Writing a Research paper based on a thesis

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The task is to write a research paper based on a thesis. Attached are all the files you need.

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Prepare a Research Paper at any conference or journal article format about your project (at least 6000 words and at least 20 references).

Please make the necessary changes in your research paper and do not directly copy and paste from thesis!

Please include below sections in your research paper;

Abstract (with key words)

I. Introduction

II. Literature Review

III. Research Methodology (Solution method, data collection, etc)

IV. Results and Discussion

V. Conclusion ( summary of results, future research, etc.)

VI. References ( articles cited in this research paper)

*******THE THESIS IS NAMED "SENIOR%202... << THAT THE RESEARCH PAPER IS BASED ON, AN EXAMPLE OF A RESEARCH PAPER IS NAMED INFLUENCE OF CASTING...., AN EXAMPLE OF THE FORMAT IS IEOM_DC2018_PAPER******

Please make sure that the idea of the research paper is clear. Fuzzy logic is applied for IRR and NPV and a comparison is made.

NPV was applied on Investment A,B and E.

IRR on Investment A and B.


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AMERICAN UNIVERSITY OF THE MIDDLE EAST COLLEGE OF ENGINEERING AND TECHNOLOGY INDUSTRIAL ENGINEERING DEPARTMENT B. Sc. Senior Project Industrial Engineering Senior II: Final Report Spring, 2018 Investment Analysis with Fuzzy Logic Prepared By: Abdullah AlHajri 17417, Khalid AlHajri 20702, Omar AlAjmi 20204, Salman ALTeenan 16823, Zeyad ALShikhany 19482 Supervised By: Dr. Ilkan Sarigol Abstract Fuzzy Logic is often used by businesses to make critical decisions which will affect the performance of the business. Fuzzy logic is a fairly new technique where truth values are given a real number between 0 and 1 instead of either 0 and 1. This project illustrates the importance of combining fuzzy logic with investment techniques in order to benefit and creating a view in the future to help investors decide and make decision. Five case studies were investigated, NPV analysis was applied to three real estate projects (A,B and E) and IRR analysis was applied to two healthcare projects (A and B). The whole analysis was run twice, once for the crispy values and once using fuzzy logic. Results showed that project E was the ideal project from the real estate projects to invest in both by fuzzy and crispy results whereas project B was the ideal project from the the healthcare projects to invest in. 2 Table of Contents Abstract ........................................................................................................................................... 2 1 Introduction: ................................................................................................................................. 6 2.1 Background: .............................................................................................................................. 7 2.2 Literature review ....................................................................................................................... 8 3 Fuzzy Logic Technique............................................................................................................. 17 3.1 Operation of Triangular Fuzzy Number: ............................................................................. 20 3.2 Investment Analysis Techniques: ........................................................................................ 21 4 Methodology .............................................................................................................................. 25 5 Results ........................................................................................................................................ 28 5.1 Triangular Fuzzy Numbers & Fuzzy Net Present Value (NPV) ......................................... 28 5.1.2 Investment(A) ................................................................................................................... 28 Graphical Solution for Investment(A) .......................................................................................... 32 5.1.3 Investment (B) ..................................................................................................................... 33 Graphical Solution for Investment(B) .......................................................................................... 37 5.1.4 Investment (E) and fuzzy net present value ......................................................................... 38 Graphical Solution for Investment (E) .......................................................................................... 41 3 5.1.5 Comparison of investments (A & B & E) ............................................................................ 41 5.2 Triangular Fuzzy Numbers & Interest rate of return (IRR) .................................................... 44 5.2.1 Project A ........................................................................................................................... 44 5.2.2 Project (B)......................................................................................................................... 46 5.3.3 Interval comparison of fuzzy between project A and B: .................................................. 48 6 PROJECT MANAGEMENT ..................................................................................................... 51 REFRENCES ................................................................................................................................ 54 List of Figures Figure 1: Union Operation ............................................................................................................ 18 Figure 2: Intersection Operation ................................................................................................... 18 Figure 3: Complement Operation ................................................................................................. 19 Figure 4: Triangular Fuzzy Number ............................................................................................. 20 Figure 5: Project A (Real Estate) .................................................................................................. 29 Figure 6: Triangular Fuzzy numbers Investment (A) ................................................................... 32 Figure 7: Project B (Real Estate) .................................................................................................. 36 Figure 8: Triangular Fuzzy Number Investment (B) .................................................................... 37 Figure 9: Project E (Real Estate) .................................................................................................. 38 Figure 10: Triangular Fuzzy Number Investment (E) .................................................................. 41 Figure 11: Triangular fuzzy number of project A and B (Healthcare) ......................................... 48 4 Figure 12: Comparison between project A and B ......................................................................... 49 Figure 13: Gantt Chart .................................................................................................................. 53 List of Tables Table 1: Typical cases of interval comparison ............................................................................. 42 Table 2: Typical cases of interval comparison ............................................................................. 43 Table 3: Contribution Table .......................................................................................................... 53 5 1 Introduction The word fuzzy means that using the normal human language in order to describe the situation, but without using specific details and getting into deep meaning but giving the correct idea of the situation. For example when someone asks about the weather the answer will be good, bad or so-so but most of the time the exact number of the temperature for example 22℃ will not be interpretted. In this case fuzzy words are used by not mentioning the exact temperature. In this fuzzy words are applied in the investment in order to give a describtion of the situation of the investment in words. When fuzzy words are used in investments, the words used to describe the situation of the investment as the business is going good or bad or fine. In this project an investment company is chosen where fuzzy numbers are translated into fuzzy words, which will give a better understanding about the investment condition in terms of annual investment, capital investment and annual rate of return. This will help gain more information about the investment and it also gives an idea for the people who want to know how the business is doing. In short, this project is about applying fuzzy logic mathematical methodology into real estate and health care investment projects in order to compare and observe the differences with the crisp logic (non-fuzzy logic). This will help identify the main factors that control the investment, for example the raw materials cost, facility design and layout, etc. Also, it will help the decision makers who are in charge of controlling the investment to know the situation of the investment from these words. The real data of the business gives an exact idea of the business situation but also takes time effort. In addition, it is hard for everyone to understand so in order 6 to simplify it and give an idea of the investment, fuzzy logic is used as the ideal way to describe the business. 2.1 Background AREF Investment Group is a Kuwaiti Closed Shareholding Company “AREF” established in 1975, with a capital of KD 22,885,937, the Company is monitored by the Central Bank of Kuwait (CBK) and Capital Markets Authority (CMA). AREF is considered to be amongst the leading investment institutions in the region focusing investments in various sectors and activities. This is achieved through developing and nurturing local, regional and international partnerships. We collected data from AREF investments group. Beside its subsidiaries and associates, AREF forms a conglomerate of companies that are diversified in various sectors. This generates synergy whereby any area of specialty is covered under the leadership of AREF to form a powerful team capable of conceiving, planning and executing mega projects in growing regional markets in the following sectors: Investment, Banking and Finance, Real Estate Investment, Logistic Services (including Aviation and River Transportation), and the Public Services Sector which include Education, Health, and IT services. It has many subsidiaries including Zamzam JV, Munshaat Real Estate Projects Co. K.S.C, Al Adaa Holding Company, and Soukouk Holding Company. In deed, the team mattes of the project are aimming to apply fuzzy and crisp logic investment tools and techniques into Soukouk Holding Company, exceclusivly, in oder to compare to get a better understanding about the investment situation and to find the optimal solution throughout the investment period.. 