On the Mathematical Formulation for Determination of Natural Groups for the Generalised Case

Current global market trend shows a shift in consumers’ attitude towards the purchased products. Increase in product variety and quality requirement coupled with decrease in production volume and delivery time is a motivating factor for the industries to employ more of Flexible Manufacturing Systems (FMSs) even at a heavy initial cost since they are capable of taking care of these market factors. Machines, in FMS, are generally more flexible, and more so due to their increased tooling capability. This characteristic results into higher operational and routing flexibilities allowing a part to be manufactured in many alternative ways most economically under the stated market conditions. These alternatives provide a generalized grouping framework wherein parts and machines are divided preferably in disjoint sets so as to reap in more of economic and other benefits. Under this circumstance, an effort has been made in this paper to determine simultaneously optimal number of groups and their constitution. Along with, the solution to the machine allocation problem is also established. A numerical example is taken to illustrate the generalized framework considered for the integrated problem. From the various grouping solutions to this problem, the effectiveness and suitability of the proposed mathematical formulations are demonstrated.