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Copyright of Revista de Historia Económica / Journal of Iberian & Latin American Economic History is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Feed costs represent a significant component of milk production expenses, making up a share of 50% or more of the total cost. The optimization of feed costs is important to achieve financial stability, competitiveness, and sustainability in dairy farming. Optimizing dairy rations not only improves economic efficiency but also plays a significant role in reducing the environmental impact of dairy farming. On the other hand, dairy rations need to meet the specific nutritional requirements of cattle to ensure their health, well-being, and maximum milk production. The formulation of an optimal dairy ration is not an easy task for farmers due to the many challenges they face in this process. This study presents an intuitive web-based tool called OPTIMILK that is used for the optimization of dairy rations using the Simplex method of linear programming. This tool enables farmers to efficiently find a least-cost ration considering the nutritional needs of dairy cows, feed availability and costs, and the nutritional composition of feed. The tool was created for a dairy farmers' association in Bosnia and Herzegovina and made available to its members for free. After almost four years of operation, the tool's usage was evaluated by analyzing the collected data. The results show that after an initial period of low activity, there was evidence of an increase in the level of use, which implies the gradual adoption of the tool in dairy farming practice. [ABSTRACT FROM AUTHOR]

Let G be a connected graph. The distance between two vertices u and v in G, denoted by d G (u , v) , is the number of edges in a shortest path from u to v, while the distance between an edge e = x y and a vertex v in G is d G (e , v) = min { d G (x , v) , d G (y , v) } . For an edge e ∈ E (G) and a subset S of V(G), the representation of e with respect to S = { x 1 , ... , x k } is the vector r G (e | S) = (d 1 , ... , d k) , where d i = d G (e , x i) for i ∈ [ k ] . If r G (e | S) ≠ r G (f | S) for every two adjacent edges e and f of G, then S is called a local edge metric generator for G. The local edge metric dimension of G, denoted by edim ℓ (G) , is the minimum cardinality among all local edge metric generators in G. For two non-trivial graphs G and H, we determine edim ℓ (G ⋄ H) in the edge corona product G ⋄ H and we determine edim ℓ (G ∘ H) in the corona product G ⋄ H . We also formulate the problem of computing edim ℓ (G) as an integer linear programming model. [ABSTRACT FROM AUTHOR]

In this article, the robust scheduling of the distribution network is presented considering electric vehicles, distributed generation, and energy storage, in which the energy management of the mentioned elements is considered, and also only one scenario is needed. The proposed deterministic problem is an optimization problem whose objective function is equal to minimizing energy cost. Also, the limitations of the problem are equal to the power flow equations of the network, the limitations of the technical indicators of the network such as the voltage of the buses and the passing power of the lines, the operation equations of electric vehicles, energy storages, and distributed generation. It is worth mentioning that the mentioned problem is non-linear. In the following, to achieve the global optimal point with a high solution speed, the linear model of the mentioned problem is presented with a very low calculation error. In this research, the uncertainty parameters of the problem are equal to active and reactive loads, energy prices, parameters of electric vehicles, and renewable productions. Finally, to simplify the decision-making of the distribution network operator, a robust model of the mentioned problem was presented. Finally, the proposed problem is applied to the IEEE standard 33-bus radial distribution network using GAMS optimization software, and then the capabilities of the proposed design are evaluated.

The Combined Cooling, Heat, and Power (CCHP) System is an efficient technology that reduces primary energy consumption and carbon dioxide emissions by generating heat, cold, and electricity simultaneously from the same fuel source. This study developed an economic optimization model using linear mathematical program theory to determine the optimal sizes of different components in a CCHP system. The study found that CCHP systems with internal combustion engines have the largest optimal size due to lower capital expenditure and improved hourly changes in combined energy production by considering electrical and absorption chillers simultaneously. The analysis compared the size determination of CCHP systems with internal combustion engine (ICE), sterling engine (SE), and proton exchange membrane fuel cell (PEMFC) technologies. PEMFC had the highest annual overall cost among the technologies studied. The results of determining the size of the CCHP system are compared with ICE, SE, and PEMFC technologies. It has been noted that PEMFC has the highest annual overall cost among the studied technologies. The usefulness index of the CCHP system increased from 23% to almost 40% when electricity was sold to the grid using internal combustion engine technology.

This paper focuses on the stochastic stabilization of hidden semi-Markov jump nonlinear positive systems. First, a notion of stochastic stability is introduced for this class of systems. A criterion is addressed to ensure the stochastic stability using a stochastic copositive Lyapunov function. Then, an observed mode is proposed to estimate the emitted value of the hidden semi-Markov process and the mode-dependent controller is designed using an improved matrix decomposition approach. Some auxiliary variables are added to decouple the coupling terms in hidden semi-Markov jump nonlinear positive systems into a tractable condition. All conditions are described in terms of linear programming. Moreover, the proposed design is developed for systems with partially known emission probabilities. Two examples are provided to show the validity of the obtained results.