7 AREF Investment Group is a Kuwaiti Closed Shareholding Company “AREF” has a vision to create an integrated financial conglomerate operating in synergy in a variety of fields and sectors forming a power team under the leadership of the parent company capable of competing and implementing mega projects in existing markets, exploring new investment markets, capturing and developing investment opportunities, and achieving integration between AREF and its companies through the exchange of expertise, cooperation in a variety of projects, and coordination which leads to positive financial result. While at the current time they are focusing on the following two mission subtitles. First of their mision objectives is to Concentrate on huge projects, which reflects the professional caliber attained by the Group, with its subsidiaries, towards discovering new investment opportunities, increasing the necessary funds, and applying new strategic investors, improving the group's branches in some promising markets in kuwait, while searching for new investment opportunities in other markets. Second of their mision objectives is to support and upgrad AREF’s subsidiaries and associated companies, which operate in different markets, in addition to establishing and acquiring new companies. 2.2 Literature review In this article they highlight the benefit of using the fuzzy logic in real estate investment and they also show how the fuzzy logic helps in taking decisions in real estate. Also it shows the situation of the real estate market in order to take a decision based on the market value of the real estate. In this case study they concern of buying an office building(Del Giudice et al.,2017). 8 In this article they concerns in making decisions in public sector investments. In this article they took in consideration the needs of the stakeholders such as the citizens and the organizations in order to find the optimum choice of investments project. They also have to check if this investment is good in the long-term or not in order to make a decision of the investment chosen(Benčina,2007). In a study to select the best industry, some measures have been taken to determine the priorities of the companies to be selected. Fuzzy Logic has been used as a new technique using financial ratios according to specific criteria. The use of this method is very good and effective. The study concluded that the use of this method has given good results and effective.Doubting is the main reason that makes investors afraid from entering the market. This paper focuses on two common techniques: fundamental and technical analysis. Moreover, the paper also focuses on the financial performance to help investors evaluate and rank the companies. The methodology compares on drug and healthy product using mean test. Fuzzy logic is defined between qualitative evaluation such as 0 or 1, they are also used in a set of membership or universal to identify an exact number which is unknown( {0,1} is a valuation set). First step is applying normalization, as a when equals 1 will be considered a normal number. Secondly, Triple numbers are considered always-positive fuzzy numbers. Furthermore, the matrix is called fuzzy when one number at least is a fuzzy. The main object of the paper is answering the customer’s questions; what stock to buy and what is the price? Fundamental analysis always will help to 9 reach the correct price, and the technical analysis will not reach the value of the stock because they predict the price from previous price patterns(Tavakkoli et al.,2010). This paper illustrates how to choose the investment project in the simplest form and whether to accept or reject an investment, and also to compare between investment projects in order to select the best considering the factors. In the beginning of the project the risk adjustment increases present cost of capital to modify the data used in a method. More Investments information are required, list the type of method to be used and define the problem. First step is estimating numbers of the investment for decision making and comparing the projects. The "n" time unit is in years, therefore cash outflow and inflow is calculated at the end of the duration (yearly). Decision making (accepting or rejecting the projects) are based on the following investment analysis: 1- Revenues per one dollar method, 2- Payback period method, 3- Net present value, 4- Net future value, 5- Method of utility of the net present value, 6- The internal rate of return method, 7- The modified internal rate of return method. The previous methods are done as fuzzy numbers are given but the cash flows duration is not known precisely(Kuchta,2000). For the past years, there are amount of the research that is on the investment behavior of firm. For these sequences of the researches, there is some of important things. The amount of the investments are doing the basically of the economic development and characteristics of markets. The main target of this research is to achieve if the fuzzy logic theory could effect of the real interest rate on the totally investment spending.In this research, we have built up a simple fuzzy 10 logic technique to observationally research the correspondence between the real interest rate and total investments. The level and variance of the interest rate are grouped as far as phonetic terms of fuzzy sets, and naturally conceivable investment standards condense the connection between particular conditions of the real interest rate and the willingness to invest of a delegate firm. Things being what they are the fuzzy logic method uncovers data about the information that isn't caught by ordinary straight relapses. The commitment of the research in this manner lies in the finding of a non-direct correspondence between the real interest rate and total investment spending, and also in the utilization of a fuzzy logic methodology to discover these regularities(Lindström, 1998). Fuzzy techniques are one of the investment strategies. Fuzzy logic is an arrangement of strategies for managing methods of thinking that are estimated as opposed to correct sets by Lotfi Zadeh 1965. It changes over the subjective esteems into target esteems. Moreover, the level of truth of an announcement can extend in the vicinity of 0 and 1 and isn't compelled to the two truth esteems {true, false} as in exemplary predicate logic.This strategy was based on a sample of 50025 daily observations consisting of five basic behavioral variables taken from twenty-five companies from the stock market in the period from January 1, 2001 to December 2008. Once the fuzzification of all info esteems has been done, the subsequent stage includes the foundation of deduction rules. These tenets speak to the way in which people decide, inducing from phonetics premises. These rules can be chosen an incentive from zero to one, called Degree of Support (DOS). DOS relies upon the qualities that based on specimen. When a control is chose with DOS equivalents to zero (one), the lead is viewed as inconsequential (critical). DOS likewise takes into account esteems in the vicinity of zero and one for fractional noteworthy run 11 the show. Also, it can be distinguished by the client as a settled esteem or arbitrarily dictated by the product. The program additionally gives simulated neural systems (ANNs) that can be utilized to remove information for the manage base. ANNs perform dull assessment of the known outcomes and incrementally reinforce/debilitate the impact of the control on the demonstrating result. The results provided the best results achieved despite the lack of accuracy. Although, there is a debate between behavioral finance and efficiency on investment strategy theory. Thus, proposed model can be used to support decisions such as grazing behavior (Serguieva& Hunter,2004). ` This article explains what is happening in the market most of the time, yet this thing does not show the reality. The market suffers because it is not stable which means there is expansion and drop in the market. And that makes the investors in a shock because of unexpected movement in the market. Expertise sees that it is important to use the fuzzy approach in order to reduce the assumption of data distribution and market behavior. They recommend a fuzzy criterion to measure how risky the investment is and to estimate the project. The process is applied to 35 companies in the United Kingdom that traded on London stock exchange. According to the investigation made in the market because of the instability in the market they use this fuzzy method which is helpful in controlling of the stability of the market and having a soft, easy and quick transaction. Finally for this article I want to mention some of the investment techniques that used in this model is net present value (NPV) which means the subtraction between the present value of cash inflows and the present value outflows(Serguieva& Hunter,2004). 