Production Campaign Planning Under Learning and Decay

Problem definition. We analyze a catalyst-activated batch-production process with uncertainty in production times, learning about catalyst-productivity characteristics, and decay of catalyst performance across batches. The challenge is to determine the quality level of batches and to decide when to replenish a catalyst so as to minimize average costs, consisting of inventory holding, backlogging, and catalyst switching costs. Academic / Practical Relevance. This is an important problem in a variety of process industry sectors such as food processing, pharmaceuticals, and specialty chemicals but has not been adequately studied in the academic literature. Our paper also contributes to the stochastic economic lot-sizing literature. Methodology. We formulate this problem as a Semi-Markov Decision Process (SMDP), and develop a two-level heuristic for it. This heuristic consists of a lower-level problem which determines the quality of batches to meet an average target quality, and a higher-level problem which determines when to replace the costly catalyst as its productivity decays. To evaluate our heuristic, we present a lower bound on the optimal value of the SMDP. This bound accounts for all costs, as well as the randomness and discreteness in the process. We then extend our methods to multiple-product settings: an advanced stochastic economic lot-sizing problem. Results. We test our proposed solution methodology with data from a leading food processing company and show our methods outperform current practice with average improvements of around 22% in costs. In addition, compared to the stochastic lower bounds, our results show the simple two-level heuristic attains near-optimal performance for the intractable multi-dimensional SMDP. Managerial Implications. Our results imply three important managerial insights: first, our simulationbased lower bound provides a close approximation to the optimal cost of the SMDP and it is nearly attainable using a relatively simple two-level heuristic. Second, the re-optimization policy used in the lower-level problem adequately captures the value of information and Bayesian learning. Third, in the higher level problem of choosing when to replace a catalyst, the intractable multidimensional state of the system is efficiently summarized by a single statistic: the probability of inventory falling below a specific threshold.