Firstly an overview of the potential impact on work-in-process （WIP） and lead time is provided when transfer lot sizes are undifferentiated from processing lot sizes. Simple performance examples are compared to thos...Firstly an overview of the potential impact on work-in-process （WIP） and lead time is provided when transfer lot sizes are undifferentiated from processing lot sizes. Simple performance examples are compared to those from a shop with one-piece transfer lots. Next, a mathematical programming model for minimizing lead time in the mixed-model job shop is presented, in which one-piece transfer lots are used. Key factors affecting lead time are found by analyzing the sum of the longest setup time of individual items among the shared processes （SLST） and the longest processing time of individual items among processes （LPT）. And lead time can be minimized by cutting down the SLST and LPT. Reduction of the SLST is described as a traveling salesman problem （TSP）, and the minimum of the SLST is solved through job shop scheduling. Removing the bottleneck and leveling the production line optimize the LPT. If the number of items produced is small, the routings are relatively short, and items and facilities are changed infrequently, the optimal schedule will remain valid. Finally a brief example serves to illustrate the method.展开更多
The objective of the research discussed in this paper has been to find an optimal schedule on mixed mass production lines of two and three machines. Johnson's rule on flow shops is generalized to mixed mass produ...The objective of the research discussed in this paper has been to find an optimal schedule on mixed mass production lines of two and three machines. Johnson's rule on flow shops is generalized to mixed mass production lines. Scheduling methods on three-machine lines are proposed for six special kinds of data of processing times of jobs. The scheduling method on two-machine lines is also proposed.展开更多
Optimizing operational parameters for syngas production of Texaco coal-water slurry gasifier studied in this paper is a complicated nonlinear constrained problem concerning 3 BP(Error Back Propagation) neural networks...Optimizing operational parameters for syngas production of Texaco coal-water slurry gasifier studied in this paper is a complicated nonlinear constrained problem concerning 3 BP(Error Back Propagation) neural networks. To solve this model, a new 3-layer cultural evolving algorithm framework which has a population space, a medium space and a belief space is firstly conceived. Standard differential evolution algorithm(DE), genetic algorithm(GA), and particle swarm optimization algorithm(PSO) are embedded in this framework to build 3-layer mixed cultural DE/GA/PSO(3LM-CDE, 3LM-CGA, and 3LM-CPSO) algorithms. The accuracy and efficiency of the proposed hybrid algorithms are firstly tested in 20 benchmark nonlinear constrained functions. Then, the operational optimization model for syngas production in a Texaco coal-water slurry gasifier of a real-world chemical plant is solved effectively. The simulation results are encouraging that the 3-layer cultural algorithm evolving framework suggests ways in which the performance of DE, GA, PSO and other population-based evolutionary algorithms(EAs) can be improved,and the optimal operational parameters based on 3LM-CDE algorithm of the syngas production in the Texaco coalwater slurry gasifier shows outstanding computing results than actual industry use and other algorithms.展开更多
In this paper,an oil well production scheduling problem for the light load oil well during petroleum field exploitation was studied.The oil well production scheduling was to determine the turn on/off status and oil fl...In this paper,an oil well production scheduling problem for the light load oil well during petroleum field exploitation was studied.The oil well production scheduling was to determine the turn on/off status and oil flow rates of the wells in a given oil reservoir,subject to a number of constraints such as minimum up/down time limits and well grouping.The problem was formulated as a mixed integer nonlinear programming model that minimized the total production operating cost and start-up cost.Due to the NP-hardness of the problem,an improved particle swarm optimization(PSO) algorithm with a new velocity updating formula was developed to solve the problem approximately.Computational experiments on randomly generated instances were carried out to evaluate the performance of the model and the algorithm's effectiveness.Compared with the commercial solver CPLEX,the improved PSO can obtain high-quality schedules within a much shorter running time for all the instances.展开更多
With diversified requirements and varying manufacturing environments, the optimal production planning for a steel mill becomes more flexible and complicated. The flexibility provides operators with auxiliary requireme...With diversified requirements and varying manufacturing environments, the optimal production planning for a steel mill becomes more flexible and complicated. The flexibility provides operators with auxiliary requirements through an implementable integrated production planning. In this paper, a mixed-integer nonlinear programming(MINLP) model is proposed for the optimal planning that incorporates various manufacturing constraints and flexibility in a steel plate mill. Furthermore, two solution strategies are developed to overcome the weakness in solving the MINLP problem directly. The first one is to transform the original MINLP formulation to an approximate mixed integer linear programming using a classic linearization method. The second one is to decompose the original model using a branch-and-bound based iterative method. Computational experiments on various instances are presented in terms of the effectiveness and applicability. The result shows that the second method performs better in computational efforts and solution accuracy.展开更多
