Download free beranek model of cash management pdf. Beranek has developed a probabilistic model for controlling cash which involves management. Models on cash balance management have been. Proposed by Baumol (1952), Archer (1966), Beranek. (1963), Miller and Orr (1966), (Pigou, 1970), Lockyer. (1973), and Gibbs (1976) among others. William Baumol (1952) was the first person to provide a. Formal model of cash management.
Nationality American Alma mater Known for Acoustics Music, Acoustics, and Architecture Awards (1961) (1975) in Engineering (2002) Scientific career Fields Institutions (MIT) Doctoral students Leo Leroy Beranek (September 15, 1914 – October 10, 2016) was an American expert, former professor, and a founder and former president of (now BBN Technologies). He authored Acoustics, considered a classic textbook in this field, and its updated and extended version published in 2012 under the title Acoustics: Sound Fields and Transducers. He was also an expert in the design and evaluation of and, and authored the classic textbook Music, Acoustics, and Architecture, revised and extended in 2004 under the title Concert Halls and Opera Houses: Music, Acoustics, and Architecture. Contents. Early life and education Beranek was born in 1914 in.
His father was a farmer whose ancestors came from (in what is now the ) and his mother, previously a schoolteacher, had become a farmwife. Beranek first started school in a in. After his first year, he rode in a horse-drawn school bus on a two-hour trip to a somewhat larger school. In 1922 his family moved back to Solon, where he was soon skipped over third grade and moved directly into fourth grade classes.: 5 Around that time, a baby brother was born, named Lyle Edward Beranek.
In 1924 Beranek's father brought home a battery-powered radio containing a single. His eldest son became fascinated with both the technology and the musical aspects of radio. In the harsh winter of January 1926, Beranek's mother died suddenly, leaving his father with huge debts and forcing his father to sell the farm within two months. In junior high school Beranek earned his first independent money by selling and fabric. Beranek's father remarried and moved the family to the nearby town of, where he became co-owner of a. At his father's suggestion, Beranek learned radio repair via a, and to an older repairman. The younger Beranek quickly learned the trade, and was soon able to buy a automobile.
He also earned some spare cash by playing in a 6-person dance band. He continued to excel in his studies, including a typing class (rarely studied by boys) where he was the top performer.: 11 Beranek applied for and was accepted at nearby in. In the aftermath of the, money was tight, but he had managed to save $500.
Worried about the shaky financial situation, he went to his bank and managed to withdraw $400 to pay his college tuition in advance. The the next day, and Beranek lost the remaining $100.: 12 During freshman year at college, Beranek was told by his father that he could not expect any family money and that he was on his own. In the summers of 1932 and 1933 Beranek worked as a on local farms, to earn tuition money and to improve his physical condition. Beranek moved into two rooms above a bakery, shared with three other students to save money. He also continued to repair radios and played in a dance band, but falling income forced him to consider dropping down to a single class (in mathematics) during the next academic year.
In August 1933 Beranek was invited to accompany the family of a local dentist to the in. This was his first trip to a big city and it was a revelation. He attended concert performances by the and daily, was dazzled by the displays of industrial products and technology, and fascinated by the international pavilions. He lived on a shoestring, spending a total of $12 for four days, and felt compelled to make a return trip the following summer.: 14–15 In college Beranek became friends with a fellow student who had an setup, inspiring him to study and to earn his own.
In fall of 1933, he bought an early to earn a modest fee by recording students before and after taking a class. This was his first hands-on experience with the developing science of.
By early 1934 he was forced to drop out of college and work full-time to earn more tuition money. He found a position at the fledgling of, where he studied in his spare time. While there, he also met and dated Florence 'Floss' Martin, a student. He was able to save enough money to attend the Spring 1935 semester at Cornell College, then returned to Collins Radio for the summer.
In August 1935 Beranek had a chance encounter with a stranger whose car had developed a while passing through Mount Vernon. While helping the stranger (who turned out to be ), he learned that the passing motorist had written a technical paper on radio technology.
