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Large varieties of mathematical programming models have been developed to provide decision support to the design engineer. The paper deals with some of the problems and offers practical solutions. [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]

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]

Project management is a process that schemes and controls the project life cycle via the easiest and the best way to achieve project goals. Project managers always aim to simultaneously handle conflicting goals in the organization. In this paper, a new mathematical model is proposed that simultaneously minimizes total cost and completion time and maximizes the quality in the project management decision problem. Contractual penalty cost and contractual reward cost with a new method are the other consideration in the proposed model. In the projects, the relation between time and direct cost is a nonlinear function. Hence, a linearization technique is presented with attention to variable change and piecewise linearization, in which nonlinear function is converted to the linear programming model. On the other hand, in real conditions according to uncertainty in environmental situations and incomplete information, there can be ambiguity in parameters and variables of the problem. The uncertainty of the parameters and variables is expressed with fuzzy sets theory and fuzzy mathematical programming. The other aim of this paper is to introduce a modified version of fully fuzzy multi-objective linear programming for the problem. For analyzing a fully fuzzy time–cost–quality project management model, a practical example of the literature is provided. By examining the results of the model with conflicting objectives, two scenarios are presented to explore the interactions of conflicting objectives on the project, and the results are reported. [ABSTRACT FROM AUTHOR]

The paper proposes a method to integrate numerically an interconnected system, based on an idea of orthogonal approximation of functions. Here, block pulse functions (BPFs) are chosen as the orthogonal set. The main advantage of using this technique is its ability to transform the original optimal control problem to a mathematical programming problem relatively easier to solve. The primary focus of this paper is to exploit and rigorously develop the BPFs parametrization technique for the synthesis of a decentralized observer-based optimal control for large-scale interconnected systems. In addition, we develop a mathematical model of a double-parallel inverted pendulum coupled by a spring, taking into account all possible changes of the connecting position of the elastic spring. In so doing, we conducted advanced simulations applying the new optimal control method to the studied interconnected system. Our results demonstrate the validity and the effectiveness of the developed decentralized observer-based optimal control approach. [ABSTRACT FROM AUTHOR]

Single-valued neutrosophic numbers (SVNNs) are very much useful to express uncertain environments. In real-life problems, there are many situations where players of a matrix game can not assess their payoffs by using ordinary fuzzy sets or intuitionistic fuzzy sets. In these situations, single-valued trapezoidal neutrosophic numbers (SVTNNs) play a vital role in game theory, as it includes indeterminacy in the information besides truth and falsity. The objectives of this paper are to explore matrix games with SVTNN payoffs and to investigate two different solution methodologies. To solve such games, a pair of neutrosophic mathematical programming problems have been formulated. In the first approach, the two neutrosophic mathematical programming models are converted into interval-valued multi-objective programming problems by using a new ranking order relation of SVTNNs. Finally, the reduced problems are solved using the weighted average approach and utilizing LINGO 17.0 software. It is worth mentioning that the values of the game for both the players are obtained in SVTNN forms, which is desirable. In the second approach, each neutrosophic mathematical programming model is transformed into a crisp one by using the idea of α -weighted possibility mean value for SVTNNs. A market share problem and another numerical example are illustrated to show the validity and applicability of the proposed approaches. [ABSTRACT FROM AUTHOR]

The aim of this study is to provide a balanced distribution of air traffic controller workload (ATCW) across airspace sectors taking into account the complexity of airspace sectors and the factors affecting ATCW, both objective and perceived. Almost all the studies focusing on the airspace sectorisation problem use heuristic or metaheuristic algorithms in dynamic simulation environments instead of a mathematical modelling approach. The paper proposes a multi-objective mixed integer mathematical model for airspace sectorisation. The model is applied to the upper, en-route level of Turkish airspace. Geographical information systems (GIS) are used to advantage for airspace analysis. The multi-objective model developed in this paper is scalarised by using the conic scalarisation method. For solving the scalarised problem, the CPLEX and DICOPT solvers of GAMS software are implemented. Finally, the optimal sector boundaries of Turkish airspace are defined. [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]

