Linear Programming Methodology Research Articles

Designing a centralized storage hydrogen supply chain network with multi-period and bi-objective optimization

This study introduces a multi-period centralized storage optimization model aimed at designing an efficient hydrogen supply chain system, considering cost and emissions as dual objectives. It integrates multiple energy sources, production and storage methods, transport combinations, demand scenarios, and carbon capture systems, offering a comprehensive decision-making approach for hydrogen network design. Employing the mixed-integer linear programming methodology, the proposed model resolves these complexities. The research applies this model to a case study in France, generating six unique scenarios for 10 and 15 cities, and compares them against two distinct decentralized models. The findings consistently highlight the centralized storage model’s cost benefits across various demand scenarios, including cases of unrestricted emissions as well as cases with limited emission targets. The cost-effectiveness of this proposed model enhances its feasibility within the current context of decarbonization.

Sustainable waste solutions: Optimizing location-allocation of 3R waste management sites in Gondokusuman, Yogyakarta, Indonesia through multi-maximal covering location approach

Developing a Multi-Maximal Covering Location Model (MMCLM) for waste management in Gondokusuman Sub-district, Yogyakarta, Indonesia, is urgently needed. The closure of the Piyungan landfill has resulted in the need for additional Reduce, Reuse, and Recycle Waste Management Sites (3R-WMSs) to reduce waste that the landfill cannot accommodate. The primary objective of this model is to optimize the location and allocation of demand volume nodes, representing the resident population, to a specific set of 3R-WMS. These demand nodes are located at different distances from 3R-WMSs, including high and low coverage areas. The research in the Gondokusuman Sub-district employed MMCLM with facility capacity constraints and was developed using mixed integer linear programming methodology. The study identified five optimal locations for a 3R-WMS establishment that comprehensively cover all demand nodes (15301) and population clusters (45903) in the sub-district, including both high (5085) and low coverage areas (10216). This research represents a significant step forward in developing a sustainable environment by ensuring easy access to reducing, reusing, and recycling-based waste management facilities for residents.

Development of a Model for Analyzing the Optimal Utilization of Classroom Space at the Federal Polytechnic, Nasarawa.

Managing the distribution of limited resources to meet the needs of people has always been a global issue that faces managers, administrators, business owners, leaders of institution and individuals alike. With the increase in number of students admitted in Federal Polytechnic Nasarawa, with a large population of about 10,000, there would be undue stress on the facilities on campus. The class rooms are not sufficient or adequate and not well-assigned compared to the measurable number of students available. This has given rise to the reduction in the length of time a lecturer spends in class, distractions from students because of classroom proximity, amongst others. These cause extreme distress on the students and lecturers alike as they are unable to study or teach, respectively, to their highest potential as a result of resources or amenities that are inadequate or wanting. Data were collected from Federal Polytechnic Nasarawa Central Examination Committee for 2022/2023 Academic Session. The linear and integer programming methodology was employed. From the result of the linear programming (LP), seven (7) out of the seventy-eight (78) available classrooms has been fully utilized. The study revealed that if the remaining seventy-one (71) classrooms are fully utilized and maximized, they will improve the current objective function with a seating capacity of 4, 640. The result of the integer programming (IP) using the branch and bound method revealed that fourteen (14) out of the seventy-eight (78) available classrooms has been fully utilized. It asserted that if the remaining sixty-four (64) classrooms are fully utilized and maximized they will improve the current objective function with a seating capacity of 7,131. The result of the sensitivity analysis indicates that the entire classroom has an allowable increase thus validating the proposed models. The study therefore concludes that classroom space utilization is being underutilized leading to congestion and overflow in the utilized classrooms.

