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Abstract: To overcome declining markets and low-cost competition, Canadian pulp and paper (P&P) mills are considering the diversification of their product platform. Investing in bioenergy is emerging as a promising way to boost the sector. In this paper, we present a mathematical programming approach to evaluate the profitability of bioenergy investments in the case of a P&P mill, while assessing technical and associated economic risks. The mill, called the integrated forest biorefinery (IFBR), could produce a set of high-value bioproducts from biomass generated in the mill or supplied from outside. P&P activity generates residues, such as black liquor and pulp sludge, which could be used to produce bioenergy. P&P activity should then be well managed, by considering the possibility of temporarily stopping the production of P&P, while assuming the costs associated with the shutdowns. The objective is to develop a mathematically-based approach for investors and stakeholders, within the forest sector that aims to optimise the value creation network of the IFBR and to maximise the profitability of future investments in bioenergy, while optimising the existing P&P activity. [Copyright &y& Elsevier]

This paper introduces a simultaneous optimization approach to synthesizing work and heat exchange networks (WHENs). The proposed work and heat integration (WHI) superstructure enables different thermodynamic paths of pressure and temperature-changing streams. The superstructure is connected to a heat exchanger network (HEN) superstructure, enabling the heat integration of hot and cold streams identified within the WHI superstructure. A two-step solution strategy is proposed, consisting of initialization and design steps. In the first step, a thermodynamic path model based on the WHI superstructure is combined with a model for simultaneous optimization and heat integration. This nonlinear programming (NLP) model aims to minimize operating expenditures and provide an initial solution for the second optimization step. In addition, hot and cold streams are identified, enabling additional model reduction. In the second step of the proposed solution approach, a thermodynamic path model is combined with the modified HEN model to minimize the network's total annualized cost (TAC). The proposed mixed integer nonlinear programming (MINLP) model is validated by several examples, exploring the impact of the equipment costing and annualization factor on the optimal network design. The results from these case studies clearly indicate that the new synthesis approach proposed in this paper produces solutions that are consistently similar to or better than the designs presented in the literature using other methodologies. [ABSTRACT FROM AUTHOR]

In recent years, there has been an increasing need to understand the complex interdependencies between critical infrastructure systems, for example, electric power, natural gas, and potable water. Whereas open-source and commercial tools for the independent simulation of these systems are well established, frameworks for cosimulation with other systems are nascent and tools for co-optimization are scarce—the major challenge being the hidden combinatorics that arise when connecting multiple-infrastructure system models. Building toward a comprehensive solution for modeling interdependent infrastructure systems, this work presents InfrastructureModels, an extensible, open-source mathematical programming framework for co-optimizing multiple interdependent infrastructures. This work provides new insights into methods and programming abstractions that make state-of-the-art independent infrastructure models composable with minimal additional effort. To that end, this paper presents the design of the InfrastructureModels framework, documents key components of the software's implementation, and demonstrates its effectiveness with three case studies on canonical co-optimization tasks arising in interdependent infrastructure systems. History: Accepted by Ted Ralphs, Area Editor for Software Tools. Funding: The work was funded by Los Alamos National Laboratory's Directed Research and Development project "The Optimization of Machine Learning: Imposing Requirements on Artificial Intelligence" and the U.S. Department of Energy's Office of Electricity Advanced Grid Modeling projects "Joint Power System and Natural Gas Pipeline Optimal Expansion Planning" and "Coordinated Planning and Operation of Water and Power Infrastructures for Increased Resilience and Reliability." This work was carried out under the U.S. DOE contract no. [DE-AC52-06NA25396]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0118) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0118). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

The emerging digitalization in today's industrial environments allows manufacturers to store online knowledge about production and use it to make better informed management decisions. This paper proposes a multi-agent framework enhanced with digital twin (DT) for production scheduling and optimization. Decentralized scheduling agents interact to efficiently manage the work allocation in different segments of production. A DT is used to evaluate the performance of different scheduling decisions and to avoid potential risks and bottlenecks. Production managers can supervise the system's decision-making processes and manually regulate them online. The multi-agent system (MAS) uses asset administration shells (AASs) for data modelling and communication, enabling interoperability and scalability. The framework was deployed and tested in an industrial pilot coming from the bicycle production industry, optimizing and controlling the short-term production schedule of the different departments. The evaluation resulted in a higher production rate, thus achieving higher production volume in a shorter time span. Managers were also able to coordinate schedules from different departments in a dynamic way and achieve early bottleneck detection. [ABSTRACT FROM AUTHOR]

This paper presents an approach to community detection in complex networks by simultaneously incorporating a connectivity-based metric and Max-Min Modularity. By leveraging the connectivity-based metric and employing a heuristic algorithm, we develop a novel complementary graph for the Max-Min Modularity that enhances its effectiveness. We formulate community detection as an integer programming problem of an equivalent yet more compact counterpart model of the revised Max-Min Modularity maximization problem. Using a row generation technique alongside the heuristic approach, we then provide a hybrid procedure for near-optimally solving the model and discovering high-quality communities. Through a series of experiments, we demonstrate the success of our algorithm, showcasing its efficiency in detecting communities, particularly in extensive networks. [ABSTRACT FROM AUTHOR]

LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered when solving an optimization problem. Standard floating-point algorithms are highly efficient but remain susceptible to the accumulation of round-off errors, which can lead solvers to return feasibility and optimality claims that are actually invalid. This paper introduces a novel direct solution approach for solving sequences of closely related SLEs encountered in nonlinear programming efficiently and without round-off errors. Specifically, it introduces rank-one update algorithms for the round-off error–free factorization framework, a tool set built on integer-preserving arithmetic that has led to the development and implementation of extremely reliable subroutines for solving SLEs occurring in linear programming. The formal guarantees of the presented algorithms are established through the derivation of theoretical insights. Their advantages are supported with computational experiments, which demonstrate upward of 75× improvements over exact factorization runtimes on fully dense matrices with more than one million entries. A significant advantage of the featured integer-preserving framework is that the length of any matrix coefficient produced by its algorithms is bounded polynomially in the size of the inputs without having to resort to greatest common divisor operations, which are required by and thereby hinder an efficient implementation of exact rational arithmetic approaches. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0331) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0331). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

In most project portfolio selection (PPS) situations, the presence of multiple attributes and decision-maker preference is inevitable. As Multi-criteria Decision Analysis (MCDA) methods provide a framework well-suited to deal with these challenges in PPS problems, the use of MCDA methods in real-life PPS problems has increased in recent years. This paper provides a comprehensive literature review of the use of different MCDA methods and their individual or combined utilization with other modeling techniques to support PPS problems. First, we summarize how MCDA methods are used in different modeling approaches. Second, we examine the mathematical models that are generally used to combine MCDA with mathematical programming techniques to solve PPS problems with resource constraints. Third, we present the drawbacks of combined utilization and discuss recent advances. Finally, we visualize the summary of the reviewed papers as a decision tree to assist researchers and practitioners in the use of MCDA methods in a specific PPS context and propose some future research directions. [ABSTRACT FROM AUTHOR]