Inventory–production coordination for customer orders is becoming increasingly important for companies to increase customer responsiveness and achieve economic purposes. In this paper, the joint optimization of inventory and production is considered for stochastic customer orders to maximize the throughput. Demands of customer orders dynamically arrive at the inventory department, and each incoming order consists of multiple product types with random workloads. To process the workloads, certain amounts of a common raw material are required and need to be drawn from the inventory department. A customer order will be lost if there do not exist enough raw materials in the inventory department. With the necessary materials, workloads of accepted orders will be assigned to a set of unrelated parallel servers to be processed in the production department. This paper intends to maximize the effective throughput through proper coordination of the inventory and the production departments. For this problem, system bottlenecks are identified and analyzed, and mathematical programming models are developed to determine the optimal throughput and the corresponding inventory and production policies. Several special cases are also explored to provide intuitive insights into the relationship between the system parameters and optimal throughput. Relationships between key model parameters and effective throughput are identified through sensitivity analysis and further validated by the results of computational experiments. Note to Practitioners—Coordination of production and inventory is crucial for system efficiency improvement. In order to better operate the system and respond to customer demands, this paper explores such coordination for stochastic customer orders to achieve the maximum effective throughput. Particularly, we consider the case where production is constrained by material inventory. System bottlenecks for various cases are identified, which can facilitate system diagnosis and performance evaluation. Based on the bottleneck analysis, an optimization problem is formulated to provide the optimal throughput and policy. Several important practical cases are also discussed, including single product type, identical/uniform servers, and speed-identical/uniform product types. Besides, sensitivity analysis is conducted to show how the changes of parameters such as expected workload and server speed will affect throughput performance. In the future research, more complex production environments and cost-related constraints will be further considered to help practitioners achieve desirable system outputs. [ABSTRACT FROM AUTHOR]

This paper proposes a new multi-objective interior search algorithm (MOISA) for solving multi-objective optimization problems. Multi-objective complex mathematical models need to be solved by meta-heuristic algorithms in such a way that Pareto-optimal solutions are obtained; therefore, a new algorithm is presented in this paper for solving such models. The process of the interior search algorithm (ISA) is based on principles of interior design and decoration. This algorithm divides all elements, except the most suitable one, into two groups. In the first group, which is called the artistic composition group, algorithm changes the composition of elements to achieve a more desirable view. In the second group, which is called the mirror group, the algorithm places a mirror between the group elements and the most suitable element to find a better view. This paper uses the principles of the ISA in conjunction with the concepts of the non-dominated sorting and crowding distance to present the proposed MOISA, which is capable of obtaining near-optimal non-dominated solutions from solution space and identifying accurate Pareto fronts. To evaluate the performance of the foregoing algorithm, the related results of solving six models and a maximal covering location-allocation model are compared with several standard multi-objective evolutionary algorithms in terms of different metrics. This comparison shows that the results of the proposed MOISA are better than those obtained from other tested algorithms. Based on the solved numerical examples, the algorithm presented in this paper has many advantages over existing algorithms. [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]

In this paper, a new group of optimization algorithms named Human Strategy Algorithm (HS) is proposed which is inspired by human strategies to problem solving. The main idea of HS is based on human actions to find the problem’s optima by means of accessible instruments. As the environment of an unknown problem assumed to be a black box, it is supposed that the environment of our problem is a dark room occupied by several men named blind men. The main mission of these men is to look for the optimum solution. Each man has at least one instrument as his assistance. Like real life, the instrument might be any tool such as stick, billy, rope, stone, yoyo, sweep. Any instrument by its unique features is suitable in some situations. In fact, this algorithm maps problem space and searches agents to dark room and people, respectively. In this paper, one sample algorithm of the group of human strategy, YOYO Blind Man Algorithm (YOYO-BMA), is introduced which uses yoyos as men’s accessible instruments. The performance of the YOYO-BMA is evaluated on a set of benchmark problems provided for CEC’2010 Special Session and Competition on Large-Scale Global Optimization (Tang et al. 2010). The results show superior performance of proposed algorithm in comparison with others. Moreover, the problem of designing urban traffic network is solve to evaluate the algorithm using a real complex problem. [ABSTRACT FROM AUTHOR]