Optimization and benefit analysis of the supply chain for sweet sorghum bioenergy production in China

<p>Bio-liquid fuel is one of the effective ways to alleviate energy shortages and reduce greenhouse gas emissions. Sweet sorghum, as an energy crop used in fuel ethanol production, has enormous potential for development. However, due to seasonality, vulnerability, and logistical scheduling costs during transportation, the sweet sorghum ethanol supply chain faces significant difficulties and challenges in its development. To address the research gap, this paper proposes a multi-objective sustainable supply chain optimization model for Chinese sweet sorghum bioenergy based on mixed-integer linear programming. In this framework, the crop growth process model is first spatially extended to obtain the feedstock sources of the sweet sorghum ethanol supply chain. Then a site selection model for the feedstock collection stations and ethanol processing plants is constructed based on the geographic information system (GIS) to determine the candidate locations of the basic units of the sweet sorghum ethanol supply chain. Finally, a multi-objective supply chain optimization model based on the mixed-integer linear programming methodology is created to achieve the sweet sorghum ethanol supply chain layout and optimization at the national level. This framework takes into account the fuel ethanol market demand in China and the current state of the sweet sorghum ethanol supply chain industry, achieving national-level layout and optimization of the sweet sorghum ethanol supply chain. The total aboveground biomass (dry weight) of sweet sorghum on marginal land in China can be converted into approximately 37.212 million tons of fuel ethanol production, meeting the requirement to promote a nationwide 10% substitution rate for automotive ethanol gasoline. The lowest-cost supply chain layout scheme suggests establishing large ethanol processing plants near the Hu Huanyong Line, as this area benefits from abundant sweet sorghum yield on marginal lands and lower east-west direction transportation costs. However, the lowest carbon emission supply chain layout scheme recommends reducing the raw material supply area and increasing the ethanol transportation route to lower carbon emissions. The results of the sensitivity analyses indicate that lowering feedstock production and increasing ethanol demand increases the overall cost and carbon emissions of the sweet sorghum ethanol supply chain, while using rail transportation methods, increasing feedstock production, and decreasing ethanol demand reduces costs and carbon emissions.</p>

Digital twin-driven real-time planning, monitoring, and controlling in food supply chains

There needs to be more clarity about when and how the digital twin approach could benefit the food supply chains. In this study, we develop and solve an integrated problem of procurement, production, and distribution strategies (PPDs) in a medium-scale food processing company. Using the digital twin approach, the model considers the industrial symbiosis opportunities between the supplier, manufacturer, and customer using interval and sequence variables operating in a constrained environment using mixed-integer linear programming (MILP) and agent-based simulation (ABS) methodology. The study optimizes the make-span and lead time, simultaneously achieving a higher level of digitalization. The analysis demonstrates how digital twin accelerates supply chain productivity by improving makespan time, data redundancy (DR), optimal scheduling plan (OSP), overall operations effectiveness (OOE), overall equipment effectiveness (OEE), and capacity utilization. Our findings provide compelling evidence that the seamless integration PPDs enormously enhance production flexibility, resulting in an excellent service level of 94 %. Managers leverage real-time simulation to accurately estimate the replenishment point with minimal lead time, ensuring optimized operations.Furthermore, our results demonstrate that implementing PPDs has yielded considerable benefits. Specifically, we observed a remarkable 65 % utilization of the pasteurizer and aging vessel and an impressive 97 % utilization of the freezer. Moreover, by applying the DT model, the present model found a notable 6 % reduction in backlog, further streamlining operations and enhancing efficiency.

How a Game Theoretic Approach Can Minimize the Cost of Train Passenger Services: An Intermodal Competition between Rail and Road Transport

Game theory models provide very powerful tools for evaluating strategies that are beneficial to both rail and road operators competing for passengers on parallel routes. This study examines how game theory can help rail operators who are incurring losses on passenger transport to identify strategies that can minimise costs, using the methodology of dual linear programming to analyse strategies. In identifying the best strategies for minimising costs for the railway operator, the best strategies for maximising profits for the road operators are also identified. The game model is set up between two passenger transport operators (rail and road) and is based on the income earned by the road operators from passengers. This study illustrates the following: how the strategies of the two competitors (rail and road) are determined; the formation of the payoff matrix and the presentation of the mathematical problem for the two competitors; and the results and verification of the best strategies for both competitors. The Leonid Hurwicz criterion was used to verify the optimal strategies.

