scholarly journals Bi-objective facility location under uncertainty with an application in last-mile disaster relief

2021 ◽  
Author(s):  
Najmesadat Nazemi ◽  
Sophie N. Parragh ◽  
Walter J. Gutjahr
Keyword(s):  
Real World ◽  
Value At Risk ◽  
Demand Uncertainty ◽  
Disaster Relief ◽  
Pareto Frontier ◽  
Data Uncertainty ◽  
Conditional Value At Risk ◽  
Two Stage ◽  
Last Mile ◽  
Conflicting Objectives

AbstractMultiple and usually conflicting objectives subject to data uncertainty are main features in many real-world problems. Consequently, in practice, decision-makers need to understand the trade-off between the objectives, considering different levels of uncertainty in order to choose a suitable solution. In this paper, we consider a two-stage bi-objective single source capacitated model as a base formulation for designing a last-mile network in disaster relief where one of the objectives is subject to demand uncertainty. We analyze scenario-based two-stage risk-neutral stochastic programming, adaptive (two-stage) robust optimization, and a two-stage risk-averse stochastic approach using conditional value-at-risk (CVaR). To cope with the bi-objective nature of the problem, we embed these concepts into two criterion space search frameworks, the $$\epsilon $$ ϵ -constraint method and the balanced box method, to determine the Pareto frontier. Additionally, a matheuristic technique is developed to obtain high-quality approximations of the Pareto frontier for large-size instances. In an extensive computational experiment, we evaluate and compare the performance of the applied approaches based on real-world data from a Thies drought case, Senegal.

scholarly journals Convex approximations for two-stage mixed-integer mean-risk recourse models with conditional value-at-risk

2019 ◽  
Vol 181 (2) ◽  
pp. 473-507 ◽  
Author(s):  
E. Ruben van Beesten ◽  
Ward Romeijnders
Keyword(s):  
At Risk ◽  
Error Bounds ◽  
Value At Risk ◽  
Risk Measure ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Two Stage ◽  
Special Cases ◽  
Integer Recourse ◽  
Mean Risk

Abstract In traditional two-stage mixed-integer recourse models, the expected value of the total costs is minimized. In order to address risk-averse attitudes of decision makers, we consider a weighted mean-risk objective instead. Conditional value-at-risk is used as our risk measure. Integrality conditions on decision variables make the model non-convex and hence, hard to solve. To tackle this problem, we derive convex approximation models and corresponding error bounds, that depend on the total variations of the density functions of the random right-hand side variables in the model. We show that the error bounds converge to zero if these total variations go to zero. In addition, for the special cases of totally unimodular and simple integer recourse models we derive sharper error bounds.

scholarly journals A Two-Stage Optimal Dispatching Model for Micro Energy Grid Considering the Dual Goals of Economy and Environmental Protection under CVaR

2021 ◽  
Vol 13 (18) ◽  
pp. 10173
Author(s):  
Jun Dong ◽  
Yaoyu Zhang ◽  
Yuanyuan Wang ◽  
Yao Liu
Keyword(s):  
Renewable Energy ◽  
Environmental Protection ◽  
Value At Risk ◽  
Operating Cost ◽  
Optimal Scheduling ◽  
Pollutant Emission ◽  
Conditional Value At Risk ◽  
Two Stage ◽  
Environmental Objectives ◽  
Energy Grid

With the development of distributed renewable energy, a micro-energy grid (MEG) is an important way to solve the problem of energy supply in the future. A two-stage optimal scheduling model considering economy and environmental protection is proposed to solve the problem of optimal scheduling of micro-energy grid with high proportion of renewable energy system (RES) and multiple energy storage systems (ESS), in which the risk is measured by conditional value-at-risk (CVaR). The results show that (a) this model can realize the optimal power of various energy equipment, promote the consumption of renewable energy, and the optimal operating cost of the system is 34873 USD. (b) The dispatch of generating units is different under different risk coefficients λ, which leads to different dispatch cost and risk cost, and the two costs cannot be optimal at the same time. The risk coefficient λ shall be determined according to the degree of risk preference of the decision-maker. (c) The proposed optimal model could balance economic objectives and environmental objectives, and rationally control its pollutant emission level while pursuing the minimum operation costs. Therefore, the proposed model can not only reduce the operation cost based on the consideration of system carbon emissions but also provide decision-makers with decision-making support by measuring the risk.

