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Papers by Tolulope Latunde

Research paper thumbnail of Optimal Value and Post Optimal Solution in a Transportation Problem

Research paper thumbnail of Uncertain Controllability and Observability of an Optimal Control Model

The interest of this paper is to examine the controllability and observability of a control syste... more The interest of this paper is to examine the controllability and observability of a control system in the configuration state-space of an uncertain optimal control system. The control system is designed based on the realization of capital asset values where a special case of asset management is modelled and optimized. Thus some necessary and sufficient conditions of the controllability and observability of the deterministic systems and the corresponding uncertain systems for the case of the uncertain optimal control system with application in capital asset management are considered.

Research paper thumbnail of Sensitivity of Parameters in the Approach of Linear Programming to a Transportation Problem

Journal of the Nigerian Society of Physical Sciences

Linear programming has served as a great tool in dealing with transportation problems to make a p... more Linear programming has served as a great tool in dealing with transportation problems to make a positive difference in economic and social activity. In this work, data of the National Union Of Road Transport Workers (NURTW) is analysed to minimizing the cost of maintenance and repair of buses taking the route from Sango park to different routes. Data collected from the park are represented using tables and solved using the Maple computer software application. The transportation problem is solved such that the transportation cost is minimized which leads to the profit being maximized. This is achieved by estimating the values of some identified parameters in the problem. This work will be beneficial to every other motor parks controllers to decide on some decision making that may bring to the union profit. This work will help the NURTW in Sango to spend less on the vehicles and save more as income.

Research paper thumbnail of On the Stochastic Optimal Control Model of the Investments of Defined Contribution (DC) Pension Funds

Journal of Applied Sciences and Environmental Management

One of the major problems faced in the management of pension funds and plan is how to allocate an... more One of the major problems faced in the management of pension funds and plan is how to allocate and control the future flow of contribution likewise the proportion of portfolio value and investments in risky assets. In this work, optimal investment for a stochastic model of a Defined contribution (DC) is investigated such that the model design is analysed yielding an optimized expected utility of the members’ terminal wealth. An optimized solution is derived using the Hamilton Jacobi equation in solving the problem of investment strategy formulated by Constant absolute risk aversion (CARA). However, to consider the changes that occur in the dimension of optimal solutions in optimization problems, mostly, the optimal behaviour of parameters, the sensitivity analysis is considered. Thus, the analysis of the model is carried out herein by utilising the approach of the sensitivity analysis of parameters. This is carried out by using Maple software and varying the values of some model par...

Research paper thumbnail of Control Policy and Sustainability for Decision-Making in Asset Management

ATBU Journal of Science, Technology and Education, 2020

The essential factor determining decision-making in private investors and public corporations is ... more The essential factor determining decision-making in private investors and public corporations is controlled asset management. In a developed asset allocation and in a time of debt crisis, an important issue on which investors base their decisions is when and how to more or fewer investments such that expected net values of assets are maximized with minimal risks for sustainability in the management of capital assets. The acknowledgement of this enables investors to make rational decisions. The aim of this paper is to provide control policy to help investors make necessary decisions for sustainability in asset management. This is done by applying an optimal control model to a real-life problem asset-liability, thus derive the control policy .

Research paper thumbnail of Sensitivity of Parameters in the Approach of Linear Programming to a Transportation Problem

Linear programming has served as a great tool in dealing with transportation problems to make a p... more Linear programming has served as a great tool in dealing with transportation problems to make a positive difference in economic and social activity. In this work, data of the National Union Of Road Transport Workers (NURTW) is analysed to minimizing the cost of maintenance and repair of buses taking the route from Sango park to different routes. Data collected from the park are represented using tables and solved using the Maple computer software application. The transportation problem is solved such that the transportation cost is minimized which leads to the pro t being maximized. This is achieved by estimating the values of some identifi ed parameters in the problem. This work will be benefi cial to every other motor parks controllers to decide on some decision making that may bring to the union profi t. This work will help theNURTW in Sango to spend less on the vehicles and save more as income.

