An Alternative Approach for Solving Bi-Level Programming Problems

An algorithm is proposed in this paper for solving two-dimensional bi-level linear programming problems without making a graph. Based on the classification of constraints, algorithm removes all redundant constraints, which eliminate the possibility of cycling and the solution of the problem is reached in a finite number of steps. Example to illustrate the method is also included in the paper.

A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM

The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.

Bi-level programming model for reconstruction of urban branch road network

Considering the decision-making variables of the capacities of branch roads and the optimization targets of lowering the saturation of arterial roads and the reconstruction expense of branch roads, the bi-level programming model for reconstructing the branch roads was set up. The upper level model was for determining the enlarged capacities of the branch roads, and the lower level model was for calculating the flows of road sections via the user equilibrium traffic assignment method. The genetic algorithm for solving the bi-level model was designed to obtain the reconstruction capacities of the branch roads. The results show that by the bi-level model and its algorithm, the optimum scheme of urban branch roads reconstruction can be gained, which reduces the saturation of arterial roads apparently, and alleviates traffic congestion. In the data analysis the arterial saturation decreases from 1.100 to 0.996, which verifies the micro-circulation transportation's function of urban branch road network.

An Optimal DASH Diet Model for People with Hypertension Using Linear Programming Approach

Selecting diets by quantitative techniques is becoming increasingly common. Linear programming is the most popular technique for the selection of least cost mixes of food to meet specific nutritional requirements for a particular group of persons for either general health or disease-related reason. Hypertension is a silent killer and its prevalence rate especially in the developing countries, which has been mostly associated to demographic, environmental and genetic factors, is becoming alarming. The DASH diet has been clinically proven to prevent and control hypertension. In this paper, a model that provides a Daily Optimal (minimum cost) DASH Diet plan for people with hypertension is formulated. The objective is to obtain daily minimum cost diet plans that satisfy the DASH Diets’ nutrients Tolerable Upper and Lower Intake for different daily Calorie Levels. The formulated DASH diet model was further illustrated using real data set with food samples gotten from the DASH eating plan chart. A DASH diet model for a hypertensive person with a 2000-daily-caloric need was formulated and its optimal diet plan for a day obtained with a total cost of 944.41 Naira. Optimal diet plans for other recommended daily calorie levels were also obtained.

Enhancing Data Analysis and Automation: Integrating Python with Microsoft Excel for Non-Programmers

Microsoft Excel is essential for the End-User Approach (EUA), offering versatility in data organization, analysis, and visualization, as well as widespread accessibility. It fosters collaboration and informed decision-making across diverse domains. Conversely, Python is indispensable for professional programming due to its versatility, readability, extensive libraries, and robust community support. It enables efficient development, advanced data analysis, data mining, and automation, catering to diverse industries and applications. However, one primary issue when using Microsoft Excel with Python libraries is compatibility and interoperability. While Excel is a widely used tool for data storage and analysis, it may not seamlessly integrate with Python libraries, leading to challenges in reading and writing data, especially in complex or large datasets. Additionally, manipulating Excel files with Python may not always preserve formatting or formulas accurately, potentially affecting data integrity. Moreover, dependency on Excel’s graphical user interface (GUI) for automation can limit scalability and reproducibility compared to Python’s scripting capabilities. This paper covers the integration solution of empowering non-programmers to leverage Python’s capabilities within the familiar Excel environment. This enables users to perform advanced data analysis and automation tasks without requiring extensive programming knowledge. Based on Soliciting feedback from non-programmers who have tested the integration solution, the case study shows how the solution evaluates the ease of implementation, performance, and compatibility of Python with Excel versions.

Two-Phase Multi Objective Fuzzy Linear Programming Approach for Sustainable Irrigation Planning

The objective of the present study is to develop the irrigation planning model and to apply the same in the form of Two-Phase Multi Objective Fuzzy Linear Programming (TPMOFLP) approach for crop planning in command area of Jayakwadi Project Stage I, Maharashtra State, India. The development of TPMOFLP model is on the basis of various Linear Programming (LP) models and Multi Objective Fuzzy Linear Programming (MOFLP) models, these models have been applied for maximization of the Net Benefits (NB), Crop production (CP), Employment Generation (EG) and Manure Utilization (MU) respectively. The significant increase in the value of level of satisfaction (λ) has been found from 0.58 to 0.65 by using the TPMOFLP approach as compare to that of MOFLP model based on maxmin approach. The two-phase approach solution provides NB = 1503.56 Million Rupees, CP = 335729.30 Tons, EG = 29.74 Million Man days and MU = 160233.70 Tons respectively. The proposed model will be helpful for the Decision Maker (DM) to take a decision under conflicting situation while planning for different conflicting objectives simultaneously and has potential to find out an integrated irrigation planning with prime consideration for economic, social and environmental issue.

