Robust optimization and mixed-integer linear programming model for LNG supply chain planning problem

The robust Mixed-Integer Linear Programming (MILP) model is an approach to address uncertainty in linear optimization involving integer and continuous variables, which can be solved using the Benders Decomposition method. One of its applications is facility location problems, which often face demand, costs, and capacity uncertainties. This article presents a systematic literature review (SLR) on solving robust MILP models using the Benders Decomposition method and its application to facility location problems. The objectives are to explore the state-of-the-art and research trends, identify issues modeled as robust MILP and solved using Benders Decomposition, and determine the most frequently used uncertainty sets. SLR was conducted using the Preferred Reporting Items for Systematic Review and Meta-Analysis (PRISMA) method on the Scopus, Science Direct, and Dimensions databases for the last five years of publication, with bibliometric analysis using VOSviewer and RStudio. The results show that there are limited articles that discuss the solution of the robust MILP model on the problem of facility location with the ellipsoidal uncertainty set. In addition, the Benders Decomposition method is widely used to solve robust MILP problems in energy, logistics, supply chains, and scheduling, with interval uncertainty sets being the most common. This topic is an influential theme and has the potential to be explored further.

The various robust linear programming models investigated so far in the literature essentially appear to be based either on what is referred to as rowwise uncertainty models or on columnwise uncertainty models (these basically assume that the rows, or the columns, of the constraint matrix are subject to changes within a well-specified uncertainty set). In this chapter, we discuss a special case of columnwise uncertainty, namely the subclass of robust linear programming (LP) models with uncertainty limited to the right hand side (RHS) only (this subclass does not appear to have been significantly investigated so far). In this context we introduce the concept of a ‘two-stage robust LP model’ as opposed to the standard case (which might be referred to as a ‘single-stage robust LP model’) and we address the question of whether LP duality can be used to convert a LP problem with RHS uncertainty into a robust LP problem with uncertainty on the objective function. We show how to derive both statements of (a) the dual to the robust model and (b) the robust version of the dual. The resulting expressions of the objective function to be optimized in both cases, appear to be clearly distinct. Moreover, from a complexity point of view, one appears to be efficiently solvable (it reduces to a convex optimization problem), whereas the other, as a nonconvex optimization problem, is expected to be computationally difficult in the general case. As an application of the two-stage robust LP model introduced here, we next investigate the PERT (program evaluation and review technique) scheduling problem, considering two possible natural ways of specifying the uncertainty set for the task durations: the case where the uncertainty set is a scaled ball with respect to the L ∞ norm; the case where the uncertainty set is a scaled Hamming ball of bounded radius (which, though leading to a quite different model, bears some resemblance to the well-known Bertsimas–Sim approach to robustness). We show that in both cases the resulting robust optimization problem can be efficiently solved in polynomial time.

In order to overcome the drawback of the conventional signal timing optimization, a robust optimization algorithm for signal control parameters based on Tabu search-artificial bee colony algorithm is proposed under unsaturated flow condition. Based on the analysis of the characteristics of traffic signal control, a robust optimization model of signal control parameters is constructed by considering the minimum the average delay and the mean square error of average delay. As a consequence, the formation process of the initial solution to the bee colony is improved and the robust optimization model is solved by using the Tabu search-artificial bee colony algorithm. The proposed robust optimization model is validated by using an intersection in Zhangye City of China. The simulation results have shown that the robust optimization model and the algorithm are feasible and practicable. This robust model and algorithm can effectively deal with the volatility of traffic flow and reduce traffic delays.

Comparison of variant robust SCUC models for operational security and economics of power systems under uncertainty

Dynamic supply chain network design for the supply of blood in disasters: A robust model with real world application

A robust optimization framework for energy management of CCHP users with integrated demand response in electricity market

Managing the limited resources of money, time and space poses a real problem in the livestock business in general and the poultry sector in particular. The stochastic linear programming with recourse will permit the formulation of a mathematical model that could easily be solved in order to attain the objective of maximizing profit but this will be hindered by the presence of some parameters like demand and supply which have no predetermined probability distributions. In an attempt to address the problem of unavailable probability distribution functions, this research is aimed at proposing a robust linear programming model which can handle problems and others in similar circumstances with the need of probability distributions.The robust model thus constructed is based on a modification of the stochastic model by Soyster. An application of this model on a real life data produced results showing an increase in profit made by a local poultry farmer from 241,485 FCFA to 362,580FCFA representing an increase in profit of more than 50% in over that obtained when using the ordinary Linear Programming Technique. The belief therefore is that, if models like this are implemented, not only would the livelihood of the poultry farmers be improved, but it will go a long way to better the economy and satisfy the ever increasing need of poultry products by the communities. Key words: Maximization, livestock, stochastic, robust, linear programming, optimization. &nbsp

A robust home health care routing-scheduling problem with temporal dependencies under uncertainty

There are various mathematical optimization problems that can be effectively solved by meta-heuristic algorithms. The improvement of these algorithms is that they carry out iterative search processes which resourcefully act upon exploration and exploitation in spatial domain containing global and local optima. An innovative robust Cuckoo Optimization Algorithm (COA) with adaptive thresholding is proposed to solve the problem of detection and estimation of surface defects on metal coating surfaces. The proposed method is developed through implementing changes to COA and improved the performance. For improving capability of local search as well to keep the global search effect, the enhanced methods such as level set is associated with the proposed method. Also, the method adapts dynamic step size, adaptively changing with the search process for improving the rate of convergence and the ability of local search. The algorithm performance is scrutinized from the experimental analysis and results. Also, the segmentation effectiveness is further enhanced by adapting suitable methods for preprocessing and post processing. The comparison and analysis of the results accomplished with the proposed method and results of earlier methods shows superior performance of the proposed method.

