ABSTRACT:The use of Mathematical models for manpower planning has increased in recent times for better manpower planning quantitatively. In respect of organizational management, numerous previous studies have applied Markov chain models in describing title or level promotions, demotions, recruitments, withdrawals, or changes of different career development paths to confirm the actual manpower needs of an organization or predict the future manpower needs. The movements of staff called transitions are usually the consequences of promotions, transfer between segments or wastage and recruitment into the system. The objective of the study is to determine the proportions of staff recruited, promoted and withdrawn from the various grades and to forecast the academic staff structure of the university in the next five years. In this paper, we studied the academic staff structure of university of Uyo, Nigeria using Markov chain models. The results showed that there is a steady increase in the number of Graduate Assistants, Senior Lecturer and Associate professors, while, there is a steady decrease in the number of Assistant Lecturer, Lecturer II, Lecturer I, and Professor in the next five years. The model so developed can only be applied when there is no control on recruitment but the research can be extended to include control on recruitment. The model can also be applied in school enrollment projection. ©JASEM https://dx.doi.org/10.4314/jasem.v21i3.17

In this paper, analysis of single queue, multi-server with limited system capacity under first come first served discipline was carried out using iterative method. The arrivals of customers and service times of customers are assumed poisson and exponential distributions respectively. This queuing model is an extension of single queue, single server with limited system capacity. Performance measures of the model, such as the expected number of customers in the queue and in the system, the expected waiting times of customers in the queue and in the system respectively were derived. The performance measures so derived were compared with that of single queue, single server with limited capacity {M/M/1:(N/FCFS)} model. The numerical illustration indicates that single queue, multi-server with limited capacity {M/M/c:(N/FCFS)} model is more effective and efficient in handling congestions.

Markov decision processes have been applied in solving a wide range of optimization problems over the years. This study provides a review of Markov decision processes and investigates its suitability for solutions to portfolio allocation problems under vendor managed inventory in an uncertain market environment. The problem was formulated in the frame work of Markov decision process and a value iteration algorithm was implemented to obtain the expected reward and the optimal policy that maps an action to a given state. Two challenges were examined -the uncertainty about the value of the item which follows a stochastic model and the small state/action spaces that can be solved via value iteration. It was observed that the optimal policy is expected to always short the stock when in state 0 because of its large return. However, while the return is not as large as in state 0, the probability of staying in state 2 is high enough that the vendor should long the stock because he expects high reward for several periods. We also obtained the expected reward for each state every ten iterations using a discount factor of 95 . 0 = λ . In spite of the small state/action spaces, the vendor is able to optimize its reward by the use of Markov decision process. ©JASEM http://dx.doi.org/10.4314/jasem.v20i4.29