In this study, Simplex Method, a Linear Programming technique was used to create a mathematical model that optimized the financial portfolio of Golden Guinea Breweries Plc, Nigeria. This work was motivated by the obse...In this study, Simplex Method, a Linear Programming technique was used to create a mathematical model that optimized the financial portfolio of Golden Guinea Breweries Plc, Nigeria. This work was motivated by the observed and anticipated miscalculations which Golden Guinea Breweries was bound to face if appropriate linear programming techniques were not applied in determining the profit level. This study therefore aims at using Simplex Method to create a Mathematical Model that will optimize the production of brewed drinks for Golden Guinea Breweries Plc. The first methodology involved the collection of sample data from the company, analyzed and the relevant coefficients were deployed for the coding of the model. Secondly, the indices collected from the first method were deployed in the software model called PHP simplex, an online software for solving Linear Programming Problem to access the profitability of the organization. The study showed that Linear Programming Model would give a high profit coefficient of N9,190,862,833 when compared with the result obtained from the manual computation which gave a profit coefficient of N7,172,093,375. Also, Bergedoff Lager, Eagle Stout and Bergedoff Malta were found not to contribute to overall profitability of the company and it was therefore recommended that their productions should be discontinued. It also recommends that various quantities of Golden Guinea Lager (1 × 12) and Golden Guinea Lager (1 × 24) should be produced.展开更多
In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of...In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4<sup>+</sup>T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.展开更多
The refugee immigration problem can be considered as a special “transportation problem”. Linear Programming Model is built, where two objectives with weight in the objective function, for the shortest routes that th...The refugee immigration problem can be considered as a special “transportation problem”. Linear Programming Model is built, where two objectives with weight in the objective function, for the shortest routes that the refugees go along and the minimum number of refugees stayed in each country. An example of EU is introduced and calculated on Lingo software. The results show that the model is available to solve the refugee immigration problem in different scale.展开更多
With the rapid development of highway construction and formation of the highway network in China,the man- agement of pavement maintenance and rehabilitation （MR） activities has become important.In this paper,four di...With the rapid development of highway construction and formation of the highway network in China,the man- agement of pavement maintenance and rehabilitation （MR） activities has become important.In this paper,four discrete optimization models are proposed for different parties involved in the management system： government,highway agent,con- tractor and the common users.These four optimal decision models are formulated as linear integer programming problems with binary decision variables.The objective function and constraints are based on the pavement performance and prediction model using the pavement condition index （PCI）.Numerical experiments are carried out with the data from a highway system in Sichuan Province which show the feasibility and effectiveness of the proposed models.展开更多
This paper deals with the modeling, analysis and optimization of a specific kind of real industrial problems. This class of problems is known in the literature as Cyclic Hoist Scheduling Problem （CHSP）. In such clas...This paper deals with the modeling, analysis and optimization of a specific kind of real industrial problems. This class of problems is known in the literature as Cyclic Hoist Scheduling Problem （CHSP）. In such class of problems, several jobs have to flow through a production line according to an ordered bath sequence. The CHSPs appear in the manufacturing facilities to achieve a mass production and to search a repetitive sequence of moves for the hoist. In this paper, we develop P-Temporal Petri Net models to represent the behavior and validate certain qualitative properties of the basic production line. Afterward, complex configurations of the production line are modeled and their properties such as reachability of desired functioning （cyclic operation）, deadlock-free, resource sharing and management are checked and validated. A mathematical analysis and a simulation study of all proposed Petri net models are carried out using mathematical fundaments of Petri nets and a Visual Object Net ＋＋ tool. The second part of the paper deals with the development of a mixed integer linear programming models to optimize processing of each line configuration. Optimal manufacturing plans of the studied system with cyclic processing sequences are defined and the feasibility of optimal cyclic scheduling of each configuration is proved.展开更多