Since the decision of the State Council in 1985 on expanding the export of electromechanical products, China’s exports of electrome-chanical products has freed itself from long fluctuation and realized fast growth. A...Since the decision of the State Council in 1985 on expanding the export of electromechanical products, China’s exports of electrome-chanical products has freed itself from long fluctuation and realized fast growth. According to statistics from the Customs Office, China’s exports of electro-mechanical products in 1995 reached US$43.86 billion, increasing 25 times in 10 years, and becoming China’s first pillar products for export. While achieving fast growth in exports, product mix has also seen sig-展开更多
Hunyou No. 2 is a three-line hybrid rice suitable for mechanical seed pro- duction and developed by Rice Research Institute of Anhui Academy of Agricultural Sciences. It performs well in yielding, lodging resistance, ...Hunyou No. 2 is a three-line hybrid rice suitable for mechanical seed pro- duction and developed by Rice Research Institute of Anhui Academy of Agricultural Sciences. It performs well in yielding, lodging resistance, disease resistance, with a short duration of growth. Therefore, it is suitable to be grown in tropical areas and countries such as Myanmar and Indonesia. The male parent contains herbicide susceptible lethality gene and it is possible for mechanical mixed planting. The research analyzed performance of Hunyou No. 2 growth in Myanmar and the results showed that Hunyou No. 2 performed better in yield, panicle length, the number of seed per panicle, setting percentage, and thousand-seed weight than She thwe yin, as well as lodging resistance, disease resistance and quality. Some high-yielding cultivation measures have been concluded including sparsely sowing, densely planting, highlighting base fertilizers, and avoiding early water breaking.展开更多
This paper treats multi-objective problem for manufacturing process design. A purpose of the process design is to decide combinations of work elements assigned to different work centers. Multiple work elements are ord...This paper treats multi-objective problem for manufacturing process design. A purpose of the process design is to decide combinations of work elements assigned to different work centers. Multiple work elements are ordinarily assigned to each center. Here, infeasible solutions are easily generated by precedence relationship of work elements in process design. The number of infeasible solutions generated is ordinarily larger than that of feasible solutions generated in the process. Therefore, feasible and infeasible solutions are located in any neighborhood in solution space. It is difficult to seek high quality Pareto solutions in this problem by using conventional multi-objective evolutional algorithms. We consider that the problem includes difficulty to seek high quality solutions by the following characteristics： （1） Since infeasible solutions are resemble to good feasible solutions, many infeasible solutions which have good values of objective functions are easily sought in the search process, （2） Infeasible solutions are useful to select new variable conditions generating good feasible solutions in search process. In this study, a multi-objective genetic algorithm including local search is proposed using these characteristics. Maximum value of average operation times and maximum value of dispersion of operation time in all work centers are used as objective functions to promote productivity. The optimal weighted coefficient is introduced to control the ratio of feasible solutions to all solutions selected in crossover and selection process in the algorithm. This paper shows the effectiveness of the proposed algorithm on simple model.展开更多
The possibility of multiplicity in an isothermal continuous mixed suspension-mixed product removalcrystallizer is explored using the bifurcation theory. A process involving agglomeration controlled precipitationis con...The possibility of multiplicity in an isothermal continuous mixed suspension-mixed product removalcrystallizer is explored using the bifurcation theory. A process involving agglomeration controlled precipitationis considered in which secondary nucleation occurs simultaneously with primary nucleation. The determinantequations for the existence of multiple steady states are developed and the multiplicity boundaries dependent on thephysical and kinetic properties and operational parameters of the process are obtained by resolving these determinantequations. The number of steady states in the precipitator for various multiplicity regions is determined and thelinear stability of these steady states is analyzed by using the Routh criterion.展开更多
In the analysis on economic growth factors, researchers usually use the production function model to calculate and measure influencing factors’ contribution rates to economic growth. Common production functions inclu...In the analysis on economic growth factors, researchers usually use the production function model to calculate and measure influencing factors’ contribution rates to economic growth. Common production functions include the CD(Cobb-Douglas) production function, the CES(Constant Elasticity of Substitution) production function, the VES(Variable Elasticity of Substitution) production function,and so on. In consideration of the diversity and complementarity of models, the paper combines the CD production function with the CES production function and then proposes a mixed production function.With regard to the parameter estimation of model, the paper gives an improved firefly algorithm with the high precision and a fast rate of convergence. With regard to the calculation of factors’ contribution rates, traditional methods generally have big errors and are not applicable to complicated models, so the paper offers a new method which can calculate contribution rates scientifically. Finally, the paper calculates the contribution rates of factors affecting Chinese economic growth and gets a good result.展开更多
