Optimum ordering policy for an imperfect single-stage manufacturing system with safety stock and planned backorder

Manufacturing industries prefer to produce extra units as safety stock especially when demand for these units varies. The phenomena of producing additional units is also observed when processes are imperfect and production managers are sure that product can be consumed in market. In addition, customer is also willing to wait for demands to be backordered in the case of shortages. However, inventory carrying and backordering costs may play vital role if products are produced in relatively large amount. Therefore, a mathematical model is needed that can define the ordered quantity taking safety stock and planned backordering into consideration with imperfect production setup. This paper is an attempt towards development of such mathematical model that considers safety stock, lot size, and planned backorders for a single-stage imperfect production setup. Mathematical model is developed based on minimization of total average cost function. Three decision variables including order quantity, safety stock, and planned backorders have been optimized simultaneously using classical optimization approach. Numerical examples are used to illustrate the proposed model for calculation of decision variables. Impact of changes in processes imperfection, holding costs, and backordering costs over variables have been numerically computed to highlight model significance in daily industrial life. Results prove that safety stock and planned backorder reduce the total cost significantly.