designing an optimal control model of a capacity, multi-stage continuous mrp system considering delay in production lead time and the possibility of reworking and recycling

In this paper, we propose a multi-stage continuous-mrp system using an optimal control model, considering the production lead time. in the proposed model, the lead time is specified for ordering work in process during the second stage and for final product manufacturing. also, the intended dynamical system is a multi-stage production-inventory system that follows a linear-quadratic optimal control model with a time delay for the state variables. in the proposed system, inventories are considered state variables, and the delivery levels and orders are control variables. the return stage is considered for items whose production has been defective. according to their situation, there are three destinations: the reworking stage, the recycling stage, or disposal. the amount of shipment to the next stage of production is based on their bom utilization coefficient and the inventory one. this stage will consume all sent items at any time and will not create a surplus inventory. in this paper, time is considered a continuous parameter proportional to the constant production processes. for validation, the proposed optimal control model was simulated in a real study in the polymer industry.