ANALYSIS OF CERTAIN DESIGN PROBLEMS IN THE CONTEXT OF THE FLEXIBLE MANUFACTURING SYSTEM (FMS) (INVENTORY MODELS, QUEUEING THEORY)

A Flexible Manufacturing System (FMS) is a highly automated system equipped with robots or numerically controlled (NC) machines which can process a variety of jobs with very little changeover time and setup cost. Automated material handling devices (transporters) allow jobs to move between any machine and are the factor which limits the number of jobs in a system. We model the FMS system as a single stage birth and death queue with finite states. The transition rate for each state depends on system throughput which is derived through the Closed Queueing Network theory. A balanced workload for all its machines is considered in this study. Four profit maximization models are proposed. The net profit, composed of profit per unit produced, inventory carrying cost, storage size cost, additional machine cost and loss production cost, is used to choose the optimal combination of number of machines, batch size (buffer size), and reorder point.;Model II has a fixed transition rate for all its states. The closed form solution to the optimal batch size is derived for this model.;In Model III we assume the number of machines and number of transporters are fixed. The variable transition rate and loss of production are allowed to determine batch size (Q) and reorder point (s). The model is very complicated and it appears impossible to derive a closed form solution. A computer search is used to study the model and an approximation formula for Q and s are derived. It is verified that the approximation solution is very accurate.;In Model IV, lead time for delivery of material from a central warehouse or supplier is considered in the model to determine optimal batch sizing and reorder points. A normal approximation formula is derived for the system.;Model I is a single stage birth and death queue with a variable transition rate for finite Q states. The transition rate at each state depends on the throughput rate and the number of transporters in the system. Lower bound solutions to the optimal batch size are derived, and the sensitivity of the optimal number of transporters to the model's parameters is also studied.