This paper gives integer linear programming (ILP) models for scheduling the League Phase of one of the most popular professional club competitions in the world, UEFA Champion’s League. There are 36 teams in the compe...This paper gives integer linear programming (ILP) models for scheduling the League Phase of one of the most popular professional club competitions in the world, UEFA Champion’s League. There are 36 teams in the competition, but each team plays only 8 other teams in the League Phase. Thus, the difficulty or ease of a team’s opponents, known as strength of schedule (SOS), compared to other teams will be different. Our main ILP model aims to minimize the maximum difference between SOS of any two teams, thus making the schedule as fair as possible. We also give a model for creating a timetable of all the matchups obtained by the first model. The models were implemented and tested using optimization software AMPL. Our main model obtained a schedule with a difference 0.4 between the highest and the lowest SOS, while that difference is 19 for the actual 2024-2025 competition. Thus, our model returns a schedule that is significantly fairer compared to the actual competition.展开更多
The circle geometric constraint model （CGCM） was put forward for resolving the open-pit mine ore-matching problems （OMOMP）. By adopting the approaches of graph theory, block model of blasted piles was abstracted i...The circle geometric constraint model （CGCM） was put forward for resolving the open-pit mine ore-matching problems （OMOMP）. By adopting the approaches of graph theory, block model of blasted piles was abstracted into a set of nodes and directed edges, which were connected together with other nodes in the range of circle constraints, to describe the mining sequence. Also, the constructing method of CGCM was introduced in detail. The algorithm of CGCM has been realized in the DIM1NE system, and applied to a short-term （5 d） program calculation for ore-matching of a cement limestone mine in Hebei Province, China. The applications show that CGCM can well describe the mining sequence of ore blocks and its mining geometric constraints in the process of mining blasted piles. This model, which is applicable for resolving OMOMP under complicated geometric constraints with accurate results, provides effective ways to solve the problems of open-pit ore-matching.展开更多
With the widespread penetration of renewable energy sources and energy storage systems,the problem of energy management has received increasing attention.One of the systems that network owners consider today is the po...With the widespread penetration of renewable energy sources and energy storage systems,the problem of energy management has received increasing attention.One of the systems that network owners consider today is the power-to-gas(P2G)system.This system causes surplus electricity generated from renewable energy resources or batteries in the network to be converted into gas and sold to the gas network.Two reasons for the existence of gas distributed generation resources and P2G systems cause the two power and gas networks to interact.Energy management and profit making considering these two networks,as a co-optimization of integrated energy systems,is a topic that has been discussed in this study to achieve the best optimal answer.Since the production of renewable energy resources and the purchase price of energy are uncertain,a scenario-based method has been chosen for modelling.Demand-side management is also one of the important problems in optimal operation of the electricity network,which can have a significant impact on reducing peak load and increasing profits.In this paper,a mixed-integer quadratic programming model for co-optimization of electric distribution and gas networks in the presence of distributed generation resources,P2G systems,storage facilities,electric vehicles and demand-side management is presented.The 33-bus distribution network is intended to analyse the proposed model.The results of different scenarios show the efficiency of the proposed model.Several key points are deduced from the obtained results:(i)demand-side management is able to reduce the peak load of the network,(ii)the presence of renewable resources and batteries can cause the network to convert excess electricity into gas and sell it to the gas network in the market and(iii)distributed generation can reduce the purchase of energy from the upstream network and cause a 36% reduction in the cost function.展开更多
The integrated circular economy model of farming and stock raising(ICEMFSR)has attracted increased attention as an effective model for solving the current irrational allocation of agricultural resources and realizing ...The integrated circular economy model of farming and stock raising(ICEMFSR)has attracted increased attention as an effective model for solving the current irrational allocation of agricultural resources and realizing the agricultural value-added industrial chain.This study uses emergy analysis to comprehensively examine and evaluate the economic benefits,environmental pressures,and sustainable development levels of ICEMFSR in Shucheng County,China.The results show that the ICEMFSR possesses the value of popularization with optimally allocated resources in the studied region,in which the emergy yield ratio(EYR),emergy loading ratio(ELR),and emergy sustainable index(ESI)in this model accounted for 3.59,1.25,and 2.89,respectively.This result indicates a leading position in the national agricultural system.Hence,this study constructs a new model based on the coupling of emergy evaluation and multi-objective linear programming to study ICEMFSR.Consequently,the EYR,ELR,and ESI respectively varied by +24.23%,10.40%,and +38.06%after replanning of ICEMFSR.This variation implies a significant improvement in the sustainable development level of the model.In addition,the optimized scenario design for key substances is proposed based on traceability and the reduce-reuse-recycle principle,including biogasification of crop straw and enhancement of crop scientific planting capacity.展开更多