Using mathematical programming with activity-based costing (ABC) and based on the theory of constraints (TOC), this study proposed a green production model for the traditional paper industry to achieve the purpose of energy saving and carbon emission reduction. The mathematical programming model presented in this paper considers (1) revenue of main products and byproducts, (2) unit-level, batch-level, and product-level activity costs in ABC, (3) labor cost with overtime available, (4) machine cost with capacity expansion, (5) saved electric power and steam costs by using the coal as the main fuel in conjunction with Refuse Derived Fuel (RDF). This model also considers the constraint of the quantity of carbon equivalent of various gases that are allowed to be emitted from the mill paper-making process to conform to the environmental protection policy. A numerical example is used to demonstrate how to apply the model presented in this paper. In addition, sensitivity analysis on the key parameters of the model are used to provide further insights for this research. [ABSTRACT FROM AUTHOR]

• Considers supplier selection problem with uncertain demand. • Assumes that suppliers produce defective units and offer buyback contract. • Uses mathematical programming and develops a solution algorithm. • Reports interesting findings and insights. Demand and supply uncertainties are the two challenges of any supply chain. Supply uncertainty can happen if suppliers' production systems generate defective units. Demand uncertainty also indicates that the demand fluctuates over time. Suppliers may share the risk of uncertain demand with buyers by agreeing to buy back unsold inventory at the end of the season. Also, a multi-sourcing scenario can be an effective strategy to handle both uncertainties. We consider in this paper an inventory problem where a buyer purchases an item from multiple suppliers. The suppliers may have limited production capacity, produce defective units, and allow the buyer to return unsold units at the end of the season with a buyback price. To determine the order quantities from the suppliers, the buyer must evaluate them based on wholesale price, buyback price, and defective rate. We first develop a solution algorithm to solve the problem and then provide some managerial insights for both the buyers and the suppliers. [ABSTRACT FROM AUTHOR]

Electric vehicles (EVs) charging swapping stations (CSSs), as well as multi‐functional integrated charging and swapping facilities (CSFs), have become important to reduce the impact of e‐mobility on the electric power distribution system. This paper presents a coordinated planning optimization strategy for CSSs/CSFs and active distribution networks (AND) that includes distributed generation. The approach is based on the application of a specifically developed spatial‐temporal load forecasting method of both plug‐in EVs (PEVs) and swapping EVs (SEVs). The approach is formulated as a mathematical programming optimization model that provides the location and sizing of new CSSs, the best active distribution network topology, the required distributed generation, and substation capacities. The developed model is solved using CPLEX, and its characteristics and performances are evaluated through a realistic case study. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel data-driven optimization approach for trajectory-based air traffic flow management (ATFM). A key aspect of the proposed approach is the inclusion of airspace users' trajectory preferences, which are computed from traffic data by combining clustering and classification techniques. Machine learning is also used to extract consistent trajectory options, whereas optimization is applied to resolve demand-capacity imbalances by means of a mathematical programming model that judiciously assigns a feasible four-dimensional trajectory and a possible ground delay to each flight. The methodology has been tested on instances extracted from the Eurocontrol data repository. With more than 32,000 flights considered, we solve the largest instances of the ATFM problem available in the literature in short computational times that are reasonable from the practical point of view. As a by-product, we highlight the trade-off between preferences and delays as well as the potential benefits. Indeed, computing efficient solutions to the problem facilitates a consensus between the network manager and airspace users. In view of the level of accuracy of the solutions and the excellent computational performance, we are optimistic that the proposed approach can make a significant contribution to the development of the next generation of air traffic flow management tools. [ABSTRACT FROM AUTHOR]

With the emergence of the fourth industrial revolution, the use of intelligent technologies in supply chains is becoming increasingly common. The aim of this research is to propose an optimal design for an intelligent supply chain of multiple perishable products under a vendor-managed inventory management policy aided by IoT-related technologies to address the challenges associated with traditional supply chains. Various levels of the intelligent supply chain employ technologies such as Wireless Sensor Networks (WSNs), Radio Frequency Identification (RFID), and Blockchain. In this paper, we develop a bi-objective nonlinear integer mathematical programming model for designing a four-level supply chain consisting of suppliers, manufacturers, retailers, and customers. The model determines the optimal network nodes, production level, product distribution and sales, and optimal choice of technology for each level. The objective functions are total cost and delivery times. The GAMS 24.2.1 optimization software is employed to solve the mathematical model in small dimensions. Considering the NP-Hard nature of the problem, the Grey Wolf Optimizer (GWO) algorithm is employed, and its performance is compared with the Multi-Objective Whale Optimization Algorithm (MOWOA) and NSGA-III. The results indicate that the adoption of these technologies in the supply chain can reduce delivery times and total supply chain costs. [ABSTRACT FROM AUTHOR]

This paper performs a comprehensive analysis of the wind energy potential of onshore regions in Greece with emphasis on quantifying the volume risk and the spatial covariance structure. Optimization techniques are employed to derive efficient wind capacity allocation plans (also known as generation portfolios) incorporating different yield aspirations. The generation profile of minimum variance and other optimal portfolios along the efficient frontier are subject to rigorous evaluation using a fusion of descriptive and statistical methods. In particular, principal component analysis is employed to estimate factor models and investigate the spatiotemporal properties of wind power generation, providing valuable insights into the persistence of volume risk. The overarching goal of the study is to employ a set of statistical and mathematical programming tools guiding investors, aggregators and policy makers in their selection of wind energy generating assets. The findings of this research challenge the effectiveness of current policies and industry practices, offering a new perspective on wind energy harvesting with a focus on the management of volume risk. [ABSTRACT FROM AUTHOR]

As a new abstract computational model in evolutionary transfer optimization (ETO), single-objective to multi-objective optimization (SMO) is conducted at the macroscopic level rather than the intermediate level for specific algorithms or the microscopic level for specific operators; this method aims to develop systems with a profound grasp of evolutionary dynamic and learning mechanism similar to human intelligence via a "decomposition" style (in the abstract of the well-known "Transformer" article "Attention is All You Need", they use "attention" instead). To the best of our knowledge, it is the first work of SMO for discrete cases because we extend our conference paper and inherit its originality status. In this paper, by implementing the abstract SMO in specialized memetic algorithms, key knowledge from single-objective problems/tasks to the multi-objective core problem/task can be transferred or "gathered" for permutation flow shop scheduling problems, which will reduce the notorious complexity in combinatorial spaces for multi-objective settings in a straight method; this is because single-objective tasks are easier to complete than their multi-objective versions. Extensive experimental studies and theoretical results on benchmarks (1) emphasize our decomposition root in mathematical programming, such as Lagrangian relaxation and column generation; (2) provide two "where to go" strategies for both SMO and ETO; and (3) contribute to the mission of building safe and beneficial artificial general intelligence for manufacturing via evolutionary computation. [ABSTRACT FROM AUTHOR]

