A volume flexible economic production lot‐sizing problem with imperfect quality and random machine failure in fuzzy‐stochastic environment

An ‘economic production lot size’ (EPLS) model for an item with imperfect quality is developed by considering random machine failure. Breakdown of the manufacturing machines is taken into account by considering its failure rate to be random (continuous). The production rate is treated as a decision variable. It is assumed that some defective units are produced during the production process. Machine breakdown resulting in idle time of the respective machine which leads to additional cost for loss of manpower is taken into account. It is assumed that the production of the imperfect quality units is a random variable and all these units are treated as scrap items that are completely wasted. The models have been formulated as profit maximization problems in stochastic and fuzzy‐stochastic environments by considering some inventory parameters as imprecise in nature. In a fuzzy‐stochastic environment, using interval arithmetic technique, the interval objective function has been transformed into an equivalent deterministic multi‐objective problem. Finally, multi‐objective problem is solved by Global Criteria Method (GCM). Stochastic and fuzzy‐stochastic problems and their significant features are illustrated by numerical examples. Using the result of the stochastic model, sensitivity of the nearer optimal solution due to changes of some key parameters are analysed.