A dynamic control problem for a two part-type pull manufacturing system

We study the problem of dynamic part scheduling and kanban allocation on a pull manufacturing system, with finite inventory space and stochastic demand. It is assumed that a finite number of requests can be backlogged and requests finding the full system are dropped. The system is a single machine, two part-type, and the control objective is that of minimizing an infinite horizon discounted cost in the inventory and backlog level and demand losses. No setup times and costs are considered. The original scheduling and kanban allocation problem is reformulated as a “pure” scheduling problem for constant kanban systems. A continuous-time Markov decision problem is formulated, and solved by means of a uniformization procedure and discrete-time dynamic programming. Some initial analytical results are given, while the solution structure is derived numerically