Day-ahead energy and reserve dispatch problem under non-probabilistic uncertainty

The current energy transition and the underlying growth in variable and uncertain renewable-based energy generation challenge the proper operation of power systems. Classical probabilistic uncertainty models, e.g., stochastic programming or robust optimisation, have been used widely to solve problems such as the day-ahead energy and reserve dispatch problem to enhance the day-ahead decisions with a probabilistic insight of renewable energy generation in real-time. By doing so, the scheduling of the power system becomes, production and consumption of electric power, more reliable (i.e., more robust because of potential deviations) while minimising the social costs given potential balancing actions. Nevertheless, these classical models are not valid when the uncertainty is imprecise, meaning that the system operator may not rely on a unique distribution function to describe the uncertainty. Given the Distributionally Robust Optimisation method, our approach can be implemented for any non-probabilistic, e.g., interval models rather than only sets of distribution functions (ambiguity set of probability distributions). In this paper, the aim is to apply two advanced non-probabilistic uncertainty models: Interval and ϵ-contamination, where the imprecision and in-determinism in the uncertainty (uncertain parameters) are considered. We propose two kinds of theoretical solutions under two decision criteria—Maximinity and Maximality. For an illustration of our solutions, we apply our proposed approach to a case study inspired by the 24-node IEEE reliability test system

