Application of Linear Programming Algorithm in the Optimization of Financial Portfolio of Golden Guinea Breweries Plc, Nigeria

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.

Approximate Solutions for a Class of Fractional-Order Model of HIV Infection via Linear Programming Problem

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+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.

Application of Linear Programming Model to Refugee Migrating Problem

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.

Discrete optimization models and methods for management systems of pavement maintenance and rehabilitation

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.

MODELING AND OPTIMIZATION OF CYCLIC HOIST SCHEDULES IN AN ELECTROPLATING LINE

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.

Circle geometric constraint model for open-pit mine ore-matching and its applications

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.

Co-optimization of integrated energy systems in the presence of renewable energy,electric vehicles,power-to-gas systems and energy storage systems with demand-side management

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.

Evaluation and advancement of the integrated circular economy model of farming and stock raising

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.

Fair Scheduling Models for Doubles Group Competitions

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 + 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.

Optimal Antibody Puri cation Strategies Using Data-Driven Models

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.

Integer Programming Formulations for Maximum Lifetime Broadcasting Problems in Wireless Sensor Networks

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.

Unmanned Aerial Vehicle Inspection Routing and Scheduling for Engineering Management

Technological advancements in unmanned aerial vehicles(UAVs)have revolutionized various industries,enabling the widespread adoption of UAV-based solutions.In engineering management,UAV-based inspection has emerged as a highly efficient method for identifying hidden risks in high-risk construction environments,surpassing traditional inspection techniques.Building on this foundation,this paper delves into the optimization of UAV inspection routing and scheduling,addressing the complexity introduced by factors such as no-fly zones,monitoring-interval time windows,and multiple monitoring rounds.To tackle this challenging problem,we propose a mixed-integer linear programming(MILP)model that optimizes inspection task assignments,monitoring sequence schedules,and charging decisions.The comprehensive consideration of these factors differentiates our problem from conventional vehicle routing problem(VRP),leading to a mathematically intractable model for commercial solvers in the case of large-scale instances.To overcome this limitation,we design a tailored variable neighborhood search(VNS)metaheuristic,customizing the algorithm to efficiently solve our model.Extensive numerical experiments are conducted to validate the efficacy of our proposed algorithm,demonstrating its scalability for both large-scale and real-scale instances.Sensitivity experiments and a case study based on an actual engineering project are also conducted,providing valuable insights for engineering managers to enhance inspection work efficiency.

RPMS在大连石化催化料调合优化测算中的应用

RPMS模型优化原理是用线性规划方法,在满足设置的约束条件下求取目标函数最优值。利用RPMS模型对催化料调合进行优化测算,通过模型优化求解得到各方案的最优二次装置负荷、最优产品分布,并选出了效益最好的调合方案,为生产优化提供了决策支持。

基于混合整数规划的数据中心冷却能耗优化

以广州某数据中心水蓄冷冷却系统为研究对象,提出了一种基于混合整数线性规划的模型预测控制方法.该方法以数据中心冷却系统的能耗最低为优化目标,通过对冷却系统和环境条件进行建模,并结合能源成本和冷却系统效率,确定最佳的冷水机组运行策略和水蓄冷冷却系统的时序控制.在优化过程中,考虑了冷水机组的最小连续运行时间对冷却系统能耗的影响,并确定了最佳取值,提高了机组的稳定性,减少了因冷机频繁启停带来的能耗浪费.通过全年能耗模拟,相较于传统控制方法,该方法将总能耗降低了6.52%,总运行费用降低了6.93%.

线性规划的历史与发展

本文介绍了线性规划的起源与发展过程,对比了丹齐格与坎托罗维奇各自在线性规划方面的贡献.

Supply-based optimal scheduling of oil product pipelines

Oil product pipelines have features such as transporting multiple materials, ever-changing operating conditions, and synchronism between the oil input plan and the oil offloading plan. In this paper, an optimal model was established for a single-source multi-distribution oil pro- duct pipeline, and scheduling plans were made based on supply. In the model, time node constraints, oil offloading plan constraints, and migration of batch constraints were taken into consideration. The minimum deviation between the demanded oil volumes and the actual offloading volumes was chosen as the objective function, and a linear programming model was established on the basis of known time nodes＇ sequence. The ant colony optimization algo- rithm and simplex method were used to solve the model. The model was applied to a real pipeline and it performed well.

