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• 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]

Problems related to the extremization of functions have been studied for quite a long time not only by Russian experts but also by the world's leading experts in the field of applied mathematics. It should be noted that, nowadays, not all problems on this topic have a solution, despite the ongoing active research in mathematical modeling and mathematical programming. A serious work is underway on a deeper study of the properties of extremizable functions. This is especially topical in the context of our country's transition to a knowledge economy and, as a first step towards this, to the digital economy, when powerful supercomputers with performance of hundreds and thousands of petaflops have arisen and quantum computers begin to occur. The paper is a survey of results associated with a new class of functions that are useful in extremization problems and is based on joint work of the authors. [ABSTRACT FROM AUTHOR]

In the context of project management, the attention given to project portfolio management has increased in recent years. The use of mathematical programming for portfolio management is also on the rise, because it integrates the project interactions with the multiple objectives of portfolio management into a single model. Among the possible objectives, recent studies have paid special attention to the emerging objective of future preparedness, which has not yet been incorporated into the existing mathematical models. This paper presents a mixed-integer nonlinear optimization model for portfolio selection that considers four main performance measures for project management, namely, value maximization, strategic alignment, balance, and future preparedness. Given the importance of the last measure, the purpose of this paper is to provide a more complete model that provides the marginal contribution and the best combination of projects according to the needs of the company. The model is tested using real data from two companies, one in Brazil and one in Canada, and the results obtained are coherent with their respective practices. [ABSTRACT FROM AUTHOR]

In this paper, we study the quadratic assignment problem with a rank-one cost matrix (QAP-R1). Four integer-programming formulations are introduced of which three are assumed to have partial integer data. Unlike the standard quadratic assignment problem, some of our formulations can solve reasonably large instances of QAP-R1 with impressive running times and are faster than some metaheuristics. Pairwise relative strength of the LP relaxations of these formulations are also analyzed from theoretical and experimental points of view. Finally, we present a new metaheuristic algorithm to solve QAP-R1 along with its computational analysis. Our study offers the first systematic experimental analysis of integer-programming models and heuristics for QAP-R1. The benchmark instances with various characteristics generated for our study are made available to the public for future research work. Some new polynomially solvable special cases are also introduced. Summary of Contribution: This paper aims to advance our knowledge and ability in solving an important special case of the quadratic assignment problem. It shows how to exploit inherent properties of an optimization problem to achieve computational advantages, a strategy that was followed by researchers in model building and algorithm developments for decades. Our computational results attest to this time-tested general philosophy. The paper presents the first systematic computational study of the rank one quadratic assignment problem, along with new mathematical programming models and complexity analysis. We believe the theoretical and computational results of this paper will inspire further research on the topic and will be of significant value to practitioners using rank one quadratic assignment models. [ABSTRACT FROM AUTHOR]

The analytic hierarchy process (AHP) is one of the most popular multi-criteria decision-making (MCDM) methods, and so is its extension fuzzy analytic hierarchy process (FAHP). However, the FAHP, unlike the AHP, easily handles the trusted weights by the consistency index (CI) or consistency ratio (CR). We need to first derive the consistent fuzzy pairwise comparison matrix (FPCM) by the transitivity axiom and then drive fuzzy weights. We also need a flexible mechanism for users to control the spread of fuzzy weights under tolerable consistency. In this paper, we propose a novel model based on mathematical programming to derive rational fuzzy weights of the FAHP and provide a parameter for decision-makers to control the spread of fuzzy weights. Three examples are used to demonstrate the proposed method and compared with others to validate and justify the proposed method. [ABSTRACT FROM AUTHOR]

This paper systematically constructs a multi-project and a multi-objective human resource scheduling mathematical model in construction projects and puts forward an improved genetic algorithm to solve it by aiming at the problems existing in the process of human resource scheduling and optimization. Specifically, first, the basic mathematical models of GPRs and resource-constrained construction project human resource scheduling problem (RCWSP/GPRs) are established, and the multi-project equilibrium problem is extended. Then, an improved inter-cluster separation (ICS) algorithm is proposed and used to solve the RCWSP/GPRs problem. Finally, on this basis, the mathematical model of multi-project and multi-objective human resource scheduling problem and the solution method based on multi-objective-integrated circuit are proposed. At the same time, the resource-constrained multi-project and multi-skill human resource scheduling problem and the integer programming mathematical model under the generalized priority relationship are proposed. Also, the simulation results verify the accuracy of the proposed algorithm and model. [ABSTRACT FROM AUTHOR]

In the last years, many areas in science, business, and engineering have experienced an enormous growth in the amount of data that they are required to analyze. In many cases, this analysis relies intimately on data visualization and, as a result, graph drawing has emerged as a new field of research. This paper addresses the challenge of drawing hierarchical graphs, which is one of the most widely used drawing standards. We introduce a new mathematical model to automatically represent a graph based on the alignment of long arcs, which we combine with the classic arc crossing minimization objective in hierarchical drawings. We complement our proposal with a heuristic algorithm that can obtain high-quality results in the short computational time required by graph drawing systems. Our algorithm joins two methodologies, tabu search and strategic oscillation (SOS), to perform a fast and effective exploration of the search space. We conduct extensive experimentation that integrates our new mathematical programming formulation and the SOS tabu search that targets large instances. Our statistical analysis confirms the effectiveness of this proposal. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of partitioning a complete weighted graph into complete subgraphs, each having the same number of vertices, with the objective of minimizing the sum of edge weights of the resulting subgraphs. This NP-complete problem arises in many applications such as assignment and scheduling-related group partitioning problems and micro-aggregation techniques. In this paper, we present a mathematical programming model and propose a complementary column generation approach to solve the resulting model. A dual based lower bounding feature is also introduced to curtail the notorious tailing-off effects often induced when using column generation methods. Computational results are presented for a wide range of test problems. [ABSTRACT FROM AUTHOR]

