Design of optimal configuration for a multi-stage production system

A mathematical model for the design of optimal system configuration for a class of multi-stage production - inventory systems is presented. This design problem involves the determination of optimal values for the batch blocking quantity (the amount of items to be processed simultaneously using a spindle), number of spindles and batch sizes. Moreover, this particular design procedure facilitates estimation of the capacity of the facilities required in terms of the number of machines of each type and the workers required to satisfy the expected demand for the products. The basic criterion considered for optimizing the system parameters is the minimization of total system cost (TSC). The TSC consists of setup cost and inventory carrying cost. A computational scheme incorporating the direct pattern search method is suggested for the optimization of the system parameters by minimizing the TSC. An example is presented to illustrate the application and behaviour of the mathematical model.