12 Second of all, we are going to discuss about the second article which is about a fuzzy real options approach for investment project valuations. Suggest a fuzzy approach for investment project valuation under uncertain environment from the side of real is aim of this approach option. These kinds of traditional approaches has a base of (DCF) which means discounted cash flows that gives the measurement of net present value (NPV) and internal rate of return (IRR). But the DCF approach shows a couple of big issues. The first issue is that the cash flow parameter of DCF approach is impossible to be estimated accurately in the situation of uncertainty. The second issue is that the managerial flexibilities values in the project investment cannot be measured exactly by the DCF approach. These issues will lead to improper results on the strategic investment project valuation. This approach is helpful for evaluate a project under uncertainty and computing the average values of a projects fuzzy expanded net present value that demonstrate the whole value of the project(Ho& Liao,2011). To start with, this article is about model for classifying exclusive investments. Meaning that, the model uses Zadeh’s decision-making criterion, determining the degree of truth, when the investment objective is to maximize the net present value as an investment technique of the project, taking under consideration the condition of minimizing risk. In this article, the concept of a fuzzy thinking is used to calculate the net present value and reduces the risk of each investment project element. In fact, this allows to determine the degree to which a project is a good investment based on the fuzzy subset theory, and understanding this as a fuzzy event and determining the degree to which a project has a high net present value, understood as another 13 fuzzy event.The paper is structured as follows. the second section called (Calculating the probability of the fuzzy event), is about calculating the probability of the fuzzy event based on determined criteria or target “the project is a good investment” when the cash flow or operating profit of that investment is occurred (estimated returns), project life and capitalization rate are considered to be uncertain. Given the uncertainty surrounding the numerical variables, the risk of the project is a fuzzy concept and it has therefore been modeled on the basis of the fuzzy subset methods. This section includes the formulation of net present value based on the terms of fuzzy logic, membership function for the risk of the project, measure scale for risk, and degree that the investment is good according to level of risk .The third section called (Calculating the possibility of the fuzzy event), this section focuses on calculating the possibility of the fuzzy event to give a judgment whether the project has a high net present value or not when, as in the second section, estimated returns, project life and capitalization rate are considered to be uncertain. In the fourth Section called Confluence between maximizing the value of the project and minimizing risk, they created a decision making module to choose between several alternative investment projects. This section presents a numerical simulation with a fuzzy-type input data set (Gorrell,2011). To start with, this article considering that there are several qualitative risk factors of mining investment projects, the article describes evaluation information by means of linguistic neutrosophic numbers (LNNs). The advantage of LNNs is that major original information is reserved with linguistic truth, indeterminacy, and false membership degrees. However, this paper includes the following:Present a number of distance measures between two LNNs, such as the 14 Hamming distance, the Euclidean distance, and the Hausdorff distance. Equally important, prove relevant properties of these formulas, including the related formulation and definitions (Gorrell,2011). In financial indices to recognize patterns can uses added value of fuzzy system which is uses strategy of experienced traders. For traders, this is appropriate. However, a variety of strategies are often used by humans. Where strategies are exchanged according to external information and circumstances. There is therefore a great need for further research so that systems with such flexibility are available. Future research should emphasize more flexibility for these strategies by improving them(Simkovic,2011). Analytical systems of data tables are still one of the treatments that are similar to black boxes in their outputs, and takes into account the format of the data entered. The primary objective and significance of the resulting values are usually exaggerated. Thus, the analysis with ambiguous output is ambiguous by definition. It depends on wither the data is sound and testable or not. One of the characteristics that governs the strength of the software used in the analysis is its ability to analyze the sensitivity of the data used. The results of the study showed that fuzz analysis data must be used to support the MCS model to reach the best results (Byrne,1997). In a study to assess the importance of the environmental impacts of construction projects it was agreed to develop a framework on the decision support process that deals with soil, air, waste, water, and others. TO gain sufficient knowledge to support decision making on this 15 matter, fuzzy logic has been used to have the ability to mimic human perceptions and manipulate them from a computer point of view(Chen et al.,2009). The use of fuzzy logic model to support investment decision making is very useful for investors who are always looking for a good way to support risk management for their long-term investments. The model was used in our current study by several valuables used to assess in the current market situation and to give recommendations to the investor. This model has been used and tested on many data in this area(Dostál& Brož,2011). 16 3 Fuzzy Logic Technique In relation with fuzzy logic, the investment model which will be represented and created in upcoming sections will be based on some fuzzy set methods, concepts, and operations beside the types of fuzzy numbers (triangular fuzzy number, and bell-shaped fuzzy numbers.)Our first focus in this section will be to describe the following terms: fuzzy numbers, fuzzy sets, and membership function. The second part will be focusing about fuzzy set operations: union, intersection, compliment, and difference of fuzzy sets. To start with, Fuzzy numbers, are mathematically and graphically called a membership function, where each membership function defines the fuzzy set for possible values on the horizontal axis. While the vertical axis, on a scale ranging from 0 to 1, gives the membership value of a defined criteria “good investment” in the fuzzy set.There are many operations that could be applied on fuzzy sets. Our model will focus on the basic operations: union, intersection, compliment, and difference of fuzzy sets. As basic operations gives needed analysis to classify the fuzzy elements in the fuzzy set into the determined model or design late on the upcoming sections. Starting with the union operation, in order to know and classify all of the elements of set A and set B in one set, except for common elements of both sets which intersect. In other word, union is the maximum of the two (set A and set B) individual membership functions. It is called maximum criterion, Figure 1. 17 Figure 1: Union Operation Next, is the intersection operation, this operation is useful when we want to know the element in both sets (set A and set B), which are located in both sets. In other word, it is the minimum of the two individual membership functions. It is known as the minimum criterion, Figure 2. Figure 2: Intersection Operation 18 Then, the complement operation, which is useful when we want to know all the elements which doesn’t belong to set A and logically these elements will be founded in set B, C, and D, for example. This is known as the negation criterion, Figure 3. Figure 3: Complement Operation In our model or design we are going to use two types of fuzzy numbers. The first one is the triangular fuzzy number (TFN), which is represented as a membership function A={a1,a2,a3}, where a1 is represented as the lower element, a2 is represented as the prototype element, and a3 is represented as the upper element. The purpose of using (TFN) is that when we have another membership function B={b1, b2, b3} we can apply the following operations: summation, multiplication, subtraction, and division, Figure 4. 19 Figure 4: Triangular Fuzzy Number 3.1 Operation of Triangular Fuzzy Number Same important properties of operations on triangular fuzzy number are summarized. 1- The results from addition or subtraction between triangular fuzzy numbers result also triangular fuzzy numbers. 2- The results from multiplication or division are not triangular fuzzy numbers. 3- Max or min operation does not give triangular fuzzy number. But we often assume that the operational results of multiplication or division to be TFNs as approximation values. First, consider addition and subtraction. Here we need not use membership function. Suppose triangular fuzzy numbers A and B are defined as: 20 A = (a1, a2, a3), B = (b1, b2, b3) Addition: A + B = (a1+b1, a2+b2, a3+b3). Subtraction: A-B = (a1-b3, a2-b2, a3-b1). Multiplication: A*B = (min (a1b1, a1b3, a3b1, a3b3), a2b2, max (a1b1, a1b3, a3b1, a3b3)). Division: A/B = (min (a1/b1, a1/b3, a3/b1, a3/b3), a2/b2, max (a1/b1, a1/b3, a3/b1, a3/b3)). 3.2 Investment Analysis Techniques 3.2.1 Net present value (NPV) NPV(Net present value) in finance is a measurement of profit which subtracting (PV cash outflows) from (PV cash inflows) for a period of time which PV is the present value. NPV is calculating by negative cash flows (cost) and positive cash flows (benefits) over periods of an investment. The period one year, measured in quarter-years, half-years or may be in months. PV calculated for each period by discounting its future value at a periodic rate of return. Positive NPV occurred in profit and negative NPV results in a loss. To calculate the net present value, the cash flows are entered and the discount rate is used to calculate the price. The reversal of this process is the discount rate where the cash flows and the input price are entered and the discount rate is calculated. NPV formula 𝑹 𝒕 NPV(i,N)=∑𝑵 𝒕=𝟏 (𝟏+𝒊)𝒕 t– the time of the cash flow i– the discount rate 21 Rt – the net cash flow Example: Given an initial investment $7000 and the income received for five years was $2500, $4800, $1700, $3150 and $2950 respectively with annually discount rate 5% what is the net present value. Manual solution: −7000 2500 4800 1700 3150 2950 NPV=(1+0.05)1 + (1+0.05)2 + (1+0.05)3 + (1+0.05)4 + (1+0.05)5 + (1+0.05)6 NPV=5815.36 3.2.2 Present Value (PV) The present value, defined as the present value discounted in the economy and finance, is the expected income based on the valuation date. The future value is always greater than or equal to the present value because of the ability to earn interest. In other words, it is the time value of the money, and at other times when the future value is lower than the current interest rates are negative. Both current and future value calculations are used to evaluate mortgages, annual bonuses, loans, sunken funds and others. Thus, these calculations are used to make comparisons between cash flows occurring simultaneously. Formula of PV: PV = FV (1+i)n 22 - Where FV : is the future amount of money N: is the number of compounding periods where the sum is worth FV,i is the interest rate for one compounding period Example: Annuity that pays $500/month over a period of 10 years with interest rate 7% per year the payment is made at the end of the month calculate the PV. Annually rate=7% so the monthly rate=7/12 %. Manual solution: PV= 500 0.07 120 (1+ ) 12 3.2.3 Internal rate of return (IRR) The method for calculating the rate of return is the internal rate of return, where the term refers to non-reliance on external factors such as capital cost or inflation. The internal rate of return on the project or investment in the compound compound rate of the effective annual return or the return rate at which it determines the net present value of all positive and negative cash flows is equal to zero of the investment. Calculation of IRR: Given that (time, cash flow) as collection of pairs in a project, the internal rate of return follows from the NPV as a function of the rate of return. 