There is a large demand for seasonal crops year-round within Australia, even when they are considered out of season. The demand is satisfied by continually moving production throughout the year to climates where the crops are in season. Management of the supply chain for a major national grower is challenging for several reasons. Due to the large number of planting decisions, it is standard practice for a team of production planners to create the annual production plan. For fresh food production, the supply chain does not contain intermediate storage requiring that the production plan is carefully timed not to waste resources with overproduction. In this paper, we develop a supply chain model that simultaneously manages the production of multiple crops across many growing regions. Production is set to satisfy the demand of multiple end-products while considering the packing plants' throughput capacity, each growing region's harvest capacity, and farm capacity. A time delay may be applied when moving between stages of the supply chain due to the geographic scale being modelled. A deterministic Mixed Integer Program is used to find the optimal planting plan, which minimises the deviation from demand for all products year-round at a minimal cost. Due to the excessive runtime for solving the model, a heuristic solution method is introduced. Numerical experiments demonstrate the advantage of the proposed model over the current manual planning process, which can solve the problem faster and with less deviation across the planning horizon. [ABSTRACT FROM AUTHOR]

The university course timetabling is a tactical level problem that almost all academic departments encounter before each semester. Nowadays, in order to meet some standards, set by educational accreditation agencies within the scope of higher education quality assurance, it is required to generate efficient course timetables, which ensure optimal distribution of basic capabilities. Actually, these capabilities should be first specified based on the learning outcomes defined by lecturers for each course that are also associated with program outcomes and are aimed to be acquired by all of the students. Based on this motivation, a multi-objective mixed-integer non-linear programming model is developed for a novel capability-based course timetabling problem. Its validity and practicality are tested on a real-life application in an Industrial Engineering Department. When the balanced solutions provided by compromise and fuzzy goal programming techniques were compared with the existing schedules of the previous years, it was revealed that significant improvements could be achieved in terms of several conflicting objectives (i.e., optimal capability distribution over the timetable, acquisition of maximum number/variety of different capabilities by the students, meeting expectations of lecturers by minimizing total temporal difference between the periods his/her courses are assigned, total penalty cost related to soft constraints). [ABSTRACT FROM AUTHOR]

Lean production is a set of methods aimed at increasing efficiency and flexibility within a firm by eliminating waste and accurately defining value. For this reason, it is interested in eliminating activities that do not add value to the product to reduce costs. Within the scope of lean production, different methods are used based on certain priorities and simultaneously. In this study, the Lean Production Leveling-Heijunka approach, a lean production method applied in a mold sponge manufacturing firm, is discussed. In the accessible literature, it has been seen that the heijunka method has been studied little before and no linear model has been found for its application. Therefore, within the scope of this study, a multi-objective linear model that includes production leveling, sequencing and job stability elements is proposed. As the proposed model is multi-objective, the weighted sum method was used as the aim aggregation method to solve it. The problem of the firm was solved using the proposed model in GAMS/CPLEX. To evaluate the performance of the model, first a small-size sample problem was solved and then the main problem of the firm where the application was used was solved. The effectiveness of the model was evaluated by comparing the results obtained after solving the firm problem with the current case. In addition, Heijunka values for both cases were calculated to demonstrate the success of the proposed model's solution. According to the calculations, the Heijunka ratio was four in the solution obtained by applying the proposed model, while it was two in the current situation. These results demonstrate that a successful Heijunka method was implemented in the firm where the application was conducted, and the production process was made more balanced. [ABSTRACT FROM AUTHOR]

This paper addresses a job shop scheduling problem with peak power constraints, in which jobs can be processed once or multiple times on either all or a subset of the machines. The latter characteristic provides additional flexibility, nowadays present in many manufacturing systems. The problem is complicated by the need to determine both the operation sequence and starting time as well as the speed at which machines process each operation. Due to the adherence to renewable energy production and its intermittent nature, manufacturing companies need to adopt power‐flexible production schedules. The proposed power control strategies, that is, adjusting processing speed and timing to reduce peak power requirements may impact production time (makespan) and energy consumption. Therefore, we propose a bi‐objective approach that minimizes both objectives. A linear programming model is developed to provide a formal statement of the problem, which is solved to optimality for small‐sized instances. We also proposed a multi‐objective biased random key genetic algorithm framework that evolves several populations in parallel. Computational experiments provide decision and policymakers with insights into the implications of imposing or negotiating power consumption limits. Finally, the several trade‐off solutions obtained show that as the power limit is lowered, the makespan increases at an increasing rate and a similar trend is observed in energy consumption but only for very small makespan values. Furthermore, peak power demand reductions of about 25% have a limited impact on the minimum makespan value (4–6% increase), while at the same time allowing for a small reduction in energy consumption. [ABSTRACT FROM AUTHOR]

In a recent paper published in this journal, Alonso‐Pecina et al. collect several sets of benchmark instances for the label printing problem from the literature and they also propose their own instances. Due to the intractability of the problem, no optimal solutions were declared for most of these instances. In this paper, we propose an integer linear programming model for the problem. We obtain optimal solutions or show that the solutions provided in the literature are already optimal for most of these instances based on the model. For some of the rest instances, we provide better solutions compared to the previous best solutions in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we conduct an analysis of a matrix game using rough interval payoffs, which we refer to as the rough interval matrix game (RIMG). We employ three methods to address the problem at hand: linear programming, graphical method, and algebraic method. The proposed approach offers several key advantages over existing methods, which we highlight. We introduce algorithms associated with each of the three mentioned methods to obtain optimal solutions for the RIMG. To validate the effectiveness of our proposed techniques, we present two numerical examples and apply the methodologies to solve them. In conclusion, we summarize the findings of our study and discuss potential avenues for future research based on the insights provided in this paper. [ABSTRACT FROM AUTHOR]