판매촉진을 도입한 수요 불확실성 재고관리 모형

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2020. 8. 문일경.As the globalization of markets accelerates competition among companies, sales promotion, which refers to short-term incentives promoting sales of products or services, plays a prominent role. Although there are various types of sales promotions, such as price reduction, buy-x-get-y-free, and trade-in program, the common purpose is to induce the purchase of customers by offering benefits. This successful strategy has caught the attention of researchers, including operations management and supply chain management. Thus, various studies have been conducted to examine strategies for ongoing operations and to demonstrate the effects of the sales promotion, which are based on the strategic level. However, research at the tactical or operational level has been conducted insufficiently. This dissertation examines the inventory models considering (i) markdown sale, (ii) buy one get one free (BOGO), and (iii) trade-in program. First, the newsvendor model is considered. By introducing the decision variable, which represents the start time of markdown sale, the retailer can obtain the optimal combination of the start time of a markdown sale and an order quantity. Under certain conditions in a decentralized system, however, the start time of a markdown sale where the retailer obtains the highest profit is the least profitable for the manufacturer. To avoid irrational ordering behavior by a retailer against a manufacturer, a revenue-sharing contract is proposed. Second, the mobile application, ``My Own Refrigerator'', is considered in the inventory model. It enables customers to store BOGO products in their virtual storage for later use. That is, customers can drop by the store to pick up the extra freebies in the future. The promotion involves a high degree of uncertainty regarding the revisiting date because customers who buy the product do not need to take both products on the day of purchase. To deal with this uncertainty, we propose a robust multiperiod inventory model by addressing the approximation of a multistage stochastic optimization model. Third, the trade-in program is considered. It is one of the sales promotions that companies collect used old-generation products from customers and provide them with new-generation products at a discount price. It also helps to acquire the additional products which are required for the refurbishment service. A multiperiod stochastic inventory model based on the closed-loop supply chain system is proposed by incorporating the trade-in program and refurbishment service simultaneously. The stochastic optimization model is approximated to the robust counterpart, which features a deterministic second-order cone program.시장의 세계화에 따른 기업 간의 경쟁이 가속화됨에 따라, 단기 인센티브를 통해 고객의 제품 또는 서비스 구매를 유도하는 판매촉진의 역할이 중요해졌다. 가격 인하, 행사상품 증정, 트레이드인프로그램과 같은 다양한 유형의 판매촉진 전략이 존재하지만, 공통된 주요 목적은 기업이 고객에게 혜택을 제공하여 고객의 수요를 증대시키는 것이다. 판매촉진의 성공적인 전략은 경영과학 또는 공급망관리 분야를 포함한 관련 학계의 관심을 이끌었다. 지속적인 운영을 위한 전략을 검토하고 전략적 수준 계획을 기반으로 하는 판매 촉진의 효과를 입증하기 위한 다양한 연구가 수행되었습니다. 하지만 운영 수준의 소매업체 입장에서의 연구는 미흡한 실정이다. 본 논문에서는 (i) 마크 다운 (ii) buy one get one free (BOGO), 및 (iii) 트레이드인프로그램을 고려한 재고관리모형을 다룬다. 먼저, 신문가판원 모형에 마크 다운 시작 시점을 나타내는 결정 변수를 도입하여 최적의 마크 다운 시작 시점과 주문량의 조합을 제공하는 모형을 제안한다. 분산 시스템의 특정 조건에서는 소매업자가 가장 높은 이익을 얻는 시점이 제조업자에게 낮은 수익성을 야기할 수 있다. 따라서 본 연구는 제조업자에 대한 소매업자의 비합리적 주문을 막기 위한 이익분배계약을 제안한다. 이익분배계약을 통한 중앙집권화 시스템은 분산 시스템에서 얻은 이익에 비해 소매업자와 제조업자의 이익을 향상시킴을 수치실험을 통해 확인하였다. 둘째, 모바일 어플리케이션 ``나만의 냉장고''를 고려한 재고모형을 고려한다. 이 앱을 통해 BOGO 행사제품을 구매한 고객은 증정품을 구매 당일 날 가져가지 않고 미래에 재방문하여 수령할 수 있는 혜택을 받는다. 하지만 소매업자 입장에서는 고객이 증정품을 언제 수령해 갈 지에 대한 불확실성이 존재하며 이는 기존의 재고관리 운영방식에는 한계점이 있음을 시사한다. 본 연구에서는 고객의 재방문에 대한 불확실성을 고려한 복수기간 추계계획 재고모형을 수립하며 이를 효율적으로 계산하기 위한 강건최적화 모형으로 근사화하였다. 셋째, 리퍼서비스와 트레이드인프로그램을 고려한 폐회로 공급망 시스템 기반의 복수기간 재고관리모형을 제안한다. 신세대 제품, 리퍼서비스 및 트레이드인프로그램에 대한 세 가지 유형의 불확실한 수요에 대한 상관관계를 반영함에 따라 복수기간 추계계획 재고모형이 수립된다. 복수기간 추계계획 재고모형의 계산이 어렵다는 한계를 극복하고자 강건최적화 모형으로 근사화하였다.Chapter 1 Introduction 1 1.1 Sales promotion 1 1.2 Inventory management 3 1.3 Research motivations 6 1.4 Research contents and contributions 8 1.5 Outline of the dissertation 10 Chapter 2 Optimal Start Time of a Markdown Sale Under a Two-Echelon Inventory System 11 2.1 Introduction and literature review 11 2.2 Problem description 17 2.3 Analysis of the decentralized system 21 2.3.1 Newsvendor model for a retailer 21 2.3.2 Solution procedure for an optimal combination of the start time of the markdown sale and the order quantity 25 2.3.3 Profi t function of a manufacturer 25 2.3.4 Numerical experiments of the decentralized system 27 2.4 Analysis of a centralized system 35 2.4.1 Revenue-sharing contract 35 2.4.2 Numerical experiments of the centralized system 38 2.5 Summary 40 2.5.1 Managerial insights 41 Chapter 3 Robust Multiperiod Inventory Model with a New Type of Buy One Get One Promotion: "My Own Refrigerator" 43 3.1 Introduction and literature review 43 3.2 Problem description 51 3.2.1 Demand modeling 52 3.2.2 Sequences of the ordering decision 54 3.3 Mathematical formulation of the IMMOR 56 3.3.1 Mathematical formulation of the IMMOR under the deterministic demand 58 3.3.2 Mathematical formulation of the IMMOR under the stochastic demand 58 3.3.3 Distributionally robust optimization approach for the IMMOR 60 3.4 Computational experiments 76 3.4.1 Experiment 1: tractability of the RIMMOR 77 3.4.2 Experiment 2: robustness of the RIMMOR 78 3.4.3 Experiment 3: e ect of duration of the expiry date under the different customers' revisiting propensities 78 3.5 Summary 83 3.5.1 Managerial insights 83 Chapter 4 Robust Multiperiod Inventory Model Considering Refurbishment Service and Trade-in Program 85 4.1 Introduction 85 4.2 Literature review 91 4.2.1 Effects of the trade-in program and strategic-level decisions for the trade-in program 91 4.2.2 Inventory or lot-sizing model in a closed-loop supply chain system 94 4.2.3 Distinctive features of this research 97 4.3 Problem description 100 4.3.1 Demand modeling 103 4.3.2 Decision of the inventory manager 105 4.4 Mathematical formulation 108 4.4.1 Mathematical formulation of the IMRSTIP under the deterministic demand model 108 4.4.2 Mathematical formulation of the IMRSTIP under the stochastic demand model 110 4.4.3 Distributionally robust optimization approach for the IMRSTIP 111 4.5 Computational experiments 125 4.5.1 Demand process 125 4.5.2 Experiment 1: tractability of the RIMRSTIP 128 4.5.3 Experiment 2: approximation error from the expected value given perfect information 129 4.5.4 Experiment 3: protection against realized uncertain factors 130 4.5.5 Experiment 4: di erences between modeling demands from VARMA and ARMA 131 4.5.6 Experiments 5 and 6: comparisons of backlogged refurbishment service with or without trade-in program 133 4.6 Summary 136 Chapter 5 Conclusions 138 5.1 Summary 138 5.2 Future research 140 Bibliography 142 Chapter A 160 A.1 160 A.2 163 A.3 163 A.4 164 A.5 165 A.6 166 Chapter B 168 B.1 168 B.2 171 B.3 172 Chapter C 174 C.1 174 C.2 174 국문초록 179Docto

