Dynamic decision-making under uncertainties: algorithms based on linear decision rules and applications in operating models

This thesis is to propose efficient and robust algorithms based on Linear Decision Rule (LDR), which expand the applicability of the existing LDR methods. Representative and complex operation models are analyzed and solved by the proposed approaches. The research motivation and scope are provided in Chapter 1. Chapter 2 introduces the generic LDR method and the contributions of this thesis to the LDR literature. To extend the LDR method to nonlinear objectives, two methods are proposed. The first is an iterative LDR (ILDR) method that tackles general concave differentiable nonlinear terms in the objective function. The second treats quadratic terms in the objective function by a Second-Order Cone approximation. The details and implementation of the proposed methods are presented in Chapter 3 and Chapter 4. Chapter 3 utilizes the Robust Optimization approach to derive an ILDR solution for a multi-period hydropower generation problem that has a nonlinear objective function. The methodology results in tractable second-order cone formulations. The performance of the ILDR approach is compared with the Sampling Stochastic Dynamic Programming (SSDP) policy derived using historical data. In Chapter 4, a joint pricing and inventory control problem of a perishable product with a fixed lifetime is analyzed. Both the backlogging and lost-sales cases are discussed. The analytic results shed new light on perishable inventory management, and the proposed approach provides a significantly simpler proof of a classical structural result in the literature. Two heuristics were proposed, one of which is a modification and improvement of an existing heuristic. The other one is an LDR based approach, which approximates the dynamics and the objective function by robust counterparts. The robust counterpart for the backlogging case is tight, and it leads to a satisfactory performance of less than 1% loss of optimality. Although the robust counterpart for the lost-sales case is not tight in the current numerical study, the gap between the LDR method and the SDP benchmark is less than 5% on average. Chapter 5 summarizes the contributions of the thesis and discusses about potential improvements. One important working project, an approximate dynamic programming based on LDR (ADP-LDR) approach, is introduced for future research.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Systems & Entrepreneurial Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Pan, Limeng

Contributors dc:contributor

• Chen, Xin
• Beck, Carolyn L.
• Cai, Ximing
• Wang, Qiong

• dynamic decision-making
• stochastic optimization
• robust optimization
• second-order cone programming
• reservoir management
• supply chain management
• perishable product management

Statement dc:rights

• Copyright 2014 Limeng Pan

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/50389

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/50389