It is necessary to select appropriate active parameters to ensure both the accuracy and computation efficiency before the global analysis of chemical kinetic model. This paper proposes a new method for selecting the active parameters on the base of the combination of sensitivity analysis and linear programming. Compared with the usual methods for selecting active parameters, such as the local sensitive analysis, the characteristics of the proposed method is preliminary visualization of the possible influence of the selected active parameters on the model outputs in the process of parameter selection, ensuring the reliability of the selected active parameters. Considering the computation efficiency, the number of selected active parameters can be controlled in a suitable size through combining with dichotomy or other screening techniques. In the study, the pre-exponential factors of the Arrhenius equations in the USC-Mech II model were considered as the candidate parameters and the uncertainties of the pre-exponential factors were set. Taking the ignition of ethylene for example, the 10 reactions that can increase the ignition time of ethylene under a wide range of conditions with equivalence ratio of 1, 0.1 ~ 1 MPa and 1000 K ~ 1500 K were successfully selected using the proposed method. Then, the 10 active parameters were tested in each condition. The results showed that the selected active parameters can make the ignition delay time close to the target for each condition, which reflects the reliability of active parameter selection. [ABSTRACT FROM AUTHOR]

We propose a framework designed to tackle a multi-objective optimization challenge related to the placement of applications in fog computing, employing a deep reinforcement learning (DRL) approach. Unlike other optimization techniques, such as integer linear programming or genetic algorithms, DRL models are applied in real time to solve similar problem situations after training. Our model comprises a learning process featuring a graph neural network and two actor-critics, providing a holistic perspective on the priorities concerning interconnected services that constitute an application. The learning model incorporates the relationships between services as a crucial factor in placement decisions: Services with higher dependencies take precedence in location selection. Our experimental investigation involves illustrative cases where we compare our results with baseline strategies and genetic algorithms. We observed a comparable Pareto set with negligible execution times, measured in the order of milliseconds, in contrast to the hours required by alternative approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a streamlined approach to addressing the problem of allocating finite crew resources to concurrent jobs in the context of municipal drainage infrastructure maintenance. The problem was defined from the perspective of a project manager involved in planning such operations on a day-by-day basis. The problem statement was then transformed into a simplified Integer Linear Programming optimization model. Performance metrics were devised to evaluate the optimization model's effectiveness. A heuristic algorithm representing the decision-making process by a seasoned planner in the partner company was also developed. Both methods were applied to a case study and contrasted based on the same performance metrics. The findings underscored substantial optimization benefits in rendering decision support in resource-constrained drainage construction operations planning. In conclusion, this research presents an alternative strategy for navigating the complexities inherent in finite crew resource allocation on multiple concurrent drainage projects; lends a cost-effective optimization solution to improving the utilization of finite available crews while satisfying service demands from multiple clients to the largest extent possible. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a case of the inverse 1-median problem on a tree by transferring the weights of vertices which has not been raised so far. This problem considers modifying the weights of vertices via transferring weights of the vertices with the minimum cost such that a given vertex of the tree becomes the 1-median with respect to the new weights. A linear programming model is proposed for this problem. The applicability and efficiency of the presented model are shown in numerical examples and a real-life problem dealing with transferring users in a social network. [ABSTRACT FROM AUTHOR]

Considering the double uncertainty caused by the ambiguity of statistical data and the ambiguity produced by the subjective assessment of decision makers, the crisp values of criteria may be insufficient to model the multi-criteria decision-making (MCDM) problem in the real world. This paper proposes a fuzzy best-worst method (FBWM) based on a dual-interval solution algorithm to extend the best-worst method (the most recent MCDM method) to fuzzy environments. The reference comparisons for the best criteria and for the worst criteria are represented by fuzzy numbers. Then, according to the BWM method, a nonlinear constrained optimization problem with fuzzy parameters is formulated. We decompose the membership function in fuzzy numbers into several interval numbers of special form and solve the aforementioned fuzzy BWM problem by compound interval algorithm to obtain fuzzy weights of different criteria. Meanwhile, an integral type-reduced method is proposed for determining the fuzzy consistency ratio in order to assess the reliability of the FBWM results. The viability of the new algorithm to expand the BWM method into fuzzy environments has been validated through three numerical examples. In contrast to the existing FBWM method, the proposed method avoids the arithmetic operation between fuzzy numbers during the solution process, directly transfers the uncertain information in the membership function corresponding to the fuzzy comparison vector to the result, and generates fuzzy weight value, which indicates that the proposed algorithm is able to obtain accurate BWM results in fuzzy environments. The results of the study provide new solution ideas for multi-criteria optimization problems under uncertainty. [ABSTRACT FROM AUTHOR]