Operational Decision Making under Uncertainty: Inferential, Sequential, and Adversarial Approaches

Modern security threats are characterized by a stochastic, dynamic, partially observable, and ambiguous operational environment. This dissertation addresses such complex security threats using operations research techniques for decision making under uncertainty in operations planning, analysis, and assessment. First, this research develops a new method for robust queue inference with partially observable, stochastic arrival and departure times, motivated by cybersecurity and terrorism applications. In the dynamic setting, this work develops a new variant of Markov decision processes and an algorithm for robust information collection in dynamic, partially observable and ambiguous environments, with an application to a cybersecurity detection problem. In the adversarial setting, this work presents a new application of counterfactual regret minimization and robust optimization to a multi-domain cyber and air defense problem in a partially observable environment

A Multiproduct Single-Period Inventory Management Problem under Variable Possibility Distributions

In multiproduct single-period inventory management problem (MSIMP), the optimal order quantity often depends on the distributions of uncertain parameters. However, the distribution information about uncertain parameters is usually partially available. To model this situation, a MSIMP is studied by credibilistic optimization method, where the uncertain demand and carbon emission are characterized by variable possibility distributions. First, the uncertain demand and carbon emission are characterized by generalized parametric interval-valued (PIV) fuzzy variables, and the analytical expressions about the mean values and second-order moments of selection variables are established. Taking second-order moment as a risk measure, a new credibilistic multiproduct single-period inventory management model is developed under mean-moment optimization criterion. Furthermore, the proposed model is converted to its equivalent deterministic model. Taking advantage of the structural characteristics of the deterministic model, a domain decomposition method is designed to find the optimal order quantities. Finally, a numerical example is provided to illustrate the efficiency of the proposed mean-moment credibilistic optimization method. The computational results demonstrate that a small perturbation of the possibility distribution can make the nominal optimal solution infeasible. In this case, the decision makers should employ the proposed credibilistic optimization method to find the optimal order quantities

Data-driven Approximation of Distributionally Robust Chance Constraints using Bayesian Credible Intervals

The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the distributionally robust chance constraint is satisfied with high probability. To incorporate available data and prior distribution knowledge, we construct ambiguity sets for the distributionally robust chance constraint using Bayesian credible intervals. We establish the congruent relationship between the ambiguity set in Bayesian distributionally robust chance constraints and the uncertainty set in a specific robust optimization. In contrast to most existent uncertainty set construction methods which are only applicable for particular settings, our approach provides a unified framework for constructing uncertainty sets under different marginal distribution assumptions, thus making it more flexible and widely applicable. Additionally, under the concavity assumption, our method provides strong finite sample probability guarantees for optimal solutions. The practicality and effectiveness of our approach are illustrated with numerical experiments on portfolio management and queuing system problems. Overall, our approach offers a promising solution to distributionally robust chance constrained problems and has potential applications in other fields

