Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order

An evaluation of the economic cost impacts of classical forecast errors

Evidence from literature suggests that there is no shortage of studies concerned with the supply chain risk management and the associated performance by the individual echelons and functional business areas or through coordinated efforts. Literature has also demonstrated strong association between the performance of supply chain inventory management and control policies and profitability. Thus, integration of operational policies with financial decisions has been seen as an avenue to improve and to better corporate strategic financial objectives in supply chain sector organisations through optimal inventory investment. This is quite important since measures to improve financial performance implicitly influence and restrict operational performance including the management of inventory. However, on the modelling of inventory and finance and in measuring the impact of one on the other, traditional approaches tend to think of one as the input into the other without due consideration for the interconnections between the two over time. In particular, the traditional inventory cost model appears to present a disconnect between operational choices and financial decisions. This thesis models both and their interconnections explicitly and simultaneously. Supposing a periodic review inventory policy with finite horizon and single perishable product, this study proposes a simple easy to understand solution. Specifically, in evaluating the economic consequences of classical forecast error metrics on inventory control system, study improves the current approach by creating a versatile consolidative costs evaluation function that aligns both operational and financial decisions as well as captures the business contextual considerations. The research study results revealed that we can easily utilise the proposed robust costs structure at the right scale (of demand uncertainty) and in the right scope (of financial capacity) to reveal the real and correct cost effects that facilitates users to produce practically feasible plans for their businesses

On the Applications of Stochastic Dual Dynamic Programming

Multistage stochastic programming (MSP) problems belong to a class of problems that involve a sequence of decisions made over multiple time stages under uncertainty. Many real-world problems can be effectively represented using MSPs. However, MSPs pose challenges in optimization due to their inherent difficulty and complexity. In the literature, Stochastic Dual Dynamic Programming (SDDP) has emerged as a powerful and versatile methodology for solving MSPs. This thesis showcases the applications of SDDP in handling sequential decision-making under uncertainty across various domains. We begin with a comprehensive introduction to MSPs, exploring their practical applications and various solution approaches. Additionally, we trace the historical development of SDDP from Benders' Decomposition to its modern enhancements. In Chapter \ref{chap:paper1}, we conduct a comprehensive survey of the diverse applications of SDDP in the literature. This includes an analysis of statistics on the prevalence of SDDP usage in various domains. Moreover, a substantial focus is placed the most common application of SDDP in the energy sector, particularly in hydro-thermal power production scheduling. The chapter outlines compelling arguments for the prominence of this specific application. Chapter \ref{chap:paper2} introduces two valuable contributions: $\mathsf{MSPLib}$, an open-source library of problems and $\mathsf{MSPFormat}$, a standardized data format designed for benchmarking SDDP. $\mathsf{MSPLib}$ aims to facilitate the evaluation of computational performance among different SDDP implementations. It offers a wide array of instances, from real-world problems to synthetic variations with varying complexities. By incorporating $\mathsf{MSPFormat}$ into the library, a unified and consistent representation of MSPs is provided, further enhancing their usability and transferability. In Chapter \ref{chap:paper3}, we showcase an MSP application to the optimal location of COVID-19 vaccine facilities under the threat of natural disasters. We introduce a new algorithm, named \textit{shadow price approximation} (SPA), which aims at approximating the shadow price of opening flood-prone vaccine facilities by tuning the parameters of a linear value function approximation which is present in the objective function of base optimization model. We also compare the performance of SPA against stochastic dual dynamic integer programming (SDDiP). The chapter closes with a detailed account of this model's application in two cities of a developing country. Moving on to Chapter \ref{chap:paper4}, we introduce a novel problem class named the multistage stochastic facility location problem under facility disruption uncertainty (MSFLPD). This new class extends the classical stochastic \textit{capacitated} facility location problem to handle uncertainty arising from facility disruptions. We then present and compare two solution algorithms tailored for addressing this problem: stochastic dual dynamic integer programming (SDDiP) and shadow price approximation (SPA)

Operational research:methods and applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order