Advanced search
Add to list

Exact solution methodologies for time-dependent non-linear systems : the financial optimization perspective

Majid Yazdani (UGent)
(2024)
Author
Promoter
(UGent)
Organization
Abstract
In the realm of operations research, addressing time-dependent mixed integer nonlinear systems - a subset of combinatorial optimization problems - presents a formidable challenge, given the dynamic parameters and intricate inter-dependencies among its components (Du et al., 2019; Krug, 2023; Li and Liao, 2020). This complexity becomes particularly evident in scenarios related to combinatorial optimization, such as supply chain management and scheduling challenges, where discrete variables must be optimized while adhering to time-dependent constraints, failure to do so can result in a substantial impact on the overall system cost. To confront these challenges effectively, it is crucial to employ combinatorial approaches that encompass decomposition strategies and approximation techniques (F ̈ullner and Rebennack, 2022; Nowak et al., 2019). When addressing Mixed Integer Nonlinear Programming (MINLP) problems, researchers categorize solution methodologies into single-tree and multitree methods, with multitree and hybrid approaches demonstrating superior effectiveness, particularly for convex MINLPs (Belotti et al., 2013). However, non-convex MINLPs, characterized by non-convex functions, necessitate specialized strategies such as piecewise linear approximations, convex relaxations, spatial branch-and-bound, quadratic reformulations, and methods leveraging non-convex structures. These di- verse approaches collectively provide robust solutions to the complexities inherent in non-convex MINLPs, highlighting the crucial need for the utilization of the latter set of techniques. This thesis focuses on some of these specific methods - such as Benders decomposition (BD), a tool for managing large-scale systems, and approximation techniques simplifying complex sys- tems (Kuchlbauer et al., 2022; Rahmaniani et al., 2017). These methods, chosen for their ef- ficacy, address challenges in two distinct problem areas. In subsequent sections, we delve into these methods, discussing their applications and examining real-world scenarios involving two applications of time-dependent nonlinear systems to derive practical insights for decision-making. The first application explores multi-echelon inventory-transportation systems in maritime supply chains. It optimizes shipment planning and safety stock placement, considering stochastic demand and transportation times. The research delves into the intricacies of optimizing variables like shipment volumes, origin points, delivery speeds, and safety stock quotas. By integrating innovative practices and analytical insights, the study aims to enhance decision-making efficiency in maritime supply chain planning. The second application focuses on the discrete time/cost trade-off problem with discounted cash flows in project scheduling. It introduces an adapted model for joint optimization of project completion time and profitability. The study employs the Generalized Benders Decomposition (GBD) technique to address computational complexity and presents an innovative Constraint Programming approach. The goal is to provide practical recommendations for project managers in various industries, optimizing decision-making in project scheduling. This dissertation categorizes its two primary applications into three distinct research streams. The first stream focuses on developing exact solution procedures for optimizing shipment planning and safety stock placement in maritime supply chains confronted with stochastic demand and variable transportation times. The second stream delves into the application of exact de- composition techniques to address the deadline-constrained discrete time/cost trade-off problem, considering discounted cash flows. The third stream centers on the development of exact solution procedures for project payment scheduling, emphasizing a joint perspective for optimizing financing cost distribution. Chapter 2 focuses on maritime supply chain planning, addressing specific research questions related to integrating multi-product and multi-mode transportation optimization, optimizing safety stock placement, and understanding the impact of time and cost parameters on decision making. Chapter 3 tackles the discrete time/cost trade-off problem in project scheduling, adapting models to real-world payment systems and project deadlines. It explores the benefits of integrating project network representation, payment systems, and deadlines, employing GBD. Chapter 4 enhances the model introduced in Chapter 3 by providing a comprehensive analysis of the DTCTP-NPV problem from a joint perspective. Specific research questions focus on the influence of exact procedures on determining execution modes and completion times, optimization of joint NPV, and the impact of solution techniques on payment distribution in project financing. The final chapter, Chapter 5, synthesizes the contributions, provides conclusions, and outlines potential future directions for academic investigations.

Citation

Please use this url to cite or link to this publication:

MLA
Yazdani, Majid. Exact Solution Methodologies for Time-Dependent Non-Linear Systems : The Financial Optimization Perspective. Ghent University. Faculty of Economics and Business Administration, 2024.
APA
Yazdani, M. (2024). Exact solution methodologies for time-dependent non-linear systems : the financial optimization perspective. Ghent University. Faculty of Economics and Business Administration, Ghent, Belgium.
Chicago author-date
Yazdani, Majid. 2024. “Exact Solution Methodologies for Time-Dependent Non-Linear Systems : The Financial Optimization Perspective.” Ghent, Belgium: Ghent University. Faculty of Economics and Business Administration.
Chicago author-date (all authors)
Yazdani, Majid. 2024. “Exact Solution Methodologies for Time-Dependent Non-Linear Systems : The Financial Optimization Perspective.” Ghent, Belgium: Ghent University. Faculty of Economics and Business Administration.
Vancouver
1.
Yazdani M. Exact solution methodologies for time-dependent non-linear systems : the financial optimization perspective. [Ghent, Belgium]: Ghent University. Faculty of Economics and Business Administration; 2024.
IEEE
[1]
M. Yazdani, “Exact solution methodologies for time-dependent non-linear systems : the financial optimization perspective,” Ghent University. Faculty of Economics and Business Administration, Ghent, Belgium, 2024.
@phdthesis{01HYAEWH0R0YB1PF6AAAAAN7WC,
  abstract     = {{In the realm of operations research, addressing time-dependent mixed integer nonlinear systems
- a subset of combinatorial optimization problems - presents a formidable challenge, given the
dynamic parameters and intricate inter-dependencies among its components (Du et al., 2019;
Krug, 2023; Li and Liao, 2020). This complexity becomes particularly evident in scenarios related to combinatorial optimization, such as supply chain management and scheduling challenges,
where discrete variables must be optimized while adhering to time-dependent constraints, failure to do so can result in a substantial impact on the overall system cost. To confront these
challenges effectively, it is crucial to employ combinatorial approaches that encompass decomposition strategies and approximation techniques (F ̈ullner and Rebennack, 2022; Nowak et al.,
2019). When addressing Mixed Integer Nonlinear Programming (MINLP) problems, researchers
categorize solution methodologies into single-tree and multitree methods, with multitree and hybrid approaches demonstrating superior effectiveness, particularly for convex MINLPs (Belotti
et al., 2013). However, non-convex MINLPs, characterized by non-convex functions, necessitate
specialized strategies such as piecewise linear approximations, convex relaxations, spatial branch-and-bound, quadratic reformulations, and methods leveraging non-convex structures. These di-
verse approaches collectively provide robust solutions to the complexities inherent in non-convex
MINLPs, highlighting the crucial need for the utilization of the latter set of techniques.
This thesis focuses on some of these specific methods - such as Benders decomposition (BD), a
tool for managing large-scale systems, and approximation techniques simplifying complex sys-
tems (Kuchlbauer et al., 2022; Rahmaniani et al., 2017). These methods, chosen for their ef-
ficacy, address challenges in two distinct problem areas. In subsequent sections, we delve into
these methods, discussing their applications and examining real-world scenarios involving two
applications of time-dependent nonlinear systems to derive practical insights for decision-making.
The first application explores multi-echelon inventory-transportation systems in maritime supply
chains. It optimizes shipment planning and safety stock placement, considering stochastic demand and transportation times. The research delves into the intricacies of optimizing variables
like shipment volumes, origin points, delivery speeds, and safety stock quotas. By integrating innovative practices and analytical insights, the study aims to enhance decision-making efficiency
in maritime supply chain planning. The second application focuses on the discrete time/cost
trade-off problem with discounted cash flows in project scheduling. It introduces an adapted
model for joint optimization of project completion time and profitability. The study employs the
Generalized Benders Decomposition (GBD) technique to address computational complexity and
presents an innovative Constraint Programming approach. The goal is to provide practical recommendations for project managers in various industries, optimizing decision-making in project
scheduling.
This dissertation categorizes its two primary applications into three distinct research streams.
The first stream focuses on developing exact solution procedures for optimizing shipment planning and safety stock placement in maritime supply chains confronted with stochastic demand
and variable transportation times. The second stream delves into the application of exact de-
composition techniques to address the deadline-constrained discrete time/cost trade-off problem,
considering discounted cash flows. The third stream centers on the development of exact solution procedures for project payment scheduling, emphasizing a joint perspective for optimizing
financing cost distribution.
Chapter 2 focuses on maritime supply chain planning, addressing specific research questions
related to integrating multi-product and multi-mode transportation optimization, optimizing
safety stock placement, and understanding the impact of time and cost parameters on decision making. Chapter 3 tackles the discrete time/cost trade-off problem in project scheduling,
adapting models to real-world payment systems and project deadlines. It explores the benefits
of integrating project network representation, payment systems, and deadlines, employing GBD.
Chapter 4 enhances the model introduced in Chapter 3 by providing a comprehensive analysis
of the DTCTP-NPV problem from a joint perspective. Specific research questions focus on the
influence of exact procedures on determining execution modes and completion times, optimization
of joint NPV, and the impact of solution techniques on payment distribution in project financing.
The final chapter, Chapter 5, synthesizes the contributions, provides conclusions, and outlines
potential future directions for academic investigations.}},
  author       = {{Yazdani, Majid}},
  language     = {{eng}},
  pages        = {{XXVIII, 217}},
  publisher    = {{Ghent University. Faculty of Economics and Business Administration}},
  school       = {{Ghent University}},
  title        = {{Exact solution methodologies for time-dependent non-linear systems : the financial optimization perspective}},
  year         = {{2024}},
}