Int. J. Contemp. Math. Sciences, Vol. 8, 2013, no. 2, 93 - 116 HIKARI Ltd, www.m-hikari.com Fuzzy Linear Programming Model for Critical Path Analysis K. Usha Madhuri 1 , B. Pardha Saradhi 2 and N. Ravi Shankar 1 1 Dept.of Applied Mathematics, GIS, GITAM University, Visakhapatnam, India 2 Dept. of Mathematics, Dr.L.B.College, Visakhapatnam, India Abstract In this paper, a new fuzzy linear programming model is proposed to find fuzzy critical path and fuzzy completion time of a fuzzy project. All the activities in the project network are represented by trapezoidal fuzzy numbers. A new representation of trapezoidal fuzzy number is introduced to reduce the constraints in the fuzzy linear programming model. Further, an example is illustrated which shows the advantages of using the proposed representation over the existing representation of trapezoidal fuzzy numbers and will present with great clarity the proposed technique and illustrate its application for fuzzy critical path problems occurring in real life situations. Keywords: Fuzzy Critical Path Problem; Ranking function; Trapezoidal fuzzy number; LR fuzzy number; linear programming 1. Introduction In today’s highly competitive business environment, project management’s ability to schedule activities and monitor progress strictly in cost, time and performance guidelines is becoming increasingly important to obtain competitive priorities such as on-time delivery and customization. In many situations, projects can be complicated and challenging to manage. Critical Path Method (CPM) is to identify critical activities on the critical path so that resources may be concentrated on these activities in order to reduce the project length time. Further