Wasting the Percentage of Onhand Inventory in an Instantaneous Economic Order Quantity Model Due to Deterioration


 Ashley Stevens
 1 years ago
 Views:
Transcription
1 Jounal of mathematics and compute Science 7 (2013) Wasting the Pecentage of Onhand Inventoy in an Instantaneous Economic Ode Quantity Model Due to Deteioation Aticle histoy: Received Mach 2013 Accepted Api 2013 Available online May 2013 M. Pattnaik Dept. of Business Administation, Utkal Univesity, Bhubaneswa, India Abstact In this pape the taditional instantaneous economic ode quantity model is extended to allow the pecentage of onhand inventoy is wasted due to deteioation. That is, the wasted/ no wasted pecentage of onhand inventoies in instantaneous EOQ models due to deteioation ae consideed simultaneously. Fo any given numbe of eplenishment cycles the existence of a unique optimal eplenishment schedule is poved and futhe the concavity of the total pofit function of the inventoy system in the numbe of eplenishments is established. A new mathematical model is developed and consideed as an enhancement to the EOQ model so that the net pofit is maximized and the numeical analysis show that an appopiate policy can benefit the etaile and that policy is impotant, especially fo wasting of deteioating items. Finally, sensitivity analysis of the optimal solution with espect to the majo paamete, pecentage of onhand inventoy which is lost due to deteioation is also caied out. Keywods: EOQ, Deteioation, Units lost,, Pofit 1. Intoduction Inventoy management plays a cucial ole in businesses since it can help companies each the goal of ensuing pompt delivey, avoiding shotages, helping sales at competitive pices and so foth. The mathematical modeling of ealwold inventoy poblems necessitates the simplification of assumptions to make the mathematics flexible. Howeve, excessive simplification of assumptions esults in mathematical models that do not epesent the inventoy situation to be analyzed. Many models have been poposed to deal with a vaiety of inventoy poblems. The classical analysis of inventoy contol consides thee costs fo holding inventoies. These costs ae the pocuement cost, caying cost and shotage cost. The classical analysis builds a model of an inventoy system and calculates the EOQ which minimize these thee costs so that thei sum is satisfying minimization citeion. One of the unealistic assumptions is that items stocked peseve thei physical chaacteistics duing thei stay in inventoy. Items in stock ae subject to many possible isks, e.g. damage, spoilage, dyness; vapoization etc., those esults decease of usefulness of the oiginal one and a cost is incued to account fo such isks. 154
2 The EOQ inventoy contol model was intoduced in the ealiest decades of this centuy and is still widely accepted by many industies today. Compehensive eviews of inventoy models can be found in [9], [14] and [17]. In pevious deteministic inventoy models, many ae developed unde the assumption that demand is eithe constant o stock dependent fo deteioated items. [7] developed a stochastic dynamic pogamming model pesented fo detemining the optimal odeing policy fo a peishable o potentially obsolete poduct so as to satisfy known timevaying demand ove a specified planning hoizon. They assumed a andom lifetime peishability, whee, at the end of each discete peiod, the total emaining inventoy eithe becomes wothless o emains usable fo at least the next peiod. [8] exploed the inventoy model fo time dependent holding cost and deteioation with salvage value whee shotages ae allowed. [3] examined the simultaneous selection poduct duability and ode quantity fo items that deteioate ove time. Thei choice of poduct duability is modeled as the values of a single design paamete that effects the distibution of the timetoonset of deteioation (TOD) and analyzed two scenaios; the fist consides TOD as a constant and the stoe manage may choose an appopiate value, while the second assumes that TOD is a andom vaiable. [2] consides the effect of diffeent maketing policies, e.g. the pice pe unit poduct and the advetisement fequency on the demand of a peishable item. [1] consideed an economic ode quantity inventoy model fo deteioating goods developed with a linea, positive tend in demand allowing inventoy shotages and backlogging. [1] and [5] consideed the effects of inflation and the timevalue of money with the assumption of two inflation ates athe than one, i.e. the intenal (company) inflation ate and the extenal (geneal economy) inflation ate. [4] agued that the analysis of [1] contained mathematical eos fo which he poposed the coect theoy fo the poblem supplied with numeical examples. [11] explained a single item EOQ model with demand dependent unit cost and vaiable setup cost. [10] pesented an EOQ inventoy model fo peishable items with a stock dependent selling ate. They assumed that the selling ate is a function of the cuent inventoy level and the ate of deteioation is taken to be constant. Unlike the wok of [18] who studied the case of patial backlogging. [10] consideed the cases of no backlogging, and of patial and full backlogging. The most ecent wok found in the liteatue is that of [6] who extended his ealie wok by assuming a timevaying demand ove a finite planning hoizon. [11] who assumes instant deteioation of peishable items with constant demand whee discounts ae allowed. [12] pesented an entopic ode quantity (EnOQ) model unde instant