Proposed Solution Procedure Research Articles

Risk-aware microgrid operation and participation in the day-ahead electricity market

This work examines the daily bidding problem of a grid-connected microgrid with locally deployed resources for electricity generation, storage and its own electricity demand. Trading electricity in energy markets may offer economic incentives but exposes the microgrid to financial risk caused by market commitments. Hence, a multi-objective, two-stage stochastic mixed integer linear programming (MILP) model is formulated, extending prior work of a risk-neutral microgrid bidding approach. The multi-objective model minimises both expected total cost of day-ahead microgrid operations and financial risk from bidding measured by conditional value-at-risk (CVaR). Bidding curves derived as first stage decisions are always feasible under present market rules – including a limitation on the number of break points per submitted curve – while being near optimal for the microgrid’s day-ahead recourse schedule. The proposed optimisation model is embedded in a variant of the ɛ-constrained method to generate bidding curve candidates with different trade-offs between the two conflicting objectives. Moreover, scenario reduction is used to compromise accuracy of the uncertainty set for better computational performance. Particularly, the marginal relative probability distance between initial and reduced scenario set is suggested to make a decision on the extent of scenario reduction. The proposed solution procedure is tested in a computational study to demonstrate its applicability to generate optimal microgrid bidding curve candidates with different emphasis between total cost and CVaR in reasonable computational time.

Network sum-rate maximization for network-coded clustered uplink NOMA networks with SWIPT-enabled relays

This paper considers network sum-rate maximization for network-coded clustered uplink non-orthogonal multiple-access (NOMA) networks with simultaneous wireless information and power transfer (SWIPT)-enabled relays. Specifically, the aim is to perform joint power allocation, power-splitting, and relay selection (J-PA-PS-RS), subject to quality-of-service (QoS) requirements. The formulated problem is excessively computationally-intensive, as it is a non-convex optimization problem. To efficiently solve it, it is split into two sub-problems: (1) joint power allocation and power-splitting per relay, and (2) relay selection. Particularly, a solution procedure is proposed, where the joint user and relay power allocation, and power-splitting per relay sub-problem is solved via a low-complexity iterative three-layer algorithm, and then followed by optimal relay selection. Simulation results have revealed that the proposed solution procedure can efficiently be used to maximize the network sum-rate, achieve near-optimal solutions, and outperform other benchmark schemes, while satisfying QoS constraints.

The multi-factory two-stage assembly scheduling problem

The recent notable focus on distributed production management in academic and industrial contexts has underscored the importance of scheduling across multiple factories. Accordingly, this study investigates a new multi-factory configuration in which non-identical factories produce different components of a final product in the first stage. Each factory is considered as a classical flow-shop, which can manufacture a unique component. These components are assembled into final products in the assembly factory, which is located in the second stage. Unlike other distributed scheduling problems, to determine a united production sequence in such a system, there is no need to find a suitable factory to assign a job since each factory is qualified for a particular task. In real-world applications, these systems encounter challenges that span from information architectures and negotiation mechanisms to the development of scheduling algorithms. The objective of this research is to schedule the jobs in each factory to minimize the makespan of the entire process. For this purpose, a mixed-integer programming model is developed to deal with small-size instances. Then, the lower bound is derived and incorporated to develop a branch and bound method. Furthermore, to deal with larger instances, five heuristic methods are developed, and the worst-case analysis is carried out. Computational experiments are conducted for different test classes to compare and to highlight the performance of the proposed solution procedures.

An exact decomposition technique for the deadline-constrained discrete time/cost trade-off problem with discounted cash flows

