Containing The Theory Of Fuzzy Inventory Of Defective Products

The globalization of the market and the diversification of consumer behavior for customer lead to the uncertain and imprecise market demand, and due to imperfect production system, machine malfunction, natural disasters, damage or breakage in transit and so on, generation of imperfect items is inevitable in a produced/ordered lot. All of these make inventory management for enterprises face great challenge. The main focuses and innovations of this paper are summarized as follows:1. According to the classic single-period inventory problem, the single-period inventory model with imperfect products and fuzzy demand is developed. The optimal order quantity is determined using credibility theory to transform the fuzzy model into the expected model. The effect defective rate on optimal order quantity is analyzed via numerical examples.2. Considering the abusive shortage situations in reality may cause an unacceptable service level, economic order quantity model with fuzzy demand, fuzzy imperfect rate and service level constraint is constructed. At first, the optimal results are determined using a simple algebraic method and signed distance to solve the fuzzy model. Then, we provide a solution procedure to find the optimal order quantity in the fuzzy sense so that the required service level is attained and the total profit per unit time in the fuzzy sense has a maximize value.The influence service level on optimal order policy is analyzed via numerical examples.3. Considering the issue of imperfect production in the actual production inventory management, economic production quantity problems with fuzzy product defective rate and shortages are studied. According to the difference of product screening rate, two economic production quantity models with LR-fuzzy defect rate and fuzzy demand are developed.The simple algebraic method and signed distance are employed to obtain the optimal production policies. The relationship between model 1 and model 2 is revealed through theoretical analysis. Numerical examples are provided to examine the effect of screening rate and fuzziness of defective rate on optimal production policies.4. Considering service level constraint problem in production inventory management, two economic production quantity models with fuzzy demand, fuzzy defective rate and service level constraint are developed. The algorithms are designed to solve models. The influence service level on optimal production policies are analyzed via numerical examples.5. Considering the quality of imperfect products are improved, two economic production quantity models with quality improvement, fuzzy demand and fuzzy defective rate are studied, Optimal production policies are determined by using a simple algebraic method and signed distance to solve the fuzzy models. The relationship between model 1 and model 2 was revealed through theoretical analysis. Numerical examples are provided to examine the effect of scrap rate, screening rate and fuzziness of defective rate on optimal production policies.6. Considering service level constraint problem in production inventory, two economic production quantity models with fuzzy demand, fuzzy defective rate, service level constraint and quality improved are developed. The algorithms are designed to solve models. The influence service level on optimal production policies are analyzed via numerical examples.