An optimization model for a manufacturing-inventory system with rework process based on failure severity under multiple constraints

The present work investigates a manufacturing-inventory system with a single machine and multiple products, featuring returns on sales and backorders. In the proposed model, some imperfect items, including scrapped and defective items, are produced by the manufacturer. Such items can be classified, based on the severity of the failure, into several categories; as a result, the rework process is carried out at different rates. Moreover, the implementation of the quality control policy requires monitoring and checking the items during the production and reworking processes via an inspection process. The present study is aimed to calculate and obtain the optimal values of the cycle length and backorders quantity for every product in order to achieve the minimum total cost of system considering machine capacity, service level, warehouse space, and budget constraints. To solve the presented model, given as a Nonlinear Programming (NLP) problem, the GAMS software as well as four commonly used algorithms, which are categorized among the meta-heuristic algorithms, is used. These algorithms include the GA (Genetic Algorithm), IWO (Invasive Weed Optimization), GWO (Grey Wolf Optimizer) and HHO (Harris Hawks Optimization) algorithms. Along with these algorithms, the Response Surface Methodology (RSM) is applied to calibrate the parameters of the proposed algorithms. Finally, several numeric problems are solved, the results of which are then compared with each other. Moreover, an analytical hierarchy process (AHP) technique for order performance by similarity to ideal solution (TOPSIS), which is a hybrid method of decision making with multiple attributes, is used for ranking the algorithms.