When Beranek mentioned plans for graduate school, Browning encouraged him to apply to, a possibility he had regarded as financially out of reach.: 20 Beranek was very busy in his final year at Cornell, running a radio repair and sales business and then transitioning to for electricity, while carrying a full course load. He managed three major wiring jobs for Cornell, including designing and installing a in a new men's dormitory then under construction.: 23 He also continued to date his girlfriend Floss.
Beranek graduated from Cornell College in summer 1936 with a Bachelor of Arts. He continued studies at, where he received a doctorate in 1940. Career During Beranek managed Harvard's electro-acoustics laboratory, which designed communications and systems for World War II aircraft, while at the same time developing other military technologies. During this time he built the first, an extremely quiet room for studying noise effects which later would inspire 's philosophy of silence.
In 1945 Beranek became involved with a small company called, which marketed a cup that fit over the mouthpiece of a telephone receiver in order to prevent the person speaking from being overheard. Although Hush-A-Phone had been around since the 1920s, Beranek used his acoustical expertise to develop an improved version of the device. Threatened Hush-A-Phone users with termination of their telephone service. At the time, AT&T maintained a monopoly on American telephone service and telephones were leased from AT&T, rather than owned by customers. The resulting legal case, resulted in a victory for Hush-A-Phone. In finding that AT&T did not have the right to restrict use of the Hush-A-Phone, the courts established a precedent that would eventually lead to the.
Beranek joined the staff at the as professor of from 1947 to 1958. In 1948, he helped found (BBN), serving as the company's president from 1952 to 1969. He continued to serve as chief scientist of BBN through 1971, as he led Boston Broadcasters, Inc.
Which (after a court battle) took control of television station. Beranek's 1954 book, Acoustics, is considered the classic textbook in this field; it was revised in 1986. In 2012, at the age of 98, he collaborated with Tim Mellow to produce an updated and extended revision, published under the new title Acoustics: Sound Fields and Transducers. Beranek's 1962 book, Music, Acoustics, and Architecture, developed from his analysis of 55 throughout the world, also became a classic; the 2004 edition of the text expanded the study to 100 halls.
Beranek has participated in the design of numerous concert halls and, and has traveled worldwide to conduct his research and to enjoy musical performances. From 1983 to 1986, Beranek was chairman of the board of the, where he remained a Life Trustee. He also served on the, 'an international volunteer group of alumni and friends established to support the arts at the Massachusetts Institute of Technology'. In 2008 he published Riding the Waves: A Life in Sound, Science, and Industry, an about his lengthy career and research in sound and music. He in September 2014, an occasion marked by a special celebration at. Beranek died on October 10, 2016 at the age of 102. His last paper, 'Concert hall acoustics: Recent findings', had been published earlier that year.
Awards and honors. Fellow of the (1952).
of the (1961) for internationally recognized achievements in all phases of architectural acoustics, and his publications on acoustical measurements, and the world's great concert halls. Gold Medal of the (1971). Gold Medal from the (1975) for leadership in developing, in the United States and abroad, the desire and the capability for achieving good acoustics in communications, workplaces, concert halls, and communities. in Engineering (2002). (2013). of the, United Kingdom (2014) In popular culture Beranek appeared on the television game show in 1962, around the time of the opening of at in.
(All four panelists selected him as 'the real' Leo Beranek.) Bibliography. Beranek, Leo.
Concert Halls and Opera Houses: Music, Acoustics, and Architecture. Springer, New Yotk: Springer, 2nd edition, 2004. Beranek, Leo (2010). Riding the Waves: A Life in Sound, Science, and Industry. Cambridge, Massachusetts: MIT Press.
(autobiography). Leo Beranek and Tim Mellow. Acoustics: Sound Fields and Transducers. Elsevier, Oxford, First edition, 2012.
See also. References. ^ Beranek, Leo (2008). (PDF) (1st ed.). Cambridge, Massachusetts: MIT Press. Retrieved 2014-06-09.
Wu, Tim (2010). The Master Switch: The Rise and Fall of Information Empires.
London: Atlantic Books Ltd. Pp. 102–103, 113. Acoustical Society of America. October 12, 2016.
Retrieved October 13, 2016. HIFICRITIC, 9 January 2013 from the original on 17 September 2013. Massachusetts Institute of Technology. Retrieved 2014-06-09. Retrieved 2014-09-19. Bryan Marquard and Edgar J.