scholarly journals Two-Stage Robust Optimization Model for Uncertainty Investment Portfolio Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Dongqing Luan ◽  
Chuming Wang ◽  
Zhong Wu ◽  
Zhijie Xia
Keyword(s):  
Robust Optimization ◽  
Financial Management ◽  
Value At Risk ◽  
Optimization Theory ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Equal Weight ◽  
Investment Portfolio ◽  
Two Stage ◽  
Mip Model

Investment portfolio can provide investors with a more robust financial management plan, but the uncertainty of its parameters is a key factor affecting performance. This paper conducts research on investment portfolios and constructs a two-stage mixed integer programming (TS-MIP) model, which comprehensively considers the five dimensions of profit, diversity, skewness, information entropy, and conditional value at risk. But the deterministic TS-MIP model cannot cope with the uncertainty. Therefore, this paper constructs a two-stage robust optimization (TS-RO) model by introducing robust optimization theory. In case experiments, data crawler technology is used to obtain actual data from real websites, and a variety of methods are used to verify the effectiveness of the proposed model in dealing with uncertainty. The comparison of models found that, compared with the traditional equal weight model, the investment benefits of the TS-MIP model and the TS-RO model proposed have been improved. Among them, the Sharpe ratio, Sortino ratio, and Treynor ratio have the largest increase of 19.30%, 8.25%, and 7.34%, respectively.

scholarly journals Stochastic Final Pit Limits: An Efficient Frontier Analysis under Geological Uncertainty in the Open-Pit Mining Industry

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 100
Author(s):  
Enrique Jelvez ◽  
Nelson Morales ◽  
Julian M. Ortiz
Keyword(s):  
Value At Risk ◽  
Efficient Frontier ◽  
Limit Problem ◽  
Open Pit ◽  
Conditional Value At Risk ◽  
Open Pit Mining ◽  
Economic Losses ◽  
Geological Uncertainty ◽  
Frontier Analysis ◽  
Conflicting Objectives

In the context of planning the exploitation of an open-pit mine, the final pit limit problem consists of finding the volume to be extracted so that it maximizes the total profit of exploitation subject to overall slope angles to keep pit walls stable. To address this problem, the ore deposit is discretized as a block model, and efficient algorithms are used to find the optimal final pit. However, this methodology assumes a deterministic scenario, i.e., it does not consider that information, such as ore grades, is subject to several sources of uncertainty. This paper presents a model based on stochastic programming, seeking a balance between conflicting objectives: on the one hand, it maximizes the expected value of the open-pit mining business and simultaneously minimizes the risk of losses, measured as conditional value at risk, associated with the uncertainty in the estimation of the mineral content found in the deposit, which is characterized by a set of conditional simulations. This allows generating a set of optimal solutions in the expected return vs. risk space, forming the Pareto front or efficient frontier of final pit alternatives under geological uncertainty. In addition, some criteria are proposed that can be used by the decision maker of the mining company to choose which final pit best fits the return/risk trade off according to its objectives. This methodology was applied on a real case study, making a comparison with other proposals in the literature. The results show that our proposal better manages the relationship in controlling the risk of suffering economic losses without renouncing high expected profit.

scholarly journals Robust Production Planning in Fashion Apparel Industry under Demand Uncertainty via Conditional Value at Risk

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Abderrahim Ait-Alla ◽  
Michael Teucke ◽  
Michael Lütjen ◽  
Samaneh Beheshti-Kashi ◽  
Hamid Reza Karimi
Keyword(s):  
At Risk ◽  
Production Planning ◽  
Value At Risk ◽  
Demand Uncertainty ◽  
Proper Time ◽  
Risk Measure ◽  
Production Costs ◽  
Conditional Value At Risk ◽  
Fashion Apparel ◽  
Production Orders

