Optimal reliability, production lotsize and safety stock: an economic manufacturing quantity model

Reliability based maintenance provides sound guidance for managers who wish to attain high standards of maintenance at their operating systems. Basically, the amount and the type of maintenance applied for the system depend strongly on the age of components of a machinery system. The present paper describes a production policy (resumption and non-resumption) in order to find out an optimal safety stock, production lotsize and reliability parameters. A production-inventory model with stochastic machine breakdown and its corrective and regular (preventive) repairs with safety stock has been developed incorporating variable reliability parameters. The reliability parameter (theta) is a design variable. Learning effects result in the cost of technology for the design variable which is an decreasing function of (theta) and this, in turn, has an impact on the average cost. Hence the setting of optimal values of reliability parameters and production lotsize with safety stock needs to be considered jointly that achieves the smallest average integrated costs. The Kuhn-Tucker method is used to obtain an optimal solution for reliability parameters, production lotsize and safety stock. Finally, numerical examples with sensitivity analysis of key parameters are given to illustrate the proposed model. Several graphical illustrations of the model are given.