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Approximate dynamic programming application to inventory management




Katanyukul, Tatpong, author

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This study has developed a new method and investigated the performance of current Approximate Dynamic Programming (ADP) approaches in the context of common inventory circumstances that have not been adequately studied in the literature. The new method uses a technique similar to eligibility trace [113] to improve performance of the residual gradient method [7]. The ADP approach uses approximation techniques, including learning and simulation schemes, to provide the flexible and adaptive control needed for practical inventory management. However, though ADP has received extensive attention in inventory management research lately, there are still many issues left uninvestigated. Some of the issues include (1) an application of ADP with a scalable, linear operating capable, and universal approximation function, i.e., Radial Basis Function (RBF); (2) performance of bootstrapping and convergence-guaranteed learning schemes, i.e., Eligibility Trace and Residual Gradient, respectively; (3) an effect of latent state variables, introduced by recently found GARCH(1,1), to a model-free property of learning-based ADPs; and (4) a performance comparison between two main ADP families, learning-based and simulation-based ADPs. The purpose of this study is to determine appropriate ADP components and corresponding settings for practical inventory problems by examining these issues. A series of simulation-based experiments are employed to study each of the ADP issues. Due to its simplicity in implementation and popularity as a benchmark in ADP research, the Look-Ahead method is used as a benchmark in this study. Conclusions are drawn mainly based on the significance test with aggregate costs as performance measurement. The performance of each ADP method was tested to be comparable to Look-Ahead for inventory problems with low variance demand and shown to have significantly better performance than performance of Look-Ahead, at 0.05 significance level, for an inventory problem with high variance demand. The analysis of experimental results shows that (1) RBF, with evenly distributed centers and half midpoint effect scales, is an effective approximate cost-to-go method; (2) Sarsa, a widely used algorithm based on one-step temporal difference learning. (TD0), is the most efficient learning scheme compared to its eligibility trace enhancement, Sarsa(λ),or to the Residual Gradient method; (3) the new method, Direct Credit Back, works significantly better than the benchmark Look-Ahead, but it does not show significant improvement over Residual Gradient in either zero or one-period leadtime problem; (4) a model-free property of learning-based ADPs is affirmed under the presence of GARCH(1,1) latent state variables; and (5) performance of a simulation-based ADP, i.e., Rollout and Hindsight Optimization, is superior to performance of a learning-based ADP. In addition, links between ADP setting, i.e., Sarsa(λ)'s Eligibility Trace factor and Rollout's number of simulations and horizon, and conservative behavior, Le., maintaining higher inventory level, have been found. Our conclusions show agreement with theoretical and early speculations on ADP applicability, RBF and TD0 effectiveness, learning-based ADP's model-free property, and that there is an advantage of simulation-based ADP. On the other hand, our findings contradict any significance of GARCH(1,1) awareness, identified by Zhang [130], at least when a learning-based ADP is used. The work presented here has profound implications for future studies of adaptive control for practical inventory management and may one day help solve the problem associated with stochastic supply chain management.


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dynamic programming
data processing
inventory control


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