23 Given the (period, cash flow) pairs (n,Cn ) where n is a positive integer, the N (total number of periods ), NPV the IRR is given by r in: - Where N: Is period usually given in years Cn : Cash flow in period n Example: Given an initial investment of $1500 and the net revenue over 4 years were $200, $230, $225 and $265 calculate the internal rate of return (IRR) after 2 years and after 4 years respectively. Manually solution: At 2 years − 1500 200 230 + + =0 (1 + 𝑟)1 (1 + 𝑟)2 (1 + 𝑟)3 r=-54% At 4 years − 1500 200 230 225 265 + + + + =0 1 2 3 4 (1 + 𝑟) (1 + 𝑟) (1 + 𝑟) (1 + 𝑟) (1 + 𝑟)5 r=-16.48 24 4 Methodology In this project we are applying the fuzzy logic on some investments and we are comparing between the results that we get when we apply the fuzzy logic analysis techniques between two investments. The methodology of our project is that we chose investments that are under Aref investment group and apply the invetsment analysis techniques by considering all of the parameters to be fuzzy and by that we can get an idea of the situation of the investment. After we apply we finished from the fuzzy part we applied the normal investment analysis techniques on the exact data. In total we have four investments under Aref investment group. Two of these investments are real estate investments, and the other two are health care investmernts. We spoke to the excutive maneger of Aref investment group to get the data of these investments, and to know where to use the fuzzy logic. We collected the data by visiting Aref investment group by disccusing the about the investments with the emloyees and specially with the excutive maneger of the group. After collecting the data and the information we wanted to know. We used the exact data that we got from the excutive maneger to calculate the NPV, IRR, and the Payback period on the investments. We also collected another approximate data by speaking with the excutive maneger. The excutive maneger was illustarting the investment and we used his illustration of the invesments to collect these data. These data are based on the expectations of the excutive maneger of the group about some investments. We used these data to calculate the previously 25 mentioned investment analysis techniques which are the NPV, IRR, and the Payback period by cosidering all of the parameters to be fuzzy. After calculating the normal investment analysis techniques by using the exact data, and the fuzzy investment analysis techniques by using the approximate data, we campared between the results of the two results that we got from each investment. The purpose of the comparing is to know how much the fuzzy investmments analysis techniques can be helpful and close to the real results and gives correct assumptions. In this project we chose two investments from Aref invetment group that work in the real estate and we got the data of their investment. After that we applied the Net Present Value technique on both investments and we compare between the results of the two of investments to help the investor choose between the two investments. After that we chose two investments that are also under Aref invesments group that invest in the health care. After we got the data from them we applied the Interest Rate of Return on both investments and then we compare between the two investments which will also help the investors to know where to invest. These two investments of the health care are new. So, after applying this techniques by using the fuzzy logic investments analysis techniques which are the NPV on the real estate investments and the IRR of the health care investments we have an idea of the situation of the investments in the future without knowing every parameter and by 26 consider them to be fuzzy, but we have an idea of the investments situation by asking the person in charge who is the executive manager of Aref investment group. 27 5 Results 5.1 Triangular Fuzzy Numbers & Fuzzy Net Present Value (NPV) To start with, the first step in analyze and calculate the fuzzy net present value for each year on the life term of the project is to determine the number of years, which is considered in the project, in our case we are considering an investment of five years including the initial year. The following terms shows the minimum estimation and the maximum estimation from the target values for both cash flows (P) and interest rates (R). The target values for each year of investment is applied from the collected data sheet from the related investments, as mentioned in the methodology. 5.1.2 Investment(A) When we met the the compaines representatives , we asked them to provide us with the target value for each year of the investment. For the first year there is no income or profits is supjected, but the capital budget is indended to be consumed at the first year. Although, from our side, we set the interest rates Ri+1 of the project, where i=0. Pn represents the present annual cash flow at the end of each year, where n= [0, 1, 2, 3, 4]. They set the minimuim and the maximuim for the initial year (P0) to be: -P0=(3,500,000; 3,700,000; 4,000,000) R1=(7%;8%;9%) Where, the left value represents the minium required investment, while the right one represents the maximuim investment. Same procedures is applied for the remaining years, with 28 one different , which is the remaing years (P1, P2, P3,P4) are representing the annual profits of the investment, except for P1 which the year of expending the capital budget of the invesment. P1=(200,000; 230,000; 300,000) R2=(7%;9%;11%) P2=(150,000; 227,000; 300,000) R3=(6%;7%;9%) P3=(200,000; 230,000; 300,000) R4=(6%;8%;9%) P4=(200,000; 235,000; 300,000) R5=(8%;9%;10%) P4(salvage) =[4,000,000 ; 4,177,420 ; 5,000,000] Figure 5: Project A (Real Estate) 29 Setting the fuzzy intervales for each year in the life of the investment in respect to (α-cut) term, where α=[0,1] P0=[-3,500,000-200,000α; -4,000,000+300,000α] R1=[1,07+0,01α;1,09-0,01α] P1= [200,000+30,000α; 300,000-70,000α] R2=[1,07+0,02α;1,11-0,02α] P2= [150,000+77,000α ; 300,000-73,000α] R3=[1,06+0,01α;1,09-0,02α] P3=[200,000+30,000α ; 300,000-70,000α] R4=[1,06+0,02α;1,09-0,01α] Notice that in the fourth year there is two cash flows. The first cash flow interval of the fifth year (P4),is the expected amount of profites at the end of the fourth year. While, the second cash flow intervale (P4(salvage)) represents the salvage value of the investment, which is expected to be earned at the end of the fifth year in addition to (P4). P4=[200,000+35,000α ; 300,000-65,000α] P4(total): is the total sum of interval P4 and intervale P4(salvage) P4(salvage) =[4,000,000+177,420α ; 5,000,000-822,580α] P4(total) = [200,000+35,000α +4,000,000+177,420α 822,580α] We get the following result: P4(total)= [4,200,000 + 212420 α ; 5,300,000-887580α] 30 ; 300,000-65,000α + 5,000,000- Now, we need to set the left (lower portion) and the right side (upper portion) of triangular fuzzy net present values (NPV(  )). The left portion (NPVl(  )) represents the minimuim value of the investment, when plug in the equation with alpha (α) = 0. While, the right portion (NPVr(  )) represents the maximuim value of the investment by pluging in (α) = 1. In fact, the same equations (1&2) could be used to find the target value or the estimated cash flow of the investment, when plug in the equation (1&2) with (α) = 1 NPVl(  ) is the first equation (1): NPVl(  ) = (−3,500,000 − 200,000𝛼) + (200,000+30,000𝛼) (1,09−0,01𝛼)∗(1,11−0,02𝛼)∗ (1,09−0,02𝛼) (200,000+30,000𝛼) ( 1,07+0,01𝛼) 150,000+77,000𝛼 + (1,09−0,01𝛼)∗(1,11−0,02𝛼) + 4,200,000 + 212420 𝛼 + (1,09−0,01𝛼)∗( 1,11−0,02𝛼)∗( 1,09−0,02𝛼)∗(1,09−0,01𝛼) NPVr(  ) is the second equation (2): NPVr(  ) = (−4,000,000 + 300,000𝛼) + 300,000−70,000𝛼 (1,07+0,01𝛼)∗(1,07+0,02𝛼)∗(1,06+0,01𝛼) 300,000−70,000𝛼 (1,09−0,01𝛼) 300,000−73,000𝛼 + (1,07+0,01𝛼)∗(1,07+0,02𝛼) + 5,300,000−887580𝛼 + (1,07+0,01𝛼)∗(1,07+0,02𝛼)∗(1,06+0,01𝛼)∗(1,06+0,02𝛼) Notice: that all fuzzy present values (Pn) are cosidered in equation (1&2)when formulating NPVr(  ) and NPVr(  ) Finding the fuzzy net values for triangular fuzzy numbers: NPV = (NPV0, NPV1, NPV2) → (triangular fuzzy net present values) By subsituting with α=0 at equation (1) 31 NPV0= (-3500000) + (200000) / ( 1.07) + (150000) / (1.09*1.11) + (200000) / (1.09*1.11*1.09) +(4200000)/ (1.09*1.11* 1.09*1.09) = -115677.5 By subsituting with α=1 at equation (1) NPV1= (-4000000+300000) + (300000-70000) / ( 1.08) + (300000-73000) / (1.08*1.09) + (300000-70000) / (1.08*1.09*1.07) +(5300000-887580)/ (1.08*1.09*1.07*1.08)= 131928.9 By susituting with α=0 at equation (2) NPV2= (-4000000) + (300000) / (1.09) + (300000) / (1.07*1.07) + (300000) / (1.07*1.07*1.06) + (5300000) / (1.07*1.07*1.06*1.06) = 904454.6 Graphical Solution for Investment(A) Figure 6: Triangular Fuzzy numbers Investment (A) From the graphical illustration we can notic that the lower portion is NPV0 = (-115677.5), the target value of cash flows is represented by (NPV1 = 131928.9), and the higher portion of the investment (NPV2 = 904454.6).there are two important notations to be considered. The first 32 notation is the lower portion of the investment represented by NPV0 is exceding the boundy of X-axis and recording a negative value NPV0, which means that the project is not profitable. Second notation is that the variation of lifter side and the righter side of the traingular is not semetric. Moreover, this mean that the we are getting a misleading net present values , which is cumlating an error within its results. So that, we cant consider this project as one of our candidates for comparison. 