Mathematical Programming Approach Research Articles

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.

Mathematical programming methods for reducing inequity due to stock-outs of pharmaceuticals in low-resourced regions using a mobile pharmacy

Delivering essential pharmaceuticals to consumers in low- and middle-income countries (LMICs) is a complex global challenge that requires equitable solutions in the last mile of pharmaceutical supply chains. This paper proposes using a mobile pharmacy to alleviate the burden due to pharmaceutical stock-outs among rural communities from an equity lens. The Stock-out Severity Index (SSI) is used to assess inequity and is used as the equity objective in a mobile facility routing model. We develop two mathematical programming approaches for routing of the mobile pharmacy so as to minimize the mean absolute deviation of the SSI. The first is a mixed integer program (MIP) modeling approach, based on an approximation of the SSI. The second is an implicit enumeration approach that is implemented within a chronological decomposition heuristic. To help establish its applicability potential, the paper describes a case study that demonstrates how a mobile pharmacy can effectively reduce inequity in a section of rural Uganda. In the case study, costs associated with improving equity are evaluated. This paper finds that optimizing for equity only is associated with high operational costs, and demonstrates approaches that achieve equitable solutions though constrained cost increases.

A mathematical programming approach for resource allocation of data analysis workflows on heterogeneous clusters

Scientific communities are motivated to schedule their large-scale data analysis workflows in heterogeneous cluster environments because of privacy and financial issues. In such environments containing considerably diverse resources, efficient resource allocation approaches are essential for reaching high performance. Accordingly, this research addresses the scheduling problem of workflows with bag-of-task form to minimize total runtime (makespan). To this aim, we develop a mixed-integer linear programming model (MILP). The proposed model contains binary decision variables determining which tasks should be assigned to which nodes. Also, it contains linear constraints to fulfill the tasks requirements such as memory and scheduling policy. Comparative results show that our approach outperforms related approaches in most cases. As part of the post-optimality analysis, some secondary preferences are imposed on the proposed model to obtain the most preferred optimal solution. We analyze the relaxation of the makespan in the hope of significantly reducing the number of consumed nodes.

Production Scheduling Using Deep Reinforcement Learning and Discrete Event Simulation

AbstractScheduling in the process industry is a highly demanding task. Having access to optimal production schedules at short notice, for instance, after spontaneous changes, offers numerous advantages in terms of robustness, economics, and ultimately customer satisfaction, as delays are minimized. In this work, we describe our initial efforts to apply and evaluate deep reinforcement learning (DRL) for optimized scheduling in a typical fill‐and‐finish batch production plant in the chemical industry. Our pilot study demonstrates how DRL can be implemented using an approach based on discrete event simulation. We discuss the results and benefits of DRL, compare it to mathematical programming approaches, and outline a potential path forward. Our study suggests that the application of DRL in the chemical industry is a promising research direction and that DRL can complement established methods such as process simulation and mathematical programming.

A review of inverse data envelopment analysis: origins, development and future directions

AbstractData envelopment analysis (DEA) is a widely used mathematical programming approach for assessing the efficiency of decision-making units (DMUs) in various sectors. Inverse DEA is a post-DEA sensitivity analysis approach developed initially for solving resource allocation. The main objective of inverse DEA is to determine the optimal quantity of inputs and/or outputs for each DMU under input and/or output perturbation (s), which would allow them to reach a given efficiency target. Since the early 2000s, inverse DEA has been extended theoretically and applied successfully in different areas including banking, energy, education, sustainability and supply chain management. In recent years, research has demonstrated the potential of inverse DEA for solving novel inverse problems, such as estimating merger gains, minimizing production pollution, optimizing business partnerships and more. This paper provides a comprehensive survey of the latest theoretical and practical advancements in inverse DEA while also highlighting potential areas for future research and development in this field. One such area is exploring the use of heuristic algorithms and optimization techniques in conjunction with inverse DEA models to address issues of infeasibility and nonlinearity. Moreover, applying inverse DEA to new sectors such as healthcare, agriculture and environmental and climate change issues holds great promise for future research. Overall, this paper sets the stage for further advancements in this promising approach.

