Robust production control policy for a single machine and single part-type manufacturing system with inaccurate observation of production surplus

Abstract

The optimal production control policy (i.e., the hedging point policy) for a single machine and single part-type manufacturing system for the case where the production surplus is accurately known has been reported in the literature. However, the production surplus is often observed inaccurately in practice. Ignoring this inaccuracy in using the optimal policy leads to not only non-robust situations but also high production costs. To consider the effect of the inaccurate observation, robustness of the production control policy is required. The robustness can be evaluated in terms of the difference between the production surplus trajectory under the policy with an inaccurate observation and the trajectory under the policy with an accurate production surplus (i.e., the hedging point policy). A difference of zero is the ideal case; however, this is generally impossible to achieve since the extent of the observation error is generally unknown. This article proposes a new robust production control policy that can give a small difference between the two trajectories. Compared with the hedging point policy, the proposed policy is more insensitive to production surplus inaccuracy in the neighborhood of the hedging point but responds more slowly to a failure of the machine. Simulation studies show that the proposed policy has a better robustness than the hedging point policy for cases where, just as in actual industrial practice, the machine failure time is much shorter than the up time of the machine. In these cases, with an increase in the observation error, the robustness of the proposed policy becomes increasingly better than that for the hedging point policy.