Regenerative pull (Kanban) production control policies

Abstract A production system consists of a set of parallel robotic cells manufacturing parts for several distinct work stations. The stations order parts from these cells and withdraw parts from their buffers only at the rate and at the time of consumption. The desired decision vector provides for the instantaneous number of cells assigned to produce parts for each work station. Two novel tractable and optimal regenerative pull (‘Kanban’) control policies are formulated: one policy minimizes the weighted starvation penalty, while the other maximizes the weighted throughputs per unit time. Following these regenerative policies the production schedules are re-evaluated at each decision epoch to mitigate the effects of processing time variability. Several important properties regarding the inherent interaction between the structure of the optimal policy, the performance of the system and the desired allocation of productive capabilities among the manufacturing resources are examplified. It is shown that the optimal policy attempts to marginally assign as much of the cells capacity as possible to certain critical part types. Substantial changes in the structure of the optimal policy, resulting either from incrementing the number of cells or from increasing their capacity, are also identified. More generally, attention is drawn to the qualitative behavior of the optimal pull control policy in certain manufacturing systems with stochastic processing rates.