International Journal of Computational Science and Mathematics. ISSN 0974-3189 Volume 2, Number 1 (2010), pp. 285--290 © International Research Publication House http://www.irphouse.com Discrete Time, Cost and Quality Trade-Off Problem with Renewable and Nonrenewable Resources N. Ravi Shankar 1 , M.M.K. Raju 2 and P. Hima Bindu 1 1 Dept. of Applied Mathematics, GIS, GITAM University, Visakhapatnam, India 2 Dept. of Mathematics, Raghu Institue of Technology, Visakhapatnam, India Abstract The discrete time –cost trade-off problem (DTCTP) is one of the main aspects of project scheduling. In DTCTP , we treat cost as a non-renewable resource and the availability of renewable resource per period has been neglected. It was recently suggested that the quality of project should also be taken into consideration. Therefore, when renewable resources and quality are considered, the traditional DTCTP is extended to a new discrete resource quality constrained time cost-trade off problem (DRQTCTP), which involves renewable resources, non renewable resources and quality constraints. The objective of DRQTCTP involves the scheduling of project activities in order of minimizing the total cost of the project while maximizing the quality of the project and also meet a given deadline. An example is given for the DRQTCTP and it is observed that when subjected to same amount of non- renewable resources, the optimal project cost in DRQTCTP is higher than that in traditional DTCTP but there is no change in quality. Keywords: Time –cost trade-off, discrete time, Project management, cost and quality problem. Introduction Since the late 1950s, critical path method (CPM) techniques have become widely recognized as valuable tools for the planning and scheduling of projects. But most of the cases, project should be implemented before the date calculated by CPM method. To achieve this goal, more sophisticated equipments or employment of more human resources can be used. Finding the most cost- effective way to complete a project with in a specific completion time is desirable for schedule planners. Therefore, for