This paper addresses the deadline-constrained discrete time/cost trade-off problem with discounted cash flows in project scheduling optimization. Our objective is to optimize the net present value (NPV) of cash flows by selecting execution modes for activities while considering project deadlines. To address this problem, we propose an adapted model that combines the activity-on-node representation of the project network with the milestone activity payment system commonly used in real-world scenarios. This enhanced model accurately depicts project dynamics, enabling improved decision-making in NPV optimization. To solve the problem, we employ the generalized benders decomposition technique, which provides an exact solution approach to handle the computational complexity of the problem. Our approach introduces three types of feasibility cuts. The first type eliminates infeasible solutions by analyzing subproblem infeasibility. The second type enhances the generation of high-quality optimality cuts by iteratively introducing constraints to the master problem, utilizing dominated paths in the project network graph. Lastly, the third type targets the elimination of inferior infeasible solutions. Additionally, we generate a comprehensive dataset encompassing various scenarios and parameter ranges from existing literature. This dataset serves as a valuable resource for further research, with online accessibility and the latest solutions available for approximately 32,400 generated instances. Through our research, we demonstrate the superiority of our proposed solution procedure compared to existing methods in the field. By considering the specific requirements of project scheduling with NPV optimization and project deadlines, our approach contributes to more effective project planning and decision-making in real-world contexts.

A robust-fuzzy multi-objective optimization approach for a supplier selection and order allocation problem: Improving sustainability under uncertainty

Attaining sustainability objectives has received wide attention in the supplier selection and order allocation (SSOA) literature. This paper aims to investigate an SSOA problem under multiple items, multiple suppliers, multiple price levels, and multiple period using a robust-fuzzy multi-objective programming in which: (a) transportation cost, delay penalty cost, and demand are uncertain; (b) four objectives are proposed to minimize total costs and the number of defective items and to maximize environmental and social impacts; and (c) all objectives of the problem have a fuzzy membership degree that is determined by the decision-makers. A robust optimization approach is elaborated as a solution procedure to address the uncertainty of the decision variables. The significance of each objective in practice is discussed based on seven distinct scenarios that produce a specific membership degree to help practitioners make efficient decisions in selecting the suppliers and allocating the orders. Two numerical examples with different sizes are conducted to validate the mathematical model. Thereafter, the sensitivity of each scenario on objectives and total satisfaction degree is analyzed. The results of the numerical solution compare the value of four objective functions under each developed scenario to provide a trade-off insight between different objectives for practitioners. Eventually, the credibility and efficiency of the proposed solution procedure are evaluated to validate the findings.

Two-stage stochastic programming approach for gas allocation network under uncertainty

Pipelines enable enormous amounts of various products (fluids) to be transported from supply nodes to demand nodes. They have traditionally been recognized as the most efficient and secure method of transferring gases. Uncertainties in the parameters may develop in the actual world for a variety of reasons which reduces the efficiency of the gas allocation network (GAN). The amount of available gas cannot be forecasted exactly due to the uncertainty in gas supply and shared usage by other demands. Design of GAN is carried out in a two stage manner: installation and operation. During operation, there is always a chance of change in number of sources or demands than that of initial design phase. In this paper, to deal with such discrete uncertainties, a two-stage stochastic programming approach for GAN is developed. The first stage represents the installation and commissioning of supplying nodes in order to satisfy the demands, and the second stage represents the actual allocation network under different available supply stations scenarios. Illustrative examples are presented to demonstrate the proposed solution procedure and annualized investment for the examples are calculated. The calculated annualized investment is 12%, 28% and 38% less than the worst case solutions. Result explains the benefits of the model in reducing investment costs while incorporating such discrete uncertainties.

Higher-order trigonometric series-based analytical solution to free transverse vibration of suspended laminated composite slabs

Suspended floors can be designed as effective pendulum seismic isolators for high-rise buildings. However, research studies on the free vibration of suspended laminated composite slabs are relatively limited. This paper presents a comprehensive analytical solution to the free vibration problem of suspended laminated composite slabs. The equations of elasticity are used to establish the equation of motion. The critical factors influencing free vibration are explicitly considered, including the material anisotropy, number of layers, elastic properties, rotatory inertia, and transverse shear of plates. The higher-order trigonometric series are utilized to solve the dynamic equations. The developed analytical solution is a complete and realistic form of the existing analytical solutions in literature and has the capability of converging fast. The proposed analytical solution does not have a dependency on the shape function as well as separate-of-variable forms unlike the Finite Element Method (FEM). Moreover, the FEM requires an in-depth mesh convergence analysis, particularly for higher-magnitude natural frequencies, which is not the case for the proposed analytical solution for any infinite range of eigenfrequencies. The proposed solution procedure is first verified by the simplified problems available in the literature. For more complex problems, the finite element analysis results obtained from Abaqus are employed to validate the analytical solution. The comparison demonstrates that the proposed analytical solution is accurate and reliable for a wide range of case-study examples. It is found that the natural frequencies of suspended laminated composite slabs are significantly influenced by the crucial factors under investigation.

