Optimal inventory economic order quantity model for inventory system with imperfect inspection processes

Inventory management is the core of supply and demand chain management. The economic order quantity (EOQ) model is the fundamental inventory management model that is assumed to bring only perfect items out of the ordered lot. A lot undergoes a single acceptance sampling plan with an imperfect inspection process before being placed in the inventory. The traditional inventory management process fails to address real-world situations where each type of product is handled in a unique way by manufacturers. This paper formulates an EOQ model in a fuzzy environment while considering: 1) shortages and backorders; 2) the chance of misclassification; 3) fuzziness in the model parameters. An optimisation problem is developed to maximise the total profit. The existence and uniqueness of the optimal solutions are proved with the help of a theorem established for concavity conditions of the total expected profit function. A sensitivity analysis study is also conducted to examine the effect of inspection error on order quantity, backorder level, and total profit. Finally, several numerical examples are presented to illustrate the model derived.