Research paper thumbnail of Impacts of Simulation-Games on Teaching and Learning Mathematics

This study sought to determine the impact of games and simulation environment on students’ achiev... more This study sought to determine the impact of games and simulation environment on students’ achievement in attitudes to mathematics in secondary school. A total of ten thousand five hundred and thirty five (10535) students in all the twenty one (21) senior secondary schools in Ilorin-south Local Government Area of Kwara State, Nigeria constituted the population of the study. All senior secondary school students two (SS II) in six (6) randomly selected schools totaled one hundred and eighty (180) in Ilorin-south Local Government Area of Kwara State were used as the sample of the study. The finding reveals that students’ poor academic achievement in mathematics is partly due to the method of teaching used. Also, the findings revealed that, the use of games and simulation environment led to improve achievement and positive attitude towards mathematics. The study concluded that teachers’ use of stimulating teaching methods would go a long way in sustaining and motivating students’ inter...

Research paper thumbnail of Analysis of a Stochastic Optimal Control for Pension Funds and Application to Investments in Lower Middle-Income Countries

Journal of the Nigerian Society of Physical Sciences

One of the major problems faced in the management of pension funds and plan is how to allocate an... more One of the major problems faced in the management of pension funds and plan is how to allocate and control the future flow of contribution likewise the proportion of portfolio value and investments in risky assets. This work considers the management of a pension plan by means of a stochastic dynamic programming model based on Merton's model. The model is analyzed such that the conditions of optimal contribution and investment in risky assets are determined and sensitized. The case study of Nigeria, Ghana, Kenya is considered for various periods in the model simulation. Thus, the volatility condition obtained is used to estimate the efficiency of some important parameters of the model.

Research paper thumbnail of A Step-Length Formula for Conjugate Gradient Methods

MALAYSIAN JOURNAL OF COMPUTING

A new step-length formula is proposed for the conjugate gradient methods. The unified formula for... more A new step-length formula is proposed for the conjugate gradient methods. The unified formula for obtaining step-length does not involve any matrix operation. Numerical results obtained are graphically illustrated using performance profiling software. This showed that the new formula performs efficiently in terms of computational efforts and execution time compared with some existing formulae for obtaining the step-length without line search procedures.

Research paper thumbnail of Optimal Feasible Solutions to a Road Freight Transportation Problem

MALAYSIAN JOURNAL OF COMPUTING

For twenty decades, there is a visible ever forward advancement in the technology of mobility, ve... more For twenty decades, there is a visible ever forward advancement in the technology of mobility, vehicles and transportation system in general. However, there is no "cure-all" remedy ideal enough to solve all life problems but mathematics has proven that if the problem can be determined, it is most likely solvable. New methods and applications will keep coming to making sure that life problems will be solved faster and easier. This study is to adopt a mathematical transportation problem in the Coca-Cola company aiming to help the logistics department manager of the Asejire and Ikeja plant to decide on how to distribute demand by the customers and at the same time, minimize the cost of transportation. Here, different algorithms are used and compared to generate an optimal solution, namely; North West Corner Method (NWC), Least Cost Method (LCM) and Vogel’s Approximation Method (VAM). The transportation model type in this work is the Linear Programming as the problems are repr...

Research paper thumbnail of Sensitivity Analysis of Road Freight Transportation of a Mega Non-Alcoholic Beverage Industry

Journal of Applied Sciences and Environmental Management

Re-optimization can be very costly for gathering and obtaining more data for a particular problem... more Re-optimization can be very costly for gathering and obtaining more data for a particular problem, to curb this very expensive investment. Sensitivity analysis has been used in this work to determine the behaviour of input parameters of the formulated problem. The main goal of the study is to respectively provide, derive, observe, compare and discuss the sensitivity analysis of data that has been optimized using different methods of the optimal solution. The best method, saving the highest percentage of transportation cost, for the formulated problem is determined to be the North-West Corner method. This was carried out by arbitrarily assigning values to the available warehouses to determine the best possible demand and supply cases rather than the initial cases. Thus, more cases are advised to be supplied to FID from the Asejire plant for the optimum reduced value of transportation cost. Keywords: Sensitivity, Parameters, Transportation Problem.