• We develop a mathematical programming model for scheduling turnaround maintenance activities for a network of plants in a supply chain. • We propose a heuristic algorithm for solving the model when the network has large number of plants. • A case study petrochemical supply chain is used to demonstrate the utilization of the model and the effectiveness of the heuristic. Turnaround (TAM) is a periodic maintenance in which plants are shutdown to conduct inspections, repairs, preventive maintenance and overhauls. The shutdown periods range from three to four weeks and prolonging this period is expensive and therefore requires effective planning. The primary purpose of this paper is to develop a mathematical programming model to coordinate and plan TAM for several plants in an integrated supply chain network. A secondary objective is to develop a heuristic algorithm for solving the model when the network has large number of plants. The model and the algorithm are developed, tested and applied on a case study petrochemical supply chain. The exact algorithm takes 8.3 times the time of the heuristic. In addition the heuristic algorithm provides near optimal solution in much shorter time. The developed model provides a tool to plan TAM for several plants in an integrated supply in an optimal fashion. [ABSTRACT FROM AUTHOR]

Caching at mobile devices and leveraging device-to-device (D2D) communication are two promising approaches to support massive content delivery over wireless networks. The analysis of cache-enabled wireless networks is usually carried out by assuming that devices are uniformly distributed, however, in social networks, mobile devices are intrinsically grouped into disjoint clusters. In this regards, this paper proposes a spatiotemporal mathematical model that tracks the service requests arrivals and account for the clustered devices geometry. Two kinds of devices are assumed, particularly, content clients and content providers. Content providers are assumed to have a surplus memory which is exploited to proactively cache contents from a known library, following a random probabilistic caching scheme. Content clients can retrieve a requested content from the nearest content provider in their proximity (cluster), or, as a last resort, the base station (BS). The developed spatiotemporal model is leveraged to formulate a joint optimization problem of the content caching and spectrum partitioning in order to minimize the average service delay. Due to the high complexity of the optimization problem, the caching and spectrum partitioning problems are decoupled and solved iteratively using the block coordinate descent (BCD) optimization technique. To this end, an optimal and suboptimal solutions are obtained for the bandwidth partitioning and probabilistic caching subproblems, respectively. Numerical results highlight the superiority of the proposed scheme over conventional caching schemes under equal and optimized bandwidth allocations. Particularly, it is shown that the average service delay is reduced by nearly 100% and 350%, compared to the Zipf and uniform caching schemes under equal bandwidth allocations, respectively. [ABSTRACT FROM AUTHOR]

Proactive scheduling aims at the generation of robust baseline schedules, which has been studied for many years with the assumption that activity splitting is not allowed. In this paper, we focus on the proactive resource-constrained project scheduling problem in which each activity can be split at discrete time instants under the constraints of a maximum number of splitting and a minimum period of continuous execution. In this problem, setup times are also considered. A mathematical model is established and analyzed, of which two properties and one lemma are proposed. As the problem is proved to be ${\text{NP}}$ -hard in the strong sense, for solving the model, we develop a genetic algorithm (GA) in which the two proposed properties and the lemma are applied as local search operators. After linearizing the proposed model, we use a commercial mathematical programming solver as a benchmark to solve the problem. From the computational results, we find that the developed GA is effective and efficient in solving the defined problem, and activity splitting improves robustness. With the growth of the maximum number of splitting, the decline in the minimum execution time, the decrease in the setup times, and the extension of the project due date, robustness increases. [ABSTRACT FROM AUTHOR]

• Comprehensive review of mathematical programming models for shale oil & gas development. • Detailed comparison of publications in five major topic areas: (1) development planning, (2) water management, (3) production optimization, (4) supplies, gathering & processing, and (5) LCA & sustainability. • Highlight of optimization deployment success stories in industry (i.e., optimization value proposition in oil & gas). • Perspective on outstanding research opportunities in the respective field of study. In this paper, we provide a comprehensive review of mathematical programming models for shale oil & gas development, and we offer a perspective on outstanding research opportunities. We distinguish contributions in five major topic areas, namely: (1) development planning, (2) water management, (3) production optimization, (4) supplies, gathering & processing, and (5) life cycle analysis & sustainability. We highlight how various types of mathematical programming models (i.e., linear programs, nonlinear programs, mixed-integer linear programs, mixed-integer nonlinear programs) have been proposed primarily by the Process Systems Engineering community to address the respective decision-making problems, and we highlight instances of successful deployment in industry. Finally, based on a critical assessment of the existing body of work, we identify opportunities for future research across the major topic areas. [ABSTRACT FROM AUTHOR]

