Optimal adaptive Kanban-type production control

The field of adaptive Kanban-type control policies has attracted considerable attention in the research community over the years. Numerous heuristic control policies have been proposed in the literature for dynamically adjusting the number of kanban cards in a manufacturing system. However, to the authors’ knowledge, none of these approaches comes with guarantees regarding their optimality. In this research, we derive optimal adaptive Kanban-type policies using a dynamic programming approach. We investigate a single-stage system that consists of parallel machines. The demand for end-items is a Markov-modulated Poisson process, meaning that it is stochastic and periodically varying, due to seasonal fluctuations. The situation where the demand follows the Poisson distribution is also examined as a special case. The goal is to minimize the average total cost that consists of holding cost and backorder cost components. The properties of the optimal policy are investigated numerically. This analysis gives strong indications that existing, adaptive heuristics can never be optimal for seasonal demand. An extensive comparative evaluation of the optimal, the standard Kanban, and three adaptive heuristic policies is conducted. The experimental results indicate that the performance of all heuristics deteriorates as the variability of the demand increases. The Adaptive Kanban policy is found to largely outperform all other heuristics and to be a good approximation of the optimal adaptive policy in most cases.