Abstract
This article considers a production-inventory system consisting of a single imperfect unreliable machine. The items manufactured by the system are either perfect items or imperfect items, which require a rework to be restored to perfect quality. The rework rate is permitted to be different from the production rate if the rework process is different from the main manufacturing process. The fraction of the number of imperfect items is random following a general distribution function. The time to failure of the machine is random, following a general distribution function. If the machine fails before the lot is completed, the production is interrupted and the machine repair is started immediately. A random machine repair time is assumed, with a general distribution function. Unlike a common assumption in the literature, after the repair of the machine is completed, the production resumes. During the machine repair, a shortage can occur. A single-variable expected average cost function is derived to find the optimal lot size. Because of the complexity in the model, the ABC heuristic is proposed and implemented to find a near optimal value for the lot size. The article also provides a sensitivity analysis of the model's key parameters. It has been observed that the lot interruption-resumption policy leads to smaller lot sizes.
•An imperfect production system has a random time to failure and a random time to repair.•Shortages are permitted during the machine repair.•The model determines the optimal production lot size.•The lot interruption-resumption strategy leads to smaller lot sizes.•The lot size reacts significantly to changes in the machine failure rate and the repair rate.