We address in this paper linear programming (LP) models in which it is desired to find a finite set of alternate optima. An LP may have multiple alternate solutions with the same objective value or with increasing objective values. For many real life applications, it can be interesting to have a pool of solutions to compare what operations should be executed and what is the cost/benefit of doing it. To obtain a specified number of these alternate solutions in the increasing order of objective values, we propose an iterative MILP algorithm in which we successively add integer cuts on inactive constraints. We demonstrate the application and effectiveness of this algorithm on a 2 dimensional LP and on small and large supply chain problems. The proposed iterative MILP algorithm provides an effective approach for finding a specified number of alternate optima in LP models, which provides a useful tool in a variety of applications as for instance in supply chain optimization problems. [ABSTRACT FROM AUTHOR]

In this article, we develop novel mathematical models to optimize utilization of community energy storage (CES) by clustering prosumers and consumers into energy sharing communities/microgrids in the context of a smart city. Three different microgrid configurations are modeled using a unifying mixed‐integer linear programming formulation. These configurations represent three different business models, namely: the island model, the interconnected model, and the Energy Service Companies model. The proposed mathematical formulations determine the optimal households' aggregation as well as the location and sizing of CES. To overcome the computational challenges of treating operational decisions within a multi‐period decision making framework, we also propose a decomposition approach to accelerate the computational time needed to solve larger instances. We conduct a case study based on real power consumption, power generation, and location network data from Cambridge, MA. Our mathematical models and the underlying algorithmic framework can be used in operational and strategic planning studies on smart grids to incentivize the communitarian distributed renewable energy generation and to improve the self‐consumption and self‐sufficiency of the energy sharing community. The models are also targeted to policymakers of smart cities, utility companies, and Energy Service Companies as the proposed models support decision making on renewable energy related projects investments. [ABSTRACT FROM AUTHOR]

This paper examines problems in decision theory where the number of alternatives and states of nature are finite. Previous studies have defined the concept of "the value of perfect information for the problem" (VPIP). This metric allows us to obtain an upper bound on the amount a decision-maker would be willing to pay for perfect information under the specific conditions of a problem. This bound is particularly important when the decision is unrepeatable, providing a more accurately adjusted measure than the one traditionally obtained with "the expected value of perfect information" (EVPI). Supported by linear programming, this work proposes a sensitivity analysis of these bounds by seeking to identify the intervals in which the problem values can vary without essentially modifying the structure of the problem. Specifically, the study aims to determine how this variation might affect the EVPI and VPIP bounds, as well as the difference in the price a decision-maker would be willing to pay for perfect information if any of the problem values were altered. By identifying alternatives and scenarios taking into account the role they play in the problem, this research classifies the data involved in a finite decision problem to ensure the conclusions can be understood as generally as possible. Although the proposed sensitivity analysis is applied to the oil-drilling problem, a classic in decision theory, the conclusions of this work have potential applications in improving environmental decision-making processes. [ABSTRACT FROM AUTHOR]

Achieving economic and social sustainability is the goal of any policy when defining measures. We focus on the beef sector, where many challenges have arisen due to its structural characteristics, such as an unfavourable scale structure, high costs, low efficiency, and a low environmental footprint. This paper presents an example of the support provided by a mathematical programming model in the development of a Common Agricultural Policy Strategic Plan for the period 2023-2027. It is a model based on linear programming that allows such an ex-ante analysis by calculating production plans at the farm level and aggregating the results at the sector level. When defining the interventions, the question arose as to what the reform of the Common Agricultural Policy will bring and to what extent the sector should be supported in meeting these challenges. These were the concerns of agricultural policy that we sought to support by modelling different scenarios. The results show that the situation of the sector will worsen, especially for larger farms, but they also show the great importance of production-related payments to mitigate the negative trend. The applied approach proves to be suitable for supporting the design of agricultural policy and achieving greater economic and social sustainability in the sector. [ABSTRACT FROM AUTHOR]

We study an integrated optimisation problem with blending, scheduling, and routing components for a melted material blending production system. The problem is formulated as a mixed-integer linear programming model that considers the blending machine environment, due dates, target amounts, required chemical compositions of the products, and ready times of the materials in containers. This model aimed to determine the container pairings, blending plants for container pairs, and schedules for blending operations while minimising the total end time of material usage, total penalty for violating component specifications, and employee workload. Further, we propose a three-stage approach that involves solving a relaxed problem and then resolving the problem with fixed variables. We developed a combinatorial Benders decomposition algorithm with a minimal infeasible subsystem identification algorithm for the blending scheduling problem. The experimental results indicate that the proposed method can find high-quality solutions within a reasonable amount of time. [ABSTRACT FROM AUTHOR]