deteioation fo peishable items with constant demand whee discounts ae allowed. [15] studied an EOQ inventoy model in which it assumes that the pecentage of onhand inventoy wasted due to deteioation is a key featue of the inventoy conditions which goven the item stocked. [16] studied pofit maximization economic ode quantity model fo deteioated items with time and pice dependent linea and deceasing demand fo finite planning hoizon unde pomotion facto fo acquiing moe pofit. In this pape, eplenishment decision unde wasting the pecentage of onhand inventoy due to deteioation ae adjusted abitaily upwad o downwad fo pofit maximization model in esponse to the change in maket demand within the finite planning hoizon. The objective of this pape is to detemine optimal eplenishment quantities in an instantaneous eplenishment pofit maximization model. All mentioned above inventoy liteatues with deteioation o no wasting the pecentage of onhand inventoy due to deteioation have the basic assumption that the etaile owns a stoage oom with optimal ode quantity. In ecent yeas, companies have stated to ecognize that a tadeoff exists between poduct vaieties in tems of quality of the poduct fo unning in the maket smoothly. In the absence of a pope quantitative model to measue the effect of poduct quality of the poduct, these companies have mainly elied on qualitative judgment. This pape postulates that measuing the behavio of poduction systems may be achievable by incopoating the idea of etaile in making optimum decision on eplenishment with wasting the pecentage of onhand inventoy due to deteioation and then compaes the optimal esults with no wasting the pecentage of onhand inventoy due to deteioation taditional model. The majo assumptions used in the above eseach aticles ae summaized in Table1. 155
3 Table  1 Summay of the Related Reseaches Autho(s) and published Yea Haiga (1994) Tsao et al. (2008) Pattnaik (2009) Pattnaik (2011) Pesent Pape (2012) Stuctue of the model (EnOQ) Demand Time Time and Pice (Deteministic) (Deteministic) (Deteministic) Demand pattens Nonstationay Linea and Deceasing Deteioation Planning Units Lost due Deteioation Model Yes Finite No Cost Yes Finite No Pofit Yes (Instant) Yes (Instant) Yes (Wasting) Finite No Pofit Finite No Pofit Finite Yes Pofit The emainde of the pape is oganized as follows. In section 2 assumptions and notations ae povided fo the development of the model. The mathematical fomulation is developed in section 3. The solution pocedue is given in section 4. In section 5, numeical example is pesented to illustate the development of the model. The sensitivity analysis is caied out in section 6 to obseve the changes in the optimal solution. Finally section 7 deals with the summay and the concluding emaks. 2. Notations and Assumptions Consumption ate t c Cycle length h Holding cost of one unit fo one unit of time. HC (q) Holding cost pe cycle K Setup cost pe cycle c Puchasing cost pe unit P s Selling Pice pe unit α Pecentage of onhand inventoy that is lost due to deteioation q Ode quantity q** Modified economic odeing / poduction quantity (EOQ/EPQ) q* Taditional economic odeing quantity (t) Onhand inventoy level at time t (q) Net pofit pe unit of poducing q units pe cycle in cisp stategy π (q) Aveage pofit pe unit of poducing q units pe cycle in cisp stategy 3. Mathematical Model Denote (t) as the onhand inventoy level at time t. Duing a change in time fom point t to t+dt, whee t + dt> t, the onhand inventoy dops fom (t) to (t+dt). Then (t+dt) is given as: (t+dt) = (t) dt α (t) dt (1) Equation (1) can be ewitten as: (t+dt) (t) dt = α (t) (2) and dt 0, equation (2) educes to: d (t) + α (t) + = 0 (3) dt Equation (3) is a diffeential equation, solution is (t) = + (q + ) α α e αt (4) Whee q is the ode quantity which is instantaneously eplenished at the beginning of each cycle of length tc units of time. The stock is eplenished by q units each time these units ae totally depleted as a esult of outside demand and deteioation. The cycle length, tc, is 156
4 detemined by fist substituting tc into equation (4) and then setting it equal to zeo to get: t c = 1 + ln ( q ) (5) α Equation (4) and (5) ae used to develop the mathematical model. It is wothy to mention that as α appoaches to zeo, t c appoaches to q. Then the total numbe of units lost pe cycle, L, is given as: L = [ q 1 ln (αq+)] (6) α The total cost pe cycle, TC(q), is the sum of the pocuement cost pe cycle, K+cq, and the holding cost pe cycle, HC(q). HC (q) is obtained fom equation (4) as : HC(q) = tc 0 =h [ q α 1 ln( q + ) 0 hφ(t)dt =h [ + (q + ) α α e αt ] dt 2 ln (αq+ )] (7) TC(q) = K + cq + h [ q α2 ln (αq+)] (8) The total cost pe unit of time, TCU (q), is given by dividing equation (8) by equation (5) to give: TCU(q) = [K + cq + h [ q ln (αq+)] ] [ 1 + ln ( q )] 1 α α2 α = K +(c +h)q ln(1+ q ) h α As α appoaches zeo, then equation (9) educes to TCU (q) = K Whose solution is given by the taditional EOQ fomula, q = 2K 1(q). 1(q) = (ql) P s TC (q) q + c + hq 2 h (9). The total pofit pe cycle is = (ql) P s K cq h [ q α α2 ln (αq+)] (10) Whee L, the numbe of units lost pe cycle due to deteioation, and TC (q) the total cost pe cycle, ae calculated fom equations (6) and (8), espectively. The aveage pofit (q) pe unit time is obtained by dividing tc in 1(q). Hence the pofit maximization poblem is Maximize 1 (q) q > 0 (11) 4. Solution Pocedue (Optimization) The optimal odeing quantity q pe cycle can be detemined by diffeentiating equation (10) with espect to q, then setting these to zeo. In ode to show the uniqueness of the solution in, it is sufficient to show that the net pofit function thoughout the cycle is concave in tems of odeing quantity q. The second ode deivates of equation (10) with espect to q ae stictly negative. Conside the following popositions. Poposition 1.The net pofit (q) pe cycle is concave in q. Conditions fo optimal q The second ode deivative of the net pofit pe cycle with espect to q can be expessed as (12) 157