This paper gives integer linear programming models for scheduling doubles tennis group competitions. The goal is to build a fair and competitive schedule for all players. Our basic model achieves that for each player ...This paper gives integer linear programming models for scheduling doubles tennis group competitions. The goal is to build a fair and competitive schedule for all players. Our basic model achieves that for each player the average ranking of his partners in all matches is as close as possible to the average ranking of his opponents in all matches. One of the variations of the basic model provides that each matchup is fair and competitive. We also give models for the case when the number of players is 4n<span style="font-family:;" "=""> </span><span style="font-family:;" "="">+</span><span style="font-family:;" "=""> </span><span style="font-family:;" "="">2, and thus one of the matches has to be singles. Our models were implemented and tested using optimization software AMPL. Computational results along with schedules for some typical situations are also given the paper.</span>展开更多
This work addresses the multiscale optimization of the puri cation processes of antibody fragments. Chromatography decisions in the manufacturing processes are optimized, including the number of chromatography columns...This work addresses the multiscale optimization of the puri cation processes of antibody fragments. Chromatography decisions in the manufacturing processes are optimized, including the number of chromatography columns and their sizes, the number of cycles per batch, and the operational ow velocities. Data-driven models of chromatography throughput are developed considering loaded mass, ow velocity, and column bed height as the inputs, using manufacturing-scale simulated datasets based on microscale experimental data. The piecewise linear regression modeling method is adapted due to its simplicity and better prediction accuracy in comparison with other methods. Two alternative mixed-integer nonlinear programming (MINLP) models are proposed to minimize the total cost of goods per gram of the antibody puri cation process, incorporating the data-driven models. These MINLP models are then reformulated as mixed-integer linear programming (MILP) models using linearization techniques and multiparametric disaggregation. Two industrially relevant cases with different chromatography column size alternatives are investigated to demonstrate the applicability of the proposed models.展开更多
Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show th...Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show that it is possible to accommodate realistic models for energy consumption and communication protocols into integer linear programming. We analyze the maximum lifetime broadcasting topology problem and we present realistic models that are also shown to provide efficient and practical solving tools. We present a strategy to substantially speed up the convergence of the solving process of our algorithm. This strategy introduces a practical drawback, however, in the characteristics of the optimal solutions retrieved. A method to overcome this drawback is discussed. Computational experiments are reported.展开更多
文摘In this study, Simplex Method, a Linear Programming technique was used to create a mathematical model that optimized the financial portfolio of Golden Guinea Breweries Plc, Nigeria. This work was motivated by the observed and anticipated miscalculations which Golden Guinea Breweries was bound to face if appropriate linear programming techniques were not applied in determining the profit level. This study therefore aims at using Simplex Method to create a Mathematical Model that will optimize the production of brewed drinks for Golden Guinea Breweries Plc. The first methodology involved the collection of sample data from the company, analyzed and the relevant coefficients were deployed for the coding of the model. Secondly, the indices collected from the first method were deployed in the software model called PHP simplex, an online software for solving Linear Programming Problem to access the profitability of the organization. The study showed that Linear Programming Model would give a high profit coefficient of N9,190,862,833 when compared with the result obtained from the manual computation which gave a profit coefficient of N7,172,093,375. Also, Bergedoff Lager, Eagle Stout and Bergedoff Malta were found not to contribute to overall profitability of the company and it was therefore recommended that their productions should be discontinued. It also recommends that various quantities of Golden Guinea Lager (1 × 12) and Golden Guinea Lager (1 × 24) should be produced.
文摘In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4<sup>+</sup>T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.
文摘The refugee immigration problem can be considered as a special “transportation problem”. Linear Programming Model is built, where two objectives with weight in the objective function, for the shortest routes that the refugees go along and the minimum number of refugees stayed in each country. An example of EU is introduced and calculated on Lingo software. The results show that the model is available to solve the refugee immigration problem in different scale.