This paper introduces a cooperative approach of a swarm intelligence algorithm and a linear programming solver to solve the capacitated facility location problem (CFLP). Given a set of potential locations to open facilities, the aim in CFLP is to find the minimum cost, which is the sum of facility opening costs and transportation costs. The developed solution strategy decomposes CFLP into two sub-problems. The former sub-problem has a binary domain. Although most of the swarm intelligence algorithms employ additional procedures such as sigmoid function to deal with binary domains, the proposed algorithm does not require for such methods. An adaptive mutation operator enhances this algorithm. The aim of the latter sub-problem is to generate a policy that optimally assigns customers to the opened facilities. In this regard, the generated binary vectors by the proposed algorithm are passed to a solver to optimise the generated linear model. Commonly used instances available in the literature are solved by the proposed strategy. Comprehensive experimental study includes comparisons with the sate-of-the-art. According to the statistically verified results, the proposed strategy is found as promising in solving CFLP. [ABSTRACT FROM AUTHOR]

Flexible process planning (FPP) involves selecting and sequencing the requisite operations according to technological requirements, and meanwhile allocating a right machine, a right tool and a right access direction to each selected operation by a given criterion. In this article, the FPP problem is exactly and concisely formulated as linear integer programming models based on the topology of the AND/OR-network under two criteria: production cost minimisation and completion time minimisation. Distinctively, more flexible manufacturing elements and process plan evaluation criteria are considered; more complicated tool and access direction changeover identifications are linearly expressed without the big-M parameter. Compared with the latest mathematical programming models for process planning, the proposed models have lower complexity and better performance. The results from numerous comparative experiments indicate that (i) the number of decision variables of the proposed models reduces approximately by 68% and the number of constraints of the proposed models dramatically reduces by 99%; (ii) within the same running time, the proposed models can exactly solve more benchmark cases than the latest models; and (iii) the solutions obtained by the proposed models are also better than the best ones founded by some state-of-the-art meta-heuristic algorithms. [ABSTRACT FROM AUTHOR]

We address three variants of the two-dimensional cutting stock problem in which the guillotine cutting of large objects produces a set of demanded items. The characteristics of the variants are the rectangular shape of the objects and items; the number of two or three orthogonal guillotine stages; and a sequencing constraint that limits the number of open stacks to a scalar associated with the number of automatic compartments or available space near the cutting machine. These problems arise in manufacturing environments that seek minimum waste solutions with limited levels of work-in-process. Despite their practical relevance, we are not aware of mathematical models for them. In this paper, we propose an integer linear programming (ILP) formulation for each of these variants based on modelling strategies for the two-dimensional guillotine cutting stock problem and the minimisation of the open stacks problem. The first two variants deal with exact and non-exact 2-stage patterns, and the third with a specific type of 3-stage patterns. Using a general-purpose ILP solver, we performed computational experiments to evaluate these approaches with benchmark instances. The results show that several equivalent solutions of the cutting problem allow obtaining satisfactory solutions with a reduced number of open stacks. [ABSTRACT FROM AUTHOR]

This note comments on the study of [Diri Kenger, Zülal, Çağrı Koç, and Eren Özceylan. 2020. "Integrated Disassembly Line Balancing and Routing Problem." International Journal of Production Research 58 (23): 7250–7268.] which studies an integrated disassembly line balancing and routing problem and develops two mixed integer linear programming (MILP) models and three mixed integer nonlinear programming (MINLP) models to handle five different scenarios, respectively. The purpose is twofold. First, we demonstrate that the two MILP models can be separated into two parallel subproblems whose optimal solutions can be combined to obtain the optimal solution of the original models. Second, we show that the three MINLP models can be linearised and propose two different linearisation techniques to reformulate them as equivalent MILP models. Computational results indicate that the linearised model outperforms the original nonlinear model in most cases. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a special type of scheduling problem. There are two classes of jobs to be processed on a single machine. Jobs of class A are directly delivered to the customers and we want to minimise their total flow time. Jobs of class B do not contribute to the objective function but must respect a no-idle constraint (i.e. they are required to keep an external downstream machine busy). This problem arises in some real-world production environments where the downstream process must not be interrupted because of technological constraints, economic viability or because the firm is bound to keep the external process continuously active (e.g. a contract with a downstream firm imposing penalties if the supply is interrupted). We prove that the general problem is NP-Hard. We introduce two mathematical programming-based approaches and some constructive heuristics. The various approaches are compared on the basis of a large computational campaign. [ABSTRACT FROM AUTHOR]

The Single-Row Facility Layout Problem (SRFLP) is one of the most studied facility layout problems in the literature. It asks for an optimal arrangement of departments with given lengths on a row such that the weighted sum of all centre-to-centre distances between department pairs is minimised. Real-world facility layouts may require taking different restrictions on the placement of departments into account, such as arrangement on a fixed position, pairwise placement, or precedence considerations. Therefore, we consider the constrained Single-Row Facility Layout Problem (cSRFLP) that additionally considers positioning, ordering, and relation constraints on single-row facility layouts. In this work, we suggest a new Integer Linear Programming (ILP) formulation for the cSRFLP, which outperforms the best available exact approach in literature. In an extensive computational study, we apply our ILP approach as well as an LP-based cutting plane algorithm on SRFLP and cSRFLP instances from the literature. We provide optimal cSRFLP layouts as well as strong lower bounds for instances with up to 42 departments. Further, we present new results for SRFLP instances from the literature. Additionally, we demonstrate the individual impact of the constraint sets on the run times of cSRFLP instances to emphasise further research on this rarely studied practice-oriented Facility Layout Problem. [ABSTRACT FROM AUTHOR]