• A shape feature controlled topology optimization method of PZT for structure vibration control is proposed. • A modified K-means clustering method is proposed to obtain the explicit shape control functions. • An explicit optimization model with SPI as its objective and shape control functions as its constraints is presented. • Sensitivity analysis is performed based on chain rule, the Lyapunov equation and the adjoint method. This paper proposes a method for shape feature controlled topology optimization of attached piezoelectric actuators of thin-walled smart structures, aiming at both vibration control performance as well as possible manufacturing constraints. This paper first proposes a modified K-means clustering method to derive the shape feature control functions. Then, an optimization model with system performance index (SPI) as its objectiveness and shape feature control functions as its explicit constraints is organized. Based on the Lyapunov equation, the adjoint method and the chain rule, the sensitivity analysis of both objective and constraints in optimization model is performed. A mathematical programming method is applied to solve the optimization model once the sensitivities is calculated. Then the LQR control algorithm is used in the optimized structure for vibration control. Numerical examples as well as engineering application are applied to prove effectiveness of the proposed methods. The results show feasibility of the proposed methods. [ABSTRACT FROM AUTHOR]

The issue of transportation is a particular type of mathematical programming that facilitates searching for and determining an optimal distribution network, considering the set of suppliers and recipients. This paper uses a numerical example to present a solution to a transport problem utilizing classical computation methods, i.e., the northwest corner, the least cost in a matrix, and the VAM approximation method. The objective of the paper was to develop tools in the form of algorithms that would then be implemented in three various computing environments (R, GNU Octave, and Matlab) that allow us to optimize transport costs within an assumed supply network. The model involved determining decision variables and indicating limiting conditions. Furthermore, the authors interpreted and visualized the obtained results. The implementation of the proposed solution enables users to determine an optimal transport plan for individually defined criteria. [ABSTRACT FROM AUTHOR]

In order to reduce complexity when designing multi-media communication networks, researchers often consider spanning tree problems defined on edge-labeled graphs. The earliest setting addressed in the literature aims to minimize the number of different media types, i.e., distinct labels, used in the network. Despite being extensively addressed, such a setting completely ignores edge costs. This led to the definition of more realistic versions, where budgets for the total cost, or the number of distinct labels allowed, were introduced. In this paper, we introduce and prove the NP-hardness of the Budgeted Labeled Minimum Spanning Tree problem, consisting in minimizing the cost of a spanning tree while satisfying specified budget constraints for each label type. This problem combines the challenges of cost efficiency and label diversity within a fixed budgetary framework, providing a more realistic and practical approach to network design. We provide three distinct mathematical programming formulations of the problem and design a Lagrangian approach to derive tighter lower bounds for the optimal solution of the problem. The performances of the proposed methods are assessed by conducting a series of computational experiments on a variety of randomly generated instances, which showed how the complexity of the problem increases as the size of the network, as well as the number of labels, increase and the budget restrictions are tightened. [ABSTRACT FROM AUTHOR]

This paper is the fruit of a partnership with Renault. Their reverse logistic requires solving a continent-scale multiattribute inventory routing problem (IRP). With an average of 30 commodities, 16 depots, and 600 customers spread across a continent, our instances are orders of magnitude larger than those in the literature. Existing algorithms do not scale, so we propose a large neighborhood search (LNS). To make it work, (1) we generalize existing split delivery vehicle routing problems and IRP neighborhoods to this context, (2) we turn a state-of-the-art matheuristic for medium-scale IRP into a large neighborhood, and (3) we introduce two novel perturbations: the reinsertion of a customer and that of a commodity into the IRP solution. We also derive a new lower bound based on a flow relaxation. In order to stimulate the research on large-scale IRP, we introduce a library of industrial instances. We benchmark our algorithms on these instances and make our code open source. Extensive numerical experiments highlight the relevance of each component of our LNS. Funding: This work was supported by Renault Group. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0342. [ABSTRACT FROM AUTHOR]

This paper presents an efficient model for optimal planning of electrical energy management in a smart residential microgrid (SRMG) by considering energy interactions among smart homes and with the purpose of SRMG's resilience improvement. A two-state linearized mathematical programming framework is given for the development of such notions. The first state proclaims a regular, disruption-free SRMG state, whereas the second state declares a disturbed SRMG state. In the initial state, two steps are taken into account. In the first stage, the minimum energy cost for each smart home, and in the second stage, minimum load profile deviation for SRMG is considered. In the second state energy interactions among in-home energy management systems to enhance the resilience is deliberated. The main objective of these two states is to advance SRMG's resiliency by considering modified SRMG's load profile and minimized smart homes' daily energy cost. Based on the obtained numerical results, energy interactions among smart homes have diminished smart home's energy cost about 3.34% in normal state, modified SRMG's load profile deviation about 3.62% in normal state, and improved SRMG's resilience about 32% in disrupted state. [ABSTRACT FROM AUTHOR]

Minimax fractional semi-infinite programming is an important research direction for semi-infinite programming, and has a wide range of applications, such as military allocation problems, economic theory, cooperative games, and other fields. Convexity theory plays a key role in many aspects of mathematical programming and is the foundation of mathematical programming research. The relevant theories of semi-infinite programming based on different types of convex functions have their own applicable scope and limitations. It is of great value to study semi-infinite programming on the basis of more generalized convex functions and obtain more general results. In this paper, we defined a new type of generalized convex function, based on the concept of the K−directional derivative, that is, uniform  (B K , ρ) − invex, strictly uniform  (B K , ρ) − invex, uniform  (B K , ρ) − pseudoinvex, strictly uniform  (B K , ρ) − pseudoinvex, uniform  (B K , ρ) − quasiinvex and weakly uniform  (B K , ρ) − quasiinvex function. Then, we studied a class of non-smooth minimax fractional semi-infinite programming problems involving this generalized convexity and obtained sufficient optimality conditions. [ABSTRACT FROM AUTHOR]