Bi-Level Programming for the Optimal Nonlinear Distance-Based Transit Fare Structure Incorporating Principal-Agent Game

The urban transit fare structure and level can largely affect passengers’travel behavior and route choices.The commonly used transit fare policies in the present transit network would lead to the unbalanced transit assignment and improper transit resources distribution.In order to distribute transit passenger flow evenly and efficiently,this paper introduces a new distance-based fare pattern with Euclidean distance.A bi-level programming model is developed for determining the optimal distance-based fare pattern,with the path-based stochastic transit assignment(STA)problem with elastic demand being proposed at the lower level.The upper-level intends to address a principal-agent game between transport authorities and transit enterprises pursing maximization of social welfare and financial interest,respectively.A genetic algorithm(GA)is implemented to solve the bi-level model,which is verified by a numerical example to illustrate that the proposed nonlinear distance-based fare pattern presents a better financial performance and distribution effect than other fare structures.

A mixed integer linear programming approach for municipal solid waste management

ＡｍｉｘｅｄｉｎｔｅｇｅｒｌｉｎｅａｒｐｒｏｇｒａｍｍｉｎｇａｐｐｒｏａｃｈｆｏｒｍｕｎｉｃｉｐａｌｓｏｌｉｄｗａｓｔｅｍａｎａｇｅｍｅｎｔＧｏｒｄｏｎＧｕｏＨｅＨｕａｎｇＥｎｖｉｒｏｎｍｅｎｔａｌＳｙｓｔｅｍｓＥｎｇｉｎｅｅｒｉｎｇ，Ｕｎｉｖｅｒ...

New Approach to Solve Cubic Objective Function Programming Problem

In this paper, a cubic objective programming problem (COPP) is defined. Introduced a new modification to solve a cubic objective programming problem. Suggested an algorithm for its solution. Also reported the algorithm of the usual simplex method. Application talks about how the developed algorithm can be used to unravel non-linear. The proposed technique, modification simplex technique, can be used with the constructed numerical examples an illustrative numerical problems are given to demonstrate the algorithms.

Bilevel Programming Model for Joint Scheduling of Arrival and Departure Flights Based on Traffic Scenario

In order to meet the needs of collaborative decision making,considering the different demands of air traffic control units,airlines,airports and passengers in various traffic scenarios,the joint scheduling problem of arrival and departure flights is studied systematically.According to the matching degree of capacity and flow,it is determined that the traffic state of arrival/departure operation in a certain period is peak or off-peak.The demands of all parties in each traffic state are analyzed,and the mathematical models of arrival/departure flight scheduling in each traffic state are established.Aiming at the four kinds of joint operation traffic scenarios of arrival and departure,the corresponding bi-level programming models for joint scheduling of arrival and departure flights are established,respectively,and the elitism genetic algorithm is designed to solve the models.The results show that:Compared with the first-come-firstserved method,in the scenarios of arrival peak&departure off-peak and arrival peak&departure peak,the departure flight equilibrium satisfaction is improved,and the runway occupation time of departure flight flow is reduced by 38.8%.In the scenarios of arrival off-peak&departure off-peak and departure peak&arrival off-peak,the arrival flight equilibrium delay time is significantly reduced,the departure flight equilibrium satisfaction is improved by 77.6%,and the runway occupation time of departure flight flow is reduced by 46.6%.Compared with other four kinds of strategies,the optimal scheduling method can better balance fairness and efficiency,so the scheduling results are more reasonable.

Programmed 6-Step Approach of Improved Liposuction-Curettage for Axillary Bromhidrosis

Background Liposuction-curettage is a long-standing and effective treatment for axillary bromhidrosis.However,residual malodor and skin necrosis typically occur following this treatment.Therefore,we improved this method to ensure fewer complications and better outcomes.Here,we have presented our programmed 6-step approach of improved liposuction-curettage.Methods The programmed 6-step approach of improved liposuction-curettage was used to remove the axillary apocrine glands.We used pointed and obtuse cannulas designed for liposuction-curettage.Results Patients treated using the programmed 6-step approach of improved liposuctioncurettage did not experience any serious complications or residual malodor.Conclusion The programmed 6-step approach of improved liposuction-curettage was more effective than traditional surgery with respect to the treatment of axillary bromhidrosis.

Approach of Separately Applying Unit Testing to AspectJ Program

A unit testing approach for AspectJ programs is proposed to separately test aspect units which have their own states. In the approach, aspects under test are converted to classes before execution of unit testing. In the conversion process, the context information passed through pointcut is transformed into advices, then the advices are converted to class member methods, and conflicts in the conversion result, if any, are resolved finally. The unit testing process consists of generating test cases, executing test cases and checking results.

