Discontinuous optimization in a class of multi-stage production systems

An alternative and efficient optimization procedure for discontinuous optimization in batch production systems is presented. This method, namely, the direct pattern search method (DPSM) is an alternative approach to that suggested by Imo and Leech (1984), the sequential unconstrained minimization technique (SUMT) to minimize the processing time per unit of a finished product in a class of multi-stage production systems. Moreover, the scope for the extension of the Imo and Leech (1984) model is explained with reference to the application to just-in-time (JIT) manufacturing systems and flexible manufacturing systems (FMS). Furthermore, the model can be enriched with an objective to model more realistic production systems incorporating the cost due to queueing of batches, and batch splitting and forming using the concept of equivalent transformation. The main purpose is to motivate the extension of the model in order to enhance the scope and application of the model for modern production systems and the use of the DPSM for discontinuous batch size optimization. An example is solved and the results obtained prove that the DPSM is superior with respect to the minimum processing time per unit and the computational effort required for discontinuous optimization.