This paper attempts to optimize optimal capacities, block routing and mine sequencing problems in a mining system. The solution approach is based on a heuristics and the mixed integer programming (MIP). Unlike previou...This paper attempts to optimize optimal capacities, block routing and mine sequencing problems in a mining system. The solution approach is based on a heuristics and the mixed integer programming (MIP). Unlike previous sequential solution approaches, the problems are herein solved at the same time. Furthermore, the proposed approach guarantees practical solutions because it considers ore material distribution within orebody. The paper has two main contributions: (a) the proposed approach generates production rates in a manner that the capacities are satisfied; (b) the proposed approach does not use pre-defined marginal cut-off grades. Thus, idle capacity problem is eliminated and different scheduling combinations are allowed. To see the performance of the approach proposed, a case study is carried out using a gold data. The schedule generated shows that the approach can determine optimal production rates, block destination and sequencing effectively.展开更多
Green manufacturing is a growing trend,and an effective layout design method for production lines can reduce resource wastage in processing.This study focuses on existing problems such as low equipment utilization,lon...Green manufacturing is a growing trend,and an effective layout design method for production lines can reduce resource wastage in processing.This study focuses on existing problems such as low equipment utilization,long standby time,and low logistics efficiency in a mixed-flow parallel production line.To reduce the energy consumption,a novel method considering an independent buffer configuration and idle energy consumption analysis is proposed for this production line’s layout design.A logistics intensity model and a machine tool availability model are established to investigate the influences of independent buffer area configuration on the logistics intensity and machine tool availability.To solve the coupling problem between machine tools in such production lines,a decoupling strategy for the relationship between machine tool processing rates is explored.An energy consumption model for the machine tools,based on an optimized configuration of independent buffers,is proposed.This model can effectively reduce the idle energy consumption of the machine tools while designing the workshop layout.Subsequently,considering the problems encountered in workshop production,a comprehensive optimization model for the mixed-flow production line is developed.To verify the effectiveness of the mathematical model,it is applied to an aviation cabin production line.The results indicate that it can effectively solve the layout problem of mixed-flow parallel production lines and reduce the idle energy consumption of machine tools during production.The proposed buffer configuration and layout design method can serve as a theoretical and practical reference for the layout design of mixed-flow parallel production lines.展开更多
Wang and Zhang defined a type of Lp-dual mixed quermassintegrals based on the Lp-radial combinations and dual quermassintegrals of star bodies. In the article, the product inequalities for this Lp-dual mixed quermassi...Wang and Zhang defined a type of Lp-dual mixed quermassintegrals based on the Lp-radial combinations and dual quermassintegrals of star bodies. In the article, the product inequalities for this Lp-dual mixed quermassintegrals are established. As the applications, we obtain the lower bounds of dual quermassintegrals product. Further, the Brunn-Minkowski type inequality and the cycle inequality for the Lp-dual mixed quermassintegrals are given.展开更多
Let S = K[x1,..., xn; y1,..., ym] be the polynomial ring in two sets of variables over a field K. We investigate some classes of graph ideals of S, namely the generalized graph ideals, in order to classify ideals of l...Let S = K[x1,..., xn; y1,..., ym] be the polynomial ring in two sets of variables over a field K. We investigate some classes of graph ideals of S, namely the generalized graph ideals, in order to classify ideals of linear type.展开更多
This paper provides intelligent simulation approach using manufacturing uncertainty in the form of simulation intelligence to improve the performances of manufacturing production system.It shows how simulation can be ...This paper provides intelligent simulation approach using manufacturing uncertainty in the form of simulation intelligence to improve the performances of manufacturing production system.It shows how simulation can be used to evaluate alternative designs in an uncertain manufacturing environment.Fuzzy rule-based manufacturing uncertainties are addressed in this study.A combination of product mix and production volume is analyzed using intelligent simulation model for an optimal production design.The intelligent simulation approach would improve the modeling accuracy in terms of more realistic presentation of uncertain activities.The proposed intelligent simulation modeling shows significant improvement and validated with real life application.展开更多
基金This project is supported by National Natural Science Foundation of China (No.70372062, No.70572044)Program for New Century Excellent Talents in University of China (No.NCET-04-0240).