The concept of eco-industrial park (EIP) has recently become the subject of a great deal of attention from industry and academic research groups. This paper proposes a series of systematic approaches for multi-level modelling and optimisation in EIPs. The novelties of this work include, (1) building a four-level modelling framework (from unit level to process level, plant level and industrial network level) for EIP research, (2) applying advanced mathematical modelling methods to describe each level operation, (3) developing efficient methodologies for solving optimisation problems at different EIP levels, (4) considering symbiotic relations amongst the three networks (material, water and energy networks) at the top EIP level with the boundary conditions of economic, social and legal requirements. For methodology demonstration, two cases at process level and industrial network level respectively are tested and solved with the developed modelling and optimisation strategies. Finally, the challenges and applications in future EIP research are also discussed, including data collection, the extension of the current networks to EIPs, and the feasibility of the proposed methodologies for complex EIP problems. The extended EIPs include the combination of material exchanges, energy systems and waste-water treatment networks. The aspects considered for future industrial ecology are carbon emission, by-product reuse, water consumption, and energy consumption. The main object of this paper is to explain the detailed model construction process and the development of optimisation approaches for a complex EIP system. In future work, this system is expected to share services, utility, and product resources amongst industrial plants to add value, reduce costs, improve environment, and consequently achieve sustainable development in a symbiosis community. [ABSTRACT FROM AUTHOR]

The paper presents the solution methodology of a multi-objective probabilistic fractional programming problem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In first step, multi-objective probabilistic fractional programming problem is converted to deterministic multi-objective fractional mathematical programming problem. In the second step, it is converted to its equivalent multi-objective mathematical programming problem. Finally, -constraint method is applied to find the best compromise solution. A numerical example and application are presented to demonstrate the procedure of proposed mathematical model. [ABSTRACT FROM AUTHOR]

This work presents a mathematical modelling based approach including many constraints encountered at Universities in Turkey. As in many other countries also in Turkey it appears that universities are too autonomous, and they have medley of individual requirements and constraints. This condition makes it very difficult to suggest a generalized model and a solution algorithm for university timetabling problem (UTP). In general, in this paper it is aimed to design compatible and flexible approach to generate timetable so as to meet all the requirements of Turkish universities. First, by reviewing the studies in which mathematical modelling approaches were used, comprehensive information about the subject has been presented. Then, proposed hierarchical mathematical modelling approach is described (HMMA). Since (UTP) is highly context-dependent the results of this study couldn't been compared to those of the studies which are published already. Proposed approach is tested 2015-2016 academic year winter term data of Atatürk University Engineering Faculty and obtained results are presented comparatively with results obtained from manual preparation in terms of seven objectives. [ABSTRACT FROM AUTHOR]

In the field of service management plays a decisive role the location of the facilities to improve the quality of services. The maximal covering location problem allows locating a known number of facilities in order to maximize the demand covered. An important aspect to take into account is the varying of demand of the nodes with respect to the time (multi-period model). In addition, each facility could be of different types. A model that takes into account the existence of different types of facilities in order to cover the demand in multi-period environments has not been found in the literature. In this paper we propose a new generalization of the dynamic maximal covering location problem where different types of facilities (with different radius of coverage) could be open in each location. In this work we used the model on case study with the objective to locate the police patrol. [ABSTRACT FROM AUTHOR]

Highlights • A new rigorous bilevel decomposition strategy for MILPs with strong linking constraints. • An extended cross decomposition method based on the bilevel decomposition strategy. • Application of the extended cross decomposition method to stochastic programming with CVaR constraints. • Case studies with a variety of scenario instances showing significant computational advantages of the proposed methods. Abstract Large-scale mixed-integer linear programming (MILP) problems, such as those from two-stage stochastic programming, usually have a decomposable structure that can be exploited to design efficient optimization methods. Classical Benders decomposition can solve MILPs with weak linking constraints (which are decomposable when linking variables are fixed) but not strong linking constraints (which are not decomposable even when linking variables are fixed). In this paper, we first propose a new rigorous bilevel decomposition strategy for solving MILPs with strong and weak linking constraints, then extend a recently developed cross decomposition method based on this strategy. We also show how to apply the extended cross decomposition method to two-stage stochastic programming problems with conditional-value-at-risk (CVaR) constraints. In the case studies, we demonstrate the significant computational advantage of the proposed extended cross decomposition method as well as the benefit of including CVaR constraints in stochastic programming. [ABSTRACT FROM AUTHOR]

This paper proposed a panel data clustering model based on D-vine and C-vine and supported a semiparametric estimation for parameters. These models include a two-step inference function for margins, two-step semiparameter estimation, and stepwise semiparametric estimation. In similarity measurement, similarity coefficients are constructed by a multivariate Hierarchical Nested Archimedean Copula (HNAC) model and compound PCC models, which are HNAC and D-vine compound model and HNAC and C-vine compound model. Estimation solutions and models evaluation are given for these models. In the case study, the clustering results of HNAC and D-vine compound model and HNAC and C-vine compound model are given, and the effect of different copula families on clustering results is also discussed. The result shows the models are effective and useful. [ABSTRACT FROM AUTHOR]

