Stochastic Modeling for Inventory and Production Planning in the Paper Industry

Stochastic Modeling for Inventory and Production
Planning in the Paper Industry
K. Karen Yin
Dept. of Bio-based Products, University of Minnesota, St. Paul, MN 55108

G. George Yin
Dept. of Mathematics, Wayne State University, Detroit, MI 48202

Hu Liu
3M Commerce Services, 3M Center, St. Paul, MN 55144
DOI 10.1002/aic.10251
Published online in Wiley InterScience (www.interscience.wiley.com).

Problem formulations and solution procedures of production planning and inventory management for manufacturing systems under uncertainties is discussed. Markov decision processes and controlled Markovian dynamic systems are used in the models. Considering an inventory problem in discrete time and formulating it by a finite-state Markov chain lead to a Markov decision process model. Using the policy-improvement algorithm yields the optimal inventory policy. In controlled dynamic system modeling, the random demand and capacity processes involved in planning are described by two finite-state continuoustime Markov chains. Such an approach enables us to embed the randomness in the differential equations of the system. The optimal production rates that minimize an expected cost are obtained by numerically solving the corresponding Hamilton–Jacobi–
Bellman (HJB) equations. To overcome the so-called curse of dimensionality, frequently encountered in computation, we resort to a hierarchical approach. Illustrative examples using data collected from a large paper manufacturer are provided. © 2004 American
Institute of Chemical Engineers AIChE J, 50: 2877–2890, 2004

Keywords: inventory management; production planning; Markov chain; optimal policy; hierarchical approach

Introduction
In the pulp and paper industry, the search for good inventory control policies and production plans started several decades ago. Many models have been developed and used (see
Leiviska, 1999 and references therein). Nevertheless, similar to
¨
the situation in many other

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