Mathematical Programming Approach Research Articles

Advancing Decarbonization Efforts in the Glass Manufacturing Industry through Mathematical Optimization and Management Accounting

This study explores the integration of activity-based costing (ABC) and the theory of constraints (TOC) with carbon tax policies to drive decarbonization in the Taiwanese glass industry. Employing a mathematical programming approach, four distinct models are developed to assess the impact of different carbon tax structures, carbon trading mechanisms, and recycled material utilization on corporate profitability and carbon emissions. The findings reveal that strategically applying ABC and the TOC with well-designed carbon tax policies can effectively incentivize emission reduction while maintaining industrial competitiveness. The models incorporating carbon trading and tax allowances demonstrate the potential for creating win–win situations, where companies can increase profitability by investing in cleaner technologies and processes. This study contributes to the literature on sustainable manufacturing and provides actionable insights for policymakers and industry leaders seeking to implement effective carbon pricing mechanisms that drive economic growth and environmental sustainability in tandem.

Optimizing Last-Mile Delivery: A Multi-Criteria Approach with Automated Smart Lockers, Capillary Distribution and Crowdshipping

Background: This publication presents a review, multiple criteria optimization models, and a practical example pertaining to the integration of automated smart locker systems, capillary distribution networks, crowdshipping, last-mile delivery and supply chain management. This publication addresses challenges in logistics and transportation, aiming to enhance efficiency, reduce costs and improve customer satisfaction. This study integrates automated smart locker systems, capillary distribution networks, crowdshipping, last-mile delivery and supply chain management. Methods: A review of the existing literature synthesizes key concepts, such as facility location problems, vehicle routing problems and the mathematical programming approach, to optimize supply chain operations. Conceptual optimization models are formulated to solve the complex decision-making process involved in last-mile delivery, considering multiple objectives, including cost minimization, delivery time optimization, service level minimization, capacity optimization, vehicle minimization and resource utilization. Results: The multiple criteria approaches combine the vehicle routing problem and facility location problem, demonstrating the practical applicability of the proposed methodology in a real-world case study within a logistics company. Conclusions: The execution of multi-criteria models optimizes automated smart locker deployment, capillary distribution design, crowdshipping and last-mile delivery strategies, showcasing its effectiveness in the logistics sector.

Mathematical programming for simultaneous feature selection and outlier detection under l1 norm

The goal of simultaneous feature selection and outlier detection is to determine a sparse linear regression vector by fitting a dataset possibly affected by the presence of outliers.The problem is well-known in the literature. In its basic version it covers a wide range of tasks in data analysis. Simultaneously performing feature selection and outlier detection strongly improves the application potential of regression models in more general settings, where data governance is a concern. To trigger this potential, flexible training models are needed, with more parameters under control of decision makers.The use of mathematical programming, although pertinent, is scarce in this context and mostly focusing on the least-squares setting. Instead we consider the least absolute deviation criterion, proposing two mixed-integer linear programs, one adapted from existing studies, and the other obtained from a disjunctive programming argument. We show theoretically and computationally that the disjunctive-based formulation is better in terms of both continuous relaxation quality and integer optimality convergence.We experimentally benchmark against existing methodologies from the literature. We identify the characteristics of contamination patterns, in which mathematical programming is better than state-of-the-art algorithms in combining prediction quality, sparsity and robustness against outliers. Additionally, the mathematical programming approaches allow the decision maker to directly control parameters like the number of features or outliers to tolerate, those based on least absolute deviations performing best. On real world datasets, where privacy is a concern, our approach compares well to state-of-the-art methods in terms of accuracy, being at the same time more flexible.

Mathematical programming models to assist the evaluation of shipbrokers

Shipbrokers play a key role in maritime industry by acting as intermediates between shipping companies and the market. They undertake various chartering, buying or selling operations. In this paper, we propose a mathematical programming approach for the evaluation and selection of shipbrokers. Specifically, the score of each ship broker is a composite measure that is derived by aggregating a set of performance criteria, e.g., reputation, etc. The developed mathematical programming models enable the aggregation and weighting of the criteria. We employ three optimization models to explore the effect of different weighting schemes on the scores and ranking of the shipbrokers. The models that provide a common set of weights for all the shipbrokers establish the appropriate ground for comparisons among them. Also, our models facilitate the incorporation of user priorities over the criteria in the form of weight restrictions. The proposed approach is illustrated by assessing seven shipbroker offers for selling a dry-bulk ship using four criteria, namely revenue, brokerage fee, brokerage time and terms & conditions.