文摘Firstly an overview of the potential impact on work-in-process （WIP） and lead time is provided when transfer lot sizes are undifferentiated from processing lot sizes. Simple performance examples are compared to those from a shop with one-piece transfer lots. Next, a mathematical programming model for minimizing lead time in the mixed-model job shop is presented, in which one-piece transfer lots are used. Key factors affecting lead time are found by analyzing the sum of the longest setup time of individual items among the shared processes （SLST） and the longest processing time of individual items among processes （LPT）. And lead time can be minimized by cutting down the SLST and LPT. Reduction of the SLST is described as a traveling salesman problem （TSP）, and the minimum of the SLST is solved through job shop scheduling. Removing the bottleneck and leveling the production line optimize the LPT. If the number of items produced is small, the routings are relatively short, and items and facilities are changed infrequently, the optimal schedule will remain valid. Finally a brief example serves to illustrate the method.
文摘The objective of the research discussed in this paper has been to find an optimal schedule on mixed mass production lines of two and three machines. Johnson's rule on flow shops is generalized to mixed mass production lines. Scheduling methods on three-machine lines are proposed for six special kinds of data of processing times of jobs. The scheduling method on two-machine lines is also proposed.
基金Supported by the National Natural Science Foundation of China(61174040,U1162110,21206174)Shanghai Commission of Nature Science(12ZR1408100)
文摘Optimizing operational parameters for syngas production of Texaco coal-water slurry gasifier studied in this paper is a complicated nonlinear constrained problem concerning 3 BP(Error Back Propagation) neural networks. To solve this model, a new 3-layer cultural evolving algorithm framework which has a population space, a medium space and a belief space is firstly conceived. Standard differential evolution algorithm(DE), genetic algorithm(GA), and particle swarm optimization algorithm(PSO) are embedded in this framework to build 3-layer mixed cultural DE/GA/PSO(3LM-CDE, 3LM-CGA, and 3LM-CPSO) algorithms. The accuracy and efficiency of the proposed hybrid algorithms are firstly tested in 20 benchmark nonlinear constrained functions. Then, the operational optimization model for syngas production in a Texaco coal-water slurry gasifier of a real-world chemical plant is solved effectively. The simulation results are encouraging that the 3-layer cultural algorithm evolving framework suggests ways in which the performance of DE, GA, PSO and other population-based evolutionary algorithms(EAs) can be improved,and the optimal operational parameters based on 3LM-CDE algorithm of the syngas production in the Texaco coalwater slurry gasifier shows outstanding computing results than actual industry use and other algorithms.
基金Supported by National High Technology Research and Development Program of China(2013AA040704)the Fund for the National Natural Science Foundation of China(61374203)
文摘In this paper,an oil well production scheduling problem for the light load oil well during petroleum field exploitation was studied.The oil well production scheduling was to determine the turn on/off status and oil flow rates of the wells in a given oil reservoir,subject to a number of constraints such as minimum up/down time limits and well grouping.The problem was formulated as a mixed integer nonlinear programming model that minimized the total production operating cost and start-up cost.Due to the NP-hardness of the problem,an improved particle swarm optimization(PSO) algorithm with a new velocity updating formula was developed to solve the problem approximately.Computational experiments on randomly generated instances were carried out to evaluate the performance of the model and the algorithm's effectiveness.Compared with the commercial solver CPLEX,the improved PSO can obtain high-quality schedules within a much shorter running time for all the instances.
