This paper investigates a single-period production-inventory model in linguistic ‘imprecise’ and statistical ‘uncertain’ environment, where fuzziness and randomness appear simultaneously. In order to capture the stochastic variability of demand uncertainty, we consider it as a random variable. We also model the hazards of imperfect quality production due to the production process shifting from “in-control” state to “out-of-control” state. The process shifting time and fraction of imperfect quality items are characterized as fuzzy random variables (FRVs). The model restricts the budget and allowable shortages. To mitigate the effect of uncertain demand, fluctuating cost parameters, etc., the imposed constraints are considered in fuzzy sense. To model the above scenarios, we formulate a fuzzy mathematical programming problem. By employing the fuzzy expectation, signed distance, and possibility/necessity measure, the fuzzy model is transformed into an equivalent deterministic non-linear programming problem. A fuzzy simulation based particle swarm optimization (PSO) algorithm is also employed to the model. The effectiveness of the model and solution methodologies are demonstrated with the help of numerical illustrations. 
A fuzzy random EPQ model for imperfect quality items with possibility and necessity constraints