Development of a production inventory model with uncertainty and reliability considerations

This paper addresses a problem of an imperfect production system under fuzzy demand and inventory holding cost. Production process reliability is considered because of the imperfect production process. In this problem, reliability of the system in regards to producing defective and non-defective items is considered as a decision variable. The objective is to maximize the graded mean integration value (GMIV) of the expected average profit while considering revenues as well as any other relevant costs. The developed model belongs to the class of a geometric programming. We have developed a simple mathematical methodology to solve the model. Genetic algorithm and simulated annealing algorithms are also applied to solve and validate the results. A numerical example has been presented to interpret the solutions.