Integration of Distributed Energy Resources (DERs) in power systems exacerbates the existing information problems between power utilities and regulators. DER policies oblivious to the trilemma of information asymmetry between power utilities, DER aggregators, and regulators result in distorted price signals to DER investors, and socially inefficient DER roll‐out. Therefore, in this paper, a game‐theoretic approach is proposed for modeling information asymmetry in distribution network information and consumer data between the DER aggregators and the power utilities. The proposed framework is based on Single Leader Single Follower (SLSF) games, reformulated as Mathematical Programs with Equilibrium Constraints (MPECs), and solved using the Scholtes's relaxation technique. The results, based on the 7‐bus Manhattan power network, show that unless the DER aggregators have complete information about the distribution network characteristics, the welfare along with the realized installed capacity of DERs in the system decreases. Moreover, progressively decreasing DER investment costs alleviate the effects of information asymmetry, suggesting that early adopters face disproportionately high welfare losses attributed to incomplete information between the DER stakeholders. Hence, policy interventions to alleviate the rampant information problems are imperative to ensure an optimal DER roll‐out. [ABSTRACT FROM AUTHOR]

The aggressive scaling down of the feature size in modern ICs has introduced major bottlenecks in printing layouts using a conventional 193 nm immersion lithography system. As different mitigation techniques have reached their limitations, Next Generation Lithography (NGL) techniques have been gaining popularity. Extreme Ultra-violet Lithography (EUVL) system which uses light having 13. 5 nm wavelength is one of the popular NGL for printing features below 20 nm. However, EUVL faces the problem of flare caused by irregular reflection from clear-field mask surfaces used. It leads to distortion of critical dimension (CD) during layout printing which in turn degrades the performance of the circuit. In this paper, we have formulated a delay-aware global routing problem in order to minimize flare without sacrificing the delay. Two different solvers, namely ILP and SAT-SMT, are employed and the results are compared. Experimental results show a significant reduction in flare without much compromise on delay. • Flare is a phenomenon in Extreme Ultra-violet lithography, which causes layout distortions. • In order to reduce flare, it is required to distribute the layout features conforming to the global flare distribution which can be modelled as a 2D concave function. In addition to that, it is important to take care of the delay during redistribution of the layout features. • For global routing, a set of delay optimized Steiner trees are to be constructed for each of the nets. • The Steiner tree that might lead to the best possible wire distribution for minimizing flare has to be selected for each net. • We have proposed a method based on mathematical programming that can select concurrently a delay-aware Steiner tree for each net such that flare over the layout area can be minimized. We have validated our proposed approach on IBM benchmark circuits to show the effectiveness of delay-aware flare reduction at the global routing stage. [ABSTRACT FROM AUTHOR]

The focus of this paper is on analyzing the role and the choice of parameters in sociophysics diffusion models by leveraging the potentialities of sociophysics from a mathematical programming perspective. We first present a generalised version of Galam's opinion diffusion model. For a given selection of the coefficients in our model, this proposal yields the original Galam's model. The generalised model suggests guidelines for possible alternative selection of its parameters that allow it to foster diffusion. Examples of the parameters selection process as steered by numerical optimisation, taking into account various objectives, are provided. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to propose a new model called the stochastic green capacitated p-median problem with a simulation-based optimisation approach. An integer linear programming mathematical model is built considering the total emission produced by vehicles and the uncertain parameters including the travel cost for a vehicle to travel from a particular facility to a customer and the amount of CO2 emissions produced. We also develop a simulation-based optimisation algorithm for solving the problem. Design/methodology/approach: The authors proposed new algorithms to solve the problem. The proposed algorithm is a hybridisation of Monte Carlo simulation and a Variable Neighbourhood Search matheuristic. The proposed model and method are evaluated using instances that are available in the literature. Findings: Based on the results produced by the computational experiments, the developed approach can obtain interesting results. The obtained results display that the proposed method can solve the problems within a short computational time and the solutions produced have good quality (small deviations). Originality/value: To the best of our knowledge, there is no paper in the previous literature investigating the simulation-based optimisation for the stochastic green capacitated p-median problem. There are two main contributions in this paper. First, to build a new model for the capacitated p-median problem taking into account the environmental impact. Second, to design a simulation-based optimisation approach to solve the stochastic green capacitated p-median problem incorporating VNS-based matheuristic and Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

The symmetric wireless network has been expected to be a revolutionary technology for mobile communications. Due to the limited resources of the microbase stations in the wireless network, the way to jointly optimize resource allocation, traffic throughput, latency, and other key performances is a hot research issue. In this paper, we introduce a joint optimization algorithm for improving the performance and balancing the traffic load of the wireless network. For the optimal traffic routing scheme, we transfer the problem to a mixed mathematical programming model. The model contains multiple traffic constraints and a single joint objective; the objective of the joint optimization are data transmission latency, energy consumption of wireless microbase stations, and throughput of links. Moreover, in order to approximately solve the optimization problem, we propose an efficient heuristic traffic transmission and migration scheme with load balancing, called an adaptive data traffic control scheme. The main idea of the proposed scheme is to split the traffic of overloaded microbase stations and links in the symmetric wireless network, so as to achieve load balancing and reduce the energy consumption of microbase stations. At last, the evaluations and simulations verify the proposed algorithm can efficiently optimize the energy allocation of microbase stations, and the network lifetime is increased to 210 rounds. Meanwhile, the network latency is reduced to 2–3 ms, and the network throughput is increased to 1000 Mb in our simulation environment. The constructed traffic control system for the traffic engineering-based wireless network in this paper can serve the intelligent system in the future. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of multiobjective mathematical programming problems with equilibrium constraints on Hadamard manifolds (in short, (MMPEC)). We introduce the generalized Guignard constraint qualification for (MMPEC) and employ it to derive Karush–Kuhn–Tucker (KKT)-type necessary optimality criteria. Further, we derive sufficient optimality criteria for (MMPEC) using geodesic convexity assumptions. The significance of the results deduced in the paper has been demonstrated by suitable non-trivial examples. The results deduced in this article generalize several well-known results in the literature to a more general space, that is, Hadamard manifolds, and extend them to a more general class of optimization problems. To the best of our knowledge, this is the first time that generalized Guignard constraint qualification and optimality conditions have been studied for (MMPEC) in manifold settings. [ABSTRACT FROM AUTHOR]

The design of the optimum wastewater interception network is presented in our research using LINGO Program. Minimising freshwater consumption and the total cost of freshwater usage, treatment of discharged wastewater and interception units are the objective functions in the optimisation model. In our research, we presented two models; the first model can use twelve sources and twelve sinks, each source can enter five techniques of treatment, and each technique has five probabilities to decrease the mass load of contaminants. The second model draws the wastewater interception network after transferring the results of the first model. This paper achieves the minimisation of freshwater consumption in the Kotchener Drain by obtaining the environmental impact of wastewater discharge. Three interception techniques are applied to decrease the chemical oxygen demand (COD) and biological oxygen demand (BOD) of the Segaaya source. Simultaneous linear equations are proposed to get the mass load which is removed with the cost of removing contaminant COD and BOD for other sources. A mathematical approach was applied to seek the two-objective functions, minimise the freshwater consumption as the first objective function and minimise the cost of fresh water, interception units and wastewater discharge in wastewater distribution as the second objective function in Kotchener Drain. Our technique is easy to apply in drains, fertilisers, and chemical plants. [ABSTRACT FROM AUTHOR]