Effect of a Storage System in a Microgrid with EDR and Economic Dispatch Considering Renewable and Conventional Energy Sources

Due to the importance that organizations and governments have placed on environmental pollution and the policies that force organizations to comply with environmental standards, the use of renewable energy sources to meet energy requirements becomes important. The problem of the economic dispatch consists of satisfying the energy demand of the clients, establishing the most convenient source of supply at each moment, considering the established objective (minimize the operating cost of the microgrid) and satisfying the established restrictions. This paper addresses the problem of economic dispatch in a microgrid with a mathematical programming approach. The proposal to meet the energy demand considers: (a) interconnection to the main grid, (b) conventional diesel generators, (c) a photovoltaic system, (d) a hydroelectric turbine, (e) a wind system, (f) a battery-based storage system, (g) capacity to exchange energy with the main grid, (h) incentive for reducing electricity demand (EDR) by customers when an environmental contingency occurs and (i) regeneration of pollutants emitted by conventional generators. The proposal is implemented in the Lingo 17 software. The results show that by including a BESS and the EDR program, it is possible to save between 18% and 75% of the costs of the objective function and stop emitting a little more than 195 kg of pollutants into the environment.

The impact of circular economy indicators in the optimal planning of energy systems

One of the purposes of the Circular Economy is to promote the optimization of resources; most power systems planning towards renewable energy focus on the operation phase. In this sense, innovative Circular Economy indicators play a fundamental role in planning electricity generation due to the massive electrification of economic activities, offering the option of using fewer material resources in the system infrastructure to reduce the depletion of non-renewable resources. Therefore, when planning a power supply system, it is essential to assess technical, environmental, and economic aspects to guarantee the system's proper functioning and an infrastructure design with the minimum impact. This work presents a mathematical programming approach that aims to introduce rigorous metrics on the requirements of non-renewable resources used during the process and energy self-sufficiency since they have not been studied as one of the aspects of the Circular Economy within the energy sector. In addition, the model determines the optimal selection of the required infrastructure and necessary capacities in energy production to satisfy the energy demand required in a specific period. Together, the quantification of materials is normalized using the Abiotic Depletion Potential as a comparison of the depletion of non-renewable resources. The proposed Mixed Integer Nonlinear Programming (MINLP) multi-objective model is solved using the goal programming technique, allowing to determine the compensations between the total cost, CO2eq emissions (related to the production of energy in the different energy generating technologies) and Circular Economy indicators. A case study for power generation in Mexico is presented and the results show that by implementing Circular Economy indicators as an addition to the economic and environmental functions, “achievement in performance” for the different objectives ranges from 84.00 % and 89.96 %. In addition, the optimization shows a 76.17 % decrease in the total cost and 48.73 % in CO2eq emissions concerning the respective worst case (Nadir point). This paper contributes to the growing body of literature on the integration of Circular Economy metrics, specifically in optimizing the energy sector.

Fuzzy Programming Approach to Solve Multi-Objective Fully Fuzzy Transportation Problem

The aim of this study is presenting the solution methodology of multi-objective fuzzy transportation problem with fuzzy decision variables, where all the input parameters and decisions variables of the programming problems are assumed to be triangular fuzzy number and triangular fuzzy decision variables respectively. Moreover the objectives under considerations are minimization of cost of transportation and minimization of shipping time under fuzzy environment. The fuzziness of the objective functions and the fuzzy constraints of the programming problem are defuzzified using the ranking function and the equality property between two fuzzy numbers, respectively. The consequent crisp multi-objective fuzzy transportation problem is tackled by employing fuzzy mathematical programming approach. Finally fuzzy decision is made after solving the resultant mathematical programming problem using LINGO(Schrage and LINDO Systems (1997)) software. Illustrative numerical example is presented in support of the proposed methodology.

A common weights multiplicative aggregation approach for composite indicators: the case of Global City Competitiveness Index