Driscoll (October 13, 2016). Boston Globe. Retrieved October 13, 2016. Beranek (April 2016). 'Concert hall acoustics: Recent findings'. The Journal of the Acoustical Society of America: 1548–1556. American Academy of Arts and Sciences.
Retrieved June 15, 2011. External links. personal website. NAMM Oral History Library (2011) Further reading. Leo Beranek, electrical engineer, an oral history. Conducted in 1996 by Janet Abbate, IEEE History Center, Rutgers University, New Brunswick, New Jersey.
This work aims to apply genetic algorithms (GA) and particle swarm optimization (PSO) to managing cash balance, comparing performance results between computational models and the Miller-Orr model. Thus, the paper proposes the application of computational evolutionary models to minimize the total cost of cash balance maintenance, obtaining the parameters for a cash management policy, using assumptions presented in the literature, considering the cost of maintenance and opportunity for cost of cash. For such, we developed computational experiments from cash flows simulated to implement the algorithms. For a control purpose, an algorithm has been developed that uses the Miller-Orr model defining the lower bound parameter, which is not obtained by the original model. The results indicate that evolutionary algorithms present better results than the Miller-Orr model, with prevalence for PSO algorithm in results. Key words: Cash Flow; Cash Balance; Treasury; Genetic Algorithms; Particle Swarm Optimization.
1.INTRODUCTION The management of the cash available is a constant problem in all types of organizations. This is because of daily cash inflows and outflows, either by operating activities of the company or financial transactions that have been negotiated. So, there is a need to control financial resources in order to obtain the best result for the firm.
Thus, the function of cash management has the responsibility to mobilize, control and plan the financial resources of companies ( ). The use of models to support decision making becomes relevant, since they can provide a comprehensive view and optimization, which can hardly be obtained without the use of methodologies for this objective. The use of models in the problem of defining the optimal level of available cash had its origin in the work of and, where the authors start from the assumption that cash balance available may be defined as a commodity in inventory, i.e. A standard good, whose control may be daily, weekly, monthly, etc. Depending on the level of temporal detail required by the company. For these authors, the definition of the optimal cash balance follows the form of models to control inventory size, where it is considered the financial resource available as an inventory that has certain costs associated with its origin and maintenance, but also generates benefits indispensable to the firm. The definition of cash balance began to have a quantitative approach in order to promote the optimization of this financial inventory in order to minimize the costs associated with the maintenance or absence of cash available.
Later, defined cash balance as having an irregular fluctuation, being characterized as a random variable and they propose a stochastic model to manage the cash balance. 1.1 Objectives The study aims to present a comparison between two computational methodologies for determining the policy of cash management, taking as a basis the structure of the model proposed by Miller and Orr.
The objective of this research is to develop a management policy of cash balance cash, based on the assumptions of cost minimization by applying genetic algorithms (GA) and particle swarm optimization (PSO) and comparing the results with the traditional Miller-Orr model. 1.3 Research Problem Taking into consideration the aspects previously reported, as well as the importance of managing the cash balance, this paper describes and analyzes the following question: Which is the best method between the traditional Miller-Orr model, or the evolutionary genetic algorithm and particle swarm optimization models, to define a policy for managing cash balance, considering the costs involved in maintaining and obtaining cash? As this paper focuses on the qualitative methodology of financial management, so we used the techniques of genetic algorithm and particle swarm optimization in the development of the cash management policies, requiring to introduce the concepts applied to the problem dealt with and the proposed methodology for its resolution. 2.1 Models for Cash Management Cash management models had their origin in the work of, the author draws a parallel between cash and other business inventories, using an adaptation of the model of inventory management known as economic order quantity (EOQ), which aims to find the best trade-off between advantages and disadvantages of owning inventories.
