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With the gradual increase of commercial banks and the expansion of their branches, the demand for cash transportation inflates sharply, bringing opportunities to the business development of Cash-In-Transit (CIT) sectors. However, the branches are often distributed in densely populated areas where traffic jams occur from time to time, which poses a severe challenge to the route planning of CIT vehicles. In addition, risk factors need to be considered during the optimization process because the goods transported belong to valuables. In order to effectively deal with the routing problem of CIT sectors, this paper established a bi-objective model and a goal programming model of Risk-Constrained Multi Depot Vehicle Routing Problems (RCMDVRPs) using real-time traffic data. Based on the traditional genetic algorithm, a Hybrid Genetic Algorithm with Intensification procedures (HGAI) is proposed to solve the goal programming model by using a three-level linked list structure to express chromosomes visually. Then, a new Self-constrained Hybrid Genetic Algorithm (SHGA) is designed for the bi-objective model. Besides, an online path updating strategy is developed to guide remote vehicles against time-dependent traffic flows. Finally, the HGAI is performed on benchmark instances to verify its accuracy. Experimental results of performance test show that the algorithm can achieve a gap of about 3% compared with the Best Known Result (BKR). The results of a case study also show that the two models and the corresponding algorithms are feasible and can be used to solve large-scale problems according to the special preferences and goals of decision-makers. [ABSTRACT FROM AUTHOR]

Dynamic stochastic optimization models provide a powerful tool to represent sequential decision-making processes. Typically, these models use statistical predictive methods to capture the structure of the underlying stochastic process without taking into consideration estimation errors and model misspecification. In this context, we propose a data-driven prescriptive analytics framework aiming to integrate the machine learning and dynamic optimization machinery in a consistent and efficient way to build a bridge from data to decisions. The proposed framework tackles a relevant class of dynamic decision problems comprising many important practical applications. The basic building blocks of our proposed framework are: (1) a Hidden Markov Model as a predictive (machine learning) method to represent uncertainty; and (2) a distributionally robust dynamic optimization model as a prescriptive method that takes into account estimation errors associated with the predictive model and allows for control of the risk associated with decisions. Moreover, we present an evaluation framework to assess out-of-sample performance in rolling horizon schemes. A complete case study on dynamic asset allocation illustrates the proposed framework showing superior out-of-sample performance against selected benchmarks. The numerical results show the practical importance and applicability of the proposed framework since it extracts valuable information from data to obtain robustified decisions with an empirical certificate of out-of-sample performance evaluation. [ABSTRACT FROM AUTHOR]

Increasing the penetration of renewables on prosumers' side brings about operational challenges in the distribution grid due to their variable and uncertain behavior. In fact, these resources have increased the distribution grid net load fluctuation during recent years. In this article, the flexibility-oriented stochastic scheduling of a microgrid is suggested to capture the net load variability at the distribution grid level. In this scheduling, the flexibility limits are set to manage the net load fluctuation at a desirable level for the main grid operator. The uncertainties of load and renewables are considered, and their uncertainties are under control by the risk-averse strategy. Moreover, multiperiod islanding constraints are added to the problem, preparing the microgrid for a resilient response to disturbances. The model is examined on a typical distribution feeder consisting of prosumers and a microgrid. The numerical results are compared for both flexibility-oriented and traditional scheduling of a microgrid at the distribution level. The proposed model reduces the net load ramping of the distribution grid using an efficient dispatch of resources in the microgrid. A sensitivity analysis is also carried out to show the effectiveness of the model. [ABSTRACT FROM AUTHOR]

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In this paper, we search for optimal portfolio strategies in the presence of various risk measure that are common in financial applications. Particularly, we deal with the static optimization problem with respect to Value at Risk, Expected Loss and Expected Utility Loss measures. To do so, under the Black-Scholes model for the financial market, Martingale method is applied to give closed-form solutions for the optimal terminal wealths; then via representation problem the optimal portfolio strategies are achieved. We compare the performances of these measures on the terminal wealths and optimal strategies of such constrained investors. Finally, we present some numerical results to compare them in several respects to give light to further studies. [ABSTRACT FROM AUTHOR]

In order to research the new sub-synchronous oscillation (SSO) phenomenon caused by the wind power, first, this work studied the characteristics of the wind turbine in the frequency of the SSO, considering the characteristics of the wind controller simultaneously, and established the wind turbine and the power grid transmission model under the SSO propagation path. Then, the non-infinite equivalent model of the grid power model was proposed in order to change the strengthening degree. Third, a comprehensive evaluation index based on the oscillation energy was presented, and the capacity of the wind power from the frequency limit of the SSO was evaluated; meanwhile, the constraints of the SSO have been studied to maintain the stability of the power network. Finally, the rationality and effectiveness of the method were verified based on the IEEE 39-node model.