BACKGROUND AND OBJECTIVES: Agriculture plays a significant role in the overall consumption of freshwater resources, accounting for approximately 70 percent of the total use. Energy is also essential at various stages of agriculture and the food chain. On a global scale, the agricultural and food industries account for approximately 30 percent of the overall energy consumption, with a significant portion derived from fossil fuel sources. This underscores the intricate interconnection between food, energy, and water resources. This study utilizes a linear programming model to determine the optimal cropping pattern while minimizing water usage in agriculture. This study's primary contribution lies in its dual approach: it identifies the optimal cropping patterns for a specified objective function through linear programming while simultaneously conducting a comprehensive analysis of these patterns by integrating considerations of food, energy, and water nexus.METHODS: The constraints applied in linear programming involve maintaining nearly the same agricultural revenue, conserving the total cultivation area, and limiting the change intervals in cultivation area by 5 percent. Using linear programming, crop patterns were determined for the periods of 2017, 2025-2050, 2050-2075, and 2075-2100. In each scenario, calculations were conducted to assess water consumption, energy demands, agricultural income, and carbon dioxide emissions, all framed within the context of the food-energy-water nexus. The various scenarios were subsequently analyzed to assess their effects. An evaluation was conducted regarding the sustainability of water usage in agricultural production.FINDINGS: All the scenarios examined resulted in lower water usage, reduced energy requirements, and decreased carbon dioxide emissions. Throughout various time periods, scenario 6, which permits a 5 percent variation in cultivation areas without imposing a total cultivation area limit, consistently proved to be the most favorable choice. It achieved an average reduction of 3.94 percent in water usage, 2.95 percent in energy requirements, and 1.62 percent in carbon dioxide emissions compared to the base scenario. Scenario 11, allowing for a 5 percent variation in cultivation areas while maintaining a total cultivation area limit, was evaluated as the second most effective scenario in terms of water conservation. It achieved an average reduction in water use of 3.45 percent, an average reduction in energy requirements of 1.85 percent, and a minimal reduction in carbon dioxide emissions of 0.11 percent across all time periods.CONCLUSION: The outcomes of this study reveal that the proposed model can play a crucial role in advancing sustainable agricultural management strategies. The obtained results indicate that significant reductions in water usage, energy requirements, and carbon dioxide emissions can be achieved simply by modifying the crop pattern, while agricultural income remains largely at the same level. The imposition of a constraint requiring the total cultivation area to be equal to or greater than that of the baseline scenario in the linear programming model has been found to restrict the extent of these reductions.

This preliminary research will be conducted at the beginning of the operations research course. Operations research is an extension of the topic of linear programming mathematics that is taught in high school. This research aims to describe the results of the work of operations research class students regarding how to design contextual problems and solve them using GeoGebra’s help. This research uses a qualitative approach, namely through in-depth observation of the results of student work on worksheets. After data analysis, it was found that in designing problems, students could produce realistic contextual problems using two variables and a single optimum solution type. Interestingly, they use contexts that are very close to current world trends, for example, Korean boy bands, culinary delights, types of flower arrangements, and so on. Meanwhile, in the solution process, using GeoGebra has proven to facilitate problem-solving by implementing the strategy and checking the results. They use the probe concept to find the optimum solution, and GeoGebra dramatically speeds up the process

Abstract Unleashing the potential of distributed renewable energy sources (RESs), intelligent and autonomous microgrids are becoming pivotal in attaining net‐zero carbon emission goals. Hybrid AC/DC microgrids rise as cutting‐edge microgrid topologies, capitalising on the best of both AC and DC systems. However, the integration of intermittent renewables and uncertainties in loading poses stability challenges. Advanced bidirectional converter controls provide efficient power exchange, but in extreme contingencies, a resilient supervisory control framework (load management/load curtailment approach) is inevitable to withstand/avoid unplanned renewable disruptions/blackouts. Moreover, the operational paradigm shift towards achieving net‐zero emissions, isolated operation of RESs, and conventional load shedding methods are anticipated to encounter substantial challenges, necessitating the development of alternative strategies. In order to improve the stability of hybrid microgrid systems in islanding scenarios, this research presents an energy balancing and load curtailment strategy. The proposed method aims at optimising resource utilisation, prioritising essential loads, and executing an optimal load curtailment strategy (if required), thereby augmenting the stability of systems. Unlike a meta‐heuristic or exhaustive search, which depends on 2n − 1 possible combinations and become unworkable as load numbers increase, the suggested methodology is based on a mathematically modelled load restriction method. By including load criticality, this strategy effectively prevents blackouts even with an increasing number of loads, providing a significantly more useful and practical solution. Additionally, the proposed charging algorithm ensures that the energy storage system imports energy from the grid during off‐peak hours and maximises power generation from the DC subgrid. The efficacy of the proposed strategy is validated using a modified IEEE‐33 bus system as a test case for a hybrid AC/DC microgrid. Simulation results demonstrate the effectiveness of the MILP‐based load curtailment approach in maintaining system stability and preventing blackouts during unforeseen events.

