Article
Management
Xin Chen, Menglong Li
Summary: This paper proposes a new concept of S-convex functions and examines its applications in economics and operations models. The study establishes the fundamental properties and characterizations of S-convex functions, and applies them to analyze substitute structures and optimal solutions in various scenarios.
OPERATIONS RESEARCH
(2022)
Article
Engineering, Manufacturing
Florian Taube, Stefan Minner
Summary: We examine a single-item inventory model with stochastic demand and periodic review. Fixed order costs are K in the regular order period occurring every m periods, while higher fixed order costs of L>K apply in the intraperiods. Previous research on optimal inventory policies did not consider these time-dependent fixed order costs. By extending current proofs for optimal inventory policies, we fill this gap in inventory theory. The optimal policy is complex in the regular order period, while a period-dependent (s,S) policy is optimal in the intraperiods. We describe and prove this optimal policy based on the concept of K-convexity and the behavior of non-K-convex cost functions.
PRODUCTION AND OPERATIONS MANAGEMENT
(2023)
Article
Automation & Control Systems
Constantin Christof, Gerd Wachsmuth
Summary: We prove the Newton differentiability of solution operators for elliptic obstacle-type variational inequalities, which can be considered as maps between suitable Lebesgue spaces and equipped with the strong-weak Bouligand differential as a generalized set-valued derivative. By utilizing this Newton differentiability, we are able to solve optimal control problems with H1-cost terms and one-sided pointwise control constraints using a semismooth Newton method. The algorithm exhibits superlinear convergence in the infinite-dimensional setting and its mesh independence is demonstrated in numerical experiments. Our findings are expected to provide insights for the design of numerical solution procedures for quasi-variational inequalities and the optimal control of obstacle-type variational problems.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2023)
Article
Environmental Sciences
Yafei Zu, Deqiang Deng, Lianghua Chen
Summary: This paper studies the optimal strategies for reducing product carbon emissions under different contracts, finding that the consignment contract can achieve a Pareto improvement for the entire supply chain, with varying impacts on the retailer and the manufacturer.
ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH
(2021)
Article
Management
Nicky D. Van Foreest, Onur A. Kilic
Summary: In this research note, it is shown that applying Breiman's work from 1964 on optimal stopping can lead to an elementary proof of the fact that (s, S) policies minimize the long-run average cost for periodic-review inventory control problems. The proof method is appealing as it only relies on basic concepts of renewal-reward processes, optimal stopping, dynamic programming, and root-finding. Furthermore, it provides an efficient algorithm for computing the optimal policy parameters. If Breiman's paper had received the attention it deserved, computational methods for (s, S)-policies could have been discovered about three decades earlier than the famous algorithm by Zheng and Federgruen (1991).
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2023)
Article
Energy & Fuels
Pedro Nel Ovalle, Jose Vuelvas, Arturo Fajardo, Carlos Adrian Correa-Florez, Fredy Ruiz
Summary: This paper presents a methodology for determining the optimal portfolio allocation for a demand response aggregator based on Day-Ahead electricity prices. By analyzing four types of contracts, it compares different scenarios for contract portfolios to establish the benefits of each market agent. The developed methodology helps in characterizing consumer behavior, forecasting their responses to incentives, and evaluating the impact of control contracts on the aggregator's performance.
Article
Automation & Control Systems
Bohao Zhu, James Lam, Masaki Ogura
Summary: This paper investigates the finite-time optimal control problems for positive linear systems with a time-varying control input. The optimization problem with piecewise-constant matrix functions is proven to be log-log convex and can be solved via geometric programming. The log-log convex result is further extended to the optimization problem with continuous functions. An optimal control problem is investigated to verify the effectiveness of the proposed optimization framework.
Article
Management
Yi Wang, Li Xiao, Xing-Gang Luo
Summary: This study derives the optimal solution for a distributionally robust multi-product newsvendor problem, showing the relationship between capacity threshold values and product priority, and conducts sensitivity analysis.
JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY
(2022)
Article
Computer Science, Artificial Intelligence
S. D. Agashe, B. K. Lande, Vanita Jain, Gopal Chaudhary, Fadi Al-turjman
Summary: This paper proposes a new method for computing the optimal control, which steers the initial state of a system to a specified or unspecified point in the state space by minimizing a given performance index. The classical Calculus of Variations and the modern approach of variation in control that leads to Pontriagin's principle are compared. By deriving the maximum principle of Pontriagin using the classical Calculus of Variations modified with brief perturbation, an expression for the change in the value of performance index is obtained. Three examples are provided to demonstrate the feasibility of the derived methods.