Nevertheless, the EOQ has restrictions when using the assumptions of fixed and predictable demand, as well as instant supplies when applying for replacement inventory ( ). According to cash inventory can be seen as an inventory of a way of trade. In the EOQ model adapted to optimize cash the optimal configuration is achieved according to the relationship between the cost opportunity and the transfer cost. In the transfer model costs increase when the company needs to sell bonds to have more cash, as the opportunity costs increase with the existence of the cash balance, it is an application that has no profitability ( ). The model makes the analysis of the cost associated with maintaining cash, i.e., the opportunity cost determined by the interest rate that the company no longer receives by not applying the resources, and the cost of obtaining the money for the conversion of investments into cash ( ). The transfer cost represents expenditure incurred in application or redemption of funds, such as fees and taxes.
Later, present a model that meets the randomness of cash flows, while still considering the existence of only two assets, cash and investment, and the latter is an option of low risk and high liquidity ( ). Figure 1 – Variation of cash flows, adapted (Miller & Orr, 1966). This model seeks to define two bounds for the level of cash resources: the minimum and maximum, so when you reach the upper bound (moment T 1 ), represented by the high limit ( H ), investing an amount of the money in that provides the cash balance back to the optimal level of cash ( Z ). And to reach the minimum limit (moment T 2 ) in lower bound ( L ) should be made a rescue of cash to obtain the optimal level again ( ).
Thus, by working the net cash flows (inputs minus outputs) the Miller-Orr model enables the cash optimization, based on the transfer costs (represented by F ) and opportunity (represented by K ), obtaining the following formulation ( ). The “.”denotes optimal values and σ 2 is the variance of net cash flows. Even with the gain in relation to the Baumol model, considering randomization of cash flows, the Miller-Orr model assumes the definition of the lower bound ( L ), i.e. The risk of lack of cash, associated with a minimum margin safety depends on a management decision and is not treated in the model. At this point the problem addressed in this work lies, since the Miller-Orr model itself does not define the lower bound, it is the use of optimization algorithm in this problem setting the lower limit of optimal ( L. ), testing all possible L, with two decimal, to be able to minimize the cost.
Later, most of the work done uses the same assumptions as in the original models, particularly the Miller-Orr, differentiating by a stochastic modeling of the problem, as the research developed by,. Few works use a computational method for solving the problem, as proposed by that addresses the fuzzy systems as well as on the use of genetic algorithms, not being observed in the literature the application of PSO in this kind of problem.
2.2 Genetic Algorithms and Particle Swarm Optimization The evolutionary computation has its origins in the study of the theory of natural evolution, models and algorithms that seek to achieve the objective functions defined for it, starting from random resolution possibilities and, according to its development algorithm, and evolving in order to obtain better results in search to the established objective ( ). The algorithms of finding appropriate solutions, or optimization algorithms, use a series of assumptions or hypotheses about how to evaluate the fitness of a solution, so most of these models, based on gradient descent, depend on the occurrence of low oscillation problems or they will fail and obtain a local and non-global optimization ( ). But evolutionary algorithms do not rely on this kind of premise. Fundamentally, performance measurement should be able to order only two comparative solutions and determine the one that somehow is better than the other ( ).
Genetic algorithms ( ) population is a set of possible solutions to the given problem, each individual of this population with a similar structure to chromosomes. Figure 2 – General diagram of the life cycle of genetic algorithm (Rezende, 2005). The chance of survival of each individual is evaluated by a cost function; the function to be optimized, the result of this function is the fitness of each individual as the best result to the problem, working in a selection to reproduce. Finally, evolution is provided by the application of genetic operators such as selection, crossover and mutation ( ). The selection operators seek to determine the fitness of each individual, with the aim of obtaining the best solution to the problem; after that, individuals are crossed, i.e.
By joining portions of each of fit individuals, a new population of individuals is made and eventually some individuals suffer random changes mutation, according to a given probability of occurrence ( ). The model of particle swarm optimization is more recent, and differs from genetic algorithms due to the fact that each possible solution (particle) has a random speed, drifting through hyperspace, thus each particle of the swarm is evaluated by a fitness function, with the best particle solution being stored, called pbest, also stored the best overall solution, gbest ( ). These features enable the PSO convergence model to the optimal result in smaller computational times.