The study of contextual learning implementation introduces mathematical concepts by linking the material with real-life situations or contexts in Rancamulya Village, West Java, commonly known as Tofu Village, where tofu is a staple food and an affordable source of nutrition favored by the wider community. Through research using linear programming simplex method, an optimal solution was found to maximize tofu production, achieving a maximum profit of Rp 1,480,000 with the production of 364 white and 182 yellow tofu boards. Seventy-two mathematics education students at La Tansa Mashir University, Rangkasbitung, conducted this project-based ethnomathematics study. The research employed an ethnographic approach with data collection techniques through observation, documentation, and interviews. Data analysis was performed using a mixed-method approach combining qualitative and quantitative methods. The quantitative data revealed a significant difference in mathematical critical thinking skills between the Problem-Based Learning (PBL) and Numbered Heads Together with Student-Constructed Criteria for Success (NHT-SCCS) learning models. Students taught with the PBL model demonstrated higher critical thinking skills compared to those using the NHT-SCCS model.

The confined aquifer dewatering for long-deep excavations usually encounters challenges due to complicated geotechnical conditions, large excavation sizes, and high hydraulic pressures. To propose the most efficient scheme of confined aquifer dewatering for long-deep excavations, dewatering optimizations were performed using the simulation–optimization method. An open cut tunnel of the Jiangyin-Jingjiang Yangtze River Tunnel Project was taken as an example. The methods of finite element and linear programming (LP) were combined to optimize the dewatering process. A three-dimensional finite element model was developed. After simulating the pumping tests, hydraulic conductivity was inverted. Then, necessary parameters in the LP method were determined by simulating dewatering with each pumping well, and various LP models were developed based on some important influence factors such as dewatering sequence, considered pumping wells, and pumping rate limitation. Finally, the optimal pumping rates were solved and applied to the numerical model, with induced drawdown and ground settlement computed for comparison. The results indicate that the optimization can significantly reduce the required wells in the original design. Dewatering in the deepest zone exhibits the highest efficiency for long-deep excavations with gradually varying depths. For the dewatering sequence from the shallowest to the deepest zone, more pumping wells are required but less energy is consumed. Higher quantity and more advantageous locations of pumping wells in the LP model usually result in lower total pumping rate, drawdown, and ground settlement. If more pumping wells are considered in the deepest zone, pumping rate limitation of single well will only slightly increase the total pumping rate, number of required pumping wells, drawdown, and ground settlement.

Purpose – The purpose of this study is to develop a novel general mathematical model to find the optimal product mix of commercial graphite products, which has a complex production process with alternative sub-processes in the graphite mining production process. Design/methodology/approach – The network optimization was adopted to model the complex graphite mining production process through the optimal allocation of raw graphite, byproducts, and saleable products with comparable sub-processes, which has different processing capacities and costs. The model was tested on a selected graphite manufacturing company, and the optimal graphite product mix was determined through the selection of the optimal production process. In addition, sensitivity and scenario analyses were carried out to accommodate uncertainties and to facilitate further managerial decisions. Findings – The selected graphite mining company mines approximately 400 metric tons of raw graphite per month to produce ten types of graphite products. According to the optimum solution obtained, the company should produce only six graphite products to maximize its total profit. In addition, the study demonstrated how to reveal optimum managerial decisions based on optimum solutions. Originality/value – This study has made a significant contribution to the graphite manufacturing industry by modeling the complex graphite mining production process with a network optimization technique that has yet to be addressed at this level of detail. The sensitivity and scenario analyses support for further managerial decisions.

We propose an adaptive method for building a multivariate regression given by a weighted linear convolution of known scalar functions of deterministic input variables with unknown coefficients. As, for example, when multivariate regression is given by a multivariate polynomial. In contrast to the general procedure of the least squares method that minimizes only a single scalar quantitative measure, the adaptive method uses six different quantitative measures and represents a systemically connected set of different algorithms which allow each applied problem to be solved on their basis by an individual adaptive algorithm that, in the case of an active experiment, even for a relatively small volume of experimental data, implements a strategy of a statistically justified solving. The small amount of data of the active experiment we use in the sense that, for such an amount, the variances of estimates of unknown coefficients obtained by the general procedure of the least squares method do not allow to guarantee the accuracy acceptable for practice. We also proposed to significantly increase the efficiency of the proposed by O. A. Pavlov. and M. M. Holovchenko modified group method of data handling for building a multivariate regression which is linear with respect to unknown coefficients and given by a redundant representation. We improve it by including some criteria and algorithms of the adaptive method for building a multivariate regression. For the multivariate polynomial regression problem, the inclusion of a partial case of the new version of the modified group method of data handling in the synthetic method proposed by O. A. Pavlov, M. M. Golovchenko, and V. V. Drozd, for building a multivariate polynomial regression given by a redundant representation, also significantly increases its efficiency.