Pseudo-random number generators (PRNGs) are software algorithms generating a sequence of numbers approximating the properties of random numbers. They are critical components in many information systems that require unpredictable and nonarbitrary behaviors, such as parameter configuration in machine learning, gaming, cryptography, and simulation. A PRNG is commonly validated through a statistical test suite, such as NIST SP 800-22rev1a (NIST test suite), to evaluate its robustness and the randomness of the numbers. In this paper, we propose a Wasserstein distance-based generative adversarial network (WGAN) approach to generating PRNGs that fully satisfy the NIST test suite. In this approach, the existing Mersenne Twister (MT) PRNG is learned without implementing any mathematical programming code. We remove the dropout layers from the conventional WGAN network to learn random numbers distributed in the entire feature space because the nearly infinite amount of data can suppress the overfitting problems that occur without dropout layers. We conduct experimental studies to evaluate our learned pseudo-random number generator (LPRNG) by adopting cosine-function-based numbers with poor random number properties according to the NIST test suite as seed numbers. The experimental results show that our LPRNG successfully converted the sequence of seed numbers to random numbers that fully satisfy the NIST test suite. This study opens the way for the "democratization" of PRNGs through the end-to-end learning of conventional PRNGs, which means that PRNGs can be generated without deep mathematical know-how. Such tailor-made PRNGs will effectively enhance the unpredictability and nonarbitrariness of a wide range of information systems, even if the seed numbers can be revealed by reverse engineering. The experimental results also show that overfitting was observed after about 450,000 trials of learning, suggesting that there is an upper limit to the number of learning counts for a fixed-size neural network, even when learning with unlimited data. [ABSTRACT FROM AUTHOR]

This study investigates a flow shop scheduling problem with queue time limits and skipping jobs, which are common scheduling requirements for semiconductor and printed circuit board manufacturing systems. These manufacturing systems involve the most complex processes, which are strictly controlled and constrained to manufacture high-quality products and satisfy dynamic customer orders. Further, queue times between consecutive stages are limited. Given that the queue times are limited, jobs must begin the next step within the maximum queue time after the jobs in the previous step are completed. In the considered flow shop, several jobs can skip the first step, referred to as skipping jobs. Skipping jobs exist because of multiple types of products processed in the same flow shop. For the considered flow shop, this paper proposes a mathematical programming formulation and a genetic algorithm to minimize the makespan. The GA demonstrated its strengths through comprehensive computational experiments, demonstrating its effectiveness and efficiency. As the problem size increased, the GA's performance improved noticeably, while maintaining acceptable computation times for real-world fab facilities. We also validated its performance in various scenarios involving queue time limits and skipping jobs, to further emphasize its capabilities. [ABSTRACT FROM AUTHOR]

Motivated by recent investigations relating the sharpness of the Jensen inequality, this paper concerns with the sharpness of the converse of the Jensen inequality. For this reason, the Jensen inequality has become one of the most discussed developmental inequalities in the current literature on mathematical inequalities. In this Special Issue, we present new results related to classical inequalities, such as the Jensen inequality, Jensen-Steffensen inequality, Jessen inequality, Grüss inequality, Chebyshev inequality, etc. [Extracted from the article]

The paper deals with the mathematical programming problems with switching constraints that are defined with continuously differentiable functions. The main results are the upper approximations of the Frèchet normal cone of the feasible set for the problem. As applications of the main results, we present some stationary conditions of the considered problem. [ABSTRACT FROM AUTHOR]

The transition towards climate neutrality will result in an increase in electrical vehicles, as well as other electric loads, leading to higher loads on electrical distribution grids. This paper presents an optimisation algorithm that enables the integration of more loads into distribution grid infrastructure using information from smart meters and/or smart meter gateways. To achieve this, a mathematical programming formulation was developed and implemented. The algorithm determines the optimal charging schedule for all electric vehicles connected to the distribution grid, taking into account various criteria to avoid violating physical grid limitations and ensuring non-discriminatory charging of all electric vehicles on the grid while also optimising grid operation. Additionally, the expandability of the infrastructure and fail-safe operation are considered through the decentralisation of all components. Various scenarios are modelled and evaluated in a simulation environment. The results demonstrate that the developed optimisation algorithm allows for higher transformer loads compared to a P(U) control approach, without causing grid overload as observed in scenarios without optimisation or P(U) control. [ABSTRACT FROM AUTHOR]

In view of the traditional branch line end express delivery centralized mode cannot adapt to the growing demand of high-speed rail (HSR) express, resulting in poor connection between trunk and branch line, high cost and poor timeliness. In this paper, the problem of scheduling optimization of branch-line flexible distribution vehicles relying on intermodal transportation of trunk and branch lines is proposed. Considering the number of vehicles, vehicle capacity, customer service time window and other constraints, an integer linear programming mathematical model with the minimum total cost of vehicle transportation cost, usage cost and time window penalty cost as the optimization objective is established. A two-level nested heuristic algorithm with two-level coding structure is proposed to solve the problem. Finally, a simulation example is given to verify the effectiveness of the model and the algorithm. The results show that the vehicle scheduling optimization problem studied in this paper can effectively improve the timeliness and accuracy of HSR express delivery, and can significantly reduce the total vehicle delivery cost. [ABSTRACT FROM AUTHOR]