This paper deals with contact analysis of rolling bearings. A new mathematical model and numeric method are presented in this paper for the purpose of contact analysis of rolling bearings based on the principle of mathematical programming method. Three-dimensional (3D), finite element method (FEM) is introduced to calculate deformation influence coefficients and gaps of assumed pairs of contact points between the contact surfaces in the mathematical model. Special software is developed to realize numeric calculation procedures of the contact analysis. With the help of the developed software, loaded bearing contact analyses are conducted for a deep groove ball bearing and a cylindrical roller bearing. In the case of the ball bearing, it is found that calculated contact pressure on the ball surfaces is correct elliptical distribution (usually called contact ellipse). This result is more reasonable than the results obtained by commercial software SolidWorks and other researchers. In the case of the roller bearing, it is found that edge-loads (non-Hertz contact that cannot be analyzed with Hertz theory) on the roller surface are analyzed when the roller is not crowned. It is also found that the edge-loads disappear and contact pressure on the roller surface becomes uniform distribution when the roller is crowned with Johson-Gohar curve. Since the most important features (contact ellipse and edge-loads) of the bearing contacts are analyzed successfully by the developed software and these results cannot be obtained simply by general methods, the mathematical model and numeric method presented in this paper are of practical meaning in engineering design and the developed software can be used as a tool for contact strength and rigidity calculations of the rolling bearings. [ABSTRACT FROM AUTHOR]

This paper proposes a new type of transformable wheel-legged mobile robot that could be applied on both flat and rugged terrains. It integrates stability and maneuverability of wheeled robot and obstacle climbing capability of legged robot by means of a wheel-legged transformable mechanism. These two modes can be switched easily with two spokes touching terrain. In this paper, the motion analysis of the proposed robot under wheeled mode, legged mode and transformable mode are carried out after briefly introducing the concept and control system design. Then, the obstacle climbing strategies under wheeled and legged modes are obtained. Finally, a prototype of the proposed robot is designed and manufactured based upon the simulation analysis. And the experiment results validate the effectiveness of the proposed transformable wheel-legged mobile robot. [ABSTRACT FROM AUTHOR]

It is a challenging task to solve a large-scale Inter-Plant Heat Integration (IPHI) problem, especially for simultaneous optimization for intra- and inter-plant heat integration. In the companion paper (Part I), a novel screening algorithm named Nearest and Largest Q r e c -based Screening Algorithm (NLQSA) was proposed. It can be used to divide a large-scale IPHI problem into several small ones, each of which includes two or three plants, while keeping the theoretical maximum inter-plant heat recovery potential Q r e c max almost unchanged. NLQSA provides a prior solution before determination of inter-plant Heat Exchanger Network (HEN) configuration for each achieved small IPHI scheme. In this paper, a modified MINLP model with an objective of minimum Total Annual Cost (TAC) is proposed to determine the final inter-plant HEN configurations of achieved segregated IPHI schemes. With the addition of stream data extraction method and NLQSA which were proposed in Part I of this paper series, a complete three-step strategy is established in order to solve the large-scale IPHI problem. Theoretically, a large-scale IPHI problem can be solved no matter how many plants involved. A case study with seven plants is introduced to illustrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Let G = (V , E) be a graph. A subset S ⊆ V of vertices is a dominating set if every vertex in V − S is adjacent to at least one vertex of S. The domination number is the minimum cardinality of a dominating set. Let u , v ∈ V. Then, u strongly dominates v and v weakly dominates u if (i) u v ∈ E and (ii) deg u ≥ deg v. A subset D of V is a strong (weak) dominating set of G if every vertex in V − D is strongly (weakly) dominated by at least one vertex in D. The strong (weak) domination number of G is the minimum cardinality of a strong (weak) dominating set. A set D ⊆ V is an independent (or stable) set if no two vertices of D are adjacent. The independent domination number of G (independent strong domination number, independent weak domination number, respectively) is the minimum size of an independent dominating set (independent strong dominating set, independent weak dominating set, respectively) of G. In this paper, mathematical models are developed for the problems of independent domination and independent strong (weak) domination of a graph. Then test problems are solved by the GAMS software, the optima and execution times are implemented. To the best of our knowledge, this is the first mathematical programming formulations for the problems, and computational results show that the proposed models are capable of finding optimal solutions within a reasonable amount of time. [ABSTRACT FROM AUTHOR]

