Optimal batch sizing in a multi-stage production system with rework consideration

In a production system, rework process plays an important role in eliminating waste and effectively controlling the cost of manufacturing. Determining the optimal batch size in a system that allows for rework is, therefore, a worthwhile objective to minimize the inventory cost of work-in-processes and the finished goods. In this paper, models for the optimum batch quantity in a multi-stage system with rework process have been developed for two different operational policies. Policy 1 deals with the rework within the same cycle with no shortage and policy 2 deals with the rework done after N cycles, incurring shortages in each cycle. The major components that play a role in minimizing this cost of the system are manufacturing setups, work-in-processes, storage of finished goods, rework processing, waiting-time, and penalty costs to discourage the generation of defectives. The mathematical structure of this rework processing model falls under a nonlinear convex programming problems for which a closed-form solution has been proposed and results are demonstrated through numerical examples, followed by sensitivity analyses of different important parameters. It is concluded that the total cost in policy 2 tends to be smaller than that in policy 1 at lower proportion of defectives if the in-process carrying cost is low. Policy 2 may be preferred when the work-in-process carrying cost is low and the penalty cost is negligible.