Purpose: Human resources are considered a competitive advantage in organizations, and according to the executive position of staff, the relative importance of the competitive advantage is enhanced so that the executive managers, and the senior staffs particularly in the production line, are of particular importance to company owners. Selecting competent and committed senior staff as well as maintaining them based on their satisfaction is one of the key factors in the success of organizations. Therefore, this paper aims to study the selection and assignment of senior staff problems so that they are selected based on their competency to manage the production workshops, and then they are assigned to the workshops based on their preferences. For this purpose, an integrated model of mathematical programming and Multi-Attribute Decision-Making (MCDM) is developed to select competent senior staff and assign them to the workshops based on their preferences. Design/methodology/approach: In this paper, some of the staff as potential options have been determined, and then, their preferences to manage all workshops have been calculated using the TOPSIS technique. Also, a multi-objective integer programming model has been developed to select competent senior staff among all potential options and to assign them to the workshops based on their preferences. In this paper, a multi-objective global criteria method has been proposed as an approach to solving the selection and assignment problem. Findings: The required data were collected through questionnaires and interviews with potential options. Consequently, the results indicated that the proposed method (weighted global criteria) outperforms the simple global criteria approach as well as the traditional method based on the decision of the managers and experts. Research limitations/implications: The results were limited to the case of production workshops in an appliances plant, and all data were deterministic. Respectively, some directions as opportunities for future research were suggested. The first suggestion is to apply the current model in other production systems, and the second suggestion is to use fuzzy logic for developing both the fuzzy TOPSIS and fuzzy mathematical programming model based on the expert’s knowledge. Practical implications: Since the non-optimal assignment of the staff to the workplaces increases the costs, and assigning them disregarding their preferences leads to staff dissatisfaction, the production system would be affected. Therefore, the lifecycle of the organization can be threatened. Therefore, the optimal staff assignment problem can be one of the most critical management challenges in industries. Originality/value: To the best of our knowledge, there is no research in the literature on the staff assignment problem that considers preferences and competencies simultaneously as studied in this paper. Therefore, the following contributions to the literature are underlined: - - Selecting and assigning senior staff to production workshops, considering a multi-objective problem - - Collecting the evaluation criteria of preferences for the problem from the literature to determine final preferences for selecting the workshop - Integrating the integer programming (IP) model and TOPSIS to extend the new model of staff assignment problem [ABSTRACT FROM AUTHOR]

This article reviews the accomplishments of studies in which optimization tools were used to develop energy-efficient and sustainable construction schedules. With the increase in global awareness of environmental issues, the construction industry has been forced to explore innovative techniques to make the building process more energy-efficient and sustainable. Project managers can use optimization tools in their scheduling procedures to address these issues in the early stages of the project. Therefore, this paper examines different optimization-based construction scheduling methods and their impact on schedule energy efficiency and the three key sustainability goals: economic viability, social equity, and environmental protection. Such a review has not yet been conducted to the best of our knowledge. This research aims to fill the gap and contribute to understanding advanced optimization tools that can pave the way to energy-efficient and sustainable scheduling practices. After a brief introduction, the background of optimization-based construction scheduling techniques that aim to improve construction management and incorporate these aspects into the decision-making process is explained. Then, these approaches are addressed in detail. It is determined for each study whether it adopted energy efficiency goals and which sustainability dimensions it considered within the proposed optimization model. The results of this study indicate a wide heuristic algorithms application for complex scheduling problems. Meanwhile, mathematical programming is still quite unexplored, especially methods that utilize algebraic modeling languages. This study provides a foundation for further research by addressing the current reach in development and possible knowledge gaps that could be researched in future studies. The paper also discusses the advantages and limitations of different approaches and illustrates the potential for utilizing these methods. Supported by the main review findings, conclusions and recommendations for further research are provided. [ABSTRACT FROM AUTHOR]

This paper is devoted to the management of advance admission requests for obstetric care. Pregnant women in China select one hospital and request admission for both antenatal and postnatal care after nine weeks of pregnancy. Schedulers must make the admission decision instantly based on the availability of the most critical resource, that is, hospital beds for postnatal care. The random delay between admission requests and postnatal care has created a distinct advance admission control problem. To address this issue, we propose a basic model that assumes a unit bed requirement for one day. Each admission generates a unit of revenue and each unit of overcapacity use incurs an overcapacity cost. With the objective of maximizing the expected net revenue, we establish an optimal policy for unlimited requests, that is, an expected arrival time quota (EATQ) policy that accepts a fixed quota of advance admission requests with the same expected date of confinement. We then propose an extended model for general capacity requirements. Using the Poisson approximation, we establish the optimality of the EATQ policy, which is shown to be solvable by a simple linear programming model. We compare the numerical results from the different policies and conduct a sensitivity analysis. The EATQ policy is demonstrated to be the best option in all test instances and notably outperforms the current admission rules used in hospitals, which usually accept admission requests according to some empirical monthly quota of the expected delivery month. The Poisson approximation is shown to be effective for determining the optimal EATQ policy for both stationary and nonstationary arrivals. Summary of Contribution: First, this paper investigates the advance admission control problem for obstetric care. Pregnant women in China choose one hospital and request admission for both antenatal and postnatal care after nine weeks of pregnancy but the most critical resource is hospitalization beds needed for postnatal care. The random delay between admission request and postnatal care makes the problem unique and challenging to solve. It belongs to the scope of computing and operations research. Second, this paper formulates a dynamic programming model, analyzes the structural properties of the optimal control policy, and finally proposes a mathematical programming model to determine the optimal quota. Numerical experiments show the validity of the proposed approach. It covers the research contents of theories on dynamic stochastic control, mathematic programming model, and experiments. Moreover, this paper is motivated by the practical problem (advance admission control) in obstetric units of Shanghai. Using these optimality properties, solution approaches, and numerical results, this paper provides guidance on how to manage advance obstetric admission requests. [ABSTRACT FROM AUTHOR]

This paper deals with the mixed-model assembly line balancing problem. This type of line is applied to more than one similar model of a product in an intermixed order. Despite their widespread use, these lines have received little attention in the literature. Metaheuristics, heuristics, and mathematical programming techniques are developed to solve these types of assembly line balancing problems. However, linear physical programming method has never been used. In this paper, a linear physical programming model is proposed for balancing a mixed-model assembly line. The performance of the proposed model is applied to a numerical example to analyze the usage of the methodology. Five objectives are considered in the model, and the outperformance of the methodology is demonstrated by comparing it to a different approach. According to the results, it has been seen that the proposed linear physical programming model is practical and useful approach for mixed-model assembly line balancing problems. [ABSTRACT FROM AUTHOR]

In the emerging modern technology of additive manufacturing, the need for optimization can be found in literature in many places. Additive manufacturing (AM) is making an object layer by layer directly from digital data. Previous works of literature have classified additive manufacturing processes into seven types. However, there is a lack of comprehensive review describing the optimization challenges and opportunities in the material extrusion process (polymer technology) and also the need for FDM polymer materials application in impeller making. In this review paper, a specific optimization method called multicriteria decision-making (MCDM) from the mathematical programming technique used in additive manufacturing polymer technology (AMPT) is discussed. The other topics such as different types of optimization techniques, applications of different MCDM tools and their applications in different fields including AM, and the optimization challenges and opportunities in AMPT particularly impeller application are discussed. [ABSTRACT FROM AUTHOR]