Analytic contact solutions of the Boussinesq and Cattaneo problems for an ellipsoidal power-law indenter

Based on Galin’s theorem for the indentation of an elastic half-space by a polynomial punch and Barber’s theorem for the determination of the contact area in elastic normal contact problems, an exact contact solution is developed for the frictionless indentation of an elastic half-space by an ellipsoidal power-law punch. Within the Cattaneo–Mindlin-approximation of tangential contacts, the tangential contact problem with friction can be reduced to the frictionless normal contact via the Ciavarella–Jäger principle, based on which also the tangential contact solution for the ellipsoidal power-law indenter is given. All known solutions for special cases (axisymmetric contact, elliptical Hertzian contact) are exactly recovered. A comparison of the pressure distribution obtained analytically for the 4-th power ellipsoidal indenter with a corresponding numerical solution based on the boundary element method shows no noticeable differences. The proposed solution procedure can also be used exactly for an arbitrary finite superposition of ellipsoidal power-law profiles, and, in an approximate sense, is applicable for arbitrary monotonous ellipsoidal profiles.

Manufacturing project scheduling considering human factors to minimize total cost and carbon footprints

Make-to-order (MTO) or engineer-to-order (ETO) systems produce complex and highly customized products and, therefore, there is a need for advanced project scheduling approaches for production planning in these systems. An important aspect of production scheduling is the assignment of operators with specific human factors to activities in a manufacturing project. This assignment impacts the duration of the activities, the total wage cost of the project and even the energy consumption during production. With increasing concern regarding low-carbon production in manufacturing, the human factors of operators thus cannot be ignored in the decision-making process in production project scheduling. In this context, our study considers an extension of the well-known resource-constrained project scheduling problem for manufacturing. This problem is represented as a bi-objective optimization problem with the conjoint objectives of minimizing the total cost of the project and its carbon footprint. Two variants of a genetic algorithm-based memetic algorithm (MA) are proposed to solve this problem and a set of artificial, realistic project instances are generated to evaluate the proposed solution procedure. Experimental results show that the proposed MA outperforms the well-known non-dominated sorting genetic algorithms (NSGA-II and NSGA-III) and its enhanced approach (ENSGA-II) in terms of both solution quality and computational efficiency. The experiments are conducted on both real-life case study data from an MTO project in the furniture industry and a large set of artificial data instances. Our research allows project managers to select appropriate operators to execute activities based on human factors, wage and power consumption with the objectives of minimum total cost and carbon footprint.

Fault Diagnosis of Wafer Acceptance Test and Chip Probing Between Front-End-of-Line and Back-End-of-Line Processes

With the rapid development of the semiconductor industry, fault diagnosis is an important task in routine operations to determine the root cause for faults that occur. A tool in manufacturing processes is equipped with a wide variety of sensors that record different types of process data. Wafers being processed are accompanied by a considerable amount of process data as a multivariate time series. Identifying the key process parameters and the corresponding process operations where faults occur can be used to facilitate the tasks of monitoring the process, maintaining the stability of the process, and stabilizing wafer production yield. This article proposes a novel solution procedure for fault diagnosis of wafer acceptance test (WAT) and chip probing (CP) using machine learning (ML). Based on the process flow of wafers and the corresponding process data, a sampling method, called synthetic minority oversampling technique (SMOTE), is first used to augment classification models with an imbalanced process dataset, and the best-practice SMOTE ratio is sought by using four competitive classifiers. By means of principal component analysis (PCA), the original data are transformed into visualizations to explore the distributions of good and bad lots of wafers. Based on the comparison of the four classifiers used in the test, the proposed logistic regression with data augmentation (LR-SMOTE) performs best. The ten most important features identified by using the LR are collected to determine potential failure operations. The identified failures in operations returned by using the proposed solution procedure for fault diagnosis of WAT and CP were confirmed by the engineers who work in the domain. Note to Practitioners—In semiconductor manufacturing practice, during the WAT and CP, domain engineers need to trace upstream the key process parameters and the corresponding key operations in the front-end-of-line (FEOL) process if any faults are detected in the back-end-of-line (BEOL) process. In fact, the FEOL and the BEOL are located in completely separate plants with different clean room standards. Bridging the information gap between these two different processes merits thorough scrutiny. Another challenge posed by fault diagnosis of WAT and CP is that the total number of features (i.e., process parameters) involved in the FEOL can be tens of thousands, leading to an adverse effect of data sparsity on model building.