Research paper thumbnail of Modelling and Forecasting Climate Time Series with State-Space Model

Journal of the Nigerian Society of Physical Sciences

This study modelled and estimated climatic data using the state-space model. The study was specif... more This study modelled and estimated climatic data using the state-space model. The study was specifically to identify the pattern of the trend movement i.e., increase or decrease in the occurrence of the climatic change; to use of Univariate Kalman Filter for the computation of the likelihood function for climatic projections; to modelling the climatic dataset using the state-space model and to assess the forecasting power of the state-space models. The data used for the work includes temperature and rainfall for periods January 1991 to December 2017. The data are tested for normality. Shapiro-Wilk, Anderson-Darling and Kolmogorov-Smirnov test of normality for the climatic data all showed that the variables are not normally distributed. The work spans the use of breaking trend regression model to fit climatic data to estimate the slopes which show much increase in climatic data has been recorded from the initial time data collection until the present. Investigations and diagnostic are...

Research paper thumbnail of Parameter Estimation and Sensitivity Analysis of an Optimal Control Model for Capital Asset Management

Advances in Fuzzy Systems

Optimal control is a very significant field of modern control theory which has been applied in ma... more Optimal control is a very significant field of modern control theory which has been applied in many areas like medicine, science, and finance. This work is based on realization of asset values as a benefit of asset management where a capital asset management problem is modelled and expressed mathematically from the perspective of an investor whose income is generated by return and capital gains on investments with price and return on assets assumed to satisfy uncertainty process. This results in an optimal control model based on uncertainty theory which relates two or more parameters that measures the condition or state of individual’s investments. These parameters enable us to know the condition of risk involved in asset management and how to maintain and manage the assets in order to maximize expected present value of the utility of asset and minimize the risk involved to aid capital investment decision-making. Parameter sensitivity analysis is an approach given to a model so as t...

Research paper thumbnail of Analysis of capital asset pricing model on Deutsche bank energy commodity

Research paper thumbnail of Mathematical Analysis of the Implication of the Proposed Rise in the Retirement Age on the Unemployment Situation in Nigeria

ATHENS JOURNAL OF SCIENCES

The objectives of this study were the physical and chemical characterization of Portuguese indust... more The objectives of this study were the physical and chemical characterization of Portuguese industrial hemp and the assessment of its suitability to produce kraft pulp. A comparison was established with a reference eucalyptus pulp, obtained by the same chemical process. Handmade paper sheets were prepared in the laboratory using hemp pulp, eucalyptus pulp and a blend of both fibres in order to compare final paper properties. The unbleached pulp was produced by batch kraft cooking (NaOH + Na 2 S) and the evaluation of pulp bleachability was carried out under a D 0 E 0 D 1 E 1 D 2 sequence. The physical properties of laboratory papers prepared with different compositions (100% hemp, 100% eucalyptus, hemp/eucalyptus 50:50) were assessed according to International Standards. Hemp fibres present two fractions, bast and core (33% and 67% of the total stem mass, respectively) with distinct biometric characteristics and cell composition. The hemp plant allowed cooking yield overlapping the wood reference, with lesser uncooked fractions. The pulp exhibited a good bleachability, even better than the reference. Hemp plant allowed a pulp with a higher gain of brightness and lower loss of intrinsic viscosity than eucalyptus. Hemp pulp also showed a better beatability, superiority in tearing resistance and a lower air permeability. The paper sheets obtained with the hemp/ eucalyptus mixture showed interesting properties, which predicts a suitable combination of these two raw materials for papermaking.

Research paper thumbnail of Multifactor modelling in asset management

International Journal of Mathematics in Operational Research

Research paper thumbnail of Parameter estimation and sensitivity analysis of a nonlinearly elastic static lung model

Optimal control is a very significant field of modern control theory which has been applied in ma... more Optimal control is a very significant field of modern control theory which has been applied in many areas like medicine, science, and finance. This work is based on realization of asset values as a benefit of asset management where a capital asset management problem is modelled and expressed mathematically from the perspective of an investor whose income is generated by return and capital gains on investments with price and return on assets assumed to satisfy uncertainty process. This results in an optimal control model based on uncertainty theory which relates two or more parameters that measures the condition or state of individual's investments. These parameters enable us to know the condition of risk involved in asset management and how to maintain and manage the assets in order to maximize expected present value of the utility of asset and minimize the risk involved to aid capital investment decision-making. Parameter sensitivity analysis is an approach given to a model so as to define significance of the factors related to the model where the whole parameter space is fully described. However, the model is applied to a real-life problem of capital asset management to deal with debt crisis of a nation's economy and the sensitivity analysis to determine the effects of the input factors on the model is investigated such that relative significance and sensitivity of each parameter on the model results are presented using parameter estimations. Finally the optimal control decision policy is obtained and discussed.