Energy-efficient control in multi-stage production lines with parallel machine workstations and production constraints

Nowadays, the growing interest in industry for enhancing manufacturing processes sustainability is a major trend. One of the most supported strategies to increase the energy-efficiency of manufacturing activities is the control of machine state towards the optimum trade-off between production rate and energy demand. This method is referred to as energy-efficient control and it triggers machines in a standby state with low power request. In this article, multi-stage production lines composed of identical parallel machine workstations are the systems of interest, and the energy-efficient control policies make use of buffer level information. Each machine can be switched off instantaneously and switched on with a stochastic startup time. Problem objective is to minimize the energy demand while ensuring production constraints. This article proposes a novel approach to solve the problem at hand. An exact model for two-stage system is formulated using a Markov Decision Process to be solved with a linear programming methodology. A novel technique, namely the Backward-Recursive approach, is used to address systems with more than two stages. Numerical experiments confirm the effectiveness of the proposed approach.

A Linear Programming Methodology to Optimize Decision-Making for Ready-Mixed Cement Products: a Case Study on Egypt’s New Administrative Capital

Egypt has started constructing its New Administrative Capital since 2015. The new capital was designed to meet smart city standards, which presents a challenge for businesses to make the optimum business decisions given the set budget for such a project. As a result, reaching the optimum solution for allocating the needed materials to each building became important. Many researchers have considered the theory of constraints in their studies to determine the optimum product mix. Frequently, research considers the target of profit maximization to reach the optimum solution with one scenario. In this paper, we aim to solve the problem of product mix in cement production, which organizations face. The problem was formulated based on a case study in Egypt with two linear programming approaches. For this problem, many scenarios were presented under the consideration of two aspects, which are resource utilization and productivity. Data visualization was used in this paper to simplify the procedure of decision-making. Also, a dashboard web application was made for the decision makers to make it easier to create, analyze, and see different business scenarios.

Optimal Sharing Electricity and Thermal Energy Integration for an Energy Community in the Perspective of 100% RES Scenario

This paper presents a study on the optimal district integration of a distributed generation (DG) system for an energy community (EC) and the implementation of sharing electricity (SE) between users. In recent years, the scientific community has frequently discussed potential pathways to achieve a 100% renewable energy source (RES) scenario, mainly through increasing electrification in all sectors. However, cooling-, heat-, and power-related technologies are expected to play a crucial role in the transition to a 100% RES scenario. For this reason, a research gap has been identified when it comes to an optimal SE solution and its effects on the optimal district heating and cooling network (DHCN) allowing both electrical and thermal integration among users. The considered system includes several components for each EC user, with a central unit and a DHCN connecting them all. Moreover, the users inside the EC can exchange electricity with each other through the existing electric grid. Furthermore, the EC considers cooling storage as well as heat storage systems. This paper applies the Mixed Integer Linear Programming (MILP) methodology for the single-objective optimization of an EC, in Northeast Italy, considering the total annual cost for owning, operating, and maintaining the entire system as the economic objective function. After the optimization, the total annual CO2 emissions were calculated to evaluate the environmental effects of the different solutions. The energy system is optimized in different scenarios, considering the usage of renewable resources and different prices for the purchase of electricity and natural gas, as well as different prices for selling electricity. Results showed that, without changing utility prices, the implementation of SE allowed for a reduction of 85% in the total electricity bought from the grid by the EC. Moreover, the total annual EC costs and CO2 emissions were reduced by 80 k€ and 280 t, respectively.

