A New Two-Stage Stochastic Model for Reverse Logistics Network Design under Government Subsidy and Low-Carbon Emission Requirement

Embargoed Access, etter IEEEs generelle retningslinjer (manuscript version for OA after 24 mnths embargo from publication date) Link to publisher's version: http://doi.org/10.1109/IEEM.2017.8289857Nowadays, increasing number of companies incorporates the reverse logistics decisions into their supply chain design in order to cope with the enforced international and national legislation and improve the resource efficiency and public image. This paper investigates a new stochastic optimization model for designing a single-period multiproduct multi-level reverse logistics system under government subsidy and low-carbon emission requirement. In order to resolve the stochastic optimization problem, a modified multi-criteria scenario-based approach is proposed to maximize the profit generation while simultaneously improve the stability of the decision-making under uncertainty. The model and solution method are tested with several numerical experiments, and managerial insights are obtained with respect to the carbon emission requirement, governmental subsidy, economy of scale, and system flexibility

Two-Stage Stochastic Model to Invest in Distributed Generation Considering the Long-Term Uncertainties

yesThis paper used different risk management indicators applied to the investment optimization performed by consumers in Distributed Generation (DG). The objective function is the total cost incurred by the consumer including the energy and capacity payments, the savings, and the revenues from the installation of DG, alongside the operation and maintenance (O&M) and investment costs. Probability density function (PDF) was used to model the price volatility in the long-term. The mathematical model uses a two-stage stochastic approach: investment and operational stages. The investment decisions are included in the first stage and which do not change with the scenarios of the uncertainty. The operation variables are in the second stage and, therefore, take different values with every realization. Three risk indicators were used to assess the uncertainty risk: Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR), and Expected Value (EV). The results showed the importance of migration from deterministic models to stochastic ones and, most importantly, the understanding of the ramifications of every risk indicator

Two-stage Stochastic Model using Benders' Decomposition for Large-scale Energy Resources Management in Smart grids

The ever-increasing penetration level of renewable energy and electric vehicles may threaten power grid operation. Dealing with uncertainty in smart grids is critical in order to mitigate possible issues. This research work proposes a two-stage stochastic model for large-scale energy resources scheduling for aggregators. The proposed model is designed for aggregators managing a smart grid. The idea is to address the challenge brought by the variability of demand, renewable energy, electric vehicles, and market price variations while pursuing cost minimization. Benders’ decomposition approach is implemented to improve the tractability of the original model and its’ computational burden. A realistic case study is presented using a real distribution network in Portugal with high penetration of renewable energy and electric vehicles. The results show the effectiveness and efficiency of the proposed approach when compared with a deterministic formulation and suggest that demand response and storage systems can mitigate the uncertainty.info:eu-repo/semantics/acceptedVersio

Genetic algorithms for the scheduling of multiproduct batch plants within uncertain environment

This study addresses the problem of batch plant scheduling. In addition uncertainty on product demands is considered through probabilistic-based methods. In the resulting two-stage stochastic programming problem, the objective is to maximize an Expected Profit Value (EPV) while respecting a constraint forcing the makespan to be lower than a time horizon. A Genetic Algorithm (GA) is proposed for the solution of a multiproduct example. The variable encoding requires special attention. Computational tests are first carried out with a deterministic model to validate the GA efficiency. Then, different runs with different scenario sets highlight the existence of various solution classes, characterized by specific numbers of batches manufactured for each product. Further analysis finally enables to discuss if each schedule is really the best-fitted to the scenario set for which it has been determined

