Multi-machine economic production quantity for items with scrapped and rework with shortages and allocation decisions

This study considers a multi-product multi-machine economic production quantity inventory problem in an imperfect production system that produces two types of defective items: items that require rework and scrapped items. The shortage is allowed and fully backordered. The scrapped items are disposed with a disposal cost and the rework is done at the end of the normal production period. Moreover, a potential set of available machines for utilization is considered such that each has a specific production rate per item. Each machine has its own utilization cost, setup time and production rate per item. The considered constraints are initial capital to utilize machines and production floor space. The proposed inventory model is a mixed integer non-linear programing mathematical model. The problem is solved using a bi-level approach, first, the set of machines to be utilized and the production allocation of items on each machine are obtained thru a genetic algorithm. Then, using the convexity attribute of the second level problem the optimum cycle length per machine is determined. The proposed hybrid genetic algorithm outperformed conventional genetic algorithm and a GAMS solver, considering solution quality and solving time. Finally, a sensitivity analysis is also given.