5 (13) Since > 0 and equation (13) is negative. Popositions 1 shows that the second ode deivative of equation (11) with espect to q ae stictly negative. The objective is to detemine the optimal values of q to maximize the unit pofit function of equation (11). It is vey difficult to deive the optimal values of q, hence unit pofit function. Thee ae seveal methods to cope with constaints optimization poblem numeically. But hee LINGO 13.0 softwae is used to deive the optimal values of the decision vaiables. 5. Numeical Example Conside an inventoy situation whee K is Rs. 200 pe ode, h is Rs. 5 pe unit pe unit of time, is 1200 units pe unit of time, c is Rs. 100 pe unit, the selling pice pe unit P s is Rs. 125 and is 5%,. The optimal solution that maximizes equation (10) and and ae detemined by using LINGO 13.0 vesion softwae and the esults ae tabulated in Table 2. Table2 Optimal Values of the Poposed Model Model Iteation q % Change 6. Sensitivity Analysis It is inteesting to investigate the influence of on etaile behaviou. The computational esults shown in Table 3 indicates the following manageial phenomena: when the pecentage of onhand inventoy that is lost due to deteioation inceases, the eplenishment cycle length, the optimal eplenishment quantity, optimal net pofit pe unit pe cycle and optimal aveage pofit pe unit pe cycle decease espectively. The optimal total numbe of units lost pe cycle inceases with inceases in the pecentage value of the majo paamete α. Table3 Sensitivity Analysis of α Iteation % Change in Conclusions In this pape, a modified EOQ model is intoduced which investigates the optimal ode quantity assumes that a pecentage of the onhand inventoy is wasted due to deteioation as a chaacteistic featue and the inventoy conditions goven the item stocked. This pape povides a useful popety fo finding the optimal pofit and odeing quantity with deteioated units of lost sales. A new mathematical model is developed and compaed to the taditional EOQ model numeically. The economic ode quantity, and the net pofit fo the modified model, wee found to be less than that of the taditional, i.e. and the net pofit espectively. But the modified aveage pofit pe unit pe cycle is moe than that of the taditional pofit pe unit pe cycle. Finally, wasting the pecentage of onhand inventoy 158
6 due to deteioation effect was demonstated numeically to have an advese effect on the aveage pofit pe unit pe cycle. Hence the utilization of units lost due to deteioation makes the scope of the application boade. Futhe, a numeical example is pesented to illustate the theoetical esults, and some obsevations ae obtained fom sensitivity analysis with espect to the majo paamete α. The model in this study is a geneal famewok that consides wasting/ no wasting the pecentage of onhand inventoy due to deteioation simultaneously. In the futue study, it is hoped to futhe incopoate the poposed model into seveal situations such as shotages ae allowed and the consideation of multiitem poblem. Futhemoe, it may also take patial backlogging into account when detemining the optimal eplenishment policy. Refeences [1] S. Bose, A. Goswami, K.S. Chaudhui, An EOQ model fo deteioating items with linea timedependent demand ate and shotages unde inflation and time discounting. Jounal of Opeational Reseach Society, (1995) 46: [2] S.K Goyal, A. Gunasekaan, An integated poductioninventoymaketing model fo deteioating items. Computes and Industial Engineeing, (1995) 28: [3] D. Gupta, Y. Gechak, Joint poduct duability and lot sizing models. Euopean Jounal of Opeational Reseach, (1995) 84: [4] M. Haiga, An EOQ model fo deteioating items with shotages and timevaying demand. Jounal of Opeational Reseach Society, (1995) 46: [5] M. Haiga, An EOQ model fo deteioating items with timevaying demand. Jounal of Opeational Reseach Society, (1996) 47: [6] M. Haiga, Economic analysis of dynamic inventoy models with nonstationay costs and demand. Intenational Jounal of Poduction Economics, (1994) 36: [7] K. Jain, E. Silve, A lot sizing fo a poduct subject to obsolescence o peishability. Euopean Jounal of Opeational Reseach, (1994) 75: [8] V.K. Misha, Inventoy model fo time dependent holding cost and deteioation with salvage value and shotages. The Jounal of Mathematics and Compute Science, (2012) 4(1): [9] J.S. Osteyoung, D.E. Mc Caty, W.L Reinhat., Use of EOQ models fo inventoy analysis. Poduction and Inventoy Management, 3 d Qt., (1986) [10] G. Padmanabhan, P. Vat, EOQ models fo peishable items unde stock dependent selling ate. Euopean Jounal of Opeational Reseach, (1995) 86: [11] M. Pattnaik, A note on nonlinea optimal inventoy policy involving instant deteioation of peishable items with pice discounts. The Jounal of Mathematics and Compute Science, (2011) 3(2): [12] M. Pattnaik, An entopic ode quantity (EnOQ) model unde instant deteioation of deishable items with pice