A dynamic programming approach to achieving an optimal end-state along a serial production line

In modern production systems, it is critical to perform maintenance, calibration, installation, and upgrade tasks during planned downtime. Otherwise, the systems become unreliable and new product introductions are delayed. For reasons of safety, testing, and access, task performance often requires the vicinity of impacted equipment to be left in a specific “end state” when production halts. Therefore, planning the shutdown of a production system to balance production goals against enabling non-production tasks yields a challenging optimization problem. This article proposes a mathematical formulation of this problem and a dynamic programming approach that efficiently finds optimal shutdown policies for deterministic serial production lines. An event-triggered re-optimization procedure that is based on the proposed deterministic dynamic programming approach is also introduced for handling uncertainties in the production line for the stochastic case. It is demonstrated numerically that in these cases with random breakdowns and repairs, the re-optimization procedure is efficient and even obtains results that are optimal or nearly optimal.