A New Heuristic Algorithm for Multi Vehicle Routing Problem with AND/OR-Type Precedence Constraints and Hard Time Windows

In this paper the classic known Multi Vehicle Routing Problem (VRP) is studied where classically several vehicles are set in a central depot, depending on the allocation strategy, each vehicle starts traveling to visit a set of nodes one after another to provide a service of gathering or delivering commodities with the aim of minimizing total traveling distances and costs. In the current paper, this classic problem is extended by new approach of AND/OR precedence constraints (PC) which have not been considered so far in the related literature. Traditionally, PC have been considered in VRPs as the 'AND' type, where the immediate successor of a node cannot be visited until its predecessor nodes have reached their end of services. However by additional OR-type precedence constraints, there are some interconnected nodes through the concept of OR, therein no mandatory need to visit all predecessors of a successor node is acquired before it can be met, and only finishing a part of them can let to that particular node to get visited. This fact is widely observed in pickup and routing and distribution real cases where requisites for some specific products can be fulfilled via various potential suppliers. Implementation of this type of PC graph in VRP is considered as the first introduction and application in the category of this problem. So, initially, the problem is mathematically formulated, then, due to problem’s NP-hard complexity and allocation-routing characteristics, a decomposition-based technique is utilized to solve the problem. The procedure is based on recently enhanced Benders’ decomposition approach named as Branch and Search Algorithm, partitioning the original main problem into allocation and routing parts. Unlike the previous version of Benders algorithm, logic based, this newly promoted method acts in a way that at the allocation level, it generates partition of nodes with feasible solutions in lower routing level. The routing part itself has been enhanced by heuristics to cover AND/OR PC graphs. Furthermore, the efficiency of the proposed solution procedure is tested and verified by running on several generated problems in different sizes and in the larger scale it is implemented on the real case of a distribution company in Iran.

Homogeneous grouping of non-prime steel products for online auctions: a case study

Not all products meet customers’ quality expectations after the steelmaking process. Some of them, labelled as ‘non-prime’ products, are sold in a periodic online auction. These products need to be grouped into the smallest feasible number of bundles as homogeneous as possible, as this increases the attractiveness of the bundles and hence their selling prices. This results in a highly complex optimisation problem, also conditioned by other requirements, with large economic implications. It may be interpreted as a variant of the well-known bin packing problem. In this article, we formalise it mathematically by studying the real problem faced by a multinational in the steel industry. We also propose a structured, three-stage solution procedure: (i) initial division of the products according to their characteristics; (ii) cluster analysis; and (iii) allocation of products to bundles via optimisation methods. In the last stage, we implement three heuristic algorithms: FIFO, greedy, and distance-based. Building on previous works, we develop 80 test instances, which we use to compare the heuristics. We observe that the greedy algorithm generally outperforms its competitors; however, the distance-based one proves to be more appropriate for large sets of products. Last, we apply the proposed solution procedure to real-world datasets and discuss the benefits obtained by the organisation.