保障各种复杂故障工况下解优质率的电网故障诊断解析模型

经典电网故障诊断解析模型是非线性0-1整数规划模型,其难以精确求解,启发式算法虽能获得可行解,但求解准确性和一致性难以保证,且求解时间较长,不利于基于诊断结果的故障排查和设备运维。对传统故障诊断模型进行改进,降低了模型的复杂度,实现了目标函数的线性化,据此构建了基于整数线性规划的电网故障诊断解析模型。Gurobi具有将启发式算法和整数线性规划求解算法有机结合的优点,将其应用于求解基于0-1整数线性规划的诊断模型,解决了传统启发式寻优算法因算法自身的局限性而陷入仅获得局部最优解甚至错解、以及求解速度慢等问题。通过算例对新型电网故障诊断模型的有效性和优越性进行验证,结果表明:相较于基于遗传算法、模拟退火算法、粒子群算法等启发式算法的传统模型,改进模型求解的速度与精度均显著得到了提高。

考虑路径关系的干线多路径绿波优化模型

针对协调路径数目增加后绿波带宽变窄问题,本文提出一种考虑路径关系的多路径协调控制优化模型。分析路径的相关关系,构建上下行分区和路径分解模型;引入子区划分参数,改进经典多路径模型,构建子区内部协调约束;分析路径在相邻子区之间的衔接特征,构建子区间连接性约束条件;综合考虑子路径长度和流量构建权重系数,以各子路径绿波带宽加权和最大为优化目标,建立多路径协调控制优化模型。为验证模型的有效性,选取南京市典型干道为研究对象开展案例分析。实验结果表明,本文提出的模型可以有效增大绿波带宽,相较于对比模型,加权绿波带宽和提高49.44%。利用VISSIM验证了方案的应用效果,仿真结果表明,本文模型方案可以获得更高的通行效益。相较于对比方案,关键路径车均延误和车均停车次数明显降低,干道车均延误和车均停车次数分别降低了20%和27%,车辆平均速度提高了17%。本文模型可为城市道路干线协调控制提供理论基础。

基于线性规划优化小精细化工企业的生产措施

由于小精细化工企业生产灵活、工艺复杂、对成本和利润控制严格,因此,对生产工艺的优化,就成为小精细化工企业生产措施改进的主要内容之一。文章结合小精细化工企业的生产状况以及在该状况条件下相应的约束因素等,采用运筹学线性规划法构建最优计划数学模型,利用计算软件就具体数据进行求解,得到生产计划的最优解。

基于均衡性和能力利用的高速铁路标杆车运行图编制方法研究

高速铁路标杆车的服务品质对于提高铁路客运产品的竞争力具有重要意义,在现场实际编图过程中,高速铁路标杆车须优先铺画,因此标杆车运行图的编制结果决定了整个列车运行图的框架。为了提高高速铁路标杆车的服务品质,考虑标杆车区间运行时分约束、交路接续时间约束等编图基本约束,结合标杆车始发时间约束、成组约束等特殊约束,基于事件活动网络构建以OD服务均衡性和能力利用为目标的整数线性规划模型。设计分阶段迭代求解算法框架,嵌套商业求解器进行求解,第1阶段为不考虑安全间隔时间约束的标杆车分组问题,以OD服务均衡性为目标进行求解;第2阶段以求解得到的标杆车分组为输入,增加安全间隔时间约束,以能力利用为目标进行求解。最后以京广高速铁路为案例,使用实际编图参数,运用优化求解器ILOG CPLEX进行求解,验证模型的有效性和可行性。实验结果表明:优化模型可以在较短时间内高效求解,与实际图对比,上下行OD服务均衡性分别提升38.2%和51.7%,能力损失降低50%,针对不同规模的算例,在200 s内均能得到最优解。针对不同交路接续时间,得出限制标杆车在北京西站的交路接续时间在45 min以内,不会对OD服务均衡性和能力利用造成较大影响。研究结果可为高速铁路标杆车运行图编制及优化提供参考。