Integrated Planning in Hospitals: A Review

Efficient planning of scarce resources in hospitals is a challenging task for which a large variety of Operations Research and Management Science approaches have been developed since the 1950s. While efficient planning of single resources such as operating rooms, beds, or specific types of staff can already lead to enormous efficiency gains, integrated planning of several resources has been shown to hold even greater potential, and a large number of integrated planning approaches have been presented in the literature over the past decades. This paper provides the first literature review that focuses specifically on the Operations Research and Management Science literature related to integrated planning of different resources in hospitals. We collect the relevant literature and analyze it regarding different aspects such as uncertainty modeling and the use of real-life data. Several cross comparisons reveal interesting insights concerning, e.g., relations between the modeling and solution methods used and the practical implementation of the approaches developed. Moreover, we provide a high-level taxonomy for classifying different resource-focused integration approaches and point out gaps in the literature as well as promising directions for future research

Agribusiness supply chain risk management: A review of quantitative decision models

Supply chain risk management is a large and growing field of research. However, within this field, mathematical models for agricultural products have received relatively little attention. This is somewhat surprising as risk management is even more important for agricultural supply chains due to challenges associated with seasonality, supply spikes, long supply lead-times, and perishability. This paper carries out a thorough review of the relatively limited literature on quantitative risk management models for agricultural supply chains. Specifically, we identify robustness and resilience as two key techniques for managing risk. Since these terms are not used consistently in the literature, we propose clear definitions and metrics for these terms; we then use these definitions to classify the agricultural supply chain risk management literature. Implications are given for both practice and future research on agricultural supply chain risk management

A Bi-objective cap-and-trade model for minimising environmental impact in closed-loop supply chains

A Closed-Loop Supply Chain (CLSC) is a complex network with unique environmental features and attributes that requires specific managerial policies and strategies. Quantitative models can provide a solid basis for these policies and strategies. This study expands the work of Shoaeinaeini et al. (2021) on Green Supply Chain Management. We propose a bi-objective facility location, demand allocation, and pricing model for CLSC networks. The proposed model considers two conflicting objective functions: maximising profits and minimising emissions. We show consumer environmental awareness can predict the products’ rate of return and determine a more suitable price for new products and the acquisition price for used products. The cap-and-trade policy has been implemented at its fullest potential, allowing the trading of carbon quotas. Therefore, companies may decide to produce less to sell more quotas or vice-versa, effectively picking the most profitable option. The model is solved and tested with the commercial solver BARON. The model effectively shows the trade-off between generating profits and emission reduction. Companies are able to turn a profit while abiding by the government’s intention of reducing emissions. The comparison with a single-objective version of the model highlights that the concurrent optimisation of economic and environmental objectives yields better results. The acquisition price of used products is a value worthy of monitoring. The government should focus on policies to assist the reverse flow of used products

Parametric Distributionally Robust Optimisation Models for Resource and Inventory Planning Problems

Parametric probability distributions are commonly used for modelling uncertain demand and other random elements in stochastic optimisation models. However, when the distribution is not known exactly, it is more common that the distribution is either replaced by an empirical estimate or a non-parametric ambiguity set is built around this estimated distribution. In the latter case, we can then hedge against distributional ambiguity by optimising against the worst-case objective value over all distributions in the ambiguity set. This methodology is referred to as distributionally robust optimisation. When applying this approach, the ambiguity set necessarily contains non-parametric distributions. Therefore, applying this approach often means that any information about the true distribution’s parametric family is lost. This thesis introduces a novel framework for building and solving optimisation models under ambiguous parametric probability distributions. Instead of building an ambiguity set for the true distribution, we build an ambiguity set for its parameters. Every distribution considered by the model is then a member of the same parametric family as the true distribution. We reformulate the model using discretisation of the ambiguity set, which can result in a large, complex problem that is slow to solve. We first develop the parametric distributionally robust optimisation framework for a workforce planning problem under binomial demands. We then study a budgeted, multi-period new svendor model under Poisson and normal demands. In these first two cases, we develop fast heuristic cutting surface algorithms using theoretical properties of the cost function. Finally, we extend the framework into the dynamic decision making space via robust Markov decision processes. We develop a novel projectionbased bisection search algorithm that completely eliminates the need for discretisation of the ambiguity set. In each case, we perform extensive computational experiments to show that our algorithms offer significant reductions in run times with only negligible losses in solution quality