Research paper thumbnail of Optimal Value and Post Optimal Solution in a Transportation Problem

Research paper thumbnail of Uncertain Controllability and Observability of an Optimal Control Model

The interest of this paper is to examine the controllability and observability of a control syste... more The interest of this paper is to examine the controllability and observability of a control system in the configuration state-space of an uncertain optimal control system. The control system is designed based on the realization of capital asset values where a special case of asset management is modelled and optimized. Thus some necessary and sufficient conditions of the controllability and observability of the deterministic systems and the corresponding uncertain systems for the case of the uncertain optimal control system with application in capital asset management are considered.

Research paper thumbnail of Sensitivity of Parameters in the Approach of Linear Programming to a Transportation Problem

Journal of the Nigerian Society of Physical Sciences

Linear programming has served as a great tool in dealing with transportation problems to make a p... more Linear programming has served as a great tool in dealing with transportation problems to make a positive difference in economic and social activity. In this work, data of the National Union Of Road Transport Workers (NURTW) is analysed to minimizing the cost of maintenance and repair of buses taking the route from Sango park to different routes. Data collected from the park are represented using tables and solved using the Maple computer software application. The transportation problem is solved such that the transportation cost is minimized which leads to the profit being maximized. This is achieved by estimating the values of some identified parameters in the problem. This work will be beneficial to every other motor parks controllers to decide on some decision making that may bring to the union profit. This work will help the NURTW in Sango to spend less on the vehicles and save more as income.

Research paper thumbnail of On the Stochastic Optimal Control Model of the Investments of Defined Contribution (DC) Pension Funds

Journal of Applied Sciences and Environmental Management

One of the major problems faced in the management of pension funds and plan is how to allocate an... more One of the major problems faced in the management of pension funds and plan is how to allocate and control the future flow of contribution likewise the proportion of portfolio value and investments in risky assets. In this work, optimal investment for a stochastic model of a Defined contribution (DC) is investigated such that the model design is analysed yielding an optimized expected utility of the members’ terminal wealth. An optimized solution is derived using the Hamilton Jacobi equation in solving the problem of investment strategy formulated by Constant absolute risk aversion (CARA). However, to consider the changes that occur in the dimension of optimal solutions in optimization problems, mostly, the optimal behaviour of parameters, the sensitivity analysis is considered. Thus, the analysis of the model is carried out herein by utilising the approach of the sensitivity analysis of parameters. This is carried out by using Maple software and varying the values of some model par...

Research paper thumbnail of Control Policy and Sustainability for Decision-Making in Asset Management

ATBU Journal of Science, Technology and Education, 2020

The essential factor determining decision-making in private investors and public corporations is ... more The essential factor determining decision-making in private investors and public corporations is controlled asset management. In a developed asset allocation and in a time of debt crisis, an important issue on which investors base their decisions is when and how to more or fewer investments such that expected net values of assets are maximized with minimal risks for sustainability in the management of capital assets. The acknowledgement of this enables investors to make rational decisions. The aim of this paper is to provide control policy to help investors make necessary decisions for sustainability in asset management. This is done by applying an optimal control model to a real-life problem asset-liability, thus derive the control policy .

Research paper thumbnail of Sensitivity of Parameters in the Approach of Linear Programming to a Transportation Problem

Linear programming has served as a great tool in dealing with transportation problems to make a p... more Linear programming has served as a great tool in dealing with transportation problems to make a positive difference in economic and social activity. In this work, data of the National Union Of Road Transport Workers (NURTW) is analysed to minimizing the cost of maintenance and repair of buses taking the route from Sango park to different routes. Data collected from the park are represented using tables and solved using the Maple computer software application. The transportation problem is solved such that the transportation cost is minimized which leads to the pro t being maximized. This is achieved by estimating the values of some identifi ed parameters in the problem. This work will be benefi cial to every other motor parks controllers to decide on some decision making that may bring to the union profi t. This work will help theNURTW in Sango to spend less on the vehicles and save more as income.

