An analysis of an optimal promotion policy for a manpower system using a queuing approach

Management Dynamics, 2006 by Yadavalli, V S S, Setlhare, K, Mishra, S S, Rajalakshmi, R

ABSTRACT

This study introduces a queuing approach to determine the optimal promotion policy and total optimal cost of promotion in a manpower planning system. In particular, the model attempts to estimate the optimal cost of promotion where the organisation incurs the cost of keeping an employee waiting until a vacancy opens up. The variation effect of various parameters on the total optimal cost of the system of promotion is also assessed by making use of a numerical demonstration of the model.

INTRODUCTION

In today's competitive world, which is characterised by, amongst others, the existence of a large number of qualified persons, manpower planning draws the serious attention of researchers engaged in this field, since each organisation requires employees with specialised skills in various fields to accomplish its business objectives, both now and in the future. Through manpower planning, the management of any organisation can not only optimise the expertise and skills of its human resources, but can also decide on the optimal number and correct type of employees available at the right place at the right time.

Formulating manpower-planning policies is one of the most critical and difficult challenges faced by an organisation. In particular, after recruitment, formulating promotion policies from one grade to another becomes more difficult as the organisation requires more expertise, since it is linked to the productivity enhancement of the organisation.

Various models applicable to manpower planning have been developed and studied in the past by a variety of researchers such as Marshall and Olkin (1967), Smith (1970), Bartholomew (1971), and Forbes (1971). Special features associated with the methods and models relevant to manpower systems have arisen in various fields.

Considering recruitment and promotion as some of the main activities of the organisation, Vajda (1975) discussed the mathematical aspect of manpower planning. The concepts of linear programming were used to develop a graded population structure where both the recruitment rates and transfer rates between the various grades are controlled by management. Davies (1975) discussed the maintainability structures in Markov chain models under recruitment control. Leeson (1984) considered the recruitment policies and their effects on internal structures. "Recruitment control" refers to an effective control of recruitment policies to obtain an optimal supply of recruits for a system at any time. Generally, recruitment levels are connected with wastage and promotions in a system, as well as the desired growth of the system. Therefore, controlling recruitment policies may help attain the desired structure and maintain it over time.

Kalamatianou (1987) obtained an attainable and maintainable grade structure in the Markov manpower system with pressure in grades. Furthermore, the work of Vassiliou (1976) and Leeson (1982) identified the wastage and promotion rates required to bring about any desired future personnel structure. Grinold (1976) placed emphasis on uncertain requirements. The main purpose was to provide a framework to regulate the supply of adequately qualified employees for naval aviation. Sathiyamoorty (1980) discussed a cumulative damage model of manpower planning with correlated inter-arrival times of shocks. Rao (1990) proposed a dynamic programming approach to identify optimal recruitment policies. A bivariate model under efficiency and seniority conditions embedded with stochastic theory was studied by Raghvendra (1991).

Young and Vassiliou (1974) considered a non-linear model for the promotion of staff. In particular, a stochastic model of promotion was proposed, based on an ecological principle which states that promotions should be proportional to the number of skilled employees available for promotion, and the number of vacancies for promotion. Subramanian (1996a, 1996b) developed an optimal policy for time-bound promotion in a hierarchical manpower system, and a model on optimum promotion rate. Sathiyamoorty and Elangovan (1999, 1998, 1997) studied an optimal recruitment policy for training prior to placement. A semi-Markov model of a manpower system was studied by Yadavalli and Natarajan (2001) with the focus on the total number of vacancies available in the entire organisation. Recently a study on trainingdependent promotions and wastage was also carried out by Yadavalli and Natarajan (2002).

Gross and Harris (1974) and Takacs (1960) have presented basic concepts of various queuing models. Queuing and inventory concepts were grouped as interdisciplinary subjects by Morse (1958) and applied to manpower-planning problems by Yadavalli et al. (2005). Mishra and Pal (2003) discussed the computational approach to the M/M/l/N interdependent queuing model. Furthermore, Mishra and Mishra (2004) evaluated the total optimal cost of the machine interference model as an important performance measure of the system. Very recently, Rajalakshmi and Jeeva (2003), as well as Jeeva, Rajalakshmi, Charles and Yadavalli (2004) discussed stochastic programming in cluster-based optimum allocation of recruitment.