基金Project supported by the National Natural Science Foundation of China (Grant No.70671064)
文摘With the rapid development of highway construction and formation of the highway network in China,the man- agement of pavement maintenance and rehabilitation （MR） activities has become important.In this paper,four discrete optimization models are proposed for different parties involved in the management system： government,highway agent,con- tractor and the common users.These four optimal decision models are formulated as linear integer programming problems with binary decision variables.The objective function and constraints are based on the pavement performance and prediction model using the pavement condition index （PCI）.Numerical experiments are carried out with the data from a highway system in Sichuan Province which show the feasibility and effectiveness of the proposed models.
文摘This paper deals with the modeling, analysis and optimization of a specific kind of real industrial problems. This class of problems is known in the literature as Cyclic Hoist Scheduling Problem （CHSP）. In such class of problems, several jobs have to flow through a production line according to an ordered bath sequence. The CHSPs appear in the manufacturing facilities to achieve a mass production and to search a repetitive sequence of moves for the hoist. In this paper, we develop P-Temporal Petri Net models to represent the behavior and validate certain qualitative properties of the basic production line. Afterward, complex configurations of the production line are modeled and their properties such as reachability of desired functioning （cyclic operation）, deadlock-free, resource sharing and management are checked and validated. A mathematical analysis and a simulation study of all proposed Petri net models are carried out using mathematical fundaments of Petri nets and a Visual Object Net ＋＋ tool. The second part of the paper deals with the development of a mixed integer linear programming models to optimize processing of each line configuration. Optimal manufacturing plans of the studied system with cyclic processing sequences are defined and the feasibility of optimal cyclic scheduling of each configuration is proved.
文摘This paper gives integer linear programming (ILP) models for scheduling the League Phase of one of the most popular professional club competitions in the world, UEFA Champion’s League. There are 36 teams in the competition, but each team plays only 8 other teams in the League Phase. Thus, the difficulty or ease of a team’s opponents, known as strength of schedule (SOS), compared to other teams will be different. Our main ILP model aims to minimize the maximum difference between SOS of any two teams, thus making the schedule as fair as possible. We also give a model for creating a timetable of all the matchups obtained by the first model. The models were implemented and tested using optimization software AMPL. Our main model obtained a schedule with a difference 0.4 between the highest and the lowest SOS, while that difference is 19 for the actual 2024-2025 competition. Thus, our model returns a schedule that is significantly fairer compared to the actual competition.
基金Project(2011AA060407) supported by the National High Technology Research and Development Program of ChinaProject(51074073) supported by the National Natural Science Foundation of China
文摘The circle geometric constraint model （CGCM） was put forward for resolving the open-pit mine ore-matching problems （OMOMP）. By adopting the approaches of graph theory, block model of blasted piles was abstracted into a set of nodes and directed edges, which were connected together with other nodes in the range of circle constraints, to describe the mining sequence. Also, the constructing method of CGCM was introduced in detail. The algorithm of CGCM has been realized in the DIM1NE system, and applied to a short-term （5 d） program calculation for ore-matching of a cement limestone mine in Hebei Province, China. The applications show that CGCM can well describe the mining sequence of ore blocks and its mining geometric constraints in the process of mining blasted piles. This model, which is applicable for resolving OMOMP under complicated geometric constraints with accurate results, provides effective ways to solve the problems of open-pit ore-matching.
文摘With the widespread penetration of renewable energy sources and energy storage systems,the problem of energy management has received increasing attention.One of the systems that network owners consider today is the power-to-gas(P2G)system.This system causes surplus electricity generated from renewable energy resources or batteries in the network to be converted into gas and sold to the gas network.Two reasons for the existence of gas distributed generation resources and P2G systems cause the two power and gas networks to interact.Energy management and profit making considering these two networks,as a co-optimization of integrated energy systems,is a topic that has been discussed in this study to achieve the best optimal answer.Since the production of renewable energy resources and the purchase price of energy are uncertain,a scenario-based method has been chosen for modelling.Demand-side management is also one of the important problems in optimal operation of the electricity network,which can have a significant impact on reducing peak load and increasing profits.In this paper,a mixed-integer quadratic programming model for co-optimization of electric distribution and gas networks in the presence of distributed generation resources,P2G systems,storage facilities,electric vehicles and demand-side management is presented.The 33-bus distribution network is intended to analyse the proposed model.The results of different scenarios show the efficiency of the proposed model.Several key points are deduced from the obtained results:(i)demand-side management is able to reduce the peak load of the network,(ii)the presence of renewable resources and batteries can cause the network to convert excess electricity into gas and sell it to the gas network in the market and(iii)distributed generation can reduce the purchase of energy from the upstream network and cause a 36% reduction in the cost function.
