scholarly journals Decision Programming for Mixed-Integer Multi-Stage Optimization under Uncertainty

2021 ◽  
Author(s):  
Ahti Salo ◽  
Juho Andelmin ◽  
Fabricio Oliveira
Keyword(s):  
Optimization Under Uncertainty ◽  
Mixed Integer ◽  
Multi Stage

scholarly journals Risk-Averse Multi-Stage Stochastic Programming to Optimizing Vaccine Allocation and Treatment Logistics for Effective Epidemic Response

2021 ◽  
Author(s):  
Xuecheng Yin ◽  
Esra Buyuktahtakin
Keyword(s):  
Value At Risk ◽  
Virus Disease ◽  
Risk Measure ◽  
Adverse Outcomes ◽  
Mixed Integer ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Expected Number ◽  
Multi Stage ◽  
Stochastic Mixed Integer Programming

Existing compartmental-logistics models in epidemics control are limited in terms of optimizing the allocation of vaccines and treatment resources under a risk-averse objective. In this paper, we present a data-driven, mean-risk, multi-stage, stochastic epidemics-vaccination-logistics model that evaluates various disease growth scenarios under the Conditional Value-at-Risk (CVaR) risk measure to optimize the distribution of treatment centers, resources, and vaccines, while minimizing the total expected number of infections, deaths, and close contacts of infected people under a limited budget. We integrate a new ring vaccination compartment into a Susceptible-Infected-Treated-Recovered-Funeral-Burial epidemics-logistics model. Our formulation involves uncertainty both in the vaccine supply and the disease transmission rate. Here, we also consider the risk of experiencing scenarios that lead to adverse outcomes in terms of the number of infected and dead people due to the epidemic. Combining the risk-neutral objective with a risk measure allows for a trade-off between the weighted expected impact of the outbreak and the expected risks associated with experiencing extremely disastrous scenarios. We incorporate human mobility into the model and develop a new method to estimate the migration rate between each region when data on migration rates is not available. We apply our multi-stage stochastic mixed-integer programming model to the case of controlling the 2018-2020 Ebola Virus Disease (EVD) in the Democratic Republic of the Congo (DRC) using real data. Our results show that increasing the risk-aversion by emphasizing potentially disastrous outbreak scenarios reduces the expected risk related to adverse scenarios at the price of the increased expected number of infections and deaths over all possible scenarios. We also find that isolating and treating infected individuals are the most efficient ways to slow the transmission of the disease, while vaccination is supplementary to primary interventions on reducing the number of infections. Furthermore, our analysis indicates that vaccine acceptance rates affect the optimal vaccine allocation only at the initial stages of the vaccine rollout under a tight vaccine supply.

scholarly journals Bounds on risk-averse mixed-integer multi-stage stochastic programming problems with mean-CVaR

2018 ◽  
Vol 266 (2) ◽  
pp. 595-608 ◽  
Author(s):  
Ali İrfan Mahmutoğulları ◽  
Özlem Çavuş ◽  
M. Selim Aktürk
Keyword(s):  
Stochastic Programming ◽  
Mixed Integer ◽  
Risk Averse ◽  
Multi Stage

scholarly journals A multistage stochastic lot-sizing problem with cancellation and postponement under uncertain demands

2021 ◽  
Author(s):  
Carlos E Testuri ◽  
Héctor Cancela ◽  
Víctor M. Albornoz
Keyword(s):  
Information Structure ◽  
Lot Sizing ◽  
Valid Inequalities ◽  
Mixed Integer ◽  
Uncertain Demand ◽  
Programming Approach ◽  
Lead Times ◽  
Multi Stage ◽  
Lot Sizing Problem ◽  
Capacitated Lot Sizing

A multistage stochastic capacitated discrete procurement problem with lead times, cancellation and postponement is addressed.  The problem determines the procurement of a product under uncertain demand at minimal expected cost during a time horizon.  The supply of the product is made through the purchase of optional distinguishable orders of fixed size with delivery time.  Due to the unveiling of uncertainty over time it is possible to make cancellation and postponement corrective decisions on order procurement.  These decisions involve costs and times of implementation.  A model of the problem is formulated as an extension of a discrete capacitated lot-sizing problem under uncertain demand and lead times through a multi-stage stochastic mixed-integer linear programming approach.  Valid inequalities are generated, based on a conventional inequalities approach, to tighten the model formulation.  Experiments are performed for several problem instances with different uncertainty information structure.  Their results allow to conclude that the incorporation of a subset of the generated inequalities favor the model solution.