5.1.3 Investment (B) To start with, fuzzy net present invesment (NPV) is the optained methoad on investment (B). By applying same procedures as investment (A), and setting the interest rates (Ri) throughout the life time of the investment to be, also the same as investment (A) in order to be able to compaire between the investments. -P0=(4,000,000 ; 4,500,000 ; 5,000,000) R1=(7%;8%;9%) P1=(300,000 ; 340,000 ; 420,000) R2=(7%;9%;11%) P2=(320,000 ; 375,000 ; 500,000) R3=(6%;7%;9%) P3=(300,000 ; 390,000 ; 450,000) R4=(6%;8%;9%) P4=(350,000 ; 400,000 ; 450,000) R5=(8%;9%;10%) Setting the fuzzy intervales for each year in the life of the investment in respect to (α-cut) term, where α=[0,1] P0=[-4,000,000-500,000α ; -5,000,000+500,000α] 33 R1=[1,07+0,01α;1,09-0,01α] P1=[300,000+40,000α ; 420,000-80,000α] R2=[1,07+0,02α;1,11-0,02α] P2=[320,000+55,000α ; 500,000-125,000α] R3=[1,06+0,01α;1,09-0,02α] P3=[300,000+90,000α ; 450,000-60,000α] R4=[1,06+0,02α;1,09-0,01α] P4=[350,000+50,000α ; 450,000-50,000α] Same as investment (A), the salvage value is earned fromt the invesment in the fifth year (P4) P4(salvage) = [6,000,000+617,133α ; 7,000,000-382,867α] P4(total) = [6,000,000+617,133α + 350,000+50,000α ; 7,000,000-382,867α + 450,000-50,000α] We get the following result: P(total)=[6, 350,000+667133α; 7, 450,000-432867α] Same as invesment (A), we need to set the left (lower portion) and the right side (upper portion) of triangular fuzzy net present values (NPV(  )). The left portion (NPVl(  )) represents the minimuim value of the investment, when plug in the equation with alpha (α) = 0. While, the right portion (NPVr(  )) represents the maximuim value of the investment by pluging in (α) = 1. In fact, the same equations (3&4) could be used to find the target value or the estimated cash flow of the investment, when plug in the equation (3&4) with (α) = 1 NPVl(  ) is the first equation (3): NPVl(  ) = (−4,000,000 − 500,000𝛼) + 300,000+90,000𝛼 (1,09−0,01𝛼)∗(1,11−0,02𝛼)∗(1,09−0,02𝛼) + 300,000+40,000𝛼 (1,07+0,01𝛼) 320,000+55,000𝛼 + (1,09−0,01𝛼)∗(1,11−0,02𝛼) + 6,350,000+667133𝛼 (1,11−0,02𝛼)∗( 1,09−0,02𝛼)∗(1,09−0,01𝛼)∗(1,09−0,01𝛼) While, NPVr(  ) is the second equation (4): 34 NPVr(  )=(−5,000,000 + 500,000𝛼) + 450,000−60,000𝛼 (1,07+0,01𝛼)∗(1,07+0,02𝛼)∗(1,06+0,01𝛼) 420,000−80,000𝛼 (1,09+0,01𝛼) 500,000−125,000𝛼 + (1,07+0,01𝛼)∗(1,07+0,02𝛼) + 7,450,000−432867𝛼 + (1,07+0,01𝛼)∗(1,07+0,02𝛼)∗(1,06+0,01𝛼)∗(1,06+0,02𝛼) Finding the fuzzy net values for triangular fuzzy numbers: NPV = (NPV0, NPV1, NPV2) → (triangular fuzzy net present values) By subsituting with α=0 at equation (3) NPVo= (-4000000) + (300000) / (1.07) + (320000) / (1.09*1.11) + (300000) / (1.09*1.11*1.09) +(6350000)/ (1.09*1.11*1.09*1.09) = 1189785.6 By subsituting with α=1 at equation (3) NPV1 = (-4000000- 500000)+(300000+40000)/(1.06) +(320000+55000)/(1.08*1.09)+ (300000+90000)/(1.08*1.09*1.07) +(6350000+667133)/(1.08*1.07*1.09*1.08) = 1607172.8 By subsituting with α=1 at equation (4) NPV2=(-5000000)+(420000)/(1.09)+(500000)/(1.07*1.07)+(450000)/(1.07*1.07*1.06)+ (7450000)/(1.07*1.07*1.06*1.06)= 11984152.2 35 Figure 7: Project B (Real Estate) 36 Graphical Solution for Investment(B) Figure 8: Triangular Fuzzy Number Investment (B) From the graphical illustration we can notic that the lower portion is NPV0 = (1189785.6), the target value of cash flows is represented by (NPV1 = 1607172.89), and the higher portion of the investment (NPV2 = 11984152.2). the symmetricity of the fuzzy traigular shape allows for investment B to be in comparison with another investment 37 5.1.4 Investment (E) and fuzzy net present value Figure 9: Project E (Real Estate) To start with, fuzzy net present invesment (NPV) is the optained methoad on investment (B). By applying same procedures as investment (A) and investment (B), and setting the interest rates (Ri) throughout the life time of the investment to be, also the same as investment (A) in order to be able to compaire between the investments. -P0= (4,000,000 ; 5,400,000 ; 6,000,000) R1=(7%;8%;9%) P1= (300,000 ; 380,000 ; 500,000) R2=(7%;9%;11%) P2= (400,000 ; 440,000 ; 600,000) R3=(6%;7%;9%) P3= (400,000 ; 445,000 ; 600,000) R4=(6%;8%;9%) 38 P4= (400,000 ; 470,000 ; 600,000) Setting the fuzzy intervales for each year in the life of the investment in respect to (α-cut) term, where α=[0,1] P0= [-4,000,000 - 1,400,000 α ; -6,000,000 + 600,000 α] R1=[1,07+0,01α;1,09-0,01α] P1= [300,000 + 80,000 α ; 500,000 -120,000 α ] R2=[1,07+0,02α;1,11-0,02α] P2= [400,000 + 40,000 α ; 600,000 – 160,000 α] R3=[1,06+0,01α;1,09-0,02α] P3= [400,000 + 45,000 α ; 600,000 - 155,000 α ] R4=[1,06+0,02α;1,09-0,01α] P4= [400,000 + 70,000 α ; 600,000- 130,000 α] P4(salvage)= [5,400,000 + 1,500,000 α ; 7,700,000 – 800,000 α] Same as investment (A), the salvage value is earned fromt the invesment in the fifth year (P4): P4(total)= [400,000 + 70,000 α + 5,400,000 + 1,500,000 α ; 600,000 - 130,000 α + 7,700,000 – 800,000 α] P4(total) = [5,800,000+ 1,570,000 α ; 8,300,000– 9300,000 α] Same as invesment (A) and investment (B), we need to set the left (lower portion) and the right side (upper portion) of triangular fuzzy net present values (NPV(  )). The left portion (NPVl(  )) represents the minimuim value of the investment, when plug in the equation with alpha (α) = 0. While, the right portion (NPVr(  )) represents the maximuim value of the investment by pluging in (α) = 1. In fact, the same equations (5&6) could be used to find the target value or the estimated cash flow of the investment, when plug in the equation (5&6) with (α) = 1 39 NPVl(  ) is the first equation (5): NPVl(  ) = (−4,000,000 − 1,400,000 α ) + 400,000 + 45,000 α (1,09−0,01α)∗(1,11−0,02α)∗1,09−0,02α 300,000 + 80,000 α 1,07+0,01α 400,000 + 40,000 α + (1,09−0,01α)∗(1,11−0,02α) + 5,800,000+ 1,570,000 α + (1,11−0,02α)∗(1,09−0,01α)∗(1,09−0,02α)∗(1,09−0,01α) While, NPVr(  ) is the second equation (4): NPVr(  ) = (−6,000,000 + 600,000 α) + 600,000 − 155,000 α (1,07+0,01α)∗(1,07+0,02α)∗(1,06+0,01α) 500,000 −120,000 α 1,09−0,01α 600,000 – 160,000 α + (1,07+0,01α)∗(1,07+0,02α) + 8,300,000– 9300,000 α + (1,07+0,01α)∗(1,07+0,02α)∗(1,06+0,01α)∗(1,06+0,02α) NPV = (NPV0, NPV1, NPV2) → (triangular fuzzy net present values) By subsituting with α=0 at equation (5) NPV0=(−4000000) + (300000)/(1.07) + (400000)/(1.09 ∗ 1.11) + (400000)/(1.09 ∗ 1.11 ∗ 1.09) + (5800000 )/(1.11 ∗ 1.09 ∗ 1.09 ∗ 1.09)= 949120.37 By subsituting with α=1 at equation (5) NPV1=((−4000000 − 1400000 ) + (300000 + 80000)/(1.06) + (400000 + 40000)/(1.08 ∗ 1.09) + (400000 + 45000)/(1.08 ∗ 1.09 ∗ 1.07) + (5800000 + 1570000 )/(1.09 ∗ 1.08 ∗ 1.07 ∗ 1.08)= 1103178.9 By subsituting with α=0 at equation (6) NPV2=(−6000000) + (500000)/(1.09) + (600000)/(1.07 ∗ 1.07) + (600000)/(1.07 ∗ 1.07 ∗ 1.06) + (8300000)/(1.07 ∗ 1.07 ∗ 1.06 ∗ 1.06)= 1929244.1 40 Graphical Solution for Investment (E) Figure 10: Triangular Fuzzy Number Investment (E) From the graphical illustration we can notic that the lower portion is NPV0 = (949120.3), the target value of cash flows is represented by (NPV1 = 1103178.9), and the higher portion of the investment (NPV2 = 1929244.1). despite the fact that this graphical solution of investment E is not symetric, because of unequality of the lower and upper portions of net present values, the investment is qualified to be compaired with other investments. As, invesment E is profitable, where NPV0 and NPV2 are belong to the positive X-axis. 5.1.5 Comparison of investments (A & B & E) The probablistic approach is defined as one of fuzzy numbers comparison tests to order fuzzy numbers, which is based on the (α–cuts) representation of fuzzy numbers. The α–cuts based orderings are so attractive, because they can be used regardless the type of the membership function. Moreover, each α-level is an interval, so the powerful tools of interval arithmetic can be employed to solve the problem of fuzzy ordering. 41 In our case, the desigen ,which we are applying for all fuzzy investments tools (NPV&IRR) is the triangular fuzzy numbers. This desigen has three components, for example X=[x0,x1,x2], where e0 represents the minimuim value of the investment or lower range, e1 represents the target value or the most likely result, while e2 represents the maximum investment or the upper range. Indeed, our comparison method (probabilistic approach) is neglecting the target value of our design (e1), and considerate the the upper and lower ranges (e0 & e2). Now, for investment (A) we can cosiderate as a proper candidate because this mean that the we are getting a misleading net present values , which is cumlating an error within its results. let b = [b1, b2], and for investment (E), let a = [a0, a2], for investment (B) be two closed and compact intervals. In the case of triangular number comparison, the obtained results may be interpreted as a fuzzy number . Let P(Hk ) be the probability of event Hk , and P(b > a|Hk ) be the conditional probability of b > a given Hk . Hence, the composite probability may be expressed as follows: P(b > a) = n k=1 P(Hk )P(b > a|Hk ). Table 1: Typical cases of interval comparison 42 P(b > a) Table 2: Typical cases of interval comparison Case number 5 does apply, when b1>=a1 ^ b2>=a2 ^b1 a) = 1 − 2 ∗ (b2−b1)∗(a2−a1) 1 (1929244.1−1189785.6)2 P(b > a) = 1 − 2 ∗ (1929244.1−949120.3)∗(11984152.2− 1189785.6)= 0.97≈97% To conclude, there is a chance 97% that investment E is better than investment B. invesment B should be selected as real estate investment. 