A CONWIP (Constant Work-In-Progress) system is basically a hybrid system with a PUSH-PULL interface at the first machine in the line. This research addresses the most general case of a cyclic CONWIP system by incorporating two additional constraints over earlier studies namely; stochastic processing times and limited intermediate storage. One of the main issues in the design of a CONWIP system is the WIP level 'M', to be maintained. This research proposes an iterative procedure to determine this optimal level. The second main issue is the optimization of the line by determining an appropriate job sequence. This research assumes a 'permutational' scheduling policy and proposes an iterative approach to find the best sequence. The approach utilizes a controlled enumerative approach called the Fast Insertion Heuristic (FIH) coupled with a method to appraise the quality of every enumeration at each iteration. This is done by using a modified version of the Floyd's algorithm, to determine the cycle time (or Flow time) of a partial/full solution. The performance measures considered are the Flow time and the Interdeparture time (inverse of throughput). Finally, both the methods suggested for the two subproblems, are tested through computer implementations to reveal their proficiency. / Master of Science