We propose a mathematical programming approach to assess a set of entities against a composite index. The weights used to construct the composite index are derived via optimization process. Specifically, we adopt the multiplicative method for the aggregation of the components (sub-indicators) of the evaluated index, which reduces the effect of compensation between the components. Also, we model the problem of identifying a common weighting scheme for the evaluated entities as a multiple objective programming (MOP) problem, with the performance of each entity being a distinct objective-criterion. This allows for comparisons and inferences between the assessed entities as a common ground is established. We stick to the concept of multiplicative aggregation by scalarizing the MOP problem using the weighted product method. Utilizing the multiplicative aggregation method in our modelling approach results in a nonlinear model that is scale invariant. However, using logarithms we show that is straightforwardly converted to a linear equivalent model, which is translation invariant. We examine whether the derived weighting scheme is unique, and in case there are alternative optimal solutions, we employ a max–min achievement function to identify a unique solution. We demonstrate our approach using synthetic datasets and compare it to other multiplicative approaches in the literature. We show that the proposed approach has neglective computational requirements and discriminates to a greater extent than those approaches with which we are compared, while at the same time provides a similar ranking. Similarities and dissimilarities in the results are justified. Since our approach is translation invariant, it enables us to apply it to cases where the data needs translation. We further illustrate our approach for such a case using the Global City Competitiveness Index, developed by Citigroup's Economist Intelligence Unit (EIU), which evaluates the competitiveness of 120 major cities worldwide.

Drop-and-pull container drayage with flexible assignment of work break for vehicle drivers

Consideration of driver-related constraints, such as mandatory work break, in vehicle scheduling and routing is of extraordinary importance for safety driving and guaranteeing the interests of vehicle drivers. Drop-and-pull transportation is an efficient mode in container drayage services and creates interdependencies between the routes of vehicle drivers. The situation becomes even more complicated when the drivers must comply with requirements of the mandatory work break. This paper addresses a drop-and-pull container drayage problem with flexible assignment of work break. The time and location of work break for drivers can be flexibly chosen based on scheduling, routing and optimization requirements. The transportation vehicle is comprised of two parts as a tractor and a trailer. The tractor can drag at most one trailer at a time, and is separable from the trailer when executing drayage activities. The problem is formulated as a mixed-integer programming model, which is then strengthened by proposing several families of valid inequalities. To efficiently solve realistic-sized instances, a backtracking adaptive threshold accepting algorithm with a mixed-integer programming model specially coping with the assignment of work break is proposed. Mechanisms of tabu search are incorporated to enhance the searching ability of the algorithm. Experiments indicate that the proposed algorithm can efficiently handle the vehicle scheduling and routing as well as the work break assignment and outperforms the mathematical programming approach. Sensitivity analyses about different policies and varied length of the work break are also conducted with some managerial insights presented.

A fast-response mathematical programming approach for delivering disaster relief goods: an earthquake case study

ABSTRACT This paper tackles a complex logistics challenge of disaster management, encompassing warehouse location, pre-disaster inventory planning, routing, and post-disaster relief supply delivery. We establish an iterative process for optimizing relief distribution to shelters. Adaptable warehouse inventory reallocation responds to fluctuating demands, guided by a two-phase mathematical programming approach. In the first phase, a two-stage stochastic programming (TSSP) model determines optimal warehouse and shelter locations and inventory levels. In the subsequent phase, we introduce a mixed-integer programming (MIP) model to minimize the overall delivery time by making routing decisions. To streamline the process, we introduce a novel enumeration algorithm that trims down route options by considering unavailable links, effectively transforming the MIP model into an assignment-based model. This innovation results in a noticeable 74% reduction in solution time. Further efficiency is achieved by developing a branch-and-cut algorithm for swift MIP resolution. A real-world case study confirms the practicality of our approach.

Analysis of the Consequences of Agricultural Policies on the Cropping Pattern of Agricultural Products and Employment in Afghanistan

The discussion of employment and its complications in the world has attracted the attention of many politicians, government officials, and experts. Creating sustainable employment and revenue is the most important way to create economic and social welfare in all human societies. Thus, in developing countries, management policies to support producers’ revenue in the agricultural sector and increase employment in this area are considered as the main development goals for them. However, the current research used the positive mathematical programming (PMP) approach and then evaluated the economic consequences of changing the cropping pattern, especially evaluating the level of employment of the labor. Accordingly, the simulated scenarios include price variation of selected agricultural products (PMP1), Yield variation of selected agricultural products (PMP2), Change in the consumption of chemical fertilizers (PMP3), change in the consumption of pesticides (PMP4), change in the consumption of irrigation water (PMP5) and the combination of the mentioned scenarios (PMP6). The study Model was done by responding to 928 questionnaires from 16 districts in Nangarhar province, AFG. The investigators recorded and classified the data in Excel software and the analysis was done with the GAMS software. Finally, by applying the integrated model (PMP6), a suitable result is established between the policies and the amount of gross profit increases by 83 million Afghanis (1.06 percent), and the amount of employment decreases by only 391 thousand people (4.35 percent). Besides, in this model, the consumption of chemical fertilizers is 1.15%, the consumption of agricultural pesticides is 0.49%, and the consumption of irrigation water is 2.95% less than the current model of the province. According to the findings of this research, all the products under review have price elasticity lower than one.

