Hybrid capacity modeling for alternative machine types in linear programming production planning

Abstract

Processing by alternative machines is very common in today's manufacturing environment, especially in the semiconductor industry. Leachman and Carmon (1992) have presented a novel approach to model alternative machine capacitated problems for Linear Programming (LP) production planning. Their approach makes possible the modeling of complex processes with re-entry into alternative machines in large scale LP production planning. However, there are difficulties in using their approach in industrial applications. In order to use their approach, a uniform assumption must be satisfied. But in many industrial applications, this assumption cannot be satisfied. In addition, their approach creates new alternative machine sets by performing union operations on existing alternative machine sets with common machine types. This will increase the number of capacity constraints, which may increase the solution time of the LP formulation. This study compares their approach and the partition approach outlined herein in terms of CPU times used. Finally, this study proposes a hybrid capacity modeling approach that is more suitable for industrial applications.