discounts. Intenational Mathematical Foum, (2010) 5(52): [13] M. Pattnaik, Decisionmaking fo a single item EOQ model with demanddependent unit cost and dynamic setup cost. The Jounal of Mathematics and Compute Science, (2011) 3(4), [14] F. Raafat, "Suvey of liteatue on continuously deteioating inventoy models. Jounal of Opeational Reseach Society, (1991) 42: [15] M.K. Salameh, M.Y. Jabe, N. Noueihed, Effect of deteioating items on the instantaneous eplenishment model. Poduction Planning and Contol, (1993) 10(2): [16] Y.C. Tsao, G.J. Sheen, Dynamic picing, pomotion and eplenishment policies fo a deteioating item unde pemissible delay in payment. Computes and Opeations Reseach, (2008) 35: [17] C.D.J. Wates, Inventoy Contol and Management. (Chicheste: Wiley), [18] H.M. Wee, Economic Poduction lot size model fo deteioating items with patial backodeing. Computes and Industial Engineeing, (1993) 24:
Deteriorated Economic Order Quantity (EOQ) Model with Variable Ordering Cost
Thailand Statistician Januay 2014; 12(1): 8395 http://statassoc.o.th Contibuted pape Deteioated Economic Ode Quantity (EOQ) Model with Vaiable Odeing Cost Monalisha Pattnaik Depatment of Business Administation,
More informationChannel selection in ecommerce age: A strategic analysis of coop advertising models
Jounal of Industial Engineeing and Management JIEM, 013 6(1):89103 Online ISSN: 0130953 Pint ISSN: 013843 http://dx.doi.og/10.396/jiem.664 Channel selection in ecommece age: A stategic analysis of
More informationFinancing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
More information30 H. N. CHIU 1. INTRODUCTION. Recherche opérationnelle/operations Research
RAIRO Rech. Opé. (vol. 33, n 1, 1999, pp. 2945) A GOOD APPROXIMATION OF THE INVENTORY LEVEL IN A(Q ) PERISHABLE INVENTORY SYSTEM (*) by Huan Neng CHIU ( 1 ) Communicated by Shunji OSAKI Abstact. This
More informationON THE (Q, R) POLICY IN PRODUCTIONINVENTORY SYSTEMS
ON THE R POLICY IN PRODUCTIONINVENTORY SYSTEMS Saifallah Benjaafa and JoonSeok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poductioninventoy
More informationThe LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.
Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the
More informationIlona V. Tregub, ScD., Professor
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationReferral service and customer incentive in online retail supply Chain
Refeal sevice and custome incentive in online etail supply Chain Y. G. Chen 1, W. Y. Zhang, S. Q. Yang 3, Z. J. Wang 4 and S. F. Chen 5 1,,3,4 School of Infomation Zhejiang Univesity of Finance and Economics
More informationAn Analysis of Manufacturer Benefits under Vendor Managed Systems
An Analysis of Manufactue Benefits unde Vendo Managed Systems Seçil Savaşaneil Depatment of Industial Engineeing, Middle East Technical Univesity, 06531, Ankaa, TURKEY secil@ie.metu.edu.t Nesim Ekip 1
More informationPromised LeadTime Contracts Under Asymmetric Information
OPERATIONS RESEARCH Vol. 56, No. 4, July August 28, pp. 898 915 issn 3364X eissn 15265463 8 564 898 infoms doi 1.1287/ope.18.514 28 INFORMS Pomised LeadTime Contacts Unde Asymmetic Infomation Holly
More informationControlling the Money Supply: Bond Purchases in the Open Market
Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises
More informationThe transport performance evaluation system building of logistics enterprises
Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194114 Online ISSN: 213953 Pint ISSN: 2138423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics
More informationTheory and practise of the gindex
Theoy and pactise of the gindex by L. Egghe (*), Univesiteit Hasselt (UHasselt), Campus Diepenbeek, Agoalaan, B3590 Diepenbeek, Belgium Univesiteit Antwepen (UA), Campus Die Eiken, Univesiteitsplein,
More informationA framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods
A famewok fo the selection of entepise esouce planning (ERP) system based on fuzzy decision making methods Omid Golshan Tafti M.s student in Industial Management, Univesity of Yazd Omidgolshan87@yahoo.com
More informationSoftware Engineering and Development
I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining
More informationDual channel closedloop supply chain coordination with a rewarddriven remanufacturing policy
Intenational Jounal of Poduction Reseach ISSN: 753 Pint 1366588X Online Jounal homepage: http://www.tandfonline.com/loi/tps Dual channel closedloop supply chain coodination with a ewaddiven emanufactuing
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More informationFinancial Planning and Riskreturn profiles
Financial Planning and Risketun pofiles Stefan Gaf, Alexande Kling und Jochen Russ Pepint Seies: 201016 Fakultät fü Mathematik und Witschaftswissenschaften UNIERSITÄT ULM Financial Planning and Risketun
More informationChapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationProblem Set # 9 Solutions
Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new highspeed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease
More informationThe Supply of Loanable Funds: A Comment on the Misconception and Its Implications
JOURNL OF ECONOMICS ND FINNCE EDUCTION Volume 7 Numbe 2 Winte 2008 39 The Supply of Loanable Funds: Comment on the Misconception and Its Implications. Wahhab Khandke and mena Khandke* STRCT Recently FieldsHat
More informationINITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS
INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in
