Production Campaign Planning Under Learning and Decay

We formulate a planning problem for a batch production process with learning about productivity characteristics and decay of catalyst performance across batches as a semi-Markov average-cost model. We decompose the problem into a lower-level stage which determines the quality of batches within a campaign to meet an average target quality, and a higher-level stage which determines the campaign length (the number of batches that are produced together) by deciding when to replace the costly catalyst as its productivity decays. For the first stage, we develop a stochastic dynamic programming model and show that the structure of the optimal batch-planning strategy depends only on the form of the function relating the catalyst decay to its total consumption. For the second stage, we propose a heuristic based on approximate dynamic programming to minimize total average costs. We present a lower bound for the optimal performance which accounts for randomness and discreteness in the process. We then extend our methods to multiple-product settings: an economic lot sizing problem with fixed batch sizes, uncertainty in production times, learning and decay. We test our methods with data from a leading food processing company and show our methods outperform current practice with average improvements of 22%.