Hybrid Machine Learning-Mathematical Programming Approach for Optimizing Gas Production and Water Management in Shale Gas Fields

This paper presents a novel mathematical programming approach that simultaneously incorporates a mixed-integer nonlinear programming formulation with machine learning models to determine the operating conditions, gas production, and optimal water management for the completion phase in shale gas fields. The dataset for the development of an artificial neural network model has been collected from the Eagle Ford Texas formation. The total cumulative gas production and flowback water generated in shale gas wells are selected as output variables. The mathematical optimization model considers machine learning models for each well, mass balances, treatment, storage, reuse, and disposal options as well as well location selection and associated costs and revenues from the sale of the shale gas produced. A case study has been used to illustrate the benefits of the proposed approach. The compromise solution offers a water consumption per produced energy of 6.71 L/GJ in addition to the fact that 27% of the total fracture water required can be obtained by reusing the flowback water with attractive economic indicators.

Optimal Incorporation of Intermittent Renewable Energy Storage Units and Green Hydrogen Production in the Electrical Sector

This paper presents a mathematical programming approach for the strategic planning of hydrogen production from renewable energies and its use in electric power generation in conventional technologies. The proposed approach aims to determine the optimal selection of the different types of technologies, electrolyzers and storage units (energy and hydrogen). The approach considers the implementation of an optimization methodology to select a representative data set that characterizes the total annual demand. The economic objective aims to determine the minimum cost, which is composed of the capital costs in the acquisition of units, operating costs of such units, costs of production and transmission of energy, as well as the cost associated with the emissions generated, which is related to an environmental tax. A specific case study is presented in the Mexican peninsula and the results show that it is possible to produce hydrogen at a minimum sale price of 4200 $/tonH2, with a total cost of $5.1687 × 106 and 2.5243 × 105 tonCO2eq. In addition, the financial break-even point corresponds to a sale price of 6600 $/tonH2. The proposed model determines the trade-offs between the cost and the emissions generated.

Optimizing spine surgery instrument trays to immediately increase efficiency and reduce costs in the operating room

BackgroundOver-crowded surgical trays result in perioperative inefficiency and unnecessary costs. While methodologies to reduce the size of surgical trays have been described in the literature, they each have their own drawbacks. In this study, we compared three methods: (1) clinician review (CR), (2) mathematical programming (MP), and (3) a novel hybrid model (HM) based on surveys and cost analysis. While CR and MP are well documented, CR can yield suboptimal reductions and MP can be laborious and technically challenging. We hypothesized our easy-to-implement HM would result in a reduction of surgical instruments in both the laminectomy tray (LT) and basic neurosurgery tray (BNT) that is comparable to CR and MP. MethodsThree approaches were tested: CR, MP, and HM. We interviewed 5 neurosurgeons and 3 orthopedic surgeons, at our institution, who performed a total of 5437 spine cases, requiring the use of the LT and BNT over a 4-year (2017–2021) period. In CR, surgeons suggested which surgical instruments should be removed. MP was performed via the mathematical analysis of 25 observations of the use of a LT and BNT tray. The HM was performed via a structured survey of the surgeons’ estimated instrument usage, followed by a cost-based inflection point analysis. ResultsThe CR, MP, and HM approaches resulted in a total instrument reduction of 41%, 35%, and 38%, respectively, corresponding to total cost savings per annum of $50,211.20, $46,348.80, and $44,417.60, respectively. ConclusionsWhile hospitals continue to examine perioperative services for potential inefficiencies, surgical inventory will be increasingly scrutinized. Despite MP being the most accurate methodology to do so, our results suggest that savings were similar across all three methods. CR and HM are significantly less laborious and thus are practical alternatives.

On the Discrete-Time Minimum Principle in Multiple-Mode Systems

This paper presents a robust version of the discrete-time minimum principle for uncertain systems. The uncertainty enters the dynamics of the system by an unknown value that belongs to a finite set. Each element of such a set represents a possible dynamic realization of the discrete-time trajectory. Following a mathematical programming approach, we reformulate the problem to obtain general necessary conditions that allow finding the worst-case optimality in the form of a weighted sum. These conditions are then applied to the time-varying linear affine quadratic problem with multiple modes and a general cost, which includes tracking signals in both: the state and the control variables. We illustrate our result with an application to a production-inventory control problem with uncertain dynamics.