More informationA Capacitated Commodity Trading Model with Market Power
A Capacitated Commodity Tading Model with Maket Powe Victo MatínezdeAlbéniz Josep Maia Vendell Simón IESE Business School, Univesity of Navaa, Av. Peason 1, 08034 Bacelona, Spain VAlbeniz@iese.edu JMVendell@iese.edu
More informationHEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING
U.P.B. Sci. Bull., Seies C, Vol. 77, Iss. 2, 2015 ISSN 22863540 HEALTHCARE INTEGRATION BASED ON CLOUD COMPUTING Roxana MARCU 1, Dan POPESCU 2, Iulian DANILĂ 3 A high numbe of infomation systems ae available
More informationResearch on Risk Assessment of the Transformer Based on Life Cycle Cost
ntenational Jounal of Smat Gid and lean Enegy eseach on isk Assessment of the Tansfome Based on Life ycle ost Hui Zhou a, Guowei Wu a, Weiwei Pan a, Yunhe Hou b, hong Wang b * a Zhejiang Electic Powe opoation,
More informationValuation of Floating Rate Bonds 1
Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned
More informationSupplementary Material for EpiDiff
Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module
More informationCHAPTER 10 Aggregate Demand I
CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income
More informationQuestions for Review. By buying bonds This period you save s, next period you get s(1+r)
MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the twopeiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume
More informationAn application of stochastic programming in solving capacity allocation and migration planning problem under uncertainty
An application of stochastic pogamming in solving capacity allocation and migation planning poblem unde uncetainty YinYann Chen * and HsiaoYao Fan Depatment of Industial Management, National Fomosa Univesity,
More informationJapan s trading losses reach JPY20 trillion
IEEJ: Mach 2014. All Rights Reseved. Japan s tading losses each JPY20 tillion Enegy accounts fo moe than half of the tading losses YANAGISAWA Akia Senio Economist Enegy Demand, Supply and Foecast Goup
More informationEfficient Redundancy Techniques for Latency Reduction in Cloud Systems
Efficient Redundancy Techniques fo Latency Reduction in Cloud Systems 1 Gaui Joshi, Emina Soljanin, and Gegoy Wonell Abstact In cloud computing systems, assigning a task to multiple seves and waiting fo
More informationHow Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes
How Much Should a Fim Boow Chapte 19 Capital Stuctue & Copoate Taxes Financial Risk  Risk to shaeholdes esulting fom the use of debt. Financial Leveage  Incease in the vaiability of shaeholde etuns that
More informationRisk Sensitive Portfolio Management With CoxIngersollRoss Interest Rates: the HJB Equation
Risk Sensitive Potfolio Management With CoxIngesollRoss Inteest Rates: the HJB Equation Tomasz R. Bielecki Depatment of Mathematics, The Notheasten Illinois Univesity 55 Noth St. Louis Avenue, Chicago,
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More informationPerformance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation
Cicuits and Systems, 013, 4, 1171 http://dx.doi.og/10.436/cs.013.41017 Published Online Januay 013 (http://www.scip.og/jounal/cs) Pefomance Analysis of an Invese Notch Filte and Its Application to F 0
More informationStatistics and Data Analysis
Pape 27425 An Extension to SAS/OR fo Decision System Suppot Ali Emouznead Highe Education Funding Council fo England, Nothavon house, Coldhabou Lane, Bistol, BS16 1QD U.K. ABSTRACT This pape exploes the
More information9:6.4 Sample Questions/Requests for Managing Underwriter Candidates
9:6.4 INITIAL PUBLIC OFFERINGS 9:6.4 Sample Questions/Requests fo Managing Undewite Candidates Recent IPO Expeience Please povide a list of all completed o withdawn IPOs in which you fim has paticipated
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationYARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH
nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav
More informationPatent renewals and R&D incentives
RAND Jounal of Economics Vol. 30, No., Summe 999 pp. 97 3 Patent enewals and R&D incentives Fancesca Conelli* and Mak Schankeman** In a model with moal hazad and asymmetic infomation, we show that it can
More information1.4 Phase Line and Bifurcation Diag
Dynamical Systems: Pat 2 2 Bifucation Theoy In pactical applications that involve diffeential equations it vey often happens that the diffeential equation contains paametes and the value of these paametes
More informationTrading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract
Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi email: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,
More informationPersonal Saving Rate (S Households /Y) SAVING AND INVESTMENT. Federal Surplus or Deficit () Total Private Saving Rate (S Private /Y) 12/18/2009
1 Pesonal Saving Rate (S Households /Y) 2 SAVING AND INVESTMENT 16.0 14.0 12.0 10.0 80 8.0 6.0 4.0 2.0 0.02.04.0 1959 1961 1967 1969 1975 1977 1983 1985 1991 1993 1999 2001 2007 2009 Pivate Saving Rate
More informationEconomics 326: Input Demands. Ethan Kaplan
Economics 326: Input Demands Ethan Kaplan Octobe 24, 202 Outline. Tems 2. Input Demands Tems Labo Poductivity: Output pe unit of labo. Y (K; L) L What is the labo poductivity of the US? Output is ouhgly
More informationNBER WORKING PAPER SERIES FISCAL ZONING AND SALES TAXES: DO HIGHER SALES TAXES LEAD TO MORE RETAILING AND LESS MANUFACTURING?