A mathematical programming approach for recognizing binet matrices

A mathematical programming approach for recognizing binet matrices

Commodity layout in supermarkets: using the integration of the comprehensive related value method and genetic algorithm

The existing shelf layout methods do not explicitly consider the attention and relevancy of the commodity systematically and thus have failed to capture the invalid associations, resulting in poor sales impact and customer satisfaction. For such shortcomings, in this paper, we propose a mathematical programming approach for shelf layout problems based on comprehensive related value. First, we introduce the concepts of related value considering both attention and relevancy; second, we give the concept of adjacent utility value and the freedom of placement, and further analyze the impact of the same commodity on surrounding commodities due to different placement positions; third, we establish a new comprehensive related value-based commodity layout optimization model (CRV-CL) and provide the solution steps integrating with a genetic algorithm. Finally, we analyze the characteristics of CRV-CL through a specific case. The simulation results indicate the overall relevancy after applying the CRV-CL model.

Water resources management scenarios and transboundary hydro-political concerns in Iran’s eastern border areas

Motives: Since the main sources of some rivers are located in neighbouring countries, hydrological issues in the eastern part of Iran are critical. The water dispute between Iran and the neighbouring Afghanistan is related to environmental issues and human health.Aim: The aim of this study was to demonstrate how transboundary water conflicts increase human vulnerability through economic issues such as reduced productivity in the agricultural sector.Results: The study’s originality lies in the application of the positive mathematical programming approach to the agricultural sector, specifically in evaluating the impact of water pricing policies on crop selection and irrigation water use. A quadratic cost function was calibrated to develop three scenarios of water resources consumption (30%, 40%, and 70% reduction for farmers in group 1, and 10%, 25%, and 75% reduction for farmers in group 2) and price increase (70%, 80%, and 100% increase). The calibration of the quadratic cost function revealed an increase in irrigation efficiency (water resources consumption) as well as an increase in the region’s irrigated area.

Exploring Rule-Free Layout Decomposition via Deep Reinforcement Learning

Multiple patterning lithography decomposition (MPLD) and mask optimization enable the ever-shrinking device feature sizes far below the lithography system limit. Conventional MPLD is solved by mathematical programming or graph-based approaches, where a set of predetermined rules are indispensable to identify the conflicts to be resolved. In this paper, we explore rule-free layout decomposition following a simple but sweet principle, let the mask optimizer “teach” the layout decomposer how to generate suitable decompositions. Our flow includes a reinforcement-learning-based layout decomposer and a deeplearning-based mask optimizer. Without any hand-crafted rules, our framework can perform competitively and even surpass the state-of-the-art rule-based methods with notable (7×~63×) turn-around-time speedup.

Topology optimization of isotropic elastic materials in the two-dimensional design domain with changes in characteristic boundary conditions

Topology optimization (TO) has become increasingly popular as a useful tool for designers and engineers during the initial stages of design. TO aims to optimize the geometry of a design to achieve a specific objective, which can range from discrete grid-like structures to continuum structures. In essence, the geometry is parameterized pixel-by-pixel, with the material density of each element or mesh point serving as a design variable. After that, the optimization problem is addressed using mathematical programming and analytic gradient calculation-based optimization approaches. In this paper, we investigate the material distribution when performing topology optimization for an isotropic material with boundary conditions including fixed structures, supports, or external forces changing. In addition, we investigate more cases where there are material holes in the design domain, meaning that the density of the material is zero. In this study, the modified SIMP method and filter sensitivity are used for topology optimization. The results of the study are the optimized structural domains and the change in compliance according to the number of iterations. The results indicate that the compliance value of most structures reaches convergence after optimization up to the 20th iteration. Moreover, if the force applied to the design domain is symmetrical, the optimal structure also exhibits symmetry. Thus, the distribution of material is concentrated at the positions of the supports. Topology optimization produces designs that both meet boundary conditions while saving material and reducing their mass. The results obtained are important data for structural optimization design for isotropic elastomeric materials. From there, it can be applied to real objects with different requirements and conditions

A mathematical programming approach for downscaling multi-layered multi-constraint land-use models