This paper presents a mathematical model for robust production planning. The model helps fashion apparel suppliers in making decisions concerning allocation of production orders to different production plants characterized by different lead times and production costs, and in proper time scheduling and sequencing of these production orders. The model aims at optimizing these decisions concerning objectives of minimal production costs and minimal tardiness. It considers several factors such as the stochastic nature of customer demand, differences in production and transport costs and transport times between production plants in different regions. Finally, the model is applied to a case study. The results of numerical computations are presented. The implications of the model results on different fashion related product types and delivery strategies, as well as the model’s limitations and potentials for expansion, are discussed. Results indicate that the production planning model using conditional value at risk (CVaR) as the risk measure performs robustly and provides flexibility in decision analysis between different scenarios.

scholarly journals Optimal Coordinated Bidding of a Profit Maximizing, Risk-Averse EV Aggregator in Three-Settlement Markets Under Uncertainty

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1755 ◽  
Author(s):  
Yelena Vardanyan ◽  
Henrik Madsen
Keyword(s):  
Real Time ◽  
Value At Risk ◽  
Risk Measure ◽  
Convex Combination ◽  
Computation Time ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Two Stage ◽  
Mixed Integer Linear Program ◽  
Market Prices

This paper develops a two-stage stochastic and dynamically updated multi-period mixed integer linear program (SD-MILP) for optimal coordinated bidding of an electric vehicle (EV) aggregator to maximize its profit from participating in competitive day-ahead, intra-day and real-time markets. The hourly conditional value at risk (T-CVaR) is applied to model the risk of trading in different markets. The objective of two-stage SD-MILP is modeled as a convex combination of the expected profit and the T-CVaR hourly risk measure. When day-ahead, intra-day and real-time market prices and fleet mobility are uncertain, the proposed two-stage SD-MILP model yields optimal EV charging/discharging plans for day-ahead, intra-day and real-time markets at per device level. The degradation costs of EV batteries are precisely modeled. To reflect the continuous clearing nature of the intra-day and real-time markets, rolling planning is applied, which allows re-forecasting and re-dispatching. The proposed two-stage SD-MILP is used to derive a bidding curve of an aggregator managing 1000 EVs. Furthermore, the model statistics and computation time are recorded while simulating the developed algorithm with 5000 EVs.

Stochastic Last-Mile Delivery with Crowd-Shipping and Mobile Depots

2021 ◽  
Author(s):  
Kianoush Mousavi ◽  
Merve Bodur ◽  
Matthew J. Roorda
Keyword(s):  
Stochastic Model ◽  
Value At Risk ◽  
Deterministic Model ◽  
Computational Study ◽  
Branch And Cut ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Solution Algorithms ◽  
Last Mile ◽  
Last Mile Delivery

This paper proposes a two-tier last-mile delivery model that optimally selects mobile depot locations in advance of full information about the availability of crowd-shippers and then transfers packages to crowd-shippers for the final shipment to the customers. Uncertainty in crowd-shipper availability is incorporated by modeling the problem as a two-stage stochastic integer program. Enhanced decomposition solution algorithms including branch-and-cut and cut-and-project frameworks are developed. A risk-averse approach is compared against a risk-neutral approach by assessing conditional-value-at-risk. A detailed computational study based on the City of Toronto is conducted. The deterministic version of the model outperforms a capacitated vehicle routing problem on average by 20%. For the stochastic model, decomposition algorithms usually discover near-optimal solutions within two hours for instances up to a size of 30 mobile depot locations, 40 customers, and 120 crowd-shippers. The cut-and-project approach outperforms the branch-and-cut approach by up to 85% in the risk-averse setting in certain instances. The stochastic model provides solutions that are 3.35%–6.08% better than the deterministic model, and the improvements are magnified with increased uncertainty in crowd-shipper availability. A risk-averse approach leads the operator to send more mobile depots or postpone customer deliveries to reduce the risk of high penalties for nondelivery.

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