This paper studies a telecommunication network design problem. In this network, users must be connected to capacitated hubs. Then, hubs that concentrate users must be connected to each other and possibly to other hubs with no users. The connections in the network must lead to a tree topology. Hence, connection between hubs can be considered as looking for forming a Steiner tree. This problem is modeled as a bi-objective mathematical programming problem. One objective function minimizes user's latency with respect to the information packages flowing through the capacitated hubs, and the other objective function aims the minimization of the total network's connection cost. To approximate the Pareto front of this bi-objective problem, a co-evolutionary algorithm is developed. In the proposed algorithm, two populations are considered. Each population is associated with one objective function. The co-evolutionary operator consists of an information exchange between both populations that occurs after the genetic operators have been applied. As a result of this co-evolutionary operator, the non-dominated solutions are identified. Computational experimentation shows that the approximated Pareto fronts are representative despite their non-convexity, and they contain a sufficient number of non-dominated solutions over the tested instances. Also, the kth distance among non-dominated solutions is relatively small, which indicates that the approximated Pareto fronts are dense. Furthermore, the required computational time is very small for a problem with the characteristics herein considered. [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]

Cut-off grade classifies the available supply of ore (valuable) and waste material within a mineralised deposit. Given the mining, processing and refining limitations of a mining operation, an optimal cut-off grade policy ensures that the flow of ore from the mine to the processing and refining facilities is maintained at the maximum possible throughput. This policy defines a schedule of cut-off grades along with corresponding quantities of mineralised material to be mined, processed and metal refined in each period of the scheduling horizon. The criteria that controls the development of cut-off grade policy aligns with the strategic objectives of an operation in order to maximise the discounted value (net present value or NPV) over the life of operation. This paper proposes a new mixed integer linear programming (MILP) based model that maximises NPV subject to the mining, processing, refining capacity constraints and develops an optimal cut-off grade policy for an open pit mining operation with multiple processing streams. An implementation of the proposed method on hypothetical and realistic data promises a relatively higher NPV as compared to the traditional Lane's approach practiced in the mining industry. [ABSTRACT FROM AUTHOR]

In the traditional fuzzy matrix game, given a pair of strategies, the payoffs of one player are usually associated with themselves, but not linked to the payoffs of the other player. Such payoffs can be called self-evaluated payoffs. However, according to the regret theory, the decision makers may care more about what they might get than what they get. Therefore, one player in a matrix game may pay more attention to the payoffs of the other player than his/her payoffs. In this paper, motivated by the pairwise comparison matrix, we allow the players to compare their payoffs and the other ones to provide their relative payoffs, which can be called the cross-evaluated payoffs. Moreover, the players' preference about the cross-evaluated payoffs is usually distributed asymmetrically according to the law of diminishing utility. Then, the cross-evaluated payoffs of players can be expressed by using the asymmetrically distributed information, i.e., the interval-valued intuitionistic multiplicative number. Comparison laws are developed to compare the cross-evaluated payoffs of different players, and aggregation operators are introduced to obtain the expected cross-evaluated payoffs of players. Based on minimax and maximin principles, several mathematical programming models are established to obtain the solution of a matrix game with cross-evaluated payoffs. It is proved that the solution of a matrix game with cross-evaluated payoffs can be obtained by solving a pair of primal–dual linear-programming models and can avoid some unreasonable results. Two examples are finally given to illustrate that the proposed method is based on the cross-evaluated payoffs of players, and can directly provide the priority degree that one player is preferred to the other player in winning the game. [ABSTRACT FROM AUTHOR]