A Multi-Stage Optimization Approach for Energy Supply Systems With Discrete Design Decisions

2019 ◽  
Author(s):  
S. Bruche ◽  
G. Tsatsaronis
Keyword(s):  
Energy Supply ◽  
Original Problem ◽  
Superior Performance ◽  
Mixed Integer ◽  
Optimization Models ◽  
Optimization Approach ◽  
Energy Supply System ◽  
Multi Stage ◽  
Supply Systems ◽  
Energy Supply Systems

Abstract Mixed integer linear programming is frequently applied to identify promising design solutions of energy supply systems. However, application-relevant optimization models are often associated with complicating model features, e.g. numerous discrete design candidates or a large time horizon of the optimization. So, even state-of-the-art solvers may be confronted with major challenges to find satisfying solutions within reasonable time. In this paper a systematic multi-stage optimization approach is proposed that is intended to support the available algorithms in solving these complex problems. The basic idea of the approach is the distribution of the original problem into two major levels. On the first level, promising design candidates are generated using simplified optimization models. These simplifications are achieved through time series aggregation and the relaxation of operational binary variables. In the second stage, the objective values of the design candidates for the original problem are determined. The division of the problem into two stages leads to a significant reduction in required optimization time but simultaneously leads to an uncertainty regarding the quality of the found solution. Therefore, in a subsequent step, it is checked whether the objective value is within an acceptable distance from the theoretically best solution. If this is not the case, the first two steps are iteratively repeated. The proposed multi-stage approach is applied to the optimization of an energy supply system located in Germany. The results show a superior performance regarding required optimization time over conventional methods.

scholarly journals Multi-Stage Transmission Network Planning Considering Transmission Congestion in the Power Market

Energies ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4910
Author(s):  
Yixin Huang ◽  
Xinyi Liu ◽  
Zhi Zhang ◽  
Li Yang ◽  
Zhenzhi Lin ◽  
...  
Keyword(s):  
Power System ◽  
Transmission Lines ◽  
Network Planning ◽  
Power Market ◽  
Mixed Integer ◽  
Transmission Network ◽  
Planning Model ◽  
Transmission Congestion ◽  
Multi Stage ◽  
Transmission Network Planning

The uncertainty of generation and load increases in the transmission network in the power market. Considering the transmission congestion risk caused by various uncertainties of the transmission network, the optimal operation strategies of the transmission network under various operational scenarios are decided, aiming for the maximum of social benefit for the evaluation of the degree of scenario congestion. Then, a screening method for major congestion scenario is proposed based on the shadow price theory. With the goal of maximizing the difference between the social benefits and the investment and maintenance costs of transmission lines under major congestion scenarios, a multi-stage transmission network planning model based on major congestion scenarios is proposed to determine the configuration of transmission lines in each planning stage. In this paper, the multi-stage transmission network planning is a mixed integer linear programming problem. The DC power flow model and the commercial optimization software CPLEX are applied to solve the problem to obtain the planning scheme. The improved six-node Garver power system and the simplified 25-node power system of Zhejiang Province, China are used to verify the effectiveness of the proposed multi-stage planning model.

Heuristic Particle Swarm Optimization for Scheduling Chemical Flowshop with Limited Intermediate Product Storage

2014 ◽  
Vol 1037 ◽  
pp. 514-517
Author(s):  
Qi Tang ◽  
Xiao Ye Zhou ◽  
Jian Xun Tang
Keyword(s):  
Particle Swarm Optimization ◽  
Intermediate Product ◽  
Particle Swarm ◽  
Batch Scheduling ◽  
Mixed Integer ◽  
Swarm Optimization ◽  
Complicated Problem ◽  
Multi Stage ◽  
Better Than ◽  
Product Storage

This paper considers integration of batching and scheduling with features on batch scheduling such as multi-product facilities, multi-stage. For this complicated problem, we present a mixed integer model (EM) and Heuristic Particle Swarm Optimization (HPSO). We proposed Strategies to improve the HPSO. Computations show that both methods are efficient. In addition, HPSO are better than EM.

Multi-objective robust optimization for multi-stage-multi-product agile closed-loop supply chain under uncertainty in the context of circular economy

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Saeid Jafarzadeh Ghoushchi ◽  
Iman Hushyar ◽  
Kamyar Sabri-Laghaie
Keyword(s):  
Supply Chain ◽  
Robust Optimization ◽  
Circular Economy ◽  
Closed Loop ◽  
Mixed Integer ◽  
Closed Loop Supply Chain ◽  
Content Type ◽  
Multi Objective ◽  
Multi Stage ◽  
Proposed Model

PurposeA circular economy (CE) is an economic system that tries to eliminate waste and continually use resources. Due to growing environmental concerns, supply chain (SC) design should be based on the CE considerations. In addition, responding and satisfying customers are the challenges managers constantly encounter. This study aims to improve the design of an agile closed-loop supply chain (CLSC) from the CE point of view.Design/methodology/approachIn this research, a new multi-stage, multi-product and multi-period design of a CLSC network under uncertainty is proposed that aligns with the goals of CE and SC participants. Recycling of goods is an important part of the CLSC. Therefore, a multi-objective mixed-integer linear programming model (MILP) is proposed to formulate the problem. Besides, a robust counterpart of multi-objective MILP is offered based on robust optimization to cope with the uncertainty of parameters. Finally, the proposed model is solved using the e-constraint method.FindingsThe proposed model aims to provide the strategic choice of economic order to the suppliers and third-party logistic companies. The present study, which is carried out using a numerical example and sensitivity analysis, provides a robust model and solution methodology that are effective and applicable in CE-related problems.Practical implicationsThis study shows how all upstream and downstream units of the SC network must work integrated to meet customer needs considering the CE context.Originality/valueThe main goal of the CE is to optimize resources, reduce the use of raw materials, and revitalize waste by recycling. In this study, a comprehensive model that can consider both SC design and CE necessities is developed that considers all SC participants.

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