Research paper thumbnail of Impacts of Simulation-Games on Teaching and Learning Mathematics

This study sought to determine the impact of games and simulation environment on students’ achiev... more This study sought to determine the impact of games and simulation environment on students’ achievement in attitudes to mathematics in secondary school. A total of ten thousand five hundred and thirty five (10535) students in all the twenty one (21) senior secondary schools in Ilorin-south Local Government Area of Kwara State, Nigeria constituted the population of the study. All senior secondary school students two (SS II) in six (6) randomly selected schools totaled one hundred and eighty (180) in Ilorin-south Local Government Area of Kwara State were used as the sample of the study. The finding reveals that students’ poor academic achievement in mathematics is partly due to the method of teaching used. Also, the findings revealed that, the use of games and simulation environment led to improve achievement and positive attitude towards mathematics. The study concluded that teachers’ use of stimulating teaching methods would go a long way in sustaining and motivating students’ inter...

Research paper thumbnail of Analysis of a Stochastic Optimal Control for Pension Funds and Application to Investments in Lower Middle-Income Countries

Journal of the Nigerian Society of Physical Sciences

One of the major problems faced in the management of pension funds and plan is how to allocate an... more One of the major problems faced in the management of pension funds and plan is how to allocate and control the future flow of contribution likewise the proportion of portfolio value and investments in risky assets. This work considers the management of a pension plan by means of a stochastic dynamic programming model based on Merton's model. The model is analyzed such that the conditions of optimal contribution and investment in risky assets are determined and sensitized. The case study of Nigeria, Ghana, Kenya is considered for various periods in the model simulation. Thus, the volatility condition obtained is used to estimate the efficiency of some important parameters of the model.

Research paper thumbnail of A Step-Length Formula for Conjugate Gradient Methods

MALAYSIAN JOURNAL OF COMPUTING

A new step-length formula is proposed for the conjugate gradient methods. The unified formula for... more A new step-length formula is proposed for the conjugate gradient methods. The unified formula for obtaining step-length does not involve any matrix operation. Numerical results obtained are graphically illustrated using performance profiling software. This showed that the new formula performs efficiently in terms of computational efforts and execution time compared with some existing formulae for obtaining the step-length without line search procedures.

Research paper thumbnail of Optimal Feasible Solutions to a Road Freight Transportation Problem

MALAYSIAN JOURNAL OF COMPUTING

For twenty decades, there is a visible ever forward advancement in the technology of mobility, ve... more For twenty decades, there is a visible ever forward advancement in the technology of mobility, vehicles and transportation system in general. However, there is no "cure-all" remedy ideal enough to solve all life problems but mathematics has proven that if the problem can be determined, it is most likely solvable. New methods and applications will keep coming to making sure that life problems will be solved faster and easier. This study is to adopt a mathematical transportation problem in the Coca-Cola company aiming to help the logistics department manager of the Asejire and Ikeja plant to decide on how to distribute demand by the customers and at the same time, minimize the cost of transportation. Here, different algorithms are used and compared to generate an optimal solution, namely; North West Corner Method (NWC), Least Cost Method (LCM) and Vogel’s Approximation Method (VAM). The transportation model type in this work is the Linear Programming as the problems are repr...

Research paper thumbnail of Sensitivity Analysis of Road Freight Transportation of a Mega Non-Alcoholic Beverage Industry

Journal of Applied Sciences and Environmental Management

Re-optimization can be very costly for gathering and obtaining more data for a particular problem... more Re-optimization can be very costly for gathering and obtaining more data for a particular problem, to curb this very expensive investment. Sensitivity analysis has been used in this work to determine the behaviour of input parameters of the formulated problem. The main goal of the study is to respectively provide, derive, observe, compare and discuss the sensitivity analysis of data that has been optimized using different methods of the optimal solution. The best method, saving the highest percentage of transportation cost, for the formulated problem is determined to be the North-West Corner method. This was carried out by arbitrarily assigning values to the available warehouses to determine the best possible demand and supply cases rather than the initial cases. Thus, more cases are advised to be supplied to FID from the Asejire plant for the optimum reduced value of transportation cost. Keywords: Sensitivity, Parameters, Transportation Problem.

Research paper thumbnail of Modelling and Forecasting Climate Time Series with State-Space Model

Journal of the Nigerian Society of Physical Sciences

This study modelled and estimated climatic data using the state-space model. The study was specif... more This study modelled and estimated climatic data using the state-space model. The study was specifically to identify the pattern of the trend movement i.e., increase or decrease in the occurrence of the climatic change; to use of Univariate Kalman Filter for the computation of the likelihood function for climatic projections; to modelling the climatic dataset using the state-space model and to assess the forecasting power of the state-space models. The data used for the work includes temperature and rainfall for periods January 1991 to December 2017. The data are tested for normality. Shapiro-Wilk, Anderson-Darling and Kolmogorov-Smirnov test of normality for the climatic data all showed that the variables are not normally distributed. The work spans the use of breaking trend regression model to fit climatic data to estimate the slopes which show much increase in climatic data has been recorded from the initial time data collection until the present. Investigations and diagnostic are...

