate Average
Opimal Sock Selling/Buying Sraegy wih reference o he Ulimae Average Min Dai Dep of Mah, Naional Universiy of Singapore, Singapore Yifei Zhong Dep of Mah, Naional Universiy of Singapore, Singapore July
More information17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides
7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion
More informationVector Autoregressions (VARs): Operational Perspectives
Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101115. Macroeconomericians
More informationJournal Of Business & Economics Research September 2005 Volume 3, Number 9
Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy YiKang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More informationPrice elasticity of demand for crude oil: estimates for 23 countries
Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh
More informationApplied Intertemporal Optimization
. Applied Ineremporal Opimizaion Klaus Wälde Universiy of Mainz CESifo, Universiy of Brisol, UCL Louvain la Neuve www.waelde.com These lecure noes can freely be downloaded from www.waelde.com/aio. A prin
More informationPerformance Center Overview. Performance Center Overview 1
Performance Cener Overview Performance Cener Overview 1 ODJFS Performance Cener ce Cener New Performance Cener Model Performance Cener Projec Meeings Performance Cener Execuive Meeings Performance Cener
More informationPremium Income of Indian Life Insurance Industry
Premium Income of Indian Life Insurance Indusry A Toal Facor Produciviy Approach Ram Praap Sinha* Subsequen o he passage of he Insurance Regulaory and Developmen Auhoriy (IRDA) Ac, 1999, he life insurance
More informationPrincipal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.
Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one
More informationInventory Planning with Forecast Updates: Approximate Solutions and Cost Error Bounds
OPERATIONS RESEARCH Vol. 54, No. 6, November December 2006, pp. 1079 1097 issn 0030364X eissn 15265463 06 5406 1079 informs doi 10.1287/opre.1060.0338 2006 INFORMS Invenory Planning wih Forecas Updaes:
More informationpolicies are investigated through the entire product life cycle of a remanufacturable product. Benefiting from the MDP analysis, the optimal or
ABSTRACT AHISKA, SEMRA SEBNEM. Invenory Opimizaion in a One Produc Recoverable Manufacuring Sysem. (Under he direcion of Dr. Russell E. King and Dr. Thom J. Hodgson.) Environmenal regulaions or he necessiy
More informationEnergy and Performance Management of Green Data Centers: A Profit Maximization Approach
Energy and Performance Managemen of Green Daa Ceners: A Profi Maximizaion Approach Mahdi Ghamkhari, Suden Member, IEEE, and Hamed MohsenianRad, Member, IEEE Absrac While a large body of work has recenly
More informationDistributed and Secure Computation of Convex Programs over a Network of Connected Processors
DCDIS CONFERENCE GUELPH, ONTARIO, CANADA, JULY 2005 1 Disribued and Secure Compuaion of Convex Programs over a Newor of Conneced Processors Michael J. Neely Universiy of Souhern California hp://wwwrcf.usc.edu/
More informationLIFE INSURANCE WITH STOCHASTIC INTEREST RATE. L. Noviyanti a, M. Syamsuddin b
LIFE ISURACE WITH STOCHASTIC ITEREST RATE L. oviyani a, M. Syamsuddin b a Deparmen of Saisics, Universias Padjadjaran, Bandung, Indonesia b Deparmen of Mahemaics, Insiu Teknologi Bandung, Indonesia Absrac.