基金supported by National Key R&D Plan[Grant number.2016YFC0502805]National Natural Science Foundation of China[Grant number.71974116]+2 种基金Shandong Natural Science Foundation[Grant number.ZR2019MG009]Shandong Province Social Science Planning Research Project[Grant number.20CGLJ13]Taishan Scholar Project[Grant number.tsqn202103010].
文摘The integrated circular economy model of farming and stock raising(ICEMFSR)has attracted increased attention as an effective model for solving the current irrational allocation of agricultural resources and realizing the agricultural value-added industrial chain.This study uses emergy analysis to comprehensively examine and evaluate the economic benefits,environmental pressures,and sustainable development levels of ICEMFSR in Shucheng County,China.The results show that the ICEMFSR possesses the value of popularization with optimally allocated resources in the studied region,in which the emergy yield ratio(EYR),emergy loading ratio(ELR),and emergy sustainable index(ESI)in this model accounted for 3.59,1.25,and 2.89,respectively.This result indicates a leading position in the national agricultural system.Hence,this study constructs a new model based on the coupling of emergy evaluation and multi-objective linear programming to study ICEMFSR.Consequently,the EYR,ELR,and ESI respectively varied by +24.23%,10.40%,and +38.06%after replanning of ICEMFSR.This variation implies a significant improvement in the sustainable development level of the model.In addition,the optimized scenario design for key substances is proposed based on traceability and the reduce-reuse-recycle principle,including biogasification of crop straw and enhancement of crop scientific planting capacity.
文摘This paper gives integer linear programming models for scheduling doubles tennis group competitions. The goal is to build a fair and competitive schedule for all players. Our basic model achieves that for each player the average ranking of his partners in all matches is as close as possible to the average ranking of his opponents in all matches. One of the variations of the basic model provides that each matchup is fair and competitive. We also give models for the case when the number of players is 4n<span style="font-family:;" "=""> </span><span style="font-family:;" "="">+</span><span style="font-family:;" "=""> </span><span style="font-family:;" "="">2, and thus one of the matches has to be singles. Our models were implemented and tested using optimization software AMPL. Computational results along with schedules for some typical situations are also given the paper.</span>
文摘This work addresses the multiscale optimization of the puri cation processes of antibody fragments. Chromatography decisions in the manufacturing processes are optimized, including the number of chromatography columns and their sizes, the number of cycles per batch, and the operational ow velocities. Data-driven models of chromatography throughput are developed considering loaded mass, ow velocity, and column bed height as the inputs, using manufacturing-scale simulated datasets based on microscale experimental data. The piecewise linear regression modeling method is adapted due to its simplicity and better prediction accuracy in comparison with other methods. Two alternative mixed-integer nonlinear programming (MINLP) models are proposed to minimize the total cost of goods per gram of the antibody puri cation process, incorporating the data-driven models. These MINLP models are then reformulated as mixed-integer linear programming (MILP) models using linearization techniques and multiparametric disaggregation. Two industrially relevant cases with different chromatography column size alternatives are investigated to demonstrate the applicability of the proposed models.
文摘Approaches based on integer linear programming have been recently proposed for topology optimization in wireless sensor networks. They are, however, based on over-theoretical, unrealistic models. Our aim is to show that it is possible to accommodate realistic models for energy consumption and communication protocols into integer linear programming. We analyze the maximum lifetime broadcasting topology problem and we present realistic models that are also shown to provide efficient and practical solving tools. We present a strategy to substantially speed up the convergence of the solving process of our algorithm. This strategy introduces a practical drawback, however, in the characteristics of the optimal solutions retrieved. A method to overcome this drawback is discussed. Computational experiments are reported.