A benefit-cost analysis approach for determining the optimal processing of micronutrient-enriched cowpea leaf soup mixes

Cost-effective techniques are usually recommended in the dissemination and adoption of postharvest processing technologies of food products. Due to limited value addition practices for cowpea leaf, the Fruits and Vegetables for All Seasons Project undertook a study to bridge the gap in the seasonal availability of the vegetable in the arid and semi-arid lands (ASALs) of Kenya through the production of cowpea leaf soup mix. However, the adoption of these techniques has an economic perspective that guides decision-making. This study utilized a two-stage linear programming methodology using NutriSurvey and the analytic hierarchy process in a seven-step hierarchy for the production of a cowpea leaf soup mix of an optimal nutrition and sensory quality. The optimal inclusion level of cowpea leaves into the soup mix was 49%. With an R2 of 61.36%, consistency, taste, and mouthfeel were the greatest determinants of the acceptability of cowpea leaf soup mixes. The incorporation of blanching in solar drying and sun drying were the least costly options with priority vectors of 0.08 and 0.09 (CR < 0.1) respectively, whereas, in the use of mechanized processing techniques such as oven drying, priority vectors of 0.10–0.19 had higher maximum benefits than the local processing technique of sun-drying that had a priority vector of 0.08 (CR < 0.1). The benefit-cost ratio was maximal without extrusion, with the solar-drying pathway having the highest benefit-cost ratio of 1.5. The study found that resource-intensive pathways yielded maximum benefits in the retention of quality. However, with the exclusion of extrusion, the benefit-cost ratio of the processes improved.

Individualizable Vehicle Lane Keeping Assistance System Design: A Linear-Programming-Based Model Predictive Control Approach

Model predictive control (MPC), a control technique that can systematically and explicitly cope with system constraints, has become increasingly prevalent in the field of automotive engineering. Respecting the advanced driver-assistance systems (ADAS) design, the MPC has found its applications in various kinds of ground vehicular lane-keeping assistance systems (LKAS). In this paper, an MPC-based LKAS is synthesized by leveraging the linear programming (LP) methodology. Compared to the conventional MPC-based LKAS that is based on quadratic programming (QP), the LP alternative is less computationally demanding, which is desired for commercial vehicular electronic control units. Besides, the LP scheme enables the designer to formulate the MPC's performance criterion in the sense of L1/L∞ norms, which differs from the QP's L2-norm-based measure. The proposed LP-based MPC-LKAS is examined in CarSim-Simulink joint simulations and its performance is compared with a QP-based solution.

Selection of an alternative based on interval-valued hesitant picture fuzzy sets

Motivated by interval-valued hesitant fuzzy sets (IVHFSs) and picture fuzzy sets (PcFSs), a notion of interval-valued hesitant picture fuzzy sets (IVHPcFSs) is presented in this article. The concept of IVHPcFSs is put forward and some operational rules are developed to deal with it. The cosine similarity measures (SMs) are modified for IVHPcFSs to deal with interval-valued hesitant picture fuzzy (IVHPcF) data and the linear programming (LP) methodology is used to find out the criteria’s weights. A multiple criteria decision making (MCDM) approach is then developed to tackle the vague and ambiguous information involved in MCDM problems under the framework of IVHPcFSs. For the validation and strengthen of the proposed MCDM approach a practical example is put forward to select the educational expert at the end.

Analysis of CO2 Emissions in the Whole Production Process of Coal-Fired Power Plant

The linear programming (LP) model has been used to identify a cost-effective strategy for reducing CO2 emissions in power plants considering coal washing, pollutant removal, and carbon capture processes, thus CO2 emissions in different production processes can be obtained. The direct emissions (combustion emissions and desulfurization emissions) and indirect emissions (pollutant removal, coal washing, and carbon capture) of CO2 were all considered in the LP model. Three planning periods were set with different CO2 emission control desirability to simulate CO2 emissions of the different reduction requirements. The results can reflect the CO2 emissions across the whole production process of a coal-fired power plant overall. The simulation results showed that for a coal-fired power plant containing two 1000 MW ultra super-critical sets, when the desirability was 0.9, the CO2 total emissions were 2.15, 1.84, and 1.59 million tons for the three planning periods. The research results suggest that the methodology of LP combined with fuzzy desirability function is applicable to represent the whole production process of industry sectors such as coal-fired power plants. The government policy makers could predict CO2 emissions by this method and use the results as a reference to conduct effective industrial and energy structure adjustment.