In this paper, we address the non-permutation flowshop scheduling problem with minimal and maximal time lags between successive operations of each job. For this problem, the set of permutation schedules is not a dominant set but not all non-permutation schedules are feasible because they are not always able to satisfy all time lag constraints. We present a theoretical study, limited to the two-machine case, and related to the change on one machine of the order of two successive jobs of a permutation schedule. This study gives first the necessary conditions to make such move with regard to the feasibility of the schedule; secondly the necessary conditions to make such move interesting with regard to either the makespan or the number of tardy jobs. Through this analysis, we obtain new properties of dominance of permutation schedules. The results of the study are incorporated into a heuristic algorithm which starts the search with optimal permutation schedules and tries to improve them so as to obtain better non-permutation schedules. We also propose a mixed integer linear programming model. The objective function is to minimize lexicographically the number of tardy jobs as primary criterion and the makespan as secondary one. Computational experiments are performed to compare permutation with non-permutation schedules. [ABSTRACT FROM AUTHOR]

In today's business world, oil companies cannot be productive and competitive, and thus, will not survive without taking the supply chain management concepts into account. Consequently, the management of a crude oil supply chain (COSC) is increasingly receiving substantial importance. The growing number of papers and books on this topic is a further witness of this fact. To foster insight into issues intertwined with COSC problems, this paper is devoted to an extensive review of mathematical programming models in this context. The classification approach for this review is based on a taxonomy framework. In this framework, ongoing and emerging challenges surrounding the strategic and tactical decisions of COSC problems are investigated. As a main goal, the gaps of literature are analyzed to recommend possible research directions. [ABSTRACT FROM AUTHOR]

Holographic algorithms introduced by Valiant have two ingredients: matchgates, which are gadgets realizing local constraint functions by weighted planar perfect matchings, and holographic reductions, which show equivalences among problems with different descriptions via basis transformations. In this paper, we replace matchgates in the paradigm above by the affine type and the product type constraint functions, which are known to be tractable in general (not necessarily planar) graphs. We present polynomial-time algorithms to decide if a given counting problem has a holographic reduction to another problem defined by the affine or product-type functions. We also give polynomial-time algorithms to the same problems for symmetric functions, where the complexity is measured in terms of the (exponentially more) succinct representations. The latter result implies that the symmetric Boolean Holant dichotomy (Cai, Guo, and Williams, SICOMP 2016) is efficiently decidable. Our proof techniques are mainly algebraic. [ABSTRACT FROM AUTHOR]

This paper presents an effective use of hybrid metaheuristics algorithm for solving Job Shop Scheduling Problem (JSSP). Integration of three metaheuristics algorithms: Shuffled Frog Leaping Algorithm (SFLA), Intelligent Water Drops algorithm (IWD) and Path Relinking (PR) algorithm were put together to solve JSSP. First, simulation model was developed and tested on the test data of Traveller Salesman Problem (TSP). Second, the model was tested on real world production line to solve the problem of Minimum Needed Workers (MNW) at the production line. The model enables individual test of three mentioned algorithms and calculation of new proposed Random Multi- Neighbourhood based Shuffled Frog Leaping Algorithm with Path Relinking (RMN-SFLA-PR). Experiments were tested on two software environments MATLAB and Simio, which gives us reliable, robust and tangible results. Results show that the new proposed RMN-SFLA-PR algorithm converged to optimum almost ten times faster than individual algorithms. The most important thing is the successful rate of all independent runs of the proposed RMN-SFLA-PR is 100 % in low-dimensional cases of the 4 benchmarks (dj38) and in JSSP to solve MNW for the real world production line. [ABSTRACT FROM AUTHOR]

Water inrush from coal floor is one of the main disasters in underground coal mining operations. When establishing or selecting control methods, various factors, such as cost, risk and operability, should be taken into consideration. However, due to the lack of effective mathematical models, the selecting process in practice relies solely on engineering experiences, which may not lead to an optimal and effective decision. This paper proposes a method that considers the parameters, variables, and constraints in water inrush control and it adopts economic factors as the objective function to construct a multi-objective optimization model. Using this method, one can not only rank different control measures but also obtain a preferred control effect level, which is a trade-off between efficiency and economy. A case study is used to demonstrate the robustness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new mathematical programming model for integrating production and procurement transport planning decisions in manufacturing systems in a unique optimization model. This problem was introduced conceptually and dubbed as MRP IV by Díaz-Madroñero et al. (2012) to extend the current MRP (material requirement planning) systems. This proposal simultaneously considers material, production resources capacities and procurement transport planning decisions with different shipping modes (such as full-truckload, less-than-truckload and milk-run) in the supply chain to avoid suboptimal results, which are usually generated due to sequential and independent plans. We considered an industrial automobile company to validate the proposed model using real world data. The results obtained by the MRP IV proposed model, in terms of total planning costs and transport efficiency indicators, are better than those obtained in the current heuristic procedures followed in the company under study. [ABSTRACT FROM AUTHOR]

In the planning phase of district energy systems, optimization models based on mathematical programming are a widely used approach. Most optimization models determine the optimal energy system design based on a single representative year. However, this approach is unable to consider changing economic and technological boundary conditions over the system's lifetime. As a result, these one-period models fall short for districts with 5th generation district heating and cooling (5GDHC) networks, which are typically developed over long time periods and are built in multiple construction phases. In this paper, we present two multi-period optimization approaches for designing 5GDHC districts: The first approach is a forward-looking model which determines the optimal investment pathway by using a perfect foresight of future parameter developments. In the second approach, a one-period model is solved repeatedly for every investment period without knowledge of future parameter developments. Both approaches are compared to a one-period model for a real-world 5GDHC district in Germany. In comparison with a one-period design approach, the forward-looking method leads to total cost savings of up to 17 % and the sequential method of up to 11 %. By using a forward-looking model, gas-fired technologies are sized smaller while the capacity of electricity-driven technologies in the energy hub as well as photovoltaic modules and thermal energy storages in buildings increases compared to a one-period model. The case study shows that a multi-period modeling approach is an important addition to design optimization models for 5GDHC networks and can have a significant impact on the optimal design. [ABSTRACT FROM AUTHOR]