NBER WORKING PAPER SERIES FISCAL ZONING AND SALES TAXES: DO HIGHER SALES TAXES LEAD TO MORE RETAILING AND LESS MANUFACTURING? Daia Bunes David Neumak Michelle J. White Woking Pape 16932 http://www.nbe.og/papes/w16932
More informationConverting knowledge Into Practice
Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading
More informationGravitational Mechanics of the MarsPhobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning
Gavitational Mechanics of the MasPhobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This
More informationMonte Carlo SimulationBased Supply Chain Disruption Management for Wargames
CREATE Reseach Achive Nonpublished Reseach Repots 21 Monte Calo SimulationBased Supply Chain Disuption Management fo Wagames Jun Zhuang Univesity of Buffalo, The State Univesity of New Yok, jzhuang@buffalo.edu
More informationDatabase Management Systems
Contents Database Management Systems (COP 5725) D. Makus Schneide Depatment of Compute & Infomation Science & Engineeing (CISE) Database Systems Reseach & Development Cente Couse Syllabus 1 Sping 2012
More informationMagnetic Bearing with Radial Magnetized Permanent Magnets
Wold Applied Sciences Jounal 23 (4): 495499, 2013 ISSN 18184952 IDOSI Publications, 2013 DOI: 10.5829/idosi.wasj.2013.23.04.23080 Magnetic eaing with Radial Magnetized Pemanent Magnets Vyacheslav Evgenevich
More informationPRICING MODEL FOR COMPETING ONLINE AND RETAIL CHANNEL WITH ONLINE BUYING RISK
PRICING MODEL FOR COMPETING ONLINE AND RETAIL CHANNEL WITH ONLINE BUYING RISK Vaanya Vaanyuwatana Chutikan Anunyavanit Manoat Pinthong Puthapon Jaupash Aussaavut Dumongsii Siinhon Intenational Institute
More informationOptimal Capital Structure with Endogenous Bankruptcy:
Univesity of Pisa Ph.D. Pogam in Mathematics fo Economic Decisions Leonado Fibonacci School cotutelle with Institut de Mathématique de Toulouse Ph.D. Dissetation Optimal Capital Stuctue with Endogenous
More informationThe Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing?
The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Glenn Boyle Depatment of Economics and Finance Univesity of Cantebuy Yanhui Li Depatment of Economics and Finance Univesity
More informationThings to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.
Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to
More informationSUPPORT VECTOR MACHINE FOR BANDWIDTH ANALYSIS OF SLOTTED MICROSTRIP ANTENNA
Intenational Jounal of Compute Science, Systems Engineeing and Infomation Technology, 4(), 20, pp. 677 SUPPORT VECTOR MACHIE FOR BADWIDTH AALYSIS OF SLOTTED MICROSTRIP ATEA Venmathi A.R. & Vanitha L.
More informationThe impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011
The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility
More informationChris J. Skinner The probability of identification: applying ideas from forensic statistics to disclosure risk assessment
Chis J. Skinne The pobability of identification: applying ideas fom foensic statistics to disclosue isk assessment Aticle (Accepted vesion) (Refeeed) Oiginal citation: Skinne, Chis J. (2007) The pobability
More informationElectricity transmission network optimization model of supply and demand the case in Taiwan electricity transmission system
Electicity tansmission netwok optimization model of supply and demand the case in Taiwan electicity tansmission system MiaoSheng Chen a ChienLiang Wang b,c, ShengChuan Wang d,e a Taichung Banch Gaduate
More informationYIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE
YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE Septembe 1999 Quoted Rate Teasuy Bills [Called Banke's Discount Rate] d = [ P 1  P 1 P 0 ] * 360 [ N ] d = Bankes discount yield P 1 = face
More informationAutomatic Testing of Neighbor Discovery Protocol Based on FSM and TTCN*
Automatic Testing of Neighbo Discovey Potocol Based on FSM and TTCN* Zhiliang Wang, Xia Yin, Haibin Wang, and Jianping Wu Depatment of Compute Science, Tsinghua Univesity Beijing, P. R. China, 100084 Email:
More informationWe address the value of quick response production practices when selling to a forwardlooking consumer
MANAGEMENT SCIENCE Vol. 57, No. 10, Octobe 2011, pp. 1737 1751 issn 00251909 ó eissn 15265501 ó 11 ó 5710 ó 1737 http://dx.doi.og/10.1287/mnsc.1110.1360 2011 INFORMS Selling to Stategic Consumes When
More informationLoyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques
Loyalty Rewads and Gift Cad Pogams: Basic Actuaial Estimation Techniques Tim A. Gault, ACAS, MAAA, Len Llaguno, FCAS, MAAA and Matin Ménad, FCAS, MAAA Abstact In this pape we establish an actuaial famewok
More informationMETHODOLOGICAL APPROACH TO STRATEGIC PERFORMANCE OPTIMIZATION
ETHODOOGICA APPOACH TO STATEGIC PEFOANCE OPTIIZATION ao Hell * Stjepan Vidačić ** Željo Gaača *** eceived: 4. 07. 2009 Peliminay communication Accepted: 5. 0. 2009 UDC 65.02.4 This pape pesents a matix
More informationModeling and Verifying a Price Model for Congestion Control in Computer Networks Using PROMELA/SPIN
Modeling and Veifying a Pice Model fo Congestion Contol in Compute Netwoks Using PROMELA/SPIN Clement Yuen and Wei Tjioe Depatment of Compute Science Univesity of Toonto 1 King s College Road, Toonto,
More informationHow do investments in heat pumps affect household energy consumption?