43 5.2 Triangular Fuzzy Numbers & Interest rate of return (IRR) 5.2.1 Project A A Healthcare Project with the following specifications in *millions: -P0 = (46.1, 52.7, 59.3) P1 = (8.8,13.2,17.6) P2 = (12.9,15.2,16.4) P3 = (15.6,17.2,20) P4= (14.7,18.7,22.6) Sample shows the difference between minimum, target and maximum: -C0 = (46.1/52.7, 52.7/59.3), C1 = (8.8/13.2, 13.2/17.6), C2 = (12.9/15.2, 15.2/16.4), C3 = (15.6/17.2, 17.2/20), C4 = (14.7/18.7, 18.7/22.6), Next, calculate the left (f1) and right (f2) function: f1 (y/C0) = 6.6y + 46.1 and f2 (y/C0) = 59.3 – 6.6y f1 (y/C1) = 4.4y + 8.8 and f2 (y/C1) = 17.6 - 4.4y f1 (y/C2) = 2.3y + 12.9 and f2 (y/C2) = 16.4 - 1.2y f1 (y/C3) = 1.6y + 15.6 and f2 (y/C3) = 20 - 2.8y f1 (y/C4) = 4y + 14.7 and f2 (y/C4) = 22.6 - 3.9y 44 The correct fractions of the fuzzy internal efficiency ratio are expressed as f1 (y / i) = (i2 -i1) y + i1 and f2 (y / i) = (i3-i4) y + i4. The equation of the left function to calculate i3 and i4: 6.6y + 46.1 = (4.4y+8.8) [(i3-i4) y + i4 + 1]-1 + (2.3y+12.9) [(i3–i4) y + i4+1]-2 + (1.6y+15.6) [(i3– i4) y + i4+1]-3+(4y+14.7) [(i3–i4) y + i4+1]-4 The equation of the right function to calculate i1 and i2: 59.3- 6.6y = (17.6-4.4y) [(i2-i1) y + i1 + 1]-1 + (16.4-1.2y) [(i2–i1) y + i1+1]-2+(20-2.8y) [(i2–i1) y + i1+1]-3+(22.6-3.9y) [(i2–i1) y + i1+1]-4 Let y = 0 and y = 1, respectively for the upper two equations: y=0: 46.1 = 8.8(1 + i4)-1 + 12.9(1+i4)-2+15.6(1 + i4)-3 + 14.7(1+i4)-4 y=0: 59.5 = 17.6(1 + i1)-1 + 16.4(1+i1)-2 + 20(1 + i1)-3 + 22.6(1+i1)-4 y=1: 52.7= 13.2(1 + i3)-1 + 15.2(1+i3)-2 + 17.2(1 + i3)-3 + 18.7(1+i3)-4 y=1: 52.7 = 13.2(1 + i2)-1 + 15.2(1+i2)-2 + 17.2(1 + i2)-3 + 18.7(1+i2)-4 Respectively From these equations we calculated interest rate: i1 = 10.3% (The better interest rate) i2 = 7.9% i3 = 7.9% i4 = 4.6% 45 5.2.2 Project (B) A Healthcare Project with the following specifications in *millions: -P0 = (33.6, 40.3, 44.7) P1 = (7.6,8.7,10.9) P2 = (9,10.2,12) P3 = (9,12,13.5) P4= (12,15.1,17.1) Sample shows the difference between minimum, target and maximum: -C0 = (33.6/40.3, 40.3/44.7), C1 = (7.6/8.7, 8.7/10.9), C2 = (9/10.2, 10.2/12), C3 = (9/12, 12/13.5), C4 = (12/15.1, 15.1/17.1), Next, calculate the left (f1) and right (f2) function: f1 (y/C0) = 6.7y + 33.6 and f2 (y/C0) = 44.7 – 6.7y f1 (y/C1) = 1.1y + 7.6 and f2 (y/C1) = 10.9 – 2.2y f1 (y/C2) = 1.2y + 9 and f2 (y/C2) = 12 - 1.8y f1 (y/C3) = 3y + 9 and f2 (y/C3) = 13.5 – 1.5y f1 (y/C4) = 3.1y + 12 and f2 (y/C4) = 17.1 – 2y 46 The correct fractions of the fuzzy internal efficiency ratio are expressed as f1 (y / i) = (i2 -i1) y + i1 and f2 (y / i) = (i3-i4) y + i4. The equation of the left function to calculate i3 and i4: 6.7y + 33.6 = (1.1y+7.6) [(i3-i4)y + i4 + 1]-1 + (1.2y+9) [(i3–i4)y + i4+1]-2 + (3y+9) [(i3–i4)y + i4+1]-3+(3.1y+12) [(i3–i4)y + i4+1]-4 The equation of the right function to calculate i1 and i2: 44.7 – 4.4y = (10.9-2.2y) [(i2-i1)y + i1 + 1]-1 + (12-1.8y) [(i2–i1)y + i1+1]-2+(13.5-1.5y) [(i2–i1)y + i1+1]-3+(17.1-2y) [(i2–i1)y + i1+1]-4 Let y = 0 and y = 1, respectively for the upper two equations: Y=0: 33.6= 7.6(1 + i4)-1 + 9(1+i4)-2+9(1 + i4)-3 + 12(1+i4)-4 Y=0: 44.7 = 10.9(1 + i1)-1 + 12(1+i1)-2 + 13.5(1 + i1)-3 + 17.1(1+i1)-4 Y=1: 40.3 = 8.7(1 + i3)-1 + 10.2(1+i3)-2 + 12(1 + i3)-3 + 15.1(1+i3)-4 Y=1: 40.3 = 8.7(1 + i2)-1 + 10.2(1+i3)-2 + 12(1 + i3)-3 + 15.1(1+i3)-4 Respectively From these equations we calculated interest rate: i1=7% (The better interest rate) i2=5% i3=5% i4=4.3% 47 B A 1.0 y 0 0 4.3 4.6 5.0 i1 i1 i2,3 7.0 7.9 i4 i2,3 10.3 i4 Figure 11: Triangular fuzzy number of project A and B (Healthcare) Comments regarding the results: A decrease in the interest rate will require investors to spend more in the investment cost. However, whenever the interest rate increases, it will benefit the investment as the income will increase and investment cost will decrease. In both projects, the larger interest rate is used from the four I’s. 5.3.3 Interval comparison of fuzzy between project A and B: Using Probabilistic Approach 48 IRR project (A): I1=10.3% I2=7.9% I3=7.9% I4=4.6% IRR project (B): I1=7% I2=5% I3=5% I4=4.3% • Let project B = [a1, a2] and project A= [b1, b2] Example of overlapping intervals: BA B A 4.3 a1 4.6 b1 7 a2 Figure 12: Comparison between project A and B 49 10.3 b2 Using the following formula: (𝑎2 − 𝑏1 )2 1 𝑃(𝑎 > 𝑏) = 1 − 2 (𝑎2 − 𝑎1 )(𝑏2 − 𝑏1 ) Therefore: 𝑃(𝑎 > 𝑏) = 1 − (7 − 4.6)2 1 2 (7 − 4.3)(10.3 − 4.6) P (a > b) = 0.813 Therefore, the probability shows that 81.3% project A is better than B. We knew the better project as we decrease the investment cost and increase the income using the higher interest rate compared between the projects. Whenever the fuzzy technique is used the benefit will increase but the risk will increase, in the other hand, the crispy(normal) technique has less risk and benefit than the fuzzy. 50 6 Conclusion After viewing the results, fuzzy logic proved to be advantagous to the normal crispy technique however it is important to mention that with fuzzy logic comes greater risk. Using fuzzy logic in investment is very useful because it will give more clear idea of the business case for the people without going into details and that will help for better understanding of the company’s situation. Advantages of fuzzy logic include: Fuzzy logic represents a system that combines the numeric and linguistic approaches. Fuzzy logic investments methods take less development time than the normal investments methods. Fuzzy logic helps the investor take a decision in choosing between different investments without knowing the exact data. Fuzzy logic makes the inventors more comfortable in taking decisions. It is very accurate because its based on the experience of experts and their knowledge. Results showed that project E for the NPV analysis was the best to invest in as project A and B showed lower profit margins. In addition, IRR analysis showed that project A is better than B to invest in. 51 7 PROJECT MANAGEMENT The project was divided into tasks between the group members as shown below: Task1: Assign group leader. Task2: Get the feedback about the senior project one final report. Task3: Find three companies and choose the best option. Task4: Work on deliverable 4 and submit the work. Task5: Visit the company to get the data needed for the project. Task6: Start applying the fuzzy logic on the company. Task7: Submit deliverable 5. Task8: Submit deliverable 6. Task9: Get the results using the normal investment techniques. Task10: Apply the fuzzy logic on the data we have. Task11: Get the results of using the fuzzy logic on the company’s data. Task12: Submit the deliverable 7. Task13: Compare between the results after and before applying the fuzzy logic. Task14: Submit the final report. Task15: Do the presentation. Task16: Submit the research paper. Table 3 shows the contributitly. Addiotnally, we conducted a Gantt Chart in order to accomplish these tasks on time as shown in Figure 7. 52 Name contribution Abdullah ALHajri Worked on Fuzzy NPV and IRR results and Project Management. Salman ALTeenan Worked on Methodology, conclusion and Design. Khaled ALHajri Worked on Abstract, Fuzzy NPV and IRR results and Background. Zeyad ALShikhany Worked on Introduction, Fuzzy NPV results Design and Gantt Chart. Omar ALAjmi Worked on Crispy NPV and IRR results and Design. Table 3: Contribution Table task 16 task 15 task 14 task 13 task 12 task 11 task 10 task 9 task 8 task 7 task 6 task 5 task 4 task 3 task 2 task 1 28-Jan 17-Feb 09-Mar 29-Mar Figure 13: Gantt Chart 53 18-Apr 08-May 28-May REFRENCES Amedeo De Cesari, Susanne Espenlaub, Arif Khurshed and Michael Simkovic, "The Effects of Ownership and Stock Liquidity on the Timing of Repurchase Transactions", 2010 Benčina, J. (2007). The use of fuzzy logic in coordinating investment projects in the public sector. The Proceedings of Rijeka Faculty of Economics–Journal of Economics and Business, 25(1), 113-136 Berk, Johnathan; DeMarzo, Peter; Stangeland, David (2015). Corporate Finance(3rd Canadian ed.). Toronto: Pearson Canada. p. 64. ISBN 978-0133552683. Broverman, Samuel (2010). Mathematics of Investment and Credit. Winsted: ACTEX Publishers. pp. 4–229. ISBN 9781566987677. Byrne, P. (1997). Fuzzy DCF: a contradiction in terms, or a way to better investment appraisal. Proceedings Cutting Edge ‘97, RICS. Del Giudice, V., De Paola, P., &Cantisani, G. B. (2017). Valuation of real estate investments through Fuzzy Logic. Buildings, 7(1), 26. Dostál, P., & Brož, Z. (2011). Fuzzy logic investment support on the financial market. In 31th International Symposium on Forecasting, Praha, CZ. Education 2020 Homeschool Console, class "Economic Math"; definition of FUTURE VALUE: "Future value is the value of an asset at a specific date." EDUCATION 2020 HOMESCHOOL CONSOLE. FORMULA FOR CALCULATING THE FUTURE VALUE OF AN ANNUITY. 54 Farris, Paul W.; Neil T. Bendle; Phillip E. Pfeifer; David J. Reibstein (2010). Marketing Metrics: The Definitive Guide to Measuring Marketing Performance. Upper Saddle River, 26New Gorrell, M. G. (2011). E-books on EBSCOhost: Combining NetLibrary E-books with the EBSCOhost Platform. Information Standards Quarterly,23(2), 31. doi:10.3789/isqv23n2.2011.07 Ho, S. H., & Liao, S. H. (2011). A fuzzy real option approach for investment project valuation. Expert Systems with Applications, 38(12), 15296-15302. Ibon Galarraga, M. González-Eguino, Anil Markandya (1 January 2011). "Handbook of Sustainable Energy". Edward Elgar Publishing. p. 37. ISBN 0857936387. Retrieved 9 May 2017 – via Google Books. Jersey: Pearson Education, Inc. ISBN 0-13-705829-2. The Marketing Accountability Standards Board (MASB) endorses the definitions, purposes, and constructs of classes of measures that appear in Marketing Metrics as part of its ongoing Common Language: Marketing Activities and Metrics Project. Kuchta, D. (2000). Fuzzy capital budgeting. Fuzzy sets and systems, 111(3), 367-385. Kurt, Daniel (2003-11-24). "Net Present Value (NPV) Definition | Investopedia". Investopedia. Retrieved 2016-05-05. Lindström, T. (1998). A fuzzy design of the willingness to invest in Sweden. Journal of economic behavior & organization, 36(1), 1-17. Liu, K. F., Liang, H. H., Yeh, K., & Chen, C. W. (2009). A qualitative decision support for environmental impact assessment using fuzzy logic. Journal of Environmental Informatics, 13(2). 