Land-use and land-cover change (LULCC) models are important tools for environmental policy planning. LULCC models are frequently constrained to the generation of projections at a specific resolution. However, subsequent studies or models may require finer resolutions. In this work, a downscaling method for LULCC models is proposed that uses a mathematical programming approach to disaggregate the multiple layers of the land-use change projections while respecting a series of constraints. The method is calibrated and validated with MapBiomas data for the years 2000 and 2018 converted for the GLOBIOM-Brazil model, successfully predicting land-use at a finer resolution. Also, as proof of concept, the calibrated model is also applied for GLOBIOM-Brazil projections for 2050. This paper advances the state-of-the-art by proposing and testing a downscaling method using a mathematical programming approach with spatial effects, that operates on multi-layered land-use projections with a range of constraints while allowing flexibility on the number and type of the specific layers and constraints.

Optimal expansion for a clean power sector transition in Mexico based on predicted electricity demand using deep learning scheme

This study presents a mathematical programming approach for the strategic planning of electrical energy production. The proposed approach seeks the optimal selection of conventional and clean technologies and their production capacity in a given period. In addition, it aims to assess the amount of emissions generated and water consumption, without neglecting economic aspects. The planning considered in this study extends from 2020 to 2040, where the approach considers the implementation of deep learning models to forecast the future electricity demand of each year through historical data; thus obtaining a more precise energy configuration. Fossil fuels and biofuels are used as primary energy in the operation of different technologies. Therefore, both economic and environmental objectives are considered. The economic objective function determines the minimum total discounted cost, which encompasses energy production, operation, maintenance, primary energy, and investment costs. While the environmental objective focuses on reducing water consumption and emissions. Through Pareto curves, using the ɛ-constraint method, the proposed model determines the trade-offs between the total discounted cost and the CO2eq emissions generated. The Mexican electrical system is presented as a specific case study with real production data and available resources. The results show that it is possible to reduce the total discounted cost by up to 11.02%, while in environmental aspects, up to 28.27% in emissions and up to 20.23% in water consumption, achieving that the power produced by renewable energies increases progressively until reaching 70% of the energy demand in 2040, where the system is committed to implementing clean technologies and replaces a percentage of fossil fuels with biofuels in conventional technologies. The results highlight that by increasing the investment cost with clean technologies, the system is balanced with a lower total future cost in the planning presented, thus reducing the environmental burden, and determining trade-offs between cost and environmental aspects.

A Mathematical Programming Approach for Multi-Objective Optimization in Designing Flexible Manufacturing Cells

The study aims to design flexible manufacturing cells with routing flexibility. A weighted mixed-integer linear mathematical programming model that aims to find optimal routing of parts in flexible manufacturing cells under constraints such as minimum machine utilization rate, maximum machine utilization rate, tool capacities, the utilization rate of workers, and labor-system unbalance is developed. The mathematical programming model aims to minimize the weighted sum of five objective functions: (1) the total number of intracellular movements; (2) the total number of intercellular movements; (3) the total workload unbalance of the machine system; (4) the total number of tools in all machines in the cells; and (5) the total labor-system workload unbalance. The main contribution of this study is to obtain these five objectives simultaneously, which have not been encountered to handle together before. By integrating these factors, the study presents a comprehensive approach to optimizing the design of flexible manufacturing cells. This study also has the potential to enhance system performance by addressing these factors. An illustrative problem tests the developed model, and the LINGO 17.0 optimization program is used to solve the generated mathematical programming model. Moreover, the related sensitivity analysis is performed with some parameters to examine the obtained results.

Strategic planning for sustainable electric system operations: Integrating renewables and energy storage

This work proposes a mathematical programming approach for strategic planning in power system operations with the aim of promoting a sustainable energy transition. The approach identifies optimal operating policies that integrate conventional generation plants and renewable energies to meet user demand while considering energy generation, transmission, and distribution. Additionally, the formulation determines the optimal storage units required in the energy transmission network to improve system stability and reduce operating costs by balancing energy supply and demand. However, the operation of the power system is limited by several factors, such as economic and environmental factors as well as energy losses. Therefore, the purpose is to operate the electricity system with the lowest operating cost while minimizing CO2 emissions generated by electricity production. Since there is a conflict between these objectives, a multi-objective approach is necessary to propose a compromise solution. The compromise solution represents a balance between technical, economic, and environmental factors; the results demonstrate that it is possible to achieve a balance between these factors. Finally, we present a case study of the Mexican Electricity System (SEN) to apply the developed model. The case study includes a maximum load operation analysis to determine the system’s limits and ranges. This analysis will enable system expansion or improvement planning to meet future energy demands.