TOPSİS YÖNTEMİ İLE ORTODONTİK TEDARİKÇİ SEÇİMİ

Dental supplier selection is a process that allows companies to choose their suppliers correctly in the light of evaluations. Choosing the right dental suppliers is an important factor both for the efficiency of dental treatment and handling an impressive supply chain. Dental supplier selection is a multi-criterion group decision-making (MCDM) problem that contains many different criterion about the decision-makers generally ambiguous information. TOPSIS method integrated intuitionistic fuzzy set is used in this study. Real-life problems include many unpredictability and defects. Experts are involved in assigning the weights of the criterion in this study. Linear programming (LP) methodology has applied for the ranking of these weights of criterion. Then, the LP methodology is carried out and it was ensured that the appropriate orthodontic bracket suppliers were selected. This is a specific multi-criterion decision making problem. The study was followed together with the sensitivity analyses of the results. At the end of the study, it is foreseen that with the right selection of suppliers, The competitive power of companies in the market and end user satisfaction will increase.

Design of a Power System Supervisory Control with Linear Optimization for Electrical Load Management in an Aircraft On-Board DC Microgrid

In modern aircraft, energy supply management has become a critical matter, since many aboard electrical loads have to be supplied, especially those related to flight safety. However, at the same time, the size and weight of electrical generators must be limited because of their on-board installation. In this paper, the Mixed Integrated Linear Programming (MILP) methodology has been used to formulate the Supervisor definition of the direct current (DC) microgrid (MG) on-board system with an extension for the programmable loads. Due to the problem of dimension increase, two methods have been presented and tested to perform optimal energy management (EM) aboard an aircraft: the Branch and Bound (B&B) and the Linear Regression Approximation (LRA). Finally, numerical simulations and results have been provided to validate the proposed optimization methodologies, according to the dimensions and the complexity of the problem.

ПРОГНОЗУВАННЯ ОБСЯГІВ РЕАЛІЗАЦІЇ ПРОДУКЦІЇ ЗА МЕТОДОМ ЛІНІЙНОГО ПРОГРАМУВАННЯ (НА МАТЕРІАЛАХ НЕМИРІВСЬКОГО КХП, М. НЕМИРІВ ВІННИЦЬКОЇ ОБЛ.)

In this article reveals an example of forecasting the volumes of sales goods through ways of implement optimization analysis, that is by linear programming method. For example, volume of production goods for realization her consumers no must to exceed of determined out maximum or to be lower by minimum, what can to foreseeing in this task. For decision tasks of linear programming with a large number of variables and constraints, decomposition methods are used, which allow instead of the original problem to solve tasks of little volume. In general methodology of linear programming together with simplex-method is considered on the example Nemyriv bakery, where determined out profit on unit bakery products, obtained through the optimal ratio of material resources and costs incurred. In analysis and treatment of economic activities the each enterprises, particularly at composition forecast as to volumes of sales goods with aim of receiving profit, linear programming maybe successfully used out for decision tasks with optimization of development and organization trade processes upon regarding the sale of its products. With point of view management a tasks of linear programming – this tasks of optimal using resources. In each event planning of production goods necessity have on attention, which different productions resources (workforce, raw, materials, means of production) are limited, and also which known norm of costs these resources on different kinds goods, or possible are multiples variants to separating production resources. In our work, we ascertained that in analysis, compliance is checked of demand for bakery products to stocks of most-important kinds raw and materials together with costs as most important conditions for receive profit on enterprises and avoiding of excessive and unforeseen losses. With aim of rise efficiency of enterprises activities necessary and further to look at question of renewing assortment goods and increase quality her, increasing volumes of production, maximum of loading production powers equipment, efficiency using of available resources.

