Fuzzy production inventory models with defective rate and shortages

Considering the issue of imperfect production and shortages in the actual inventory management, production inventory strategy of crisp and fuzzy product defective rate with backorder were studied. The production inventory models with LR-fuzzy defective rate, fuzzy demand, fuzzy screening cost and fuzzy order cost were developed. The optimal production strategy were determined by transforming the fuzzy model into crisp model based on signed distance method. The relationships between fuzzy and classical production inventory models were revealed through theoretical analysis. The influence of fuzziness of defective rate and screening rate on the optimal production quantity and total cost were analyzed via numerical examples.