Thus, from the current position of the particle ( x i ) that corresponds to the current solution, its current speed ( v i ), its best past position ( pbest i ) and the best global position of all particles in the swarm ( gbest ), each particle is updated interactively ( ) in accordance with the previous attributes ( ). Figure 3 – Particle swarm optimization algorithm (Adapted Chen & Jiang, 2010). There are implications for the outcome of the models according to parameters and techniques of these operators in the case of GA function selection, ordering the fittest individuals, ensuring that the best alternatives found to the problem is always maintained, since the PSO function inertia, which keeps the solution in its original path, as well as the social and cognitive behavior, seeking forward towards the solution of best results already obtained, allowing its evolution and convergence in search of the optimal result. 3 Methodology The methodology of this work is focused on computational experiment of developing GA and PSO algorithms that are able to get the definition of the three parameters of a cash balance policy: the optimal level of cash ( Z ), the upper bound ( H ) and lower bound ( L ). Therefore, it is necessary to develop experiments in different scenarios for obtaining series of net cash flows to enable the validation of the developed models.
In the specific case of the problem addressed, the referenced benchmarks in, and highlight the cash balance as a random variable with normal distribution. For the experiment we used parameters of mean and standard deviation of the samples at three different levels (low, intermediate and high). The definition of the intervals follows the assumption that the two parameters that compose the normal distribution (mean and standard deviation) should vary in ranges, enabling an assessment of the sensitivity of the models to potential real effects in organizations, in order to compare them together. The definition of these parameters, shown in, was performed empirically by previous tests, since no information supporting its definition in the literature has been found. Random Number Generation Mean Standard Deviation Class 1 1,000 500 Class 2 1,000 5,000 Class 3 1,000 50,000 Class 4 20,000 500 Class 5 20,000 5,000 Class 6 20,000 50,000 Class 7 100,000 500 Class 8 100,000 5,000 Class 9 100,000 50,000 Thus, a total of 9 classes of problems, and for each class of problem 100 samples were randomly generated, called 'Problems' with 500 value points each (Table 2).
Subsequently, all the problems (900 samples for each of the 500 values) were tested for normal distribution using the Chi-Square Test ( X 2 ) and Kolmogorov-Smirnoff Test (KS), with a significance level of 95%, while those not complying with the precept of normality were replaced before the trial. The aim was to validate the algorithms according to flows with different means and variances, obtaining flows more or less risky of presenting negative values in net cash.
An optimization algorithm was applied initially using the Miller-Orr model by changing the lower bound of cash ( L ) in order to obtain the lowest cost. The variable L was defined empirically between $ 0.00 and $ 50,000.00. Considering the variation of L in $0.01, with two decimal, for a total of 5,000,000 possible values, we obtain the value of L that gives the lowest cost by the Miller-Orr model. So GA and PSO models have been applied to the problems, being programmed to minimize the cost of the cash based on the definition of the parameters Z, H and L simultaneously. The development of algorithms considers the following issues: - Initial cash balance: all series of cash balances left from a starting balance of $ 10,000.00, plus every time the value arising from the series of cash flows. The determination of a fixed initial balance does not affect the relevance of flows, it is set just after the first calculation of the cash flow; - The transfer cost ( F ) was set at $ 100.00 per transaction, be it investment (cash outflow for investment) when the balance reaches the upper bound, or disinvestment (output of investment to cash) when the balance reaches the minimum limit defined. The cost of transfer corresponds to the financial cost that the company incurs when making investment and divestment operations.
As the Miller-Orr model only deals with the transfer cost as being a fixed amount of currency, in this case $ 100, the other models follow the same pattern. However, in practice, it is common to the composition of the cost of transfer to be formed by a fixed amount and a percentage value on the transaction value of investment / disinvestment.
The $100 value was assigned empirically based on previous tests, similar to that used by Miller and Orr in their model; - The opportunity cost ( K ), given by the financial cost of obtaining cash when cash rupture occurs, having borrowed from the organization the obtained feature of 0.0261158% per day on this value, a rate which is equivalent to 10% per year. The opportunity cost is the interest rate that the organization would have to pay for borrowing money to make the necessary payments. 4 RESULTS The results obtained with the function of minimizing the total cost of ownership of cash, based on the lower bound ( L ) from the Miller-Orr model are presented in Optimal Algorithm.