The daily production planning of sawmills is a critical task in pursuing the optimal exploitation of forest resources. Production planning determines which logs are to be processed, taking into account their characteristics with the aim of satisfying the demand for final products. Logs are turned into lumber when they are cut according to a set of available cutting patterns (CPs). The development of efficient production planning is a key factor in improving the productivity of sawmills, and mathematical modeling is a suitable technique to achieve this objective. In this paper, a mixed integer linear programming (MILP) model for optimal daily production planning in sawmills is proposed. The model involves a set of CPs for each type of log, which is obtained through an exhaustive algorithm, attaining all possible feasible CPs. The proposed approach determines the optimal number of logs of each type to be cut, the selected CPs to be used, material inventory, demand fulfillment, and other industrial and commercial issues with the objective of maximizing the firm's benefit, in reasonable computational time, considering the size of the problem. [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]

This paper considers the design of an input signal for minimizing the time and energy required to detect and isolate faults in the outputs of a system. Faults are represented by discrete switches between affine models with bounded disturbances and bounded measurement errors. Within this framework, previous work has demonstrated that a minimally harmful input guaranteeing fault diagnosis can be obtained by solving a Mixed Integer Quadratic Program (MIQP). A closed-loop approach allows to reduce the length and/or norm of this input by solving an MIQP at each time instant with the newly available measurements. However, solving such programs online can be computationally demanding. In this paper, we employ multi-parametric (mp) programming to move most of the computation offline, thus allowing the application of the closed-loop approach to fast processes. Still, the mp-MIQP complexity becomes quickly prohibitive as the number of faulty models increases. In order to overcome this problem, we propose a strategy based on mp-optimization and graph theory that takes into account only two models at a time. While this approach is suboptimal compared to the case in which all the models are considered simultaneously, simulations show that, in practice, the performance is comparable. [ABSTRACT FROM AUTHOR]

The fractional transportation problem (FTP) plays an important role in logistics and supply management for reducing cost and improving service. In the real world, however, the parameters in the models are seldom known exactly and have to be estimated. This paper investigates the FTP where the cost coefficients and right-hand sides are represented by fuzzy parameters. Intuitively, when the parameters in the FTP are fuzzy numbers, the derived objective value should be also a fuzzy number. Based on Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the fuzzy objective value of the FTP with fuzzy parameters. By applying the dual formulation of linear fractional programming and variable substitution techniques, the two-level mathematical programs are transformed into ordinary one-level linear programs to solve. At a specific $$\alpha $$ -cut, solving the pair of linear programs produces the bounds of the objective value of the fuzzy FTP. By collecting the bounds from different $$\alpha $$ levels, one can depict the shape of the membership function. An example illustrates how to apply the concept of this paper to solve the fuzzy FTP problem. [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]

Abstract Inter-plant hydrogen network with reuse/recycle optimization is important for saving hydrogen resource. Thus, it's necessary to optimize the inter-plant hydrogen network. In this paper, a novel two-step method that combines the pinch insight with mathematical programming is developed to optimize the inter-plant hydrogen network with purification reuse/recycle. A new transhipment model for targeting inter-plant hydrogen network is built to target the hydrogen utility consumption for each refinery. After the hydrogen consumption is determined, individual plant hydrogen networks are designed separately. The mathematical model is linear to guarantee global optimal solution. Furthermore, the model can also optimize the number of inter-plant connections of the hydrogen network. Case study indicates the effectiveness of model. Highlights • A two-step method to target and design inter-plant hydrogen network with purification reuse/recycle is proposed. • The hydrogen utilities for inter-plant network can be reduced further by inter-plant streams. • The number of inter-plant connections can be optimized. [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]

Analyzing the behavior and stability properties of a local optimum in an optimization problem, when small perturbations are added to the objective functions, are important considerations in optimization. The tilt stability of a local minimum in a scalar optimization problem is a well-studied concept in optimization which is a version of the Lipschitzian stability condition for a local minimum. In this paper, we define a new concept of stability pertinent to the study of multiobjective optimization problems. We prove that our new concept of stability is equivalent to tilt stability when scalar optimizations are available. We then use our new notions of stability to establish new necessary and sufficient conditions on when strict locally efficient solutions of a multiobjective optimization problem will have small changes when correspondingly small perturbations are added to the objective functions. [ABSTRACT FROM AUTHOR]

