Dynamic Multi Period Production Planning Problem with Semi Markovian Variable Cost (TECHNICAL NOTE)

This paper develops a method for solving the single product multi-period production-planning problem, in which the production and the inventory costs of each period arc concave and backlogging is not permitted. It is also assumed that the unit variable cost of the production evolves according to a continuous time Markov process. We prove that this production-planning problem can be Stated as a problem of finding the dynamic shortest path from the source node to the sink node, Finally, we apply the stochastic dynamic programming to find the dynamic shortest path from the source node to the sink node and obtain the optimal production scheduled for each period.