This paper, attempts to propose a new multi-stage production-inventory system with and without lead-times via an optimal control model. The proposed optimal control model for lead-times contains some delays in the state variables. The considered dynamical system is a multi-stage production-inventory one which obeys a linear quadratic optimal control model with time delays in the states. Production lead-times can be considered as required time for production. In the proposed system, the inventories of stocks are considered as state variables while the demand and ordering levels are control variables. In the proposed multi- stage system, returned items from one stock to the previous one is allowed with recycling. The exact solution of non-delay model along with the approximate solution of delayed system are obtained and compared in a real case study in granular polymer industry which the products are 3D panels and Expanded Poly Styrene (EPS) blocks.

Keywords