Optimal inventory control for assemble-to-order systems: A stochastic programming based asymptotic analysis framework

This dissertation focuses on the study of optimal inventory control of Assemble-to-Order (ATO) systems, a common strategy developed in supply chain management to address the mismatch between supply and demand. Historically, the optimal control of ATO systems has been shown to be a notoriously difficult problem. To tackle the technical challenges, we develop a four-step Stochastic Programming (SP) based asymptotic analysis framework. The SP model, as a surrogate model to ATO systems, is easier to solve and can provide vital guidance in developing novel inventory control policies. And asymptotic analysis can be used to show that the inventory control policies are asymptotically optimal. Asymptotic optimality, although a weaker standard than exact optimality, is a good alternative criterion in evaluating the performance of inventory control policies, especially when meeting exact optimality is usually analytically intractable. We first derive lower bounds about the long run average expected inventory cost on any feasible control policies for ATO inventory systems with deterministic lead times. The cost lower bounds are obtained from SP models with relaxed constraints to the original ATO systems, and are used to set performance benchmarks for evaluating our inventory control policies. Instead of developing efficient algorithms to solve the SP models, which is beyond the domain of this dissertation, we focus on investigating the stability of SP solutions. We first prove that the solution sets to the SP models are uniformly Lipschitz continuous in model inputs. Next we establish procedures to select Lipschitz continuous solutions to the SP models, which will be used to develop our inventory control policies. This Lipschitz continuity is also necessary to prove the asymptotic optimality of our inventory control policies. We develop two different replenishment polices for ATO inventory systems with deterministic lead times. The first one is Independent Base Stock (IBS) policy, where the corresponding base stock levels are constants formulated from solutions to a two-stage SP. The second one is the SP based replenishment policy formulated from solutions to a multi-stage SP. Unlike IBS policy, the inventory targets in the SP based policy depend on the system states, or ultimately on the inputs to the SP model that are changing in the control of real ATO systems. We also derive the optimality gaps from using these two replenishment policies along with any feasible allocation policy. Our allocation policy builds on the solutions to a Linear Program (LP) using component balance processes as inputs, and follows the Allocation Principle. We show that the optimality gap under the joint use of IBS replenishment policy and this LP based allocation policy diminishes to zero on the diffusion scale when lead times grow to infinity and the ratio of longest lead time to shortest lead time converges to unity. For ATO inventory systems with general deterministic lead times, we first develop a Stochastic Tracking Model and associated convergence results. With these convergence results, we prove that under the joint use of the SP based replenishment policy and the LP based allocation policy, the optimality gap converges to zero on the diffusion scale as the longest lead time grows to infinity. We also demonstrate the use of the LP based allocation policy to ATO production-inventory systems and show that it is also asymptotically optimal on the diffusion scale. Our allocation policy also has several advantages over some existing ones. Incidentally, we find in many ATO production-inventory systems, achieving asymptotic optimality necessitates component reservation. Finally, we conduct extensive numerical studies by simulating the application of our policies to some simple ATO inventory systems with deterministic lead times. The observation from simulations about the performance of our polices with increasing lead times is consistent with the established asymptotic optimality result. In addition, the simulation results also show that our policies can perform well in many non-asymptotic regimes.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Industrial Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2019

Author dc:creator

• Wan, Haohua

Contributors dc:contributor

• Wang, Qiong
• Stolyar, Aleksandr
• Reiman, Martin I.
• Seshadri, Sridhar

• Assemble-to-Order
• Stochastic Programming
• Asymptotic Analysis

Statement dc:rights

• Copyright 2019 Haohua Wan

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/105894

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/105894