We consider, within a Markovian complete financial market, the problem of finding the least expensive portfolio process meeting, at each payment date, three different types of risk criterion. Two of them encompass an expected utility-based measure and a quantile hedging constraint imposed at inception on all the future payment dates, while the other one is a quantile hedging constraint set at each payment date over the next one. The quantile risk measures are defined with respect to a stochastic benchmark and the expected utility-based constraint is applied to random payment dates. We explicit the Legendre-Fenchel transform of the pricing function. We also provide, for each quantile hedging problem, a backward dual algorithm allowing to compute their associated value function by backward recursion. The algorithms are illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

In order to research the new sub-synchronous oscillation (SSO) phenomenon caused by the wind power, first, this work studied the characteristics of the wind turbine in the frequency of the SSO, considering the characteristics of the wind controller simultaneously, and established the wind turbine and the power grid transmission model under the SSO propagation path. Then, the non-infinite equivalent model of the grid power model was proposed in order to change the strengthening degree. Third, a comprehensive evaluation index based on the oscillation energy was presented, and the capacity of the wind power from the frequency limit of the SSO was evaluated; meanwhile, the constraints of the SSO have been studied to maintain the stability of the power network. Finally, the rationality and effectiveness of the method were verified based on the IEEE 39-node model. [ABSTRACT FROM AUTHOR]

This paper introduces various models for optimal and maximal utility-based distributed generation penetration in the radial distribution systems. Several problems with different probabilistic indices as objective functions constrained by power flow equations, distributed generation penetration, voltage, and thermal limits are proposed to obtain the optimal penetration of distributed generations on rural distribution networks. There are tradeoffs between interests and risks that the distribution network operators or distribution companies may be willing to take on. Thus, to have an effective method for maximal allocation of distributed generations, new indices are proposed, and the problems are formulated as a risk-constrained optimization model. The obtained problems have mixed-integer nonlinear programming and nonconvex forms because of nonlinearity and nonconvexity of the optimal power flow (OPF) equations and indices, leading to computationally nondeterministic polynomial-time-hard problems. Accordingly, in this paper, convex relaxations of OPF are introduced instead of the conventional nonlinear equations. Efficient linear equivalents of the objective function and constraints are introduced to reduce the computational burden. Test results of the proposed models on a radial distribution system are presented and discussed. [ABSTRACT FROM AUTHOR]

Recently, representations and methods aimed at analysing decision problems where probabilities and values (utilities) are associated with distributions over them (second-order representations) have been suggested. In this paper we present an approach to how imprecise information can be modelled by means of second-order distributions and how a risk evaluation process can be elaborated by integrating procedures for numerically imprecise probabilities and utilities. We discuss some shortcomings of the use of the principle of maximising the expected utility and of utility theory in general, and offer remedies by the introduction of supplementary decision rules based on a concept of risk constraints taking advantage of second-order distributions.

Optimization models have been widely used in the power industry to aid the decision-making process of scheduling and dispatching electric power generation resources, a process known as unit commitment (UC). Since UC’s birth, there have been two major waves of revolution on UC research and real life practice. The first wave has made mixed integer programming stand out from the early solution and modeling approaches for deterministic UC, such as priority list, dynamic programming, and Lagrangian relaxation. With the high penetration of renewable energy, increasing deregulation of the electricity industry, and growing demands on system reliability, the next wave is focused on transitioning from traditional deterministic approaches to stochastic optimization for unit commitment. Since the literature has grown rapidly in the past several years, this paper is to review the works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC. Relevant lines of future research are also discussed to help transform research advances into real-world applications. [ABSTRACT FROM PUBLISHER]

Recently, representations and methods aimed at analysing decision problems where probabilities and values (utilities) are associated with distributions over them (second-order representations) have been suggested. In this paper we present an approach to how imprecise information can be modelled by means of second-order distributions and how a risk evaluation process can be elaborated by integrating procedures for numerically imprecise probabilities and utilities. We discuss some shortcomings of the use of the principle of maximising the expected utility and of utility theory in general, and offer remedies by the introduction of supplementary decision rules based on a concept of risk constraints taking advantage of second-order distributions. [ABSTRACT FROM AUTHOR]

We consider an investor who wants to maximize expected utility of terminal wealth. Stock returns are modelled by a stochastic differential equation with non-constant coefficients. If the drift of the stock returns depends on some process independent of the driving Brownian motion, it may not be adapted to the filtration generated by the stock prices. In such a model with partial information, due to the non-constant drift, the position in the stocks varies between extreme long and short positions making these strategies very risky when trading on a daily basis. To reduce the corresponding shortfall risk, motivated by Cuoco, He and Issaenko [Operations Research, 2008, 56, pp. 358–368.] we impose a class of risk constraints on the strategy, computed on a short horizon, and then find the optimal policy in this class. This leads to much more stable strategies that can be computed for both classical drift models, a mean reverting Ornstein–Uhlenbeck process and a continuous-time Markov chain with finitely many states. The risk constraints also reduce the influence of certain parameters that may be difficult to estimate. We provide a sensitivity analysis for the trading strategy with respect to the model parameters in the constrained and unconstrained case. The results are applied to historical stock prices. [ABSTRACT FROM AUTHOR]