The analysis of the principal-agent problem usually requires the classical first-order approach (FOA). However, the validity of the FOA makes restrictive assumptions on the problem under consideration such as the convexity of the distribution function condition. The main aim of this paper is to compute the optimal wages and characterize a closed form solution to the risk-neutral principal-agent problem with limited liability constraints. The development in this paper mainly invokes certain techniques in the semi-infinite programming rather than the FOA. [ABSTRACT FROM AUTHOR]

In this paper, global optimization model is designed for grid computing system. It is provided as a promising model for grid resource scheduling algorithm. It aims at solving the problem of optimally allocating services on the grid to optimize the grid service reliability, deadline and cost. In this paper, the problem of optimizing the reliability of grid systems has been modeled as a multi-objective optimization problem where apart from the grid system reliability; the system cost, deadline and redundancy are also considered as its constraints. The algorithm considers failure rate of computational and network resources to do the reliability analysis of the grid system. Based on the service reliability of the grid system, the proposed RORS algorithm selects the set of optimal resources among the candidate resources based on reliability, application execution time and cost that achieves optimal performance using a genetic algorithm. The proposed algorithm has been demonstrated using Java-based GridSim tool. [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]

This paper studies the ordinal and additive inconsistency problems of linguistic preference relations. First, the definition of ordinal consistency of a linguistic preference relation is proposed. Based on the definition of adjacency matrix of a linguistic preference relation, the necessary and sufficient conditions of a linguistic preference relation being ordinally consistent are given. Then, a distance-based nonlinear programming method is developed to identify and adjust the ordinal and additive inconsistencies for linguistic preference relations. The proposed methods can not only solve the ordinal inconsistency, additive inconsistency problems, respectively, but also solve the ordinal and additive inconsistency problems simultaneously. Finally, numerical examples and comparative analysis are provided to show the effectiveness and advantages of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, a grey linear programming problem with grey coefficients is discussed. In particular, the duality results as one of the important results on linear programming with grey parameters is established. First, some definitions and concepts of Grey System Theory are introduced and then a dual problem is defined for the primal grey linear programming problem. In particular, for establishing the duality theory, the fundamental theorems and results, such as weak and strong duality and optimality condition is proved. The study emphasizes that the established results can be usefulfor providing a new approach to solve the dual problem directly on the primal simplex tableau. [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]

Depending on whether a mathematical program with equilibrium constraints (MPEC) is considered in its original or its enhanced (via KKT conditions) form, the assumed qualification conditions as well as the derived necessary optimality conditions may differ significantly. In this paper, we study this issue when imposing one of the weakest possible qualification conditions, namely the calmness of the perturbation mapping associated with the respective generalized equations in both forms of the MPEC. It is well known that the calmness property allows one to derive the so-called M-stationarity conditions. The restrictiveness of assumptions and the strength of conclusions in the two forms of the MPEC is also strongly related to the qualification conditions on the “lower level”. For instance, even under the linear independence constraint qualification (LICQ) for a lower level feasible set described by C1 functions, the calmness properties of the original and the enhanced perturbation mapping are drastically different. When passing to C1,1 data, this difference still remains true under the weaker Mangasarian–Fromovitz constraint qualification, whereas under LICQ both the calmness assumption and the derived optimality conditions are fully equivalent for the original and the enhanced form of the MPEC. After clarifying these relations, we provide a compilation of practically relevant consequences of our analysis in the derivation of necessary optimality conditions. The obtained results are finally applied to MPECs with structured equilibria. [ABSTRACT FROM AUTHOR]

The forward-backward splitting technique is a popular method for solving monotone inclusions that have applications in optimization. In this paper, we explore the behaviour of the algorithm when the inclusion problem has no solution. We present a new formula to define the normal solutions using the forward-backward operator. We also provide a formula for the range of the displacement map of the forward-backward operator. Several examples illustrate our theory. [ABSTRACT FROM AUTHOR]