Inventory management and production planning under stochastic demand and production capacity processes in the paper industry

Scientific inventory management and production planning are of critical importance to the paper industry because of the complex and random nature of its production systems and the ever-changing market conditions. This work concerns problem formulation and solution procedure for efficient inventory management and production planning under random demand and stochastic production capacity processes in the paper industry.; Using demand data collected from a large paper manufacturer, we develop inventory policies for the finished paper products. To incorporate both variability and regularity of the system into mathematical formulation, we analyze probability distribution of the demand, explore its connection with the corresponding Markov chain, and integrate these into our decision making. In particular, we formulate the Markov decision model by identifying the chain's state space and the transition probabilities, specify the cost structure and evaluate its individual component, and use the policy-improvement algorithm to obtain the optimal policy. Application examples are provided for illustration.; Considering the uncertainties involved in the manufacturing systems, the system dynamics are formulated by differential equations with Markovian disturbances. Modeling the random demand and capacity processes by two finite-state continuous-time Markov chains, the production planning is formulated as a stochastic optimal control problem with the objective of minimizing the discounted surplus and production costs. By discretizing the associated Hamilton-Jacobi-Bellman (HJB) equations satisfied by the value functions, numerical algorithms are applied to a papermaking process. Using demand and capacity data collected from real industrial processes, three case studies are presented; optimal production policies are obtained, which enable one to make production decisions sequentially throughout the process lifespan.; For large-scale systems, the computation needed in numerically solving such dynamic programming equations increases with respect to the number of Markovian states. In many cases, the computational requirements to obtain an optimal policy are staggering to the point that a numerical solution becomes infeasible. To address the issue of “curse of dimensionality”, we resort to hierarchical approach and seek nearly optimal solutions. The mathematical models and time-scale separation technique are discussed, the problem formulation and numerical procedure are applied to two different examples.