Batch Sizing in Sustainable Production Systems with Imperfect Quality

In classic Economic Production Quantity (EPQ), an optimal batch size is determined to minimize total production cost including setup and inventory holding costs, and defective parts are not allowed. In this paper an imperfect EPQ system is studied to minimize the overall cost, where setup cost, scarp rate, batch size, and electrical power demand are determined by the model. In this imperfect production system, a percentage of the batch is defective in each cycle, which will be reworked at an extra charge. In addition, the model considers electrical power demand charge which accounts for a large percentage of industrial utility bills. This framework also determines the optimal level of investment on system design and flexibility which in turn, is a function of setup cost, electrical power requirement (power demand), and scrap rate. The proposed constrained cost minimization problem is formulated as a nonlinear mathematical model, and is solved using a posynomial Geometric Programming (GP) approach to present a closed form solution for the batch size, setup cost, allowable defective rate and power requirements. The model is illustrated through a numerical example and some sensitivity analysis is performed.