A Bilevel Voltage Regulation Operation for Distribution Systems With Self-Operated Microgrids

The emerging of microgrids in distribution systems has significantly enhanced the resilience of power grids. However, the operators of a distribution system and microgrids therein can be different and have accessibility to different devices. To model the operation of such a grid, this paper proposes a bilevel formulation and probes into the voltage regulation operation, considering the interaction between different systems. The proposed bilevel formulation considers the cooperation of active energy resources (AER), transformer tap-changers, and capacitor banks that are controlled by different operators. To facilitate the solution time of the target bilevel optimization, the lower-level problems with different objectives are modeled using deep neural networks (DNNs) which are then converted into a set of constraints. Hence, the bilevel problem can be reformed to a single-level problem. Lastly, the proposed solution procedures are validated using a customized joint system constructed by the IEEE 123-bus system and a real distribution system in Iowa. According to the numerical validation results, the solution time of the proposed nonlinear activation function based DNN model is 69 times faster than other methods in solving voltage regulation with a bilevel structure.

Computational structural dynamics general solution procedure using finite volumes

A method for the solution of the three-dimensional structural dynamics equations with large strains using a finite volume technique is presented. The proposed solution procedure is second order accurate in space and employs a second-order accurate dual time-stepping scheme. The momentum conservation equations are written in terms of the Piola-Kirchhoff stresses. The stress tensor is related to the Lagrangian strain tensor through the St. Venant-Kirchhoff constitutive relationship. The structural solver presented is verified through two test cases. The first test case is a three-dimensional cantilever beam subject to a gravitational load that is verified using theory and two-dimensional simulations reported in literature. The second test case is a three-dimensional highly deformable cantilever plate subject to a gravitational load. The results of this case are verified through a comparison with the modal response calculated by commercially available software. The focus of the current effort is the development and verification of the structural dynamics portion of a future fully coupled monolithic fluid-thermal-structure interaction code package.

Large Deformation Hermitian Finite Element Coupled Thermoelasticity Analysis of Wave Propagation and Reflection in a Finite Domain

In the present paper, a finite element nonlinear coupled thermoelasticity formulation is presented for analysis of the wave propagation, reflection, and mixing phenomena in the finite length isotropic solids. The governing equations are derived based on the second Piola-Kirchhoff stress and the full form of Green’s strain-displacement tensors to account for the large deformations and finite strains. In contrast to the available researches, the assumption of very small temperature changes compared to the reference temperature is released in the present research. Galerkin’s method, a weak formulation, and cubic elements are employed to obtain the time-dependent non-linear finite element governing equations. The proposed solution procedure to the resulting highly nonlinear and time-dependent governing equations employs an updating algorithm and Newmark’s numerical time integration method. The wave propagation and reflection phenomena are investigated for both the mechanical and thermal shocks and time variations of distributions of the resulting displacements, temperature rises, and stresses are illustrated graphically and discussed comprehensively. Furthermore, the effects of the non-linear terms are discussed comprehensively. Results reveal that in the non-linear analysis, no fixed speed of wave propagation can be defined.

Hierarchical‐matrix method for a class of diffusion‐dominated partial integro‐differential equations

AbstractA hierarchical matrix approach for solving diffusion‐dominated partial integro‐differential problems is presented. The corresponding diffusion‐dominated differential operator is discretized by a second‐order accurate finite‐volume scheme, while the Fredholm integral term is approximated by the trapezoidal rule. The hierarchical matrix approach is used to approximate the resulting algebraic problem and includes the implementation of an efficient preconditioned generalized minimum residue (GMRes) solver. This approach extends previous work on integral forms of boundary element methods by taking into account inherent characteristics of the diffusion‐dominated differential operator in the resultant algebraic problem. Numerical analysis estimates of the accuracy and stability of the finite‐volume and the trapezoidal rule approximation are presented and combined with estimates of the hierarchical‐matrix approximation and with the accuracy of the GMRes iterates. Results of numerical experiments are reported that successfully validate the theoretical accuracy and convergence estimates, and demonstrate the almost optimal computational complexity of the proposed solution procedure.