Discussion Papes Statistics Noway Reseach depatment No. 737 Apil 203 Bente Halvosen and Bodil Meethe Lasen How do investments in heat pumps affect household enegy consumption? Discussion Papes No. 737,
More informationData Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation
(213) 1 28 Data Cente Demand Response: Avoiding the Coincident Peak via Wokload Shifting and Local Geneation Zhenhua Liu 1, Adam Wieman 1, Yuan Chen 2, Benjamin Razon 1, Niangjun Chen 1 1 Califonia Institute
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance the availability
More informationPAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII  SPETO  1995. pod patronatem. Summary
PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8  TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC
More informationAnalyzing Ballistic Missile Defense System Effectiveness Based on Functional Dependency Network Analysis
Send Odes fo Repints to epints@benthamscience.ae 678 The Open Cybenetics & Systemics Jounal, 2015, 9, 678682 Open Access Analyzing Ballistic Missile Defense System Effectiveness Based on Functional Dependency
More informationSupply chain information sharing in a macro prediction market
Decision Suppot Systems 42 (2006) 944 958 www.elsevie.com/locate/dss Supply chain infomation shaing in a maco pediction maket Zhiling Guo a,, Fang Fang b, Andew B. Whinston c a Depatment of Infomation
More informationMultiband Microstrip Patch Antenna for Microwave Applications
IOSR Jounal of Electonics and Communication Engineeing (IOSRJECE) ISSN: 22782834, ISBN: 22788735. Volume 3, Issue 5 (Sep.  Oct. 2012), PP 4348 Multiband Micostip Patch Antenna fo Micowave Applications
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance
More informationAvoided emissions kgco 2eq /m 2 Reflecting surfaces 130
ANALYSIS OF GLOBAL WARMING MITIGATION BY WHITE REFLECTING SURFACES Fedeico Rossi, Andea Nicolini Univesity of Peugia, CIRIAF Via G.Duanti 67 0615 Peugia, Italy T: +9075585846; F: +90755848470; E: fossi@unipg.it
More informationUncertain Version Control in Open Collaborative Editing of TreeStructured Documents
Uncetain Vesion Contol in Open Collaboative Editing of TeeStuctued Documents M. Lamine Ba Institut Mines Télécom; Télécom PaisTech; LTCI Pais, Fance mouhamadou.ba@ telecompaistech.f Talel Abdessalem
More informationInsurance Pricing under Ambiguity
Insuance Picing unde Ambiguity Alois Pichle a,b, a Univesity of Vienna, Austia. Depatment of Statistics and Opeations Reseach b Actuay. Membe of the Austian Actuaial Association Abstact Stating fom the
More informationAn Approach to Optimized Resource Allocation for Cloud Simulation Platform
An Appoach to Optimized Resouce Allocation fo Cloud Simulation Platfom Haitao Yuan 1, Jing Bi 2, Bo Hu Li 1,3, Xudong Chai 3 1 School of Automation Science and Electical Engineeing, Beihang Univesity,
More informationModelbased clustering of longitudinal data. McNicholas, Paul D.; Murphy, Thomas Brendan. Canadian Journal of Statistics, 38 (1): 153168
Povided by the autho(s) and Univesity College Dublin Libay in accodance with publishe policies Please cite the published vesion when available Title Modelbased clusteing of longitudinal data Autho(s)
More informationBasic Financial Mathematics
Financial Engineeing and Computations Basic Financial Mathematics Dai, TianShy Outline Time Value of Money Annuities Amotization Yields Bonds Time Value of Money PV + n = FV (1 + FV: futue value = PV
More informationA TwoStep Tabu Search Heuristic for MultiPeriod MultiSite Assignment Problem with Joint Requirement of Multiple Resource Types
Aticle A TwoStep Tabu Seach Heuistic fo MultiPeiod MultiSite Assignment Poblem with Joint Requiement of Multiple Resouce Types Siavit Swangnop and Paveena Chaovalitwongse* Depatment of Industial Engineeing,
More informationMeanRevertingEbitBased Stock Option Evaluation: Theory and Practice
Jounal of Applied Finance & aning, vol. 3, no. 5, 03, 3536 ISSN: 796580 pint vesion, 796599 online Scienpess Ltd, 03 MeanRevetingbitased Stoc Option valuation: Theoy and Pactice Hassan l Ibami Abstact
More informationTop K Nearest Keyword Search on Large Graphs
Top K Neaest Keywod Seach on Lage Gaphs Miao Qiao, Lu Qin, Hong Cheng, Jeffey Xu Yu, Wentao Tian The Chinese Univesity of Hong Kong, Hong Kong, China {mqiao,lqin,hcheng,yu,wttian}@se.cuhk.edu.hk ABSTRACT
