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.

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 represented in tables and results are compared with the result obtained on Maple 18 software. The study shows various ways in which the initial basic feasible solutions to the problem can be obtained where the best method that saves the highest percentage of transportation cost with for this problem is the NWC. The NWC produces the optimal transportation cost which is 517,040 units.

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 parameters such that the behaviour of each parameter relating to the pension funds invested in the risky assets is determined. The results are presented graphically and using tables thus discussed such that pension investors and stakeholders are advised. Keywords: Stochastic; DC Pension funds; Sensitivity analysis; Hamilton-Jacobi-Bellman equation; Optimal investment

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.