A two-stage stochastic model for co-firing biomass supply chain networks

A sustainable alternative to fossil fuels is biomass. The design of cost-efficient biomass networks is necessary to compete with nonrenewable resources. The creation of integrated biomass supply chain (BSC) network design models and solution procedures can contribute to the achievement of this goal. In particular, the emerging bioenergy industry must take advantage of the economies of scale in transportation to minimize the final product’s cost. Hub-and-spoke networks have been proposed as a modeling approach to design large scale BSCs. The majority of these models are deterministic and do not consider the inherent variability in the biomass feedstock, such as physical and chemical properties that affect transportation, the effects of future climate on the biomass supply, overall cost, and production operations. Levels of ash and moisture are directly related to the quality of the feedstock, which negatively affects production of biofuels, increasing transportation and handling costs as well as the burden on the BSC’s efficiency. Varying weather affects biomass yield, which creates a fluctuation in the incoming supply into the network, creating a complex large scale Newsvendors Problem. In this paper, a stochastic hub-and-spoke network model and an efficient solution are proposed to minimize logistical costs by finding an optimal production and distribution network as well as optimal transportation while reducing computational burden by using metaheuristics, such as Simulated Annealing, when solving large NP-hard instances. The proposed solution procedure was compared to recent benchmark models, i.e. Bender’s Decomposition, yielding an overall solution difference of less than 7.71% and average reduction time difference of 91.4%. Case studies with several scenarios based on varying weather conditions were created using realistic data from the northeast region of the U.S.

A total‐Lagrangian material point method for coupled growth and massive deformation of incompressible soft materials

AbstractA total‐Lagrangian material point method (TLMPM) with a mixed formulation is proposed in this article for the mechanical analysis of incompressible soft materials coupling the mass growth and massive deformation. In this work, the growth‐induced large deformation behavior is handled within the framework of the material point method (MPM) based on the multiplicative decomposition of deformation gradient. To overcome the volumetric locking caused by the incompressibility of soft materials, a weak‐form equation for hydrostatic pressure is implemented into a mixed MPM framework. To deal with the massive deformation caused by growth, the total‐Lagrangian formulation is further introduced into the mixed MPM. The TLMPM discretized via the B‐spline basis functions is then developed in the proposed solution procedure. The efficiency and accuracy of the proposed method are demonstrated by several representative two‐ and three‐dimensional numerical examples with large deformation such as the free growth of blocks and constrained growth of rings. The challenging problems including the volumetric growth of bilayers with complex geometry and the strain‐driven growth of skin are further investigated using the proposed TLMPM to illustrate its ability for evaluating the growth phenomena and behaviors as observed in nature and engineering.

A unified and rigorous solution for quasi-static cylindrical cavity expansion in plasticity constitutive models

This paper presents a unified and rigorous solution for the quasi-static cylindrical cavity expansion problem in all existing plasticity constitutive models. Rigorous three-dimensional definitions of p’ and q are used as proposed by Chen & Abousleiman. Then, the p-q stress space is transformed to the three stress components in a cylindrical coordinate system. The governing partial differential equations (PDEs) for cylindrical cavity expansion, including the stress equilibrium equation, the constitutive equation, the consistency equation, the continuity equation, and the drainage conditions, are written with respect to the three stress components in a cylindrical coordinate system. The PDEs are subsequently reduced to ordinary differential equations (ODEs), which can be summarized in unified matrix form by means of a similarity transformation. A rigorous semi-analytical solution can immediately be obtained by numerically solving the ODEs using commercial ODE solvers, such as MATLAB. The proposed solution procedure is general and can be applied to both the drained and undrained conditions in all plasticity constitutive models. Finally, the partially drained effect was discussed through numerical analysis, and empirical equations considering the partially drained effect were proposed for calculating the limit effective radial stress and excess pore pressure at the cavity wall.

Development of a supply chain configuration model for new product development: a multi-objective solution approach

Early supplier involvement in new product development is strategically important for the success of most firms. We therefore discuss how to configure an appropriate supply chain network for new product development. First, we propose a supply chain configuration model under a multi-objective optimization framework. We then develop a solution procedure based on a multi-objective evolutionary algorithm, i.e. NSGA-II (Non-Sorting Genetic Algorithm-II), to minimize the total supply chain cost and time-to-market. The efficiency of the proposed solution procedure is discussed along with a laptop assembly case study. The results obtained from NSGA-II are also compared from SPEA-II (Strength Pareto Evolutionary Algorithm-II).