Assignment of Personnels when Job Completion time follows Gamma distribution using Stochastic Programming Technique

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Author(s) 
Mohammed Faisal Khan, Zaki Anwar, Qazi Shoeb Ahmad 

KEYWORDS 
Cluster analysis, Gamma distribution, Linear stochastic programming, Nonlinear programming, 

ABSTRACT 
Recruitment of persons to various jobs according to required talents in an organization plays an important role in the growth of the organization. The formation of a number of groups of the persons from the population based on their efficiency in completion of jobs is being done by using the theory of cluster analysis. In this paper we formulate the problem of assignment of persons from various groups to different jobs who may complete them in minimum time as stochastic programming problem. The job completion times are assumed to follows Gamma distribution. By using the chance constrained programming technique we transform the stochastic programming problem to an equivalent deterministic problem with linear objective function and some nonlinear (convex) constraints. First we assume that the completion time variables are identically distributed Gamma variables. The model is then extended to the case of nonidentically distributed time variables. The illustrative examples are also given for both the models. 

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