55 Marco Raugei, Pere Fullana-i-Palmer and Vasilis Fthenakis (March 2012). "The Energy Return on Energy Investment (EROI) of Photovoltaics: Methodology and Comparisons with Fossil Fuel Life Cycles" (PDF). http://www.bnl.gov/. Archived (PDF) from the original on 28 March 2015. External link in |website= (help) (n.d.). doi:10.7717/peerj.347/supp-2 (n.d.). Retrieved December 02, 2017, from https://www.doc.ic.ac.uk/~nd/surprise_96/journal/vol4/sbaa/report.fuzzysets.html Serguieva, A., & Hunter, J. (2004). Fuzzy interval methods in investment risk appraisal. Fuzzy Sets and Systems, 142(3), 443-466. Simkovic, M. (2011). The Effects of Ownership and Stock Liquidity on the Timing of Repurchase Transactions. Simkovic, Michael (2017). "The Evolution of Valuation in Bankruptcy". American Bankruptcy Law Journal. SSRN 2810622 . South-Western Publishing Co. pp. 147–498. ISBN 9780538479172. Tavakkoli, M., Jamali, A., &Ebrahimi, A. (2010). New method to evaluate financial performance of companies by fuzzy logic: case study, drug industry of Iran. Asia Pacific Journal of Finance and Banking Research, 4(4), 15 56 See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/269099709 Influence of casting speed on the structure and mechanical properties of continuous cast DHP copper tube Conference Paper · May 2014 CITATION READS 1 109 6 authors, including: Ehsaan-Reza Bagherian Colin Bell The American University of the Middle East University of Strathclyde 21 PUBLICATIONS 4 CITATIONS 5 PUBLICATIONS 3 CITATIONS SEE PROFILE SEE PROFILE Mervyn Cooper Brian Frame 5 PUBLICATIONS 3 CITATIONS University of Dundee 5 PUBLICATIONS 3 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: Rautomead R& D project View project All content following this page was uploaded by Ehsaan-Reza Bagherian on 04 December 2014. The user has requested enhancement of the downloaded file. st rd May  21  –  23  2014,  Brno,  Czech  Republic,  EU       INFLUENCE OF CASTING SPEED ON THE STRUCTURE AND MECHANICAL PROPERTIES OF CONTINUOUS CAST DHP COPPER TUBE Ehsaan-Reza BAGHERIANa, Colin BELLb, Mervyn COOPERb, Yongchang FANa, Brian FRAMEb, Amin ABDOLVANDa a University of Dundee, DD1 4HN Dundee, Scotland, United Kingdom, e.bagherian@dundee.ac.uk, y.fan@dundee.ac.uk, A.Abdolvand@dundee.ac.uk b Rautomead Ltd, DD2 4UH Dundee, Scotland, United Kingdom Colin.Bell@rautomead.com ,Mervyn.Cooper@rautomead.com, Brian.Frame@rautomead.com Abstract DHP Copper tubes are frequently used in industrial applications with their unique characteristics such as high corrosion or excellent erosion resistance. Due to the requirement of good quality production, an excellent global factor is needed for the purpose of obtaining high mechanical properties. A mechanical properties has correlation with grain size and a high mechanical properties is achieved by small grain structure. There are three ways in which grain size can be altered: by thermal means, chemical means and by mechanical means. This paper looks at the first case, thermal means, which has very substantial cost benefits over the other two types of grain refinement in that it does not require large pieces of equipment that vibrate or mix and does not use any exotic metals as feed stock. Instead what thermal methods require is a change in parameters like: casting speed, liquid metal temperature or cooling water temperature. In this work, characterization of the influence of casting speed on the structure and mechanical properties of continuous cast DHP copper tube has been carried out by drift expanding test and grain size reading. A significant different based on grain structure has been investigated and it was also found that the casting speed could improve the elongation of samples from 29 % expanding to 36 % expanding. Keywords: DHP Copper Tubes, Casting Speed, Drift Expanding Test and Grain Structure 1. INTRODUCTION In alloy castings it is usually desirable for the grain structure to be fine. The major advantage of fine grain structures over cast structures is the improvement of mechanical properties and increase uniformity of properties [1, 2]. The fine grain process development program begun in 1975 to produce a fine, equiaxed grain structure with a vacuum-cast IN713LC radial turbine wheel and since the 1980s, fundamental finegrained cast techniques have been widely developed [3]. Grain refining methods are grouped into (a) thermal such as cooling rate control, (b) chemical by adding the nucleant agents addition into the melt and (c) dynamical by mechanical agitation [4, 5]. Although a finer grain can be obtained by mechanical and chemical techniques but the problem of these methods are that, the mechanical way is expensive and inoculants introduce oxides, which as non-metallic inclusions, become nucleation sites for fatigue crack initiation [3]. The other problem of chemical method is lack of uniform dispersion of nucleant agents like metal oxides due to the ultimate problems such as poor wettability or in-compatibility between metal and oxide particles [6]. In this work, characterization of the influence of parameters of the casting process has been carried out, especially that of the casting rate was selected as the most adaptable technique and the easiest to implement in a conventional casting process. However, the casting speed is limited by several different phenomena examples of fracture of samples on high-speed solidification rate. Clearly, to increase the casting speed of a continuous casting process requires careful consideration of many different phenomena. st rd May  21  –  23  2014,  Brno,  Czech  Republic,  EU       The aim of this paper is to investigate the impact of the casting speed on the structure and mechanical properties of continuous cast DHP copper tubes. 2. EXPERIMENT The traditional method of producing copper tube is by large ingot casting and extrusion but there is a new method which use continuous casting technology to cast smaller tube. The main advantage of the continuous casting process for copper tube production is that it is an economic and flexible manufacturing process with a much smaller initial capital investment. In studying the properties of DHP copper tubes it is necessary to have detailed knowledge of mechanical properties and grain size of the samples. Mechanical properties usually gain by 3 testing methods involving; (a) Tensile test by inserting a metal plugs into the ends of pipe and then measuring the tensile strength and elongation percentage, (b) Tube drift expanding test to measuring the tube expanding percentage and (c) Flattening test for determining the ability of metallic tubes of circular cross-section to undergo plastic deformation by flattening [7, 8 and 9]. In order to understand the efficiency of casting speed, further study has been done. Four casting speed have been studied in this research (1040 (mm/min), 1140 (mm/min), 1220 (mm/min) and 1360 (mm/min) respectively) and mechanical properties of continuous cast DHP copper tubes has investigated by drift expanding test. Table 1 is given the copper tube samples tested in this study. Table 1 The Copper tube samples tested in this research Sample OD Thickness Speed (mm/min) Product (kg/hr) (mm) (mm) Cast 1 38 2.3 1040 144 Cast 2 38 2.3 1140 158 Cast 3 38 2.3 1220 169 Cast 4 38 2.3 1360 189 Drift Expanding Test – drift-expanding test is “Expansion of the end of the test piece cut from the tube, by means of a conical mandrel, until the maximum outside diameter of the expanded tube reaches the value specified in the relevant product standard” [7]. Symbols, designation and units for the driftexpanding test of tubes are presented in Table 1 and shown in Fig. 1. Fig. 2 (a and b) illustrates the test procedure, which have been carried out to identify the Influence of casting speed on the mechanical properties of continuous cast DHP copper tubes. Fig. 1 Designation of the drift-expanding test of tubes st rd May  21  –  23  2014,  Brno,  Czech  Republic,  EU       Table 2 Symbols, Designation and Units for the drift-expanding test of tubes Symbol Designation Units A Wall thickness of the tube mm D Original outside diameter of the tube mm Du Maximum outside diameter after testing mm L Length of the test piece before testing mm Β Angle of the conical mandrel Degree (a) Drift Expanding Test (b) Specimen after fracture Fig. 2 drift-expanding procedure In this research, drift expanding test done by a hydraulic press at ambient temperature and truncated-cone shaped mandrel of hardened steel. The length of the specimen was selected less than twice size of the external diameter of the tube. Finally, the drift expanding percentage, calculated by measuring the diameter of tube after fracture divided by the original diameter of tube Metallography – Metallographic analysis is the science of preparing a metal surface by grinding, polishing and etching to study the metal alloy’s microstructures, which usually determine the physical and mechanical properties of metal alloy material [10]. In this paper, all samples were ground first using coarse abrasive paper (Grade No 60) and subsequently wet & dry fine silicon carbide paper (Grit No 2500). Then the samples were polished using diamond paste beginning with 6 micron and then continuing until the grinding scratches were removed (quarter micron). After polishing, the samples were cleaned by acetone in an ultrasonic cleaner and dried with nitrogen gas. Finally, the polished samples were etched using a cotton tip dipped with distilled water and nitric acid. 3. RESULTS AND DISCUSSION Average Expanding Percentage –The results of average expanding percentage of copper tube samples are presented in Fig. 3. Table 2 shows the average expanding percentage of the continuous cast DHP copper tube samples, which explained on Table 1. It can be seen that the cast 4 samples has a higher drift expanding percentage (improved by 29 % to 36 %) st rd May  21  –  23  2014,  Brno,  Czech  Republic,  EU       Table 3 Drift expanding results Sample Test 1 Test 2 Test 3 Average Expanding Percentage (%) Cast 1 31 % 28 % 27 % 29 % Cast 2 30 % 32 % 28 % 30 % Cast 3 32 % 31 % 33 % 32 % Cast 4 38 % 35 % 36 % 36 % Fig. 3 comparison average expanding percentage of copper tube samples Grain Structure – The effect of casting speed on the structure of the continuous cast DHP copper tube is illustrate in Fig. 4. It must be noticed that fine grains can be achieved by increasing the casting speed, as seen in sample 1, 2, 3 and 4 in Fig. 4. Cast 1 Cast 2 st rd May  21  –  23  2014,  Brno,  Czech  Republic,  EU       Cast 3 Cast 4 Fig. 4 comparison grain structure of copper tube samples An easy method to expand the mechanical properties of a material is to make the grain size as small as possible, or to increase the amount of grain boundaries. It is known from the above observation on the metallography analysis of grains that the number of columnar grains increases after grain refining by increasing the casting speed. As is well known, smaller grains have greater ratios of surface area to volume, which means a bigger ratio of grain boundaries to dislocations. The more grain boundaries that occur, the higher strength. The other reason for this is increasing casting speed leads to a change in the heat conduction and solidification condition, which results in making it possible to obtain a structure with finer grains. This is based on a thermal change because the higher the casting speed gets the faster the material goes from liquid to solid. 