Research paper thumbnail of Parameter Estimation and Sensitivity Analysis of an Optimal Control Model for Capital Asset Management

Advances in Fuzzy Systems

Optimal control is a very significant field of modern control theory which has been applied in ma... more Optimal control is a very significant field of modern control theory which has been applied in many areas like medicine, science, and finance. This work is based on realization of asset values as a benefit of asset management where a capital asset management problem is modelled and expressed mathematically from the perspective of an investor whose income is generated by return and capital gains on investments with price and return on assets assumed to satisfy uncertainty process. This results in an optimal control model based on uncertainty theory which relates two or more parameters that measures the condition or state of individual’s investments. These parameters enable us to know the condition of risk involved in asset management and how to maintain and manage the assets in order to maximize expected present value of the utility of asset and minimize the risk involved to aid capital investment decision-making. Parameter sensitivity analysis is an approach given to a model so as t...

Research paper thumbnail of Analysis of capital asset pricing model on Deutsche bank energy commodity

Research paper thumbnail of Mathematical Analysis of the Implication of the Proposed Rise in the Retirement Age on the Unemployment Situation in Nigeria

ATHENS JOURNAL OF SCIENCES

The objectives of this study were the physical and chemical characterization of Portuguese indust... more The objectives of this study were the physical and chemical characterization of Portuguese industrial hemp and the assessment of its suitability to produce kraft pulp. A comparison was established with a reference eucalyptus pulp, obtained by the same chemical process. Handmade paper sheets were prepared in the laboratory using hemp pulp, eucalyptus pulp and a blend of both fibres in order to compare final paper properties. The unbleached pulp was produced by batch kraft cooking (NaOH + Na 2 S) and the evaluation of pulp bleachability was carried out under a D 0 E 0 D 1 E 1 D 2 sequence. The physical properties of laboratory papers prepared with different compositions (100% hemp, 100% eucalyptus, hemp/eucalyptus 50:50) were assessed according to International Standards. Hemp fibres present two fractions, bast and core (33% and 67% of the total stem mass, respectively) with distinct biometric characteristics and cell composition. The hemp plant allowed cooking yield overlapping the wood reference, with lesser uncooked fractions. The pulp exhibited a good bleachability, even better than the reference. Hemp plant allowed a pulp with a higher gain of brightness and lower loss of intrinsic viscosity than eucalyptus. Hemp pulp also showed a better beatability, superiority in tearing resistance and a lower air permeability. The paper sheets obtained with the hemp/ eucalyptus mixture showed interesting properties, which predicts a suitable combination of these two raw materials for papermaking.

Research paper thumbnail of Multifactor modelling in asset management

International Journal of Mathematics in Operational Research

Research paper thumbnail of Parameter estimation and sensitivity analysis of a nonlinearly elastic static lung model

Optimal control is a very significant field of modern control theory which has been applied in ma... more Optimal control is a very significant field of modern control theory which has been applied in many areas like medicine, science, and finance. This work is based on realization of asset values as a benefit of asset management where a capital asset management problem is modelled and expressed mathematically from the perspective of an investor whose income is generated by return and capital gains on investments with price and return on assets assumed to satisfy uncertainty process. This results in an optimal control model based on uncertainty theory which relates two or more parameters that measures the condition or state of individual's investments. These parameters enable us to know the condition of risk involved in asset management and how to maintain and manage the assets in order to maximize expected present value of the utility of asset and minimize the risk involved to aid capital investment decision-making. Parameter sensitivity analysis is an approach given to a model so as to define significance of the factors related to the model where the whole parameter space is fully described. However, the model is applied to a real-life problem of capital asset management to deal with debt crisis of a nation's economy and the sensitivity analysis to determine the effects of the input factors on the model is investigated such that relative significance and sensitivity of each parameter on the model results are presented using parameter estimations. Finally the optimal control decision policy is obtained and discussed.