A solving approach for fuzzy multi-objective linear fractional programming and application to an agricultural planting structure optimization problem

In this paper, an algorithm is presented to solve fuzzy multi-objective linear fractional programming (FMOLFP) problems through an approach based on superiority and inferiority measures method (SIMM). In the model for the proposed approach, each of fuzzy goals defined for the fractional objectives and some of constraints have fuzzy numbers. To achieve the highest membership value, SIMM is adopted to deal with fuzzy number in constraints, then a linear goal programming methodology is introduced to solve the problem in which the fractional objectives is fuzzy goals. A case of agricultural planting structures optimization problem is solved to illustrate the application of the algorithm. The results show that winter wheat and summer corn acreage should be 38,386.4 ha, and cotton acreage should be 20,669.6 ha. Because of high risk in cotton cultivation at present, the ratio of grain planted area to cotton planted area is unreasonable. An improved support in policy is necessary for the government to enhance the enthusiasm of farmers to plant cotton and sustain the development of cotton market in the long term.

A combined machine learning algorithms and DEA method for measuring and predicting the efficiency of Chinese manufacturing listed companies

Data Envelopment Analysis (DEA) is a linear programming methodology for measuring the efficiency of Decision Making Units (DMUs) to improve organizational performance in the private and public sectors. However, if a new DMU needs to be known its efficiency score, the DEA analysis would have to be re-conducted, especially nowadays, datasets from many fields have been growing rapidly in the real world, which will need a huge amount of computation. Following the previous studies, this paper aims to establish a linkage between the DEA method and machine learning (ML) algorithms, and proposes an alternative way that combines DEA with ML (ML-DEA) algorithms to measure and predict the DEA efficiency of DMUs. Four ML-DEA algorithms are discussed, namely DEA-CCR model combined with back-propagation neural network (BPNN-DEA), with genetic algorithm (GA) integrated with back-propagation neural network (GANN-DEA), with support vector machines (SVM-DEA), and with improved support vector machines (ISVM-DEA), respectively. To illustrate the applicability of above models, the performance of Chinese manufacturing listed companies in 2016 is measured, predicted and compared with the DEA efficiency scores obtained by the DEA-CCR model. The empirical results show that the average accuracy of the predicted efficiency of DMUs is about 94%, and the comprehensive performance order of four ML-DEA algorithms ranked from good to poor is GANN-DEA, BPNN-DEA, ISVM-DEA, and SVM-DEA.

A heuristic approach to the task planning problem in a home care business

In this paper, we study a task scheduling problem in a home care business. The company has a set of supervisors in charge of scheduling the caregivers' weekly plans. This can be a time-consuming task due to the large number of services they work with, as well as the need to consider user preferences, services required time windows and travel times between users' homes. Apart from that, it is also important to have a continuity of care, i.e., that users generally prefer not to have their caregiver changed. This problem involves both route planning and employee task planning, which are usually very challenging. We first propose to model it using integer linear programming methodology. Since the real instances that the company needs to solve are very large, we design a heuristic algorithm, based on the simulated annealing philosophy, that allows the company to obtain the caregivers' weekly schedules. Lastly, we check the algorithm's good performance, by comparing the solutions it proposes with those provided by the integer linear programming methodology, in small size problems, and we present a case study to confirm that the algorithm correctly solves real-life instances.

Airfoil–slat arrangement model design for wind turbines in fuzzy environment

In this study, a multi-element wind turbine blade that consists of NACA 6411 and NACA 4412 leading-edge slat design is investigated computationally. Optimum design parameters of the slatted wind turbine blade leading to maximum value of CL/CD related to the turbine power are obtained. In the optimization process, a new fuzzy logic linear programming methodology integrating with fuzzy linear regression and 2D CFD analysis is proposed. The aerodynamic characteristics of the slatted blade are computed by using Incompressible Navier–Stokes equations and k-omega turbulence modeling. Results are compared with the results of linear programming method and direct search optimization method. The computational results reveal that the proposed methodology for performance optimization is more effective than other methods to obtain high-performance value of the CL/CD. The maximum value of the CL/CD is obtained as 25.1 leading the maximum efficiency of 0.52.