Approximate Parametric Dynamic Programming in Inventory Management

We present an approximation method for inventory management under multiple suppliers and stochastic lead times. The method is based on parametric dynamic programming using convex piecewise linear approximations of the differential cost function in approximate relative value iteration steps and works for a range of stochastic control problems with linear dynamics and convex piecewise linear immediate costs. The obtained differential cost approximation not only defines a policy that performs well in practise, it also yields lower bounds that are useful to judge the quality of the corresponding policy or other heuristics. ∗Contact author. Email address: wor@zurich.ibm.com †IBM Research Zurich, Saeumerstrasse 4, CH-8803 Rueschlikon, Switzerland. ‡ETH Zurich, Institute for Operations Research, Raemistrasse 101, CH-8092 Zurich, Switzerland.