An economic manufacturing quantity model with probabilistic deterioration in a production system

This paper develops an economic manufacturing quantity (EMQ) model with deterioration and exponential demand in a production system over a finite time horizon under the effect of inflation and time value of money. The production rate is a dynamic variable (varying with time) in a production system. Due to a long run process, the machinery system is converted from in-control state to out-of-control state which results the production of improper items. The improper items are reworked at a fixed cost to make it as proper. With the increasing value of time, the production of improper item also increases. To reduce the production of the improper items, the systems have to be more reliable and with less amount of failure. In this direction, the model considers that the development cost, production cost, and material cost are dependent on the reliability parameter. The deterioration of the product is considered probabilistic to make the research a more realistic one. By considering the reliability parameter as a decision variable, we try to obtain the associated profit of the system which we have to maximize. To derive the maximization procedure, we use Euler-Lagrange formula from control theory. We outline some numerical examples along with graphical representations and sensitivity analysis to illustrate the model.