Abstract Background Energy system models based on linear programming have been growing in size with the increasing need to model renewables with high spatial and temporal detail. Larger models lead to high computational requirements. Furthermore, seemingly small changes in a model can lead to drastic differences in runtime. Here, we investigate measures to address this issue. Results We review the mathematical structure of a typical energy system model, and discuss issues of sparsity, degeneracy and large numerical range. We introduce and test a method to automatically scale models to improve numerical range. We test this method as well as tweaks to model formulation and solver preferences, finding that adjustments can have a substantial impact on runtime. In particular, the barrier method without crossover can be very fast, but affects the structure of the resulting optimal solution. Conclusions We conclude with a range of recommendations for energy system modellers: first, on large and difficult models, manually select the barrier method or barrier+crossover method. Second, use appropriate units that minimize the model’s numerical range or apply an automatic scaling procedure like the one we introduce here to derive them automatically. Third, be wary of model formulations with cost-free technologies and dummy costs, as those can dramatically worsen the numerical properties of the model. Finally, as a last resort, know the basic solver tolerance settings for your chosen solver and adjust them if necessary.

Discrimination-aware classification methods remedy socioeconomic disparities exacerbated by machine learning systems. In this paper, we propose a novel data pre-processing technique that assigns weights to training instances in order to reduce discrimination without changing any of the inputs or labels. While the existing reweighing approach only looks into sensitive attributes, we refine the weights by utilizing both sensitive and insensitive ones. We formulate our weight assignment as a linear programming problem. The weights can be directly used in any classification model into which they are incorporated. We demonstrate three advantages of our approach on synthetic and benchmark datasets. First, discrimination reduction comes at a small cost in accuracy. Second, our method is more scalable than most other pre-processing methods. Third, the trade-off between fairness and accuracy can be explicitly monitored by model users. Code is available at https://github.com/frnliang/refined_reweighing. [ABSTRACT FROM AUTHOR]

Developing a self‐sufficient renewable power (RP) road transport (SRPRT) system is an important future direction for transport–energy integration. More well‐developed studies must be conducted on the coordinated planning of transport, power supply, and power generation networks. This paper carries out the joint operation and planning of highway charging networks with the wind‐photovoltaic‐energy storage (HCN‐WPE) system. Under multi‐network integration and the interaction among multiple entities, a nested bi‐level optimization model is proposed to optimize the users' charging and travel behavior, charging network's deployment, and power generation system's (PGS) configuration. An H‐M‐L algorithm structure is developed, combining the heuristic algorithm, multi‐agent‐based simulation technology, and linear programming algorithm. Its convergence and applicability are verified on the Nguyen‐Dupius network. An empirical case in the Hu‐Bao‐Wu city agglomeration in China is employed to explore and discuss the managerial insights for the HCN‐WPE system. The study finds that multi‐network coordinated planning can improve the benefits of multiple entities, where the net present value, RP supply rate, and RP consumption rate increase by 12.0%, 3.2%, and 10.5%, compared to independent planning. Network‐level planning can play a management and induction role in balancing the station's load pressure. In addition, the PGS co‐configuration can leverage the complementary power supply of multiple RP generators and the peak cutting and valley filling of energy storage systems, which is essential for achieving the SRPRT goal. [ABSTRACT FROM AUTHOR]

A derivative is a financial asset whose future payoff is a function of underlying assets. Pricing a financial derivative involves setting up a market model, finding a martingale ("fair game") probability measure for the model from the existing asset prices, and using that probability measure to price the derivative. When the number of underlying assets and/or the number of market outcomes in the model is large, pricing can be computationally demanding. In this work, we first formulate the pricing problem in a linear algebra setting, including the realistic setting of incomplete markets where derivatives do not have a unique price. We show that the problem can be solved with a variety of quantum techniques such as quantum linear programming and the quantum linear systems algorithm. While in previous works the martingale measure is assumed to be given, here it is extracted from market variables akin to bootstrapping, a common practice among financial institutions. We discuss the quantum zero-sum game algorithm and the quantum simplex algorithm as viable subroutines. For quantum linear systems solvers, we formalize a new market assumption milder than market completeness, which allows the potential for large speedups. Towards prototype use cases, we conduct numerical experiments motivated by the Black–Scholes–Merton model. [ABSTRACT FROM AUTHOR]

In this paper, a fast method to generate a constant-modulus (CM) waveform for a multiple-input, multiple-output, (MIMO) radar is proposed. To simplify the optimization process, the design of the transmit waveform is decoupled from the design of transmit beamformers (TBs) and subpulses. To further improve the computational efficiency, the TBs' optimization is conducted in parallel, and a linear programming model is proposed to match the desired beampattern. Additionally, we incorporate the perturbation vectors into the TBs' optimization so that the TBs can be adjusted to satisfy the CM constraint. To quickly generate the CM subpulses with the desired range-compression (RC) performance, the classical linear frequency modulation (LFM) signal and non-LFM (NLFM) are adopted as subpulses. Meanwhile, to guarantee the RC performance of the final angular waveform, the selection of LFM signal parameters is analyzed to achieve a low cross-correlation between subpulses. Numerical simulations verify the transmit beampattern performance, RC performance, and computational efficiency of the proposed method. [ABSTRACT FROM AUTHOR]