Airport gates are the main places for aircraft to receive ground services. With the increased number of flights, limited gate resources near to the terminal make the gate assignment work more complex. Traditional solution methods based on mathematical programming models and iterative algorithms are usually used to solve these static situations, lacking learning and real-time decision-making abilities. In this paper, a two-stage hybrid algorithm based on imitation learning and genetic algorithm (IL-GA) is proposed to solve the gate assignment problem. First of all, the problem is defined from a mathematical model to a Markov decision process (MDP), with the goal of maximizing the number of flights assigned to contact gates and the total gate preferences. In the first stage of the algorithm, a deep policy network is created to obtain the gate selection probability of each flight. This policy network is trained by imitating and learning the assignment trajectory data of human experts, and this process is offline. In the second stage of the algorithm, the policy network is used to generate a good initial population for the genetic algorithm to calculate the optimal solution for an online instance. The experimental results show that the genetic algorithm combined with imitation learning can greatly shorten the iterations and improve the population convergence speed. The flight rate allocated to the contact gates is 14.9% higher than the manual allocation result and 4% higher than the traditional genetic algorithm. Learning the expert assignment data also makes the allocation scheme more consistent with the preference of the airport, which is helpful for the practical application of the algorithm. [ABSTRACT FROM AUTHOR]

Product recovery, accompanied by cradle to cradle policies from the contemporary supply chain, becomes an essential element in meeting environmental compliance and waste management policies. Incorporation of reverse logistics into the traditional supply chains becomes a complementary factor for efficient product recovery. To begin with product recovery, consumers are encouraged to return their end-of-use/end-of-life products, and the steps of collecting and planning the movement of returned products are crucial decisions. The efficient planning of a cost effective recovery process in reverse logistics requires dealing with the uncertainty underlying in the quantity and quality of the returned products. In this paper, we propose establishing an initial collection point within a permissible radius of the customer zones to overcome some of the issues of uncertainty. The uncertainty in the quantity and quality of the returned products are modelled using fuzzy triangular numbers. To capture the real world conditions of the proposed problem, our model aims at maximizing the profit incurred in the recovery process in an uncertain environment. The model was solved with the help of fuzzy mathematical programming. The model is validated by a company case belonging to the manufacturing of electronic products. To increase the applicability of the product recovery process in the industry, we propose a recovery process for the planning horizon consisting of multi periods and multi products. The outcomes of the proposed model indicate that for the successful realisation of such network, customers need to be legally enforced to return their end of used products in the channels established for value recovery. [ABSTRACT FROM AUTHOR]

Reliability is an important issue in electricity distribution systems, with strict regulatory policies and investments needed to improve it. This paper presents a mixed integer linear programming (MILP) model for clustering electrical customers, maximizing system reliability and minimizing outage costs. However, the evaluation of reliability and its corresponding nonlinear function represent a significant challenge, making the use of mathematical programming models difficult. The proposed heuristic procedure overcomes this challenge by using a linear formulation of reliability indicators and incorporating them into the MILP model for clustering electrical customers. The model is mainly defined on a density-based heuristic that constrains the set of possible medians, thus dealing with the combinatorial complexity associated with the problem of empowered p-medians. The proposed model proved to be effective in improving the reliability of real electrical distribution systems and reducing compensation costs. Three substation cluster scenarios were explored, in which the total utility compensations were reduced by approximately USD 86,000 (1.80%), USD 67,400 (1.41%), and USD 64,000 (1.3%). The solutions suggest a direct relationship between the reduction in the compensation costs and the system reliability. In addition, the alternative modeling approach to the problem served to match the performance between the distribution system reliability indicators. [ABSTRACT FROM AUTHOR]

This paper investigates the design problem of an electric bus (E-bus) route with charging stations to smooth the operations between E-bus service and charging. The design variables include the locations of E-bus stops, number of charging piles at charging stations, fare, and headway. A mathematical programming model is proposed to maximize social welfare in consideration of the uncertain charging demand at charging stations. The model solution algorithm is also designed. The model and algorithm are demonstrated on the E-bus route 931 in the city of Suzhou, China. The results of the case studies show that (i) the right number of stops on a bus route can contribute to the highest social welfare; (ii) the pile–bus ratio decreases with the increase of E-bus fleet size, thereby improving the E-bus charging efficiency at charging stations; and (iii) deploying charging stations at one end of a bus route can achieve a shorter waiting time for E-bus compared with deployment at two ends. [ABSTRACT FROM AUTHOR]

Calculus of Variations In the paper I On a Non-Newtonian Calculus of Variations i , Delfim F. M. Torres presents, for the first time in the literature, a non-Newtonian calculus of variations that involves the minimization of a function defined by a non-Newtonian integral with a Lagrangian depending on the non-Newtonian derivative. This publication is an editorial for the Special Issue of Axioms "Calculus of Variations, Optimal Control and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th birthday". This Special Issue is dedicated to Professor Delfim F. M. Torres on the occasion of his 50th birthday, as recognition of his significant contributions to Mathematics, in particular in the calculus of variations, optimal control, and mathematical biology. [Extracted from the article]

A linear problem of regression analysis is considered under the assumption of the presence of noise in the output and input variables. This approximation problem may be interpreted as an improper interpolation problem, for which it is required to correct optimally the positions of the original points in the data space so that they all lie on the same hyperplane. The use of the quadratic approximation criterion for such a problem led to the appearance of the total least squares method. In this paper, we use the minimax criterion to estimate the measure of correction of the initial data. It leads to a nonlinear mathematical programming problem. It is shown that this problem can be reduced to solving a finite number of linear programming problems. However, this number depends exponentially on the number of parameters. Some methods for overcoming this complexity of the problem are proposed. [ABSTRACT FROM AUTHOR]

The ever-growing participation of Renewable Energy Sources (RES) in modern distribution networks is replacing an important portion of Conventional Generation (CG), which brings along new challenges in the planning and operation of distribution grids. As RES such as Photovoltaic Energy (PV) and Wind Power Generation (WPG) increase in distribution networks, studies regarding their integration and coordination become more important. In this context, the purpose of this paper is to propose a Multi-period Optimal Power Flow (MOPF) model for the optimal coordination of Battery Energy Storage Systems (BESSs) with PV, WPG, and CG in modern distribution networks. The model formulation was developed in A Modeling Language for Mathematical Programming (AMPL) and solved through the Knitro solver within a time horizon of 24 h. A distinctive feature and one of the main contributions of the proposed approach is the fact that BESSs can provide both active and reactive power. The proposed optimization model reduces power losses and improves voltage profiles. To show the applicability and effectiveness of the proposed model, several tests were carried out on the 33-bus distribution test system and a real distribution system of 141 buses located in the metropolitan area of Caracas. Power loss reductions of up to 58.4% and 77% for the test systems of 33 and 141 buses were obtained, respectively, when BESSs provided both active and reactive power. The results allow us to conclude that the proposed model for optimal coordination of BESSs with RES is suitable for real-life applications, resulting in important reductions of power losses and flattening of voltage profiles. [ABSTRACT FROM AUTHOR]