The stochastic nature of emergency service requests and the unavailability of emergency vehicles when requested to serve demands are critical issues in constructing valid models representing real life emergency medical service (EMS) systems. We consider an EMS system design problem with stochastic demand and locate the emergency response facilities and vehicles in order to ensure target levels of coverage, which are quantified using risk measures on random unmet demand. The target service levels for each demand site and also for the entire service area are specified. In order to increase the possibility of representing a wider range of risk preferences we develop two types of stochastic optimization models involving alternate risk measures. The first type of the model includes integrated chance constraints (ICCs ), whereas the second type incorporates ICCs and a stochastic dominance constraint. We develop solution methods for the proposed single-stage stochastic optimization problems and present extensive numerical results demonstrating their computational effectiveness. [ABSTRACT FROM AUTHOR]

We introduce a new preference relation in the space of random variables, which we call robust stochastic dominance. We consider stochastic optimization problems where risk-aversion is expressed by a robust stochastic dominance constraint. These are composite semi-infinite optimization problems with constraints on compositions of measures of risk and utility functions. We develop necessary and sufficient conditions of optimality for such optimization problems in the convex case. In the nonconvex case, we derive necessary conditions of optimality under additional smoothness assumptions of some mappings involved in the problem. [ABSTRACT FROM AUTHOR]

Technological innovation is identified as one of the most important factors to enhance competitiveness. Despite numerous studies on the enhancing competitiveness in business organization or at a national level, the main focus of previous research has been on innovation system strategic issues, management instrument development processes, assumptions of various general benefits for innovation implementation and national innovation systems benefits. However, the analysis of technological innovations has not been concentrated on financial issues relating them to risk and high uncertainty constraints existing in technology-related markets. The specificity of financial management under uncertain innovation development process still is a recent direction of academic research, though having wide applicability on conceptual and practical basis. This article presents a framework for integration of technological innovation financing sources and risk constraints to pursue a technology following strategy of the company. [ABSTRACT FROM AUTHOR]

We address a dynamic portfolio optimization problem where the expected utility from terminal wealth has to be maximized. The special feature of this paper is an additional constraint on the portfolio strategy modeling bounded shortfall risks, which are measured by value at risk or expected loss. Using a continuous-time model of a complete financial market and applying martingale methods, analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Finally, some numerical results are presented. [ABSTRACT FROM AUTHOR]

Empirical distributions are often claimed to be superior to parametric distributions, yet to also increase the computational complexity and are therefore hard to apply in portfolio optimization. In this paper, we approach the portfolio optimization problem under constraints on the portfolio’s Value at Risk and Expected Tail Loss, respectively, under empirical distributions for the Standard and Poor’s 100 stocks. We apply a heuristic optimization method which has been found to overcome the restrictions of traditional optimization techniques. Our results indicate that empirical distributions might turn into a Pandora’s Box: Though highly reliable for predicting the assets’ risks, employing these distributions in the optimization process might result in severe mis-estimations of the resulting portfolios’ actual risk. It is found that even a simple mean-variance approach can be superior despite its known specification errors. [ABSTRACT FROM AUTHOR]

This study presents an optimal power management for a microgrid (MG) in distribution market environment. The MG operator is able to have interactions with the distribution market operator (DMO) and adjacent MG (AMG) operator to supply its local loads. The DMO regulates the electricity market, and assigns the electricity price and power profile for the MG. The motivation behind the use of The DMO is that it works as an entity between MG and independent system operator (ISO) in order to guarantee a flexible operation by reducing power fluctuation and reduce the unintentional peak loads in low market price hours. The unused power capacity in AMG is used during the islanded hours through an additional interconnection point connected to the MG. Using this method reduces the need for installing new generation resources, which will be a practical and economical solution for MG developer. This MG which is able to provide power from distribution market and the AMG with two interconnection points is named dependent MG (DMG). A market-based stochastic model containing distribution market constraints and AC power flow formulations employs conditional value at risk (CVaR) methodology to capture the loads and wind uncertainties. The effectiveness of the presented model is evaluated on a 20 kV test system using different case studies. In this test system, the operator is the owner of all generation units. The numerical analysis explicate that presented model reduces the operation cost of DMG with the aim of responsive loads, unused power capacity, energy storage system (ESS) and power generation units. The market-based scheduling also provides operational flexibility for distribution system by adjusting flexibility limit of market constraints. It is also shown that changing risk preferences level changes the power generation pattern in ESS and causes a costly operation of resources in risk-averse strategy. The competence of this model is significant when the preventive maintenance (PM) program is carried out, and the DMG should rely on its flexible resources and AMG's available power capacity, which could reduce the load shedding. • Developing a market-based stochastic scheduling of dependent MG (DMG). • Considering the risk and distribution market constraints as well as uncertainties. • Considering the unused power capacity of adjacent MGs during the scheduling horizon. • Implementing the linearized AC power flow formulations in operation modeling. • Investigating the economic and flexibility roles of responsive loads, dispatchable units, and ESS. [ABSTRACT FROM AUTHOR]