The mathematical model for airline network seat inventory control problem is usually investigated to maximize the total revenue under some constraints such as capacities and demands. This paper presents a chance-constrained programming model based on the uncertainty theory for network revenue management, in which the fares and the demands are both uncertain variables rather than random variables. The uncertain programming model can be transformed into a deterministic form by taking expected value on objective function and confidence level on the constraint functions. Based on the strategy of nested booking limits, a solution method of booking control is developed to solve the problem. Finally, this paper gives a numerical example to show that the method is practical and efficient. [ABSTRACT FROM AUTHOR]

It is one of the important issues in the field of today's sewage treatment of researching the MBR membrane flux prediction for membrane fouling. Firstly this paper used the principal component analysis method to achieve dimensionality and correlation of input variables and obtained the three major factors affecting membrane fouling most obvious:MLSS, total resistance, and operating pressure. Then it used the BP neural network to establish the system model of the MBR intelligent simulation, the relationship between three parameters, and membrane flux characterization of the degree of membrane fouling, because the BP neural network has slow training speed, is sensitive to the initial weights and the threshold, is easy to fall into local minimum points, and so on. So this paper used genetic algorithm to optimize the initial weights and the threshold of BP neural network and established the membrane fouling prediction model based on GA-BP network. As this research had shown, under the same conditions, the BP network model optimized by GA of MBR membrane fouling is better than that not optimized for prediction effect of membrane flux. It demonstrates that the GA-BP network model of MBR membrane fouling is more suitable for simulation of MBR membrane fouling process, comparing with the BP network. [ABSTRACT FROM AUTHOR]

Highlights: [•] This paper addresses the problem of the design of a gain-scheduled controller (GSC). [•] In this paper we have proposed two GSC design procedures. [•] GSC design procedure guarantees parameter dependent quadratic stability. [•] GSC design procedure ensures the guaranteed cost. [•] The proposed procedure is based on the Lyapunov theory and BMI. [Copyright &y& Elsevier]

Derive the quantitative predictions of constraint-based models require of conversion algorithms to enumerate and construct the skeleton graph conformed by the extreme points of the feasible region, where all constraints in the model are fulfilled. The conversion is problematic when the system of linear constraints is degenerate. This paper describes a conversion algorithm that combines the best of two methods: the incremental slicing of cones that defeats degeneracy and pivoting for a swift traversal of the set of extreme points. An extensive computational practice uncovers two complementary classes of conversion problems. The two classes are distinguished by a practical measure of complexity that involves the input and output sizes. Detailed characterizations of the complexity classes and the corresponding performances of the algorithm are presented. For the benefit of implementors, a simple example illustrates the stages of the exposition. [ABSTRACT FROM AUTHOR]

In recent years sampling approaches have been used more widely than optimization algorithms to find parameters of conceptual rainfall–runoff models, but the difficulty of calibration of such models remains in dispute. The problem of finding a set of optimal parameters for conceptual rainfall–runoff models is interpreted differently in various studies, ranging from simple to relatively complex and difficult. In many papers, it is claimed that novel calibration approaches, so-called metaheuristics, outperform the older ones when applied to this task, but contradictory opinions are also plentiful. The present study aims at calibration of two simple lumped conceptual hydrological models, HBV and GR4J, by means of a large number of metaheuristic algorithms. The tests are performed on four catchments located in regions with relatively similar climatic conditions, but on different continents. The comparison shows that, although parameters found may somehow differ, the performance criteria achieved with simple lumped models calibrated by various metaheuristics are very similar and differences are insignificant from the hydrological point of view. However, occasionally some algorithms find slightly better solutions than those found by the vast majority of methods. This means that the problem of calibration of simple lumped HBV or GR4J models may be deceptive from the optimization perspective, as the vast majority of algorithms that follow a common evolutionary principle of survival of the fittest lead to sub-optimal solutions. [ABSTRACT FROM PUBLISHER]

To resolve one of uncertainty features, randomness, in ontologies, this paper shows how to characterize uncertainty of concepts from a statistical viewpoint. In addition, with a focus on indirect entities, which are computed from direct entities through mathematical models, the uncertainties propagated from those direct entities are important and should be quantified. Thus, a novel algorithm, named Stochastic Reduced Order Model (SROM), is presented to be applied to quantify the ontological uncertainty propagation in presence of multiple input entities. This SROM-based method could approximate the statistics of indirect entities accurately and efficiently by using a very small amount of samples of input entities. The computational cost is considerably reduced while guaranteeing a reasonable degree of accuracy. Furthermore, the predicted statistics of output entities could be regarded as high-level information and be beneficial for other ontological operations, such as ontology filtering and ontology reasoning. The implementation of the SROM algorithm is non-intrusive to the mathematical model; therefore, this algorithm could be applicable to quantify uncertainty in ontologies with any mathematical relationships. [ABSTRACT FROM AUTHOR]