A novel topology optimization method for the design of coated structures infilled with multiple materials is proposed in this paper, where a novel material interpolation model for the topology description is developed based on the ordered SIMP scheme. With the introduction of two special Heaviside projections into the two-step filtering and projection procedure, the external coating and the substrate region can be well identified by using several modified design variables. Then, the material distribution of the multi-material infilling is obtained by multiplying the infill identification field with the piece-wisely projected design variables and optimized via the mathematical programming algorithm under the ordered SIMP framework. Using an eroded density field and its original field, the uniform thickness of the external coating can be well controlled. The proposed approach for optimizing coated structures with multi-phase infill materials is easy to implement due to its implementation relying on those frequently-used filtering and projection operations. Besides, without introducing any additional design variables, the method developed in this paper inherits the advantages of the ordered SIMP method and has great calculation efficiency and stable iteration performance. With the consideration of several issues such as different coating thicknesses and different design parameters, several 2D numerical examples are studied to demonstrate the effectiveness of the proposed approach, as well as a 3D example. The optimization results illustrate that the method developed in this paper is effective for the design of coated structures infilled with multiple materials and the advantages of considering multiple infill materials is also validated. • A new filtering and projection procedure is proposed for coated structures. • Without extra variables, coated structures with multi-material infilling are modeled. • Using frequently used filtering operations, the proposed method is easy to implement. • The proposed approach exhibits stable iteration histories. • Despite certain parameter dependencies, optimized results have suitable performance. [ABSTRACT FROM AUTHOR]

The dynamic and complex environment affects the operational efficiency of automated guided vehicles (AGVs) at automated container terminals, in which artificial intelligent approaches are applied to address optimization problems in dynamic systems. This paper proposes a digital twin-based decision support approach to improve the efficiency of AGV scheduling service. Accordingly, the factors that affect AGV scheduling performance, including conflicts, failures, and battery constraints, are discussed first. Then, the framework and main steps of the proposed approach are described. The physical operation space is mapped into the virtual space, and both spaces keep synchronized to support the verification of solutions. A mathematical programming model and Q-learning algorithm are used to generate the AGV scheduling plan considering battery charging. Numerical experiments are conducted to demonstrate the effectiveness of the proposed approach. Comparisons of the digital twin-based approach, genetic algorithm (GA), and particle swarm optimization (PSO) are also made with different scale experiments. It appears that the proposed digital twin-based approach is superior to GA and PSO when solving small- and large-scale cases. A sensitivity analysis is performed concerning the battery utilization rate, task, and AGV number. Experimental results show that an optimal configuration of AGV and task can improve the battery utilization rate and reduce the completion time. • A digital twin-based decision support approach is proposed to improve scheduling. • A mathematical programming model is developed to minimize the total completion time. • Digital twin and Q-learning are used to monitor operation and obtain solutions. • Sensitivity analysis of battery utilization is made to provide equipment maintenance. • The proposed approach is superior based on the comparison of solution performances. [ABSTRACT FROM AUTHOR]

• The model allocates safety stocks in supply chains at minimum cost. • An MIQCP reformulation with piecewise approximation greatly improves computational efficiency. • The piecewise function yields an improved estimation for the fill rates. • The GSM is extended to handle non-normally distributed demands. • Real-world case studies solved to optimality within few seconds of computational time. This paper presents a Multi-Echelon Inventory Optimization (MEIO) framework, based on the Guaranteed-Service Model (GSM), to allocate safety stocks across a supply chain with several locations and products, minimizing costs while meeting service level objectives. Extending previous work by Achkar et al. (2023), this paper enhances the Mixed-Integer Quadratically Constrained Program (MIQCP) with a highly efficient solution approach. The model introduces a piecewise linear approximation, significantly improving computational efficiency and the accuracy of the approximation for the fill rate function. It also introduces a different and more efficient approach to account for stochastic lead times using a discrete function. Moreover, an extension of the approach to account for non-normally distributed demands is proposed. The model is applied to several instances of a real-world case study from a pharmaceutical company, with more than 7300 product-location combinations, showing that optimal solutions can be obtained within few seconds of computational time. [ABSTRACT FROM AUTHOR]

Randomized decision making refers to the process of making decisions randomly according to the outcome of an independent randomization device, such as a dice roll or a coin flip. The concept is unconventional, and somehow counterintuitive, in the domain of mathematical programming, in which deterministic decisions are usually sought even when the problem parameters are uncertain. However, it has recently been shown that using a randomized, rather than a deterministic, strategy in nonconvex distributionally robust optimization (DRO) problems can lead to improvements in their objective values. It is still unknown, though, what is the magnitude of improvement that can be attained through randomization or how to numerically find the optimal randomized strategy. In this paper, we study the value of randomization in mixed-integer DRO problems and show that it is bounded by the improvement achievable through its continuous relaxation. Furthermore, we identify conditions under which the bound is tight. We then develop algorithmic procedures, based on column generation, for solving both single- and two-stage linear DRO problems with randomization that can be used with both moment-based and Wasserstein ambiguity sets. Finally, we apply the proposed algorithm to solve three classical discrete DRO problems: the assignment problem, the uncapacitated facility location problem, and the capacitated facility location problem and report numerical results that show the quality of our bounds, the computational efficiency of the proposed solution method, and the magnitude of performance improvement achieved by randomized decisions. Summary of Contribution: In this paper, we present both theoretical results and algorithmic tools to identify optimal randomized strategies for discrete distributionally robust optimization (DRO) problems and evaluate the performance improvements that can be achieved when using them rather than classical deterministic strategies. On the theory side, we provide improvement bounds based on continuous relaxation and identify the conditions under which these bound are tight. On the algorithmic side, we propose a finitely convergent, two-layer, column-generation algorithm that iterates between identifying feasible solutions and finding extreme realizations of the uncertain parameter. The proposed algorithm was implemented to solve distributionally robust stochastic versions of three classical optimization problems and extensive numerical results are reported. The paper extends a previous, purely theoretical work of the first author on the idea of randomized strategies in nonconvex DRO problems by providing useful bounds and algorithms to solve this kind of problems. [ABSTRACT FROM AUTHOR]

With the development of modern science and technology, the field of UAV has also entered the era of high-tech exploration. Among them, the task planning, allocation, path exploration, and algorithm optimization of heterogeneous multi UAV technology are our main concerns. Based on the above situation, this paper proposes a heterogeneous multi UAV task planning technology based on ant colony algorithm powered BP neural network. The planning, research, and design are mainly carried out according to the actual situation of the UAV flight test, and the mathematical programming model is established according to the UAV load degree and maximum flight distance as constraints. This paper focuses on the contribution of the ant colony optimization algorithm to benefit maximization and task minimization. The experimental results show that the BP neural network optimized by the ant colony algorithm can improve the number of iterations and training time. Compared with some comparative algorithms, its performance is better. [ABSTRACT FROM AUTHOR]