More informationVISCOSITY OF BIODIESEL FUELS
VISCOSITY OF BIODIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
More information867 Product Transfer and Resale Report
867 Poduct Tansfe and Resale Repot Functional Goup ID=PT Intoduction: This X12 Tansaction Set contains the fomat and establishes the data contents of the Poduct Tansfe and Resale Repot Tansaction Set (867)
More informationMATHEMATICAL SIMULATION OF MASS SPECTRUM
MATHEMATICA SIMUATION OF MASS SPECTUM.Beánek, J.Knížek, Z. Pulpán 3, M. Hubálek 4, V. Novák Univesity of South Bohemia, Ceske Budejovice, Chales Univesity, Hadec Kalove, 3 Univesity of Hadec Kalove, Hadec
More informationNontrivial lower bounds for the least common multiple of some finite sequences of integers
J. Numbe Theoy, 15 (007), p. 393411. Nontivial lowe bounds fo the least common multiple of some finite sequences of integes Bai FARHI bai.fahi@gmail.com Abstact We pesent hee a method which allows to
More informationLife Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109
Life Insuance Puchasing to Reach a Bequest Ehan Bayakta Depatment of Mathematics, Univesity of Michigan Ann Abo, Michigan, USA, 48109 S. David Pomislow Depatment of Mathematics, Yok Univesity Toonto, Ontaio,
More informationSpirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project
Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.
More informationContingent Convertible Bonds and Capital Structure Decisions
Contingent Convetible Bonds and Capital Stuctue Decisions Bois Albul Dwight M. Jaffee Alexei Tchistyi Apil 25, 2010 Abstact This pape povides a fomal model of contingent convetible bonds CCBs, a new instument
More informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More informationModal Characteristics study of CEM1 SingleLayer Printed Circuit Board Using Experimental Modal Analysis
Available online at www.sciencediect.com Pocedia Engineeing 41 (2012 ) 1360 1366 Intenational Symposium on Robotics and Intelligent Sensos 2012 (IRIS 2012) Modal Chaacteistics study of CEM1 SingleLaye
More informationRune Stenbacka Tuomas Takalo. Switching costs and financial stability
Rune Stenbacka Tuomas Takalo Switching costs and financial stability ank of Finland Reseach Discussion Pape 06 SWITCING COSTS ND FINNCIL STILITY* Rune Stenbacka** Tuomas Takalo*** 4 Januay 06 We establish
More informationThe Impacts of Congestion on Commercial Vehicle Tours
Figliozzi 1 The Impacts of Congestion on Commecial Vehicle Tous Miguel Andes Figliozzi Potland State Univesity Maseeh College of Engineeing and Compute Science figliozzi@pdx.edu 5124 wods + 7 Tables +
More informationExam #1 Review Answers
xam #1 Review Answes 1. Given the following pobability distibution, calculate the expected etun, vaiance and standad deviation fo Secuity J. State Pob (R) 1 0.2 10% 2 0.6 15 3 0.2 20 xpected etun = 0.2*10%
More informationGESTÃO FINANCEIRA II PROBLEM SET 1  SOLUTIONS
GESTÃO FINANCEIRA II PROBLEM SET 1  SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 20102011 Chapte 1 The Copoation 113. What is the diffeence
More informationARE BROKERS' COMMISSION RATES ON HOME SALES TOO HIGH? A CONCEPTUAL ANALYSIS. Paul Anglin. and. Richard Arnott. September 1995.
ARE ROKERS' COMMISSION RATES ON HOME SALES TOO HIGH? A CONCEPTUAL ANALYSIS Paul Anglin and Richad Anott Septembe 1995 Abstact Many people believe that pevailing commission ates fo esidential eal estate
More informationStrategic Asset Allocation and the Role of Alternative Investments
Stategic Asset Allocation and the Role of Altenative Investments DOUGLAS CUMMING *, LARS HELGE HAß, DENIS SCHWEIZER Abstact We intoduce a famewok fo stategic asset allocation with altenative investments.
More informationTHE CARLO ALBERTO NOTEBOOKS
THE CARLO ALBERTO NOTEBOOKS Meanvaiance inefficiency of CRRA and CARA utility functions fo potfolio selection in defined contibution pension schemes Woking Pape No. 108 Mach 2009 Revised, Septembe 2009)
More informationOptimal Peer Selection in a FreeMarket PeerResource Economy
Optimal Pee Selection in a FeeMaket PeeResouce Economy Micah Adle, Rakesh Kuma, Keith Ross, Dan Rubenstein, David Tune and David D Yao Dept of Compute Science Univesity of Massachusetts Amhest, MA; Email:
More information