Setup cost reduction EMQ inventory system with probabilistic defective and rework in multiple shipments management

This paper considers an economic manufacturing quantity (EMQ) model for defective products with imperfect production processes and rework, in which the setup cost is logarithmic function of capital investment. In this study, fixed quantity multiple installments of the finished batch are delivered to customers at a fixed interval of time. We also consider three types of continuous probabilistic defective function to find the associated cost. The way our basic business operations like decision making, marketing strategies, financial management, etc. are done are being reformed with the use of computers and mathematics. In view of that the mathematical modeling and computational algorithm are employed in this study for optimizing the replenishment lot-size and setup cost simultaneously with the objective of minimizing total cost of the EMQ system. The long-run average cost function is derived, its convexity is proved via differential calculus. A computer code using the software Matlab is developed to derive the optimal solution and present numerical examples to illustrate the model.