An EPQ model to study the parallel production of two items in a multistage production system

In the manufacturing world, there are certain situations in which the manufacturer produce two sets of items, first item is the original product produced by the manufacturer for direct sale. And the second product is produced using a portion of first product as a source of raw material. Such phenomenon is covered in multistage manufacturing system and it can be observed in automobile industries, electronic industry, electrical parts manufacturing units, furniture manufacturer etc, where two production units work in parallel at the same time. Further, a portion of first product is used as raw material in the production of the second product. There is no existing literature in production inventory model which can explain this phenomenon. In this paper, an attempt have been made to develop a multistage production inventory model to study the parallel production of two items. Moreover, optimal values of production rate and selling price is obtain for both the productions in order to get the maximum profit. The model is validated with numerical examples. The objective function is solved with two variants of PSO under a proposed solution procedure. Managerial implications and limitations are proposed along with sensitivity analysis.