Optimization of a small-scale LNG supply chain

The paper aims to analyze the use of helical milling in hole enlargement in aluminum alloys, considering the effects of the input variables (tool overhang, cutting speed, axial and tangential feed per tooth) on the output ones related to the hole quality such as radial force, circularity and roughness. Additionally, the robust optimization is developed through the combination of robust parameter design, mean square error, and normal boundary intersection through responses modeled by response surface methodology. The results show that hole enlargement by helical milling is feasible and could achieve good values of radial forces, circularities, and specially roughness, which presented average roughness values under 0.2 μm for all experiments. The observed relationship between input and outputs shows that the axial and tangential feed are significant for all responses in linear, quadratic, and interaction terms, and cutting speed and tool overhang have at least significant terms in linear, quadratic, or interaction models. Low values of axial feed per tooth reduce radial force and circularity. Tool overhang is a noise variable and is directly connected to the shape error, since high values increase circularity deviations. Since significant noise terms exist, the robust optimization was able to reduce the variability of tool overhang in the responses and achieve mean values of circularity, radial forces, average and total roughness of about 7 μm, 20 N, 0.1 μm, and 1.7 μm, respectively.

Container fleet renewal considering multiple sulfur reduction technologies and uncertain markets amidst COVID-19

:A robust multi-objective wing design optimization procedure using CFD is presented in this work. Instead of directly applying CFD to wing design optimization, a Kriging aerodynamic model that approximates CFD result is proposed to save computational cost. By introducing 6σ robust approach as a sub-objective function, multi-objective wing design problems can be solved with aerodynamic robustness. Non-Uniform Rational B-Spline curves (NURBS) are introduced to depict the wing geometry in design optimization process. The most important parameters of the wing geometry can then be screened by design of experiment and treated as design variables due to the local variation property of NURBS. Under this formulation, a multi-objective genetic algorithm based on non-dominated sorting is employed to handle multiple flight conditions in wing design. The optimum wing geometry is selected according to trade-off among design objects on the non-dominated front. To validate the proposed approach, two robust design optimization cases are studied for ONERA-M6-Wing. It turns out that the drag coefficient is insensitive to Mach number between Ma0.8–Ma0.9 after robust optimization. The result also verifies the effectiveness of our method in boosting performance and robustness of multiple flight conditions: the lift curve slope (Ma0.3) of optimum wing and the 6σ objective function of transonic drag (Ma0.8–Ma0.9) increase by 11.9% and 25.4%, respectively. Observations in the optimization cases are concluded as follows: 1) For wing aerodynamic design problems, the multi-objective robust optimization can both improve the performance at different flight conditions and provide robustness. 2) The Kriging aerodynamic model derived from CFD result can satisfy the precision requirement of wing design. 3) Even though the optimization result is subject to the weights of the 6σ function in sub-object, the influence is not comparable to the trade-off among design objects. 4) The optimum solution obtained by proposed approach is superior to gradient based optimization method, while the computational cost is acceptable.

Robust optimization and stochastic programming approaches for medium-term production scheduling of a large-scale steelmaking continuous casting process under demand uncertainty

Purpose The purpose of this paper is to propose robust optimization models addressing the container slot allocation problem with minimum quantity commitment (MQC) under uncertain demand, which is faced by international companies export to USA. Design/methodology/approach A novel robust optimization approach handling linear programming (LP) with right-hand-side uncertainty is developed by incorporating new parameters: uncertainty level, infeasibility tolerance and reliability level. Two types of uncertainty, namely, bounded uncertainty and symmetric uncertainty are considered, respectively. Findings The present work finds that the expected revenue increases as the uncertainty level and the MQC decrease, as well as the infeasibility tolerance and the reliability level increase, no matter which type of uncertainty is considered. Research limitations/implications Typically, the capacity constraints in a container shipping model should include two major restrictions: (1) number of slots and (2) total weight of loaded and empty containers. However, this study only addresses the first restriction for simplicity. It is recommended that future research explore the optimal solutions with additional restriction (2). Originality/value This paper fills a theoretical and practical gap for the problem of slot allocation with MQC in container liner revenue management. Deterministic and tractable mixed integer LP is formulated to derive robust solutions which immunes to demand uncertainty. Illustrative examples are presented to test the proposed models. The present work provides practical and solid advice and examples which demonstrates the application of the proposed robust optimization approach for logistics managers.