An optimal resource allocation for a financial institution and oil company in Ghana using dynamic programming

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A study was carried out to determine an Optimal Resource Allocation for: i. a financial institution ii. An oil company and iii. A joint operations set-up for the financial institution and the oil company in order to establish an overall optimal resource allocation policy for the financial institution and the oil company. In line with these objectives, investment data were collected from a financial institution labelled company A and an oil company labelled company B, both based in Accra. [Names withheld as this was the condition under which the data were provided]. Thus, these data were utilised to set-up and solve the Resource Allocation problem for each of the companies using Backward Recursion method of Dynamic Programming.. Next, a simulation of a joint investment venture for the two companies was carried out by setting up a hypothetical company C, owning all the resources and investment programmes for the two companies. The Resource Allocation of this hypothetical company was also solved, using the above-mentioned method. The following observations were made: i) The Dynamic Programming Approach provided better solution to the Resource Allocation Problem of each of the companies under consideration. ii) The sum of the individual annual mean optimal returns of the two companies viz A and B was greater than that of company C, the joint operations set-up. iii The existence of a high variability in the investment rates among the investment programmes under consideration gave an indication that the pattern of the resource allocation tends to be skewed towards the investment programme with the highest investment rate of return (i.e. gradient factor) whilst where there is low or no variability in the investment rate of returns, the pattern tends to be clustered around the mean value of the investment rate of return and iv) The higher the value of the units of the resource available for allocation, the more accurate the optimal return value obtained. In line with the observations made, it was recommended that i) it is also not advisable for the two companies A and B to operate as joint entity since the sum of the individual annual mean optimal returns of the two companies viz A and B was greater than that of company C, the joint operations set-up. and ii) the companies A and B should allocate their respective resources at any given time according to the allocations given by the solutions to their main problems using Dynamic Programming or for that matter any suitable mathematical programming method.
A thesis submitted to the Board of Postgraduate Studies, Kwame Nkrumah University of Science and Technology, Kumasi, in partial fulfilment of the requirement for the award of the Degree of Master of Science in Mathematics, 1998