Article History KeywordsAdomian polynomials Adomian decomposition method Lane-Emden.In this paper, we generate the Adomian polynomial for major nonlinear terms which are mostly common in differential equations. And we applied it to Lane-Emden type of equations whose nonlinear terms are exponential functions. The result we obtained by modified Adomian decomposition method (ADM) gave a series solution which is the same as the Taylors series of the exact solution.Contribution/ Originality: This study contributes in the existing literature on the use of Adomian decomposition method. It explicitly provide the Adomian polynomials of frequently occurring nonlinear terms in a linear functional. And, for the first time, applied to obtain an exact solution to the Lane-Emden type of equation.

Background: At the heart in the development of any organization or nation is human resource. Over the years the world over, a sharp increase in too many numbers of qualified persons is being experienced yearly. This has impacted on recruitment and promotion costs to increase immensely, thereby affecting negatively manpower system costs. Dynamic Programming (DP) approach to optimal manpower recruitment and promotion policies for the two grade system has been proposed. Methods: Considering the fact that contemporary manpower systems are not limited to just two grades -a kind of "switch-approach" to manpower systems, we first establish the link between a manpower planning problem and a dynamic decision-making process. This linkage resulted to a multistage real-life decision-making problem whose solution demands that decisions be made sequentially at different levels and at different points in time and space. Dynamic Programming is a mathematical technique well appropriate for the optimization of multistage decision problems. This allows us to give a generalization to manpower systems by modifying the model to finite grades which came out to be more robust and actionable, a constrained deterministic Dynamic Programming (CDDP) found to function computationally as the very well-known Wagner-Whitin Model in inventory/production management. Five cost variables associated with manpower planning were identified and used as inputs to the modified deterministic DP model. Results/Relevance: The data shows yearly recruitments and promotions totaling 507 and 266 staff respectively for a ten-period (year) planning horizon. Total manpower system cost (in ooo's of Nigerian Naira) occasioned by yearly recruitments and promotions exercises for the period is 11334 (7092 for recruiting, 4100 for promoting, and 142 for overstaffing). Our DP model minimizes the manpower system cost to 9462 making a significant reduction of 1872. The optimal policy for the planning period calls for recruiting and promoting respectively 79 and 41 in period 1 only, 86 and 24 in period 2 for periods 2 and 3, 86 and 46 in period 4 for periods 4 and 5, 89 and 29 in period 6 only, 85 and 70 in period 7 for periods 7 and 8, and 82 and 56 in period 9 for periods 9 and 10. The study will contribute to the growing literature on applications of OR models to problems in manpower planning. The model outcomes would provide the basis for evaluating decision policies aimed at conducting recruitment promptly and to eliminate over-stagnated promotions. Conclusion/Further research:We formulate decisions making in a finitely-graded manpower system as a multistage decision-making optimization problem which are best handled by dynamic programming. Five cost variables associated with manpower planning were identified and used as inputs to the modified deterministic DP model. Our model is resolute for minimizing manpower system costs occasioned by recruitments and promotions exercises in a wide range of multi-graded manpower systems instead of just two grades. The study's limit...