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https://hdl.handle.net/2142/125668
Description
Title
Inventory management with incomplete information
Author(s)
Bai, Xingyu
Issue Date
2024-06-18
Director of Research (if dissertation) or Advisor (if thesis)
Chen, Xin
Stolyar, Alexander
Doctoral Committee Chair(s)
Chen, Xin
Stolyar, Alexander
Committee Member(s)
Wang, Qiong
Seshadri, Sridhar
Department of Study
Industrial&Enterprise Sys Eng
Discipline
Industrial Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Inventory control
lead time
Abstract
Efficient inventory management is vital for businesses to maintain optimal levels of stock while minimizing costs. However, in real-world scenarios, the decision maker suffers from incomplete information existing widely in supply chains, which can be due to order lead times, inaccurate inventory level records, unknown demand distributions. Consequently, it is hard to obtain the optimal policy. This thesis delves into these challenges and opportunities presented by incomplete information in inventory control problems.
First, We consider a generic Markov decision process with two controls: one control taking effect immediately and the other control whose effect is delayed by a positive lead time. We analyze the so-called semi-open-loop policies, which specify open-loop controls for the delayed action and closed-loop controls for the immediate action, in the asymptotic regime where the lead time goes to infinity. For MDPs defined on general spaces with uniformly bounded cost functions and a fast mixing property, we construct a periodic semi-open-loop policy for each lead time value and show that these policies are asymptotically optimal. For MDPs defined on Euclidean spaces with linear dynamics and convex structures, we impose another set of conditions under which semi-open-loop policies (actually, constant-delayed-control policies) are asymptotically optimal. Moreover, we verify that these conditions hold for a broad class of inventory models, which supports the use of semi-open-loop policies in practice.
Second, we consider the lost-sales inventory model in which the lead time is not only large but also random. Under the assumption that the placed orders cannot cross in time, we establish the asymptotic optimality of constant-order policies as the lead time increases for the model with divisible products. For the model with indivisible products, we propose a bracket policy, which alternates deterministically between two consecutive integer order quantities, and prove that the bracket policy is asymptotically optimal. Our theoretical results can be extended to the models with order crossover, random supply functions, Markov-modulated demands and cyclic demands. In addition, we provide a comprehensive numerical study to demonstrate the good performance of the proposed open-loop policies, and derive further managerial insights.
Finally, we consider a partially observable lost-sales inventory system in which the inventory level is observed only when it reaches zero. We use the vanishing discount factor approach to prove the existence of a stationary optimal policy for the average cost minimization. As our main methodological contribution, we provide a way to verify the key condition of the vanishing discount factor approach – the uniform boundedness of the relative discounted value function.
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