More informationRealtime Particle Filters
Realime Paricle Filers Cody Kwok Dieer Fox Marina Meilă Dep. of Compuer Science & Engineering, Dep. of Saisics Universiy of Washingon Seale, WA 9895 ckwok,fox @cs.washingon.edu, mmp@sa.washingon.edu Absrac
More informationDynamic programming models and algorithms for the mutual fund cash balance problem
Submied o Managemen Science manuscrip Dynamic programming models and algorihms for he muual fund cash balance problem Juliana Nascimeno Deparmen of Operaions Research and Financial Engineering, Princeon
More informationUNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES. Nadine Gatzert
UNDERSTANDING THE DEATH BENEFIT SWITCH OPTION IN UNIVERSAL LIFE POLICIES Nadine Gazer Conac (has changed since iniial submission): Chair for Insurance Managemen Universiy of ErlangenNuremberg Lange Gasse
More informationPlanning Demand and Supply in a Supply Chain. Forecasting and Aggregate Planning
Planning Demand and Supply in a Supply Chain Forecasing and Aggregae Planning 1 Learning Objecives Overview of forecasing Forecas errors Aggregae planning in he supply chain Managing demand Managing capaciy
More information4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
More informationRelationships between Stock Prices and Accounting Information: A Review of the Residual Income and Ohlson Models. Scott Pirie* and Malcolm Smith**
Relaionships beween Sock Prices and Accouning Informaion: A Review of he Residual Income and Ohlson Models Sco Pirie* and Malcolm Smih** * Inernaional Graduae School of Managemen, Universiy of Souh Ausralia
More informationABSTRACT KEYWORDS. Markov chain, Regulation of payments, Linear regulator, Bellman equations, Constraints. 1. INTRODUCTION
QUADRATIC OPTIMIZATION OF LIFE AND PENSION INSURANCE PAYMENTS BY MOGENS STEFFENSEN ABSTRACT Quadraic opimizaion is he classical approach o opimal conrol of pension funds. Usually he paymen sream is approximaed
More informationHedging with Forwards and Futures
Hedging wih orwards and uures Hedging in mos cases is sraighforward. You plan o buy 10,000 barrels of oil in six monhs and you wish o eliminae he price risk. If you ake he buyside of a forward/fuures
More informationNetwork Effects, Pricing Strategies, and Optimal Upgrade Time in Software Provision.
Nework Effecs, Pricing Sraegies, and Opimal Upgrade Time in Sofware Provision. YiNung Yang* Deparmen of Economics Uah Sae Universiy Logan, UT 84322353 April 3, 995 (curren version Feb, 996) JEL codes:
More informationRisk Modelling of Collateralised Lending
Risk Modelling of Collaeralised Lending Dae: 4112008 Number: 8/18 Inroducion This noe explains how i is possible o handle collaeralised lending wihin Risk Conroller. The approach draws on he faciliies
More informationUSE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES
USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were
More informationTowards Optimal Capacity Segmentation with Hybrid Cloud Pricing
Towards Opimal Capaciy Segmenaion wih Hybrid Cloud Pricing Wei Wang, Baochun Li, and Ben Liang Deparmen of Elecrical and Compuer Engineering Universiy of Torono Absrac Cloud resources are usually priced
More informationOptimal Life Insurance Purchase, Consumption and Investment
Opimal Life Insurance Purchase, Consumpion and Invesmen Jinchun Ye a, Sanley R. Pliska b, a Dep. of Mahemaics, Saisics and Compuer Science, Universiy of Illinois a Chicago, Chicago, IL 667, USA b Dep.
More informationFebruary 8, 2009. An Economic Framework of Demand Response in Restructured Electricity Markets. Hungpo Chao 1 ABSTRACT
February 8, 2009 An Economic Framework of Demand Response in Resrucured Elecriciy Markes Hungpo Chao 1 ABSTRACT This paper provides a unified economic framework for assessing he effeciveness of priceresponsive
More informationForecasting and Information Sharing in Supply Chains Under QuasiARMA Demand
Forecasing and Informaion Sharing in Supply Chains Under QuasiARMA Demand Avi Giloni, Clifford Hurvich, Sridhar Seshadri July 9, 2009 Absrac In his paper, we revisi he problem of demand propagaion in
More informationModel predictive control for a smart solar tank based on weather and consumption forecasts
Available online a www.sciencedirec.com Energy Procedia 30 (2012 ) 270 278 SHC 2012 Model predicive conrol for a smar solar an based on weaher and consumpion forecass Rasmus Halvgaard a*, Peder Bacher
More informationThe Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of