Security is an issue of paramount importance, yet is it a significant challenge for wireless communications, which becomes more intricate when facing a full duplex (FD) active eavesdropper capable of performing eavesdropping and jamming simultaneously. In this paper, we investigate the physical layer security issue in the presence of an FD active eavesdropper, who launches jamming attacks to further improve the eavesdropping. The jamming, however, also results in self-interference at the eavesdropper itself. This security problem is formulated within a hierarchical game framework where the eavesdropper acts as the leader and the legitimate user is the follower. In particular, we first investigate the follower’s secrecy rate maximization problem and derive the optimal legitimate transmission strategy. Then, the leader’s wiretap rate maximization is expressed as a mathematical program with equilibrium constraints (MPEC). Leveraging the concavity of the follower’s problem, we transform the MPEC problem into a single-level optimization and obtain the jamming power allocation strategy by applying the primal-dual interior-point method. Moreover, we analyze the situations where only partial channel state information is available at the legitimate user and the corresponding impacts on the game. Finally, we present extensive simulation results to validate our theoretical analysis. [ABSTRACT FROM PUBLISHER]

In this paper we consider k -meet-semidistributive lattices and we are interested in the computation of the set-colored poset associated to an implicational base. The parameter k is of interest since for any finite lattice L there exists an integer k for which L is k -meet-semidistributive. When k = 1 they are known as meet-semidistributive lattices. We first give a polynomial time algorithm to compute an implicational base of a k -meet-semidistributive lattice from its associated colored poset. In other words, for a fixed k , finding a minimal implicational base of a k -meet-semidistributive lattice L from a context (FCA literature) of L can be done not just in output-polynomial time (which is open in the general case) but in polynomial time in the size of the input. This result generalizes that in [26] . Second, we derive an algorithm to compute a set-colored poset from an implicational base which is based on the enumeration of minimal transversals of a hypergraph and turns out to be in polynomial time for k -meet-semidistributive lattices [13,20] . Finally, we show that checking whether a given implicational base describes a k -meet-semidistributive lattice can be done in polynomial time. [ABSTRACT FROM AUTHOR]

Analysing economic efficiency of farm production always faces a problem of insufficient information. This is particularly true when the analysis is performed on the reference farm where estimates are based on the average aggregated data. The paper illustrates how the combination of different mathematical programming methods could be efficiently used to analyse the farm-production plan with the lack of the on-farm accounting data. The utilised approach shows how the holistic analysis of production planning as a multi-criteria problem could be conducted. The estimation of the missing information and the disaggregation of the endogenous farm data is enabled through different models that are based on the constrained optimisation. The developed models are linked into the spreadsheet modular tool enabling systematic analyses of the farm decision making under risky conditions. Illustration of the modular tool application is given via the analyses of three hypothetic dairy farms. The obtained results indicate that the developed approach enables holistic analyses of the production planning. The methodology applied provides also important information for the measures aimed to increase efficiency as well as to benchmarking the performance of different farm types. The results point to a discrepancy between the solutions obtained through different objective functions and shows the advantage of the multi-criteria approach. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology to optimize the trading strategies of a proactive distribution company (PDISCO) in the real-time market by mobilizing the demand response. Each distribution-level demand is considered as an elastic one. To capture the interrelation between the PDISCO and the real-time market, a bi-level model is presented for the PDISCO to render continuous offers and bids strategically. The upper-level problem expresses the PDISCO’s profit maximization, while the lower-level problem minimizes the operation cost of the transmission-level real-time market. To solve the proposed model, a primal-dual approach is used to translate this bi-level model into a single-level mathematical program with equilibrium constraints. Results of case studies are reported to show the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Job shop scheduling problem is very important one in real application of many kind of industries. In the real world applications, there exist many different kinds of disruptions with different sizes. In this situation, beyond the optimality of the final solution, its ability to absorb disruptions is vital, so that the final solution remains feasible in the case of occurring predicted disruptions. In this paper a robust job shop scheduling problem under disruptions is considered. It is intended to generate robust schedules which are able to absorb a predefined range of disruptions. For this reason, two robustness indices are proposed and the related formulas for computing the required buffer times to reach the desired robustness level are proposed. For this purpose, four methods are proposed to solve the variant defined robust job shop scheduling problem, including (1) a mathematical model, (2) a Branch and Bound algorithm, (3) a beam search algorithm, and (4) a meta-heuristic algorithm based on the particle swarm optimization (PSO) method. The first and second methods result in optimum solution. As the size of the problem increases, the required time to find the optimum solutions raises, so that no solutions can be achieved in rational amount of time, e.g. one hour. Therefore, the third and fourth methods are proposed to find good solutions even for large-scale problem in a limited amount of time. Finally, the algorithms are compared using some randomly generated instances. The results show that each algorithm can outperform the others in different conditions. [ABSTRACT FROM AUTHOR]