基金Supported in part by the National High Technology Research and Development Program of China(2012AA041701)the National Natural Science Foundation of China(61320106009) the 111 Project of China(B07031)
文摘With diversified requirements and varying manufacturing environments, the optimal production planning for a steel mill becomes more flexible and complicated. The flexibility provides operators with auxiliary requirements through an implementable integrated production planning. In this paper, a mixed-integer nonlinear programming(MINLP) model is proposed for the optimal planning that incorporates various manufacturing constraints and flexibility in a steel plate mill. Furthermore, two solution strategies are developed to overcome the weakness in solving the MINLP problem directly. The first one is to transform the original MINLP formulation to an approximate mixed integer linear programming using a classic linearization method. The second one is to decompose the original model using a branch-and-bound based iterative method. Computational experiments on various instances are presented in terms of the effectiveness and applicability. The result shows that the second method performs better in computational efforts and solution accuracy.
文摘Since the decision of the State Council in 1985 on expanding the export of electromechanical products, China’s exports of electrome-chanical products has freed itself from long fluctuation and realized fast growth. According to statistics from the Customs Office, China’s exports of electro-mechanical products in 1995 reached US$43.86 billion, increasing 25 times in 10 years, and becoming China’s first pillar products for export. While achieving fast growth in exports, product mix has also seen sig-
基金Supported by International S&T Cooperation Plan of Anhui Province(1503062031)S&T Innovation Team of Anhui Academy of Agricultural Sciences(15C0108)+1 种基金Key Project for Anhui Province during the 13thFive-year Plan(1604a0702008)Special Fund for Agro-scientific Research in the Public Interest(201503130)~~
文摘Hunyou No. 2 is a three-line hybrid rice suitable for mechanical seed pro- duction and developed by Rice Research Institute of Anhui Academy of Agricultural Sciences. It performs well in yielding, lodging resistance, disease resistance, with a short duration of growth. Therefore, it is suitable to be grown in tropical areas and countries such as Myanmar and Indonesia. The male parent contains herbicide susceptible lethality gene and it is possible for mechanical mixed planting. The research analyzed performance of Hunyou No. 2 growth in Myanmar and the results showed that Hunyou No. 2 performed better in yield, panicle length, the number of seed per panicle, setting percentage, and thousand-seed weight than She thwe yin, as well as lodging resistance, disease resistance and quality. Some high-yielding cultivation measures have been concluded including sparsely sowing, densely planting, highlighting base fertilizers, and avoiding early water breaking.
文摘This paper treats multi-objective problem for manufacturing process design. A purpose of the process design is to decide combinations of work elements assigned to different work centers. Multiple work elements are ordinarily assigned to each center. Here, infeasible solutions are easily generated by precedence relationship of work elements in process design. The number of infeasible solutions generated is ordinarily larger than that of feasible solutions generated in the process. Therefore, feasible and infeasible solutions are located in any neighborhood in solution space. It is difficult to seek high quality Pareto solutions in this problem by using conventional multi-objective evolutional algorithms. We consider that the problem includes difficulty to seek high quality solutions by the following characteristics： （1） Since infeasible solutions are resemble to good feasible solutions, many infeasible solutions which have good values of objective functions are easily sought in the search process, （2） Infeasible solutions are useful to select new variable conditions generating good feasible solutions in search process. In this study, a multi-objective genetic algorithm including local search is proposed using these characteristics. Maximum value of average operation times and maximum value of dispersion of operation time in all work centers are used as objective functions to promote productivity. The optimal weighted coefficient is introduced to control the ratio of feasible solutions to all solutions selected in crossover and selection process in the algorithm. This paper shows the effectiveness of the proposed algorithm on simple model.
文摘The possibility of multiplicity in an isothermal continuous mixed suspension-mixed product removalcrystallizer is explored using the bifurcation theory. A process involving agglomeration controlled precipitationis considered in which secondary nucleation occurs simultaneously with primary nucleation. The determinantequations for the existence of multiple steady states are developed and the multiplicity boundaries dependent on thephysical and kinetic properties and operational parameters of the process are obtained by resolving these determinantequations. The number of steady states in the precipitator for various multiplicity regions is determined and thelinear stability of these steady states is analyzed by using the Routh criterion.