Article
Acoustics
Zahra Nikooeinejad, Mohammad Heydari
Summary: The collocation method is a powerful and effective technique for solving nonlinear differential equations. This paper presents a collocation method based on the shifted fractional-order Legendre functions and applies it to solve linear and nonlinear Hamilton-Jacobi-Bellman partial differential equations in stochastic optimal control problems.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Automation & Control Systems
Franco Blanchini, Paolo Bolzern, Patrizio Colaneri, Giuseppe De Nicolao, Giulia Giordano
Summary: We present a control problem for positive compartmental systems and solve the Pontryagin equations without trial and error. The solution is binary and the switching times are easily determined. We derive an analytic cost-to-go-function by solving a simple nonlinear differential equation. In the case of an infinite horizon, we show that the HJB equation can be exactly solved, with the optimal solution being constant and the cost-to-go function being linear and copositive. We propose an iterative scheme to solve this equation and provide examples related to flood control and epidemiology.
Article
Computer Science, Information Systems
Gang Zhao, Hui He, Bingbing Di, Jie Chu
Summary: Electronic portfolios are crucial for evaluating student performance, but traditional systems cannot ensure information safety and meet access control requirements. We propose StuChain, an efficient blockchain-based platform, which integrates a hybrid access control approach to solve these issues.
MULTIMEDIA TOOLS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Dario Pighin
Summary: This article provides a counterexample to the uniqueness of global minimizers in semilinear optimal control problems. The lack of uniqueness is shown to occur for a specific selection of the state-target in the cost functional. Furthermore, it is demonstrated that there exist local minimizers which are not global for certain state-targets, potentially trapping gradient-type algorithms and missing global minimizers. The convexity of a quadratic functional in optimal control is also analyzed in an abstract setting. As a consequence of nonuniqueness, a result of nonuniqueness for a coupled elliptic system is deduced. Numerical simulations are conducted to illustrate the theoretical results. The potential impact of the multiplicity of minimizers on the turnpike property in long time horizons is also discussed.
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
(2023)
Article
Automation & Control Systems
Yuanhua Wang, Peilian Guo
Summary: This paper investigates the optimal control problem for a class of Boolean control networks, providing necessary and sufficient conditions for the solvability of SBCNs and presenting an effective algorithm to design an optimal control sequence using the controllability matrix of normalized Boolean control networks.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Mathematics
Tomasz Lukowski, Matteo Parisi, Lauren K. Williams
Summary: This paper studies the image of the positive Grassmannian and its positroid cells under two different tilde maps. It defines positroid dissections and conjectures a bijection between positroid dissections of the hypersimplex and positroid dissections of the amplituhedron. It also proves properties of the positive tropical Grassmannian and positroid polytopes.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2023)
Article
Engineering, Manufacturing
Xin Chen, Menglong Li
Summary: Discrete convexity, particularly L-convexity and M-convexity, offers a critical approach for solving classical problems in inventory theory and has gained popularity in the literature. Its significance is demonstrated through various applications such as network flow problems, stochastic inventory control, and appointment scheduling. This method helps provide new insights and simplify analyses for existing problems in the literature.
PRODUCTION AND OPERATIONS MANAGEMENT
(2021)
Article
Management
Xin Chen, Menglong Li
Summary: This paper proposes a new concept of S-convex functions and examines its applications in economics and operations models. The study establishes the fundamental properties and characterizations of S-convex functions, and applies them to analyze substitute structures and optimal solutions in various scenarios.
OPERATIONS RESEARCH
(2022)
Article
Management
Xingyu Bai, Xin Chen, Menglong Li, Alexander Stolyar
Summary: This paper investigates the decoupling of delayed action from the current state in a generic Markov decision process (MDP) through the establishment of asymptotic optimality of semi-open-loop policies. It shows that under certain conditions, these policies are asymptotically optimal as the lead time goes to infinity. The research covers MDPs defined on general spaces with uniformly bounded cost functions and fast mixing property, as well as MDPs defined on Euclidean spaces with linear dynamics and convex structures.
OPERATIONS RESEARCH
(2023)
Article
Management
Xingyu Bai, Xin Chen, Menglong Li, Alexander Stolyar
Summary: This paper investigates the decoupling of delayed actions from the current state in a generic Markov decision process (MDP) with two controls. It establishes the asymptotic optimality of semi-open-loop policies, where open-loop controls are specified for delayed actions and closed-loop controls are specified for immediate actions. The paper constructs periodic semi-open-loop policies and shows their asymptotic optimality as the lead time goes to infinity. It also imposes conditions for Euclidean MDPs with linear dynamics and convex structures, and verifies the asymptotic optimality of semi-open-loop policies in these conditions.
OPERATIONS RESEARCH
(2023)