Abstract: Since the observed values of security returns in real-world problems are sometimes imprecise or vague, an increasing effort in research is devoted to study the properties of risk measures in fuzzy portfolio optimization problems. In this paper, a new risk measure is suggested to gauge the risk resulted from fuzzy uncertainty. For this purpose, the absolute deviation and absolute semi-deviation are first defined for fuzzy variable by nonlinear fuzzy integrals. To compute effectively the absolute semi-deviations of single fuzzy variable as well as its functions, this paper discusses the methods of computing the absolute semi-deviation by classical Lebesgue–Stieltjes (L–S) integral. After that, several useful absolute deviation and absolute semi-deviation formulas are established for common triangular, trapezoidal and normal fuzzy variables. Applying the absolute semi-deviation as a new risk measure in portfolio optimization, three classes of fuzzy portfolio optimization models are developed by combining the absolute semi-deviation with expected value operator and credibility measure. Based on the analytical representation of absolute semi-deviations, the established fuzzy portfolio selection models can be turned into their equivalent piecewise linear or fractional programming problems. Since the absolute semi-deviation is a piecewise fractional function and pseudo-convex on the feasible subregions of deterministic programming models, we take advantage of the structural characteristics to design a domain decomposition method to separate a deterministic programming problem into three convex subproblems, which can be solved by conventional solution methods or general-purpose software. Finally, some numerical experiments are performed to demonstrate the new modeling idea and the effectiveness of the solution method. [Copyright &y& Elsevier]

Abstract: This paper presents new definitions for process intensification identifying two main categories called unit intensification and plant intensification. This paper also proposes general mathematical programming formulations for the different categories of intensification through a disjunctive formulation to consider the use of existing units or to include additional units. The ideas of process integration (energy, mass and property integration) are very useful for process intensification helping in maximizing throughput for a given process, minimizing process inventory for a given throughput or in minimizing utilities and feedstock for a given throughput (this means that process intensification is broader than process integration). This paper identifies that process intensification is a wider approach than single unit intensification as it was considered by most of the previous works. A case study is presented to show the applicability of the proposed models and definitions. [Copyright &y& Elsevier]

Abstract: In this paper, we study two variants of the problem of adding edges to a graph so as to reduce the resulting diameter. More precisely, given a graph , and two positive integers and , the Minimum-Cardinality Bounded-Diameter Edge Addition (MCBD) problem is to find a minimum-cardinality set of edges to be added to in such a way that the diameter of is less than or equal to , while the Bounded-Cardinality Minimum-Diameter Edge Addition (BCMD) problem is to find a set of edges to be added to in such a way that the diameter of is minimized. Both problems are well known to be NP-hard, as well as approximable within and (up to an additive term of 2), respectively. In this paper, we improve these long-standing approximation ratios to and to (up to an additive term of 2), respectively. As a consequence, we close, in an asymptotic sense, the gap on the approximability of MCBD, which was known to be not approximable within , for some constant , unless . Remarkably, as we further show in the paper, our approximation ratio remains asymptotically tight even if we allow for a solution whose diameter is optimal up to a multiplicative factor approaching . On the other hand, on the positive side, we show that at most twice of the minimal number of additional edges suffices to get at most twice of the required diameter. Some of our results extend to the edge-weighted version of the problems. [Copyright &y& Elsevier]

Abstract: This paper presents the analysis of delay-dependent bounded input bounded output (BIBO) stability for a class of switched uncertain neutral systems. The uncertainty is assumed to be of structured linear fractional form which includes the norm-bounded uncertainty as a special case. First, by introducing the general variation-of-constants formula of neutral systems with perturbation, the BIBO stability property of general linear switched neutral systems with perturbation is established. Next, combining the general variation-of-constants formula with the state-dependent switching rule, new approaches are presented to design the feedback controller and the switching rules. Furthermore, the BIBO stability criteria are obtained in terms of the so-called Lyapunov–Metzler linear matrix inequalities (LMIs). Finally, simulation examples are given to demonstrate the effectiveness and the potential of the proposed techniques in this paper. [Copyright &y& Elsevier]

Abstract: This paper considers an online hierarchical scheduling problem on parallel identical machines. We are given a set of machines and a sequence of jobs. Each machine has a different hierarchy, and each job also has a hierarchy associated with it. A job can be assigned to a machine only if its hierarchy is no less than that of the machine. The objective is to minimize the makespan, i.e., the maximum load of all machines. Two models are studied in the paper. For the fractional model, we present an improved algorithm and lower bounds. Both the algorithm and the lower bound are based on solutions of mathematical programming. For any given , our algorithm is optimal by numerical calculation. For the integral model, we present both a general algorithm for any , and an improved algorithm with better competitive ratios of 2.333 and 2.610 for and 5, respectively. [Copyright &y& Elsevier]

In this paper, we set out to illustrate and discuss how mathematical modelling could and should be applied to aid our understanding of plants and, in particular, plant–soil interactions. Our aim is to persuade members of both the biological and mathematical communities of the need to collaborate in developing quantitative mechanistic models. We believe that such models will lead to a more profound understanding of the fundamental science of plants and may help us with managing real-world problems such as food shortages and global warming. We start the paper by reviewing mathematical models that have been developed to describe nutrient and water uptake by a single root. We discuss briefly the mathematical techniques involved in analysing these models and present some of the analytical results of these models. Then, we describe how the information gained from the single-root scale models can be translated to root system and field scales. We discuss the advantages and disadvantages of different mathematical approaches and make a case that mechanistic rather than phenomenological models will in the end be more trustworthy. We also discuss the need for a considerable amount of effort on the fundamental mathematics of upscaling and homogenization methods specialized for branched networks such as roots. Finally, we discuss different future avenues of research and how we believe these should be approached so that in the long term it will be possible to develop a valid, quantitative whole-plant model. [ABSTRACT FROM AUTHOR]