基金Supported by the National Natural Science Foundation of China(11401418)
文摘In the analysis on economic growth factors, researchers usually use the production function model to calculate and measure influencing factors’ contribution rates to economic growth. Common production functions include the CD(Cobb-Douglas) production function, the CES(Constant Elasticity of Substitution) production function, the VES(Variable Elasticity of Substitution) production function,and so on. In consideration of the diversity and complementarity of models, the paper combines the CD production function with the CES production function and then proposes a mixed production function.With regard to the parameter estimation of model, the paper gives an improved firefly algorithm with the high precision and a fast rate of convergence. With regard to the calculation of factors’ contribution rates, traditional methods generally have big errors and are not applicable to complicated models, so the paper offers a new method which can calculate contribution rates scientifically. Finally, the paper calculates the contribution rates of factors affecting Chinese economic growth and gets a good result.
文摘This paper attempts to optimize optimal capacities, block routing and mine sequencing problems in a mining system. The solution approach is based on a heuristics and the mixed integer programming (MIP). Unlike previous sequential solution approaches, the problems are herein solved at the same time. Furthermore, the proposed approach guarantees practical solutions because it considers ore material distribution within orebody. The paper has two main contributions: (a) the proposed approach generates production rates in a manner that the capacities are satisfied; (b) the proposed approach does not use pre-defined marginal cut-off grades. Thus, idle capacity problem is eliminated and different scheduling combinations are allowed. To see the performance of the approach proposed, a case study is carried out using a gold data. The schedule generated shows that the approach can determine optimal production rates, block destination and sequencing effectively.
基金The authors gratefully acknowledge the financial support from the National Science and Technology Major Project of China(Grant No.2019ZX04024001)the Natural Science Foundation of Beijing Municipality(Grant No.3192003)+2 种基金the General Project of Science and Technology Plan from Beijing Educational Committee(Grant No.KM201810005013)the Tribology Science Fund of State Key Laboratory of Tribology(Grant Nos.STLEKF16A02,SKLTKF19B08)the Training Program of Rixin Talent and Outstanding Talent from Beijing University of Technology.
文摘Green manufacturing is a growing trend,and an effective layout design method for production lines can reduce resource wastage in processing.This study focuses on existing problems such as low equipment utilization,long standby time,and low logistics efficiency in a mixed-flow parallel production line.To reduce the energy consumption,a novel method considering an independent buffer configuration and idle energy consumption analysis is proposed for this production line’s layout design.A logistics intensity model and a machine tool availability model are established to investigate the influences of independent buffer area configuration on the logistics intensity and machine tool availability.To solve the coupling problem between machine tools in such production lines,a decoupling strategy for the relationship between machine tool processing rates is explored.An energy consumption model for the machine tools,based on an optimized configuration of independent buffers,is proposed.This model can effectively reduce the idle energy consumption of the machine tools while designing the workshop layout.Subsequently,considering the problems encountered in workshop production,a comprehensive optimization model for the mixed-flow production line is developed.To verify the effectiveness of the mathematical model,it is applied to an aviation cabin production line.The results indicate that it can effectively solve the layout problem of mixed-flow parallel production lines and reduce the idle energy consumption of machine tools during production.The proposed buffer configuration and layout design method can serve as a theoretical and practical reference for the layout design of mixed-flow parallel production lines.
基金Supported by the National Natural Science Foundation of China(11371224)
文摘Wang and Zhang defined a type of Lp-dual mixed quermassintegrals based on the Lp-radial combinations and dual quermassintegrals of star bodies. In the article, the product inequalities for this Lp-dual mixed quermassintegrals are established. As the applications, we obtain the lower bounds of dual quermassintegrals product. Further, the Brunn-Minkowski type inequality and the cycle inequality for the Lp-dual mixed quermassintegrals are given.
文摘Let S = K[x1,..., xn; y1,..., ym] be the polynomial ring in two sets of variables over a field K. We investigate some classes of graph ideals of S, namely the generalized graph ideals, in order to classify ideals of linear type.
文摘This paper provides intelligent simulation approach using manufacturing uncertainty in the form of simulation intelligence to improve the performances of manufacturing production system.It shows how simulation can be used to evaluate alternative designs in an uncertain manufacturing environment.Fuzzy rule-based manufacturing uncertainties are addressed in this study.A combination of product mix and production volume is analyzed using intelligent simulation model for an optimal production design.The intelligent simulation approach would improve the modeling accuracy in terms of more realistic presentation of uncertain activities.The proposed intelligent simulation modeling shows significant improvement and validated with real life application.