Prof. Harris Dellas Advanced Macroeconomics Winer 2001/01 The Real Business Cycle paradigm The RBC model emphasizes supply (echnology) disurbances as he main source of macroeconomic flucuaions in a world
More informationTo Sponsor or Not to Sponsor: Sponsored Search Auctions with Organic Links and Firm Dependent ClickThrough Rates
To Sponsor or No o Sponsor: Sponsored Search Aucions wih Organic Links and Firm Dependen ClickThrough Raes Michael Arnold, Eric Darmon and Thierry Penard June 5, 00 Draf: Preliminary and Incomplee Absrac
More informationPresent Value Methodology
Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer
More informationThe Interaction of Guarantees, Surplus Distribution, and Asset Allocation in With Profit Life Insurance Policies
1 The Ineracion of Guaranees, Surplus Disribuion, and Asse Allocaion in Wih Profi Life Insurance Policies Alexander Kling * Insiu für Finanz und Akuarwissenschafen, Helmholzsr. 22, 89081 Ulm, Germany
More informationOptimal Power Cost Management Using Stored Energy in Data Centers
Opimal Power Cos Managemen Using Sored Energy in Daa Ceners Rahul Urgaonkar, Bhuvan Urgaonkar, Michael J. Neely, Anand Sivasubramanian Advanced Neworking Dep., Dep. of CSE, Dep. of EE Rayheon BBN Technologies,
More informationMeasuring macroeconomic volatility Applications to export revenue data, 19702005
FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a
More informationEvolutionary building of stock trading experts in realtime systems
Evoluionary building of sock rading expers in realime sysems Jerzy J. Korczak Universié Louis Paseur Srasbourg, France Email: jjk@dpinfo.usrasbg.fr Absrac: This paper addresses he problem of consrucing
More informationRandom Walk in 1D. 3 possible paths x vs n. 5 For our random walk, we assume the probabilities p,q do not depend on time (n)  stationary
Random Walk in D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes
More informationARIMAbased Demand Forecasting Method Considering Probabilistic Model of Electric Vehicles Parking Lots
1 ARIMAbased Demand Forecasing Mehod Considering Probabilisic Model of Elecric Vehicles Parking Los M.H. Amini, Suden Member, IEEE, O. Karabasoglu, Maria D. Ilić, Fellow, IEEE, Kianoosh G. Borooeni Suden
More informationPRACTICES AND ISSUES IN OPERATIONAL RISK MODELING UNDER BASEL II
Lihuanian Mahemaical Journal, Vol. 51, No. 2, April, 2011, pp. 180 193 PRACTICES AND ISSUES IN OPERATIONAL RISK MODELING UNDER BASEL II Paul Embrechs and Marius Hofer 1 RiskLab, Deparmen of Mahemaics,
More informationWe consider a decentralized assembly system in which a buyer purchases components from several firsttier
MANAGEMENT SCIENCE Vol. 55, No. 4, April 2009, pp. 552 567 issn 00251909 eissn 15265501 09 5504 0552 informs doi 10.1287/mnsc.1080.0961 2009 INFORMS Dynamic Cos Reducion Through Process Improvemen in
More informationTowards Optimal Capacity Segmentation with Hybrid Cloud Pricing
Towards Opimal Capaciy Segmenaion wih Hybrid Cloud Pricing Wei Wang, Baochun Li, and Ben Liang Deparmen of Elecrical and Compuer Engineering Universiy of Torono Torono, ON M5S 3G4, Canada weiwang@eecg.orono.edu,
More informationTerm Structure of Prices of Asian Options
Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 111 Nojihigashi, Kusasu, Shiga 5258577, Japan Email:
More informationTowards Optimal Capacity Segmentation with Hybrid Cloud Pricing
Towards Opimal Capaciy Segmenaion wih Hybrid Cloud Pricing Wei Wang, Baochun Li, and Ben Liang Deparmen of Elecrical and Compuer Engineering Universiy of Torono Torono, ON M5S 3G4, Canada weiwang@eecg.orono.edu,
More informationManufacturing Planning and Control
Manufacuring Planning and Conrol Sephen C. Graves Massachuses nsiue of echnology November 999 Manufacuring planning and conrol enails he acquisiion and allocaion of limied resources o producion aciviies
More informationChapter Four: Methodology
Chaper Four: Mehodology 1 Assessmen of isk Managemen Sraegy Comparing Is Cos of isks 1.1 Inroducion If we wan o choose a appropriae risk managemen sraegy, no only we should idenify he influence ha risks
More informationCRISES AND THE FLEXIBLE PRICE MONETARY MODEL. Sarantis Kalyvitis
CRISES AND THE FLEXIBLE PRICE MONETARY MODEL Saranis Kalyviis Currency Crises In fixed exchange rae regimes, counries rarely abandon he regime volunarily. In mos cases, raders (or speculaors) exchange
More information