Given a set of spatial units, such as land parcels and grid cells, how to allocate subsets of it to activities of interest while satisfying certain criteria? Such a decision process is here called spatial allocation. Though many problems of spatial allocation share this generic construct, each may have a quite unique set of criteria and interpret even the same criteria in its own way. Such diversity makes it difficult to model spatial allocation problems in unambiguous terms that are amenable to algorithmic solution. This paper proposes a classification scheme for spatial properties that helps to address a variety of spatial properties in establishing spatial allocation criteria. The implication of the paper is that a number of spatial properties and spatial allocation criteria can be decomposed into a few kinds of primitive spatial properties and their relations. [ABSTRACT FROM AUTHOR]

In this paper the fairness of some methods of allocating seats in a proportional representation (PR) voting system is investigated. Different PR systems are in use throughout the democratic world, but the primary focus here is the method used in South Africa, namely the largest remainder method with a Droop quota. It is shown that as the number of parties increases, the number of lost votes (votes not used to allocate seats) increases when using this method. Other existing allocation methods are discussed and compared with each other as well as with three optimisation methods (based on mathematical programming) introduced in this paper. Applying these mathematical programming methods results in allocations that are more fair than the existing methods of seat allocation, if South African voting data are used. These mathematical models attempt to minimise a number of different measures of the deviation between the actual percentage of votes received and the percentage of seats allocated to a certain party. Ideally this deviation should be zero, but due to the discrete nature of seats this is virtually impossible to achieve. [ABSTRACT FROM AUTHOR]

This paper presents a new step-wise sequential solution strategy for the synthesis of heat integrated water networks (HIWNs) comprising of two mathematical models. The first model minimizes water and energy costs. The optimal freshwater and water flow rates within the HIWN are determined from this model. Using these optimal flow rates, different configurations of HIWN are evaluated for the purpose of heat integration. The second model is the stage-wise heat exchanger network (Yee and Grossmann, 1990), which is solved for each of the evaluated network configuration in a sequential manner. Using this proposed strategy, a set of locally optimal HIWNs are produced and the best one is chosen based on the minimum total annual cost (TAC). The proposed sequential strategy is applied to small and medium sized examples in the literature. The results show that the proposed new sequential solution strategy can be successfully applied to small and medium sized HIWN problems. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model for the design of a non-cooperative supply chain where transportation activities are provided by logistics companies. We consider a four-layer network comprised of manufacturers, retailers, customers, and logistics service providers (LSPs). In this problem, manufacturers, retailers, and LSPs do not collaborate or engage in any type of bargaining strategy among one other. Instead, they compete to supply products to customers at demand markets, while each agent seeks to maximize his own profit. LSPs compete among themselves to provide logistics (transportation/warehousing) services to manufacturers. It is considered that manufacturers, LSPs, and retailers collaborate to maximize services. Normally this problem cannot be modeled as an optimization problem, so we use a variational inequality approach to formulate it. To the best of our knowledge, this important problem, which helps evaluate options and make decisions when logistics activities are provided by LSPs, has not been modeled in the literature and this constitutes our main contribution. The model determines the optimal level of production for each manufacturer, the flow of products between manufacturers and retailers, the flow of products to be handled by each logistics service provider and the flow of products between retailers and demand markets in a non-cooperative environment. Numerous experiments are presented and adapted from test examples that are available in the literature, while results and important findings are discussed. [ABSTRACT FROM AUTHOR]

For using the surface electromyography (sEMG) in various applications, the process consists of three parts: an onset time detection for detecting the first point of movement signals, a feature extraction for extracting the signal attribution, and a feature classification for classifying the sEMG signals. The first and the most significant part that influences the accuracy of other parts is the onset time detection, particularly for automatic systems. In this paper, an automatic and simple algorithm for the real-time onset time detection is presented. There are two main processes in the proposed algorithm: a smoothing process for reducing the noise of the measured sEMG signals and an automatic threshold calculation process for determining the onset time. The results from the algorithm analysis demonstrate the performance of the proposed algorithm to detect the sEMG onset time in various smoothing-threshold equations. Our findings reveal that using a simple square integral as the smoothing-threshold equation with the given sEMG signals gives the best performance for the onset time detection. Additionally, our proposed algorithm is also implemented on a real hardware platform, namely NI myRIO. Using the real-time simulated sEMG data, the experimental results guarantee that the proposed algorithm can properly detect the onset time in the real-time manner. [ABSTRACT FROM AUTHOR]

Over the last few decades, research on resource constrained project scheduling has focused on the development of mathematical programming based approaches for the generation of a nominal schedule under a deterministic environment. During the implementation phase, however, the nominal schedule may need to be revised when one or more resources are disrupted for a length of time. In this paper, we formulate two discrete time based models to deal with two different disruption scenarios for multi-mode resource constrained problems. We propose a reactive re-scheduling procedure for a single, as well as a series of disruptions, without having any disruption information in advance. To test the proposed approaches, sets of ten, twenty and thirty-activity multi-mode test instances from Project Scheduling Library (PSLIB) were used after introducing randomly generated disruption events. The experimental studies were also carried out to determine the effect of different factors related to the disruption recovery process. [ABSTRACT FROM AUTHOR]