The results using the GA and PSO algorithms, with the average values calculated over the 100 problems used in the experiments in each class problem, show the cost of cash, the iteration in which the lowest cost was obtained and the computational time per seconds by achievement. Thus, comparative mean results of each class of problem are presented in. Class of Problem ARD ARD ADR Best Solution Optimal Algorithm Miller-Orr GA Algorithm PSO Algorithm GA PSO 1 24.74% 5.54% 3.04% 42.00% 58.00% 2 17.09% 15.94% 0.00% 0.00% 100.00% 3 13.28% 4.68% 0.00% 0.00% 100.00% 4 26.47% 0.93% 0.38% 43.00% 57.00% 5 32.68% 0.99% 0.24% 31.00% 69.00% 6 26.15% 3.73% 0.00% 0.00% 100.00% 7 21.37% 0.16% 0.22% 55.00% 45.00% 8 25.11% 0.20% 0.19% 54.00% 46.00% 9 40.09% 0.66% 0.09% 25.00% 75.00% General 25.22% 3.65% 0.46% 27.78% 72.22% In it can be seen that the PSO algorithm has the lowest average mean deviation overall, losing only in Class 7. Furthermore, the PSO algorithm gets the best solution in 72.22% of the time, and in classes 2, 3 and 6 it had the best result problems in 100% of the time compared with the algorithm GA.
Later we used the t Test for two samples assuming equal variances in order to verify that the cash costs obtained by the algorithms are significantly different at 5% level, indicating that the costs obtained with GA and PSO algorithms have the same characteristics distribution over 99% ( ). T-Test: two sample assuming equal variances GA PSO Mean 18,582.27 23,060.51 Variance 86,859,400.32 151,313,595.00 Observations 900 900 Stat t -8.705272018 P(T.
5 CONCLUSION The genetic algorithms and particle swarm optimization have been proven to be useful tools in the application this kind of optimization problem. When assisting in the definition of parameters for managing, cash balance can find with higher impartiality the optimal values for the cash management.
The analysis shows that the PSO algorithm gets lower costs with higher efficiency (ARD) and efficacy (greater number of hits), but not significantly different from each other. Regarding the computational time, the algorithm GA showed an average time of 2.93 seconds per problem, while the PSO algorithm had an average time of 23.47 seconds. Considering that each company would be a problem, although the computational time average PSO algorithm is much higher, a difference of 20 seconds to get the firm's cash balance policy would not be something problematic. In practice, the two kinds of algorithms are presented as a practical solution to define a policy for the management of the cash balance, obtaining significant gains in relation to cost and time obtained by the optimized Miller-Orr model.
However, given the experimental results, the PSO algorithm has higher convergence in the pursuit of lower cost, within the criteria established. This study focuses on the comparison between the Miller and Orr model and computational algorithms GA and PSO developed with the aim of setting management policy in cash, with the variables for the ideal cash (Z), upper bound (H) and lower bound (L), but the models GA and PSO can be applied for the definition of all more complex cash policies, without the limitations of the Miller-Orr model, as. Consider only a fixed cost in monetary cost transfer ( F ), when in practice these costs usually have a fixed component and a variable component as a percentage of the operation amount;. Consider the same transfer cost ( F ) in investment operations and rescue, since in practice there are different costs;.
The incidence of opportunity cost ( K ) when cash resources are left without considering obtaining profitability with the use of financial resources, which would reduce the cost of cash maintenance. So, the results point to a promising area, but further studies and experiments are needed, since the results could not be compared with other newer models, like the ones y, and e, because these models have shown reductions in limitations in the Miller-Orr Model. Nevertheless, with these diversifications, it would not be possible to apply a control algorithm as we did in this study, since computation time of the definition of three parameters simultaneously would be prohibitive, hence the great relevance of this study; we present results which demonstrate that GA and PSO algorithms can be used in more sophisticated models to the problem of cash management, signs of obtaining practical solutions acceptable. Therefore, this study presents its contribution to the validation of GA and PSO algorithms, especially with the PSO model as reliable, quick and malleable in the development of algorithms that enable the reduction of limitations, enabling the development of policies for cash management closer to reality, which are applicable for the financial management of organizations.