4. CONCLUSION AND FUTURE WORK From the above experimental results, some important conclusions can be drawn: 1. Once the speed is increased from 1040 mm/min to 1360 mm/min the end result produces an increase in the production rate from 144kg/hr to 189kg/hr. 2. When casting speed was increased from 1040 mm/min to 1360 mm/min, significant improvements of mechanical and physical properties were observed. With the increasing of the casting speed, the drift expanding percentage increased, and the grain structure tends to become finer in structure. 3. An economical process has been studied to produce continuous cast DHP copper tube fine grain structure by increasing the casting speed. A significant achievement of the fine grain process is to produce a uniform structure and enables greater reliance to be placed on the manufacturing process. 4. One limitation observed in this study is that once the casting speed is increased above the 1360 mm/min by even a minute amount it would result in a casting fracture. Thus, at high casting speed, casting speed changing should be avoided or slower speed changing rate in continuous casting should be used. 5. As for future work, this research can be extended by comparing the influence of other thermal factors on the structure and mechanical properties of continuous cast DHP copper tube such as; the temperature of liquid metal or cooling water temperature. st rd May  21  –  23  2014,  Brno,  Czech  Republic,  EU     6.   It is suggested that for extended future work to these areas, a chemical way could also be attempted. ACKNOWLEDGEMENTS The corresponding authors would like to thank Mr. Gavin Marnie, Mr. Dougie Hain and Mr. Graham Lees at Rautomed, and Professor Mervyn Rose and Dr. Mark Pridham at University of Dundee, for their technical support. LITERATURE [1] T. E. Quested, A. L. Greer, Grain refinement of Al alloys: Mechanisms determining as-cast grain size in directional solidification, Acta Materialia, Volume 53, Issue 17, October 2005, pp. 4643–4653 [2] J. R. Bringer, L. F. Norris, L. Rozenberg, Microcast-x fine grain casting a progress report, Super alloy 1984, The Metal- lurgical Society of AIME, 1984, pp. 23 - 32. [3] M. Would, H. Benson, Development of conventional fine grain casting process, The Metallurgical Society of AIME, 1984, pp. 3 -12. [4] L. F. Mondolfo, Grain refinement in the casting of non-ferrous alloys, Grain Refinement in Casting and Welds, The Metallurgical Society of AIME, 1983, pp. 3-50. [5] T. Robert, M. E. Noguez, G. Salas, S. Montejano, Influence of grain refinement on some mechanical properties of non ferrous cast alloys, Acta Metallurgica et Materialia, Volume 40, Issue 4, April 1992, Pages 771–777. [6] Gwang-Ho Kim1), Sung-Mo Hong2), Min-Ku Lee, Effect of Oxide Dispersion on Dendritic Grain Growth Characteristics of Cast Aluminum Alloy, Materials Transactions, Vol. 51 No.10 (2010) pp.1951-1957. [7] ASTM, Standard Test Methods and Definitions for Mechanical Testing of Steel Product, A 370 – 07b [8] EN ISO, Standard Test Methods and Definitions for Metallic materials – Tube - Drift-expanding test, 8493:1998. [9] EN ISO, Standard Test Methods and Definitions for Metallic materials –Tube - Flattening test, 8492:1998. [10] Metallography, Microstructure, and Analysis, Application and Innovation for Metals, Alloys, and Engineered Materials, ISSN: 2192-9270 (electronic version) Journal No. 13632. View publication stats Proceedings of the International Conference on Industrial Engineering and Operations Management Washington DC, USA, September 27-29, 2018 Paper Title (18 font) Ahad Ali and Don Reimer (12 font) A. Leon Linton Department of Mechanical Engineering (11 font) Lawrence Technological University Southfield, MI 48075, USA aali@ltu.edu, dreimer@ltu.edu Mohammad Khadem Mechanical and Industrial Engineering Department Sultan Qaboos University Muscat, Oman khadem@squ.edu.om Abstract (12 font) Use font size 11 for the abstract text. It should not be exceeding 200 words. Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Abstract Keywords (12 font) Note more than five keyword (11 font size) Page Layout • • • • • 8 1/2" X 11" paper size All margins: 1.00" Full justification Times New Roman font Maximum 12 pages 1. Headings (12 font) 1.1 Sub-Headings (11 font) Text – 10 font, no indexing. 100 80 60 East 40 West 20 North 0 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr Figure 1. Name of the figure © IEOM Society International Abstract Abstract Abstract Abstract Abstract Proceedings of the International Conference on Industrial Engineering and Operations Management Washington DC, USA, September 27-29, 2018 Table 1. Name of the table Equation numbering is optional. Do not include page numbers. Manuscript must be in MS Word. Acknowledgements Add acknowledgement if need References (12 font) Chang, T., Wysk, R., and Wang, H., Computer-Aided Manufacturing, 3rd Edition, Prentice Hall, New Jersey, 2006. Cook, V., and Ali, A., End-of-line inspection for annoying noises in automobiles: trends and perspectives, Applied Acoustic, vol. 73, no. 3, pp. 265-275, 2012. Reimer, D., Corporate Entrepreneurship, Available: http://www.ieomsociety.org/Details.aspx?id=xxx, March 5, 2012. Khadem, M., Ali, A., and Seifoddini, H., Efficacy of lean metrics in evaluating the performance of manufacturing system, International Journal of Industrial Engineering, vol. 15, no. 2, pp. 176-184, 2008. Pandian, A., and Ali, A., Automotive robotic body shop simulation for performance improvement using plant feedback, International Journal of Industrial and Systems Engineering, vol. 7, no. 3, pp. 269-291, 2011. Rahim, A., and Khan, M., Optimal determination of production run and initial settings of process parameters for a deteriorating process, International Journal of Advanced Manufacturing Technology, April 2007, vol. 32, no. 78, pp. 747-756, 2007. Rahman, M. A., Sarker, B. R., and Escobar, L. A., Peak demand forecasting for a seasonal product using Bayesian approach, Journal of the Operational Research Society, vol. 62, pp. 1019-1028, 2011. Reimer, D., and Ali, A., Engineering education and the entrepreneurial mindset at Lawrence Tech, Proceedings of the International Conference on Industrial Engineering and Operations Management, Istanbul, Turkey, July 3 – 6, 2012. Shetty, D., Ali, A., and Cummings, R., A model to assess lean thinking manufacturing initiatives, International Journal of Lean Six Sigma, vol. 1, no. 4, pp. 310-334, 2010. Srinivasan, G., Arcelus, F.J., and Pakkala, T.P.M., A retailer’s decision process when anticipating a vendor’s temporary discount offer, Computers and Industrial Engineering, vol. 57, pp. 253-260, 2009. See below guidelines for citations: For papers in a journal: Last name, first initial, title of the paper, journal name, volume (vol.), issue (no.), page number (pp.), year. (single author) Last name of first author, first initial of first author, and last name of second author, first initial of second author, title of the paper, journal name, volume (vol.), issue (no.), page number (pp.), year. (multiple authors) For papers in a conference: Last name, first initial, title of the paper, conference name, volume/issue (in any), page number (if any), city, country, date of the conference, year. (single author) Last name of first author, first initial of first author, and last name of second author, first initial of second author, title of the paper, conference name, volume/issue (in any), page number (if any), city, country, date of the conference, year. (multiple authors) For books: Last name, first initial, title of the book, edition, publisher, city/country, year. (single author) © IEOM Society International Proceedings of the International Conference on Industrial Engineering and Operations Management Washington DC, USA, September 27-29, 2018 Last name of first author, first initial of first author, and last name of second author, first initial o second author, title of the book, edition, publisher, city/country, year. (multiple authors) For internet sources: Last name, first initial, title of the article or news in online resource, name of the newspaper or online sources, Available: online link, date, year. Reimer, D., Corporate Innovation and Entrepreneurship, Available: http://www.ieomsociety.org/Details.aspx?id=xxx, March 5, 2012. Biographies Include author bio(s) of 200 words or less. Ahad Ali is an Associate Professor, and Director of Master of Engineering in Manufacturing Systems and Master of Science in Industrial Engineering in the A. Leon Linton Department of Mechanical Engineering at the Lawrence Technological University, Michigan, USA. He earned B.S. in Mechanical Engineering from Khulna University of Engineering and Technology, Bangladesh, Masters in Systems and Engineering Management from Nanyang Technological University, Singapore and PhD in Industrial Engineering from University of Wisconsin-Milwaukee. He has published journal and conference papers. Dr Ali has completed research projects with Chrysler, Ford, New Center Stamping, Whelan Co., Progressive Metal Manufacturing Company, Whitlam Label Company, DTE Energy, Delphi Automotive System, GE Medical Systems, Harley-Davidson Motor Company, International Truck and Engine Corporation (ITEC), National/Panasonic Electronics, and Rockwell Automation. His research interests include manufacturing, simulation, optimization, reliability, scheduling, manufacturing, and lean. He is member of IIE, INFORMS, SME and IEEE. Donald M. Reimer is currently a fulltime senior lecturer and Director of The Lear Entrepreneurial Program in College of Engineering at Lawrence Tech. Mr. Reimer holds a Bachelor of Science degree in Industrial Management from Lawrence Technological University and a Master of Arts degree in Political Science from University of Detroit/Mercy. He is a Certified Management Consultant with over 35 years of experience in working with closely-held businesses. He has taught courses in entrepreneurship, management and corporate entrepreneurship and innovation for engineers. Mr. Reimer served as member of the Minority Economic Development Committee of New Detroit. Mr. Reimer serves as a KEEN Fellow for The Kern Family Foundation and is a member of United States Association of Small Business and Entrepreneurship. © IEOM Society International
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