Solving Two-Stage Stochastic Steiner Tree Problems by Two-Stage Branch-and-Cut

We consider the Steiner tree problem under a two-stage stochastic model with recourse and finitely many scenarios. In this prob- lem, edges are purchased in the first stage when only probabilistic infor- mation on the set of terminals and the future edge costs is known. In the second stage, one of the given scenarios is realized and additional edges are puchased in order to interconnect the set of (now known) ter- minals. The goal is to decide on the set of edges to be purchased in the first stage while minimizing the overall expected cost of the solution. We provide a new semi-directed cut-set based integer programming formula- tion, which is stronger than the previously known undirected model. We suggest a two-stage branch-and-cut (B&C) approach in which L-shaped and integer-L-shaped cuts are generated. In our computational study we compare the performance of two variants of our algorithm with that of a B&C algorithm for the extensive form of the deterministic equiva- lent (EF). We show that, as the number of scenarios increases, the new approach significantly outperforms the (EF) approach

A production planning model considering uncertain demand using two-stage stochastic programming in a fresh vegetable supply chain context

Production planning models are achieving more interest for being used in the primary sector of the economy. The proposed model relies on the formulation of a location model representing a set of farms susceptible of being selected by a grocery shop brand to supply local fresh products under seasonal contracts. The main aim is to minimize overall procurement costs and meet future demand. This kind of problem is rather common in fresh vegetable supply chains where producers are located in proximity either to processing plants or retailers. The proposed two-stage stochastic model determines which suppliers should be selected for production contracts to ensure high quality products and minimal time from farm-to-table. Moreover, Lagrangian relaxation and parallel computing algorithms are proposed to solve these instances efficiently in a reasonable computational time. The results obtained show computational gains from our algorithmic proposals in front of the usage of plain CPLEX solver. Furthermore, the results ensure the competitive advantages of using the proposed model by purchase managers in the fresh vegetables industry.This work was supported by the MEyC under contracts TIN2011-28689-C02-02, TRA2013-48180-C3-P and TIN2014- 53234-C2-2-R. The authors are members of the research group 2014-SGR163 and 2014-SGR151, funded by the Generali- tat de Catalunya

Solving Stochastic Hydrothermal Unit Commitment with a New Primal RecoverycTechnique Based on Lagrangian Solutions

The high penetration of intermittent renewable generation has prompted the development of Stochastic Hydrothermal Unit Commitmentc(SHUC) models, which are more difficult to be solved than their thermal-basedccounterparts due to hydro generation constraints and inflow uncertainties.cThis work presents a SHUC model applied in centralized cost-based dispatch, where the uncertainty is related to the water availability in reservoirs and demand. The SHUC is represented by a two-stage stochastic model, formulated as a large-scale mixed-binary linear programming problem. The solution strategy is divided into two steps, performed sequentially, with intercalated iterations to find the optimal generation schedule. The first step is the Lagrangian Relaxation (LR) approach. The second step is given by a Primal Recovery based on LR solutions and a heuristic based on Benders' Decomposition. Both steps benefit from each other, exchanging information over the iterative process. We assess our approach in terms of the quality of the solutions and running times on space and scenario LR decompositions. The results show the advantage of our primal recovery technique compared to solving the problem via MILP solver. This is true already for the deterministic case, and the advantage grows as the problem’s size (number of plants and/or scenarios) does

A Two-Stage Approach for Routing Multiple Unmanned Aerial Vehicles with Stochastic Fuel Consumption

The past decade has seen a substantial increase in the use of small unmanned aerial vehicles (UAVs) in both civil and military applications. This article addresses an important aspect of refueling in the context of routing multiple small UAVs to complete a surveillance or data collection mission. Specifically, this article formulates a multiple-UAV routing problem with the refueling constraint of minimizing the overall fuel consumption for all of the vehicles as a two-stage stochastic optimization problem with uncertainty associated with the fuel consumption of each vehicle. The two-stage model allows for the application of sample average approximation (SAA). Although the SAA solution asymptotically converges to the optimal solution for the two-stage model, the SAA run time can be prohibitive for medium- and large-scale test instances. Hence, we develop a tabu-search-based heuristic that exploits the model structure while considering the uncertainty in fuel consumption. Extensive computational experiments corroborate the benefits of the two-stage model compared to a deterministic model and the effectiveness of the heuristic for obtaining high-quality solutions.Comment: 18 page