Estimation of CARA Preferences and Positive Mathematical Programming

The purpose of this paper is to combine the estimation of output price risk and positive mathematical programming (PMP). It reconciles the risk programming presented by Freund with a consistent estimate of the constant absolute risk aversion (CARA) coefficient. It extends the PMP approach to calibration of realized production outputs and observed input prices. The results of this specification include 1) uniqueness of the calibrating solution, 2) elimination of the tautological calibration constraints typical of the original PMP procedure, 3) equivalence between a phase I calibrating solution and a solution obtained by combining phase I and phase II of the traditional PMP procedure. In this extended PMP framework, the cost function specification involves output quantities and input prices—contrary to the myopic cost function of the traditional PMP approach. This extension allows for a phase III calibrating model that replaces the usual linear technology with relations corresponding to Shephard lemma (in the primal constraints) and the marginal cost function (in the dual constraints). An empirical example with a sample of farms producing four crops illustrates the novel procedure.

A Lagrange Relaxation Based Approach to Solve a Discrete-Continous Bi-Level Model

In this work we propose a solution method based on Lagrange relaxation for discrete-continuous bi-level problems, with binary variables in the leading problem, considering the optimistic approach in bi-level programming. For the application of the method, the two-level problem is reformulated using the Karush-Kuhn-Tucker conditions. The resulting model is linearized taking advantage of the structure of the leading problem. Using a Lagrange relaxation algorithm, it is possible to find a global solution efficiently. The algorithm was tested to show how it performs.

A Trace-state Based Approach to Specification and Design of Parallel Programs

In this paper they deal with the issue of specification and design of parallel communicatingprocesses. A trace-state based model is introduced to describe the behaviour of concurrent programs. They presenta formal system based on that model to achieve hierarchical and modular development and verification methods. Anumber of refinement rules are used to decompose the specification into smaller ones and calculate program fromthe

A Weighted Goal Programming Model for the DASH Diet Problem: Comparison with the Linear Programming DASH Diet Model

A Linear Programming DASH diet model for persons with hypertension has previously been formulated and daily minimum cost diet plans that satisfy the DASH diets’ tolerable intake level of the nutrients for 1500 mg a day Sodium level and different daily calorie levels were obtained using sample foods from the DASH diet eating plan chart. But the limitation in the use of linear programming model in selecting diet plans to meet specific nutritional requirements which normally results in the oversupply of certain nutrients was evident in the linear programming DASH diet plan obtained as the nutrient level of the diet plans obtained had wide deviations of from the DASH diets’ tolerable upper and lower intake level for the given calorie and sodium levels. Hence the need for a model that gives diet plans with minimized nutrients’ level deviations from the DASH diets’ tolerable intake level for different daily calorie and sodium level at desired cost. A weighted Goal Programming DASH diet model that minimizes the daily cost of the DASH eating plan as well as deviations of the diets’ nutrients content from the DASH diet’s tolerable intake levels is hereby presented in this work. The formulated weighted goal programming DASH diet model is further illustrated using chosen sample foods from the DASH food chart as used in the work on the linear programming DASH diet model for a 1500 mg sodium level and 2000 calories a day diet plan as well as for 1800, 2200, 2400, 2600, 2800 and 3000 daily calorie levels. A comparison of the DASH nutrients’ composition of the weighted Goal Programming DASH diet plans and those of the linear programming DASH diet plans were carried out at this sodium level and the different daily calorie levels. It was evident from the results of the comparison that the weighted goal programming DASH diet plans has minimized deviations from the DASH diet’s tolerable intake levels than those of the linear programming DASH diet plans.

国际承包商合规体系的有效性度量研究

为响应廉洁“一带一路”号召,助力国际承包商开展有效的合规管理,采用文献分析法、德尔菲法构建企业层面的合规指标体系,并基于Fuzzy-OPA形成合规体系的有效性度量模型,通过调研某国际承包商的合规体系验证模型的合理性。研究结果表明:合规指标体系包含合规准则、措施及最佳实践,基于Fuzzy-OPA构建的度量模型能够评价企业合规体系的有效性,为诊断合规薄弱环节、完善合规体系提供参考。

混合随机波动模型下带随机工资的DC型养老金最优投资策略

针对养老金的保值增值问题,分析具有利率风险和波动风险的DC(defined contribution)型养老金最优投资策略。假设金融市场包含一种无风险资产和一种股票,其中股票价格服从混合随机波动(Heston-Hull-White)模型。设定养老金计划成员的工资是随机的。基于终端财富预期效用最大化标准,在CARA效用函数下,通过建立相应的HJB(Hamilton-Jacob-Bellman)方程,求解出最优投资策略,并利用数值算例分析主要模型参数对最优投资策略的影响。结果表明:风险规避系数的增大会导致投资者对股票的投资比例下降,利率风险和波动风险对DC型养老金的最优投资策略有显著影响。所得结果对基金管理者具有一定的指导作用。

拥挤网络下OD需求重构的双层规划模型

提出了在拥挤网络下利用密度作为观测变量对Origin-Destination(OD)需求进行重构的双层规划模型。上层目标为极小化各个估计值与观测值之间的误差,下层为用户均衡模型。采用KKT条件法将该双层规划转化为相对容易求解的均衡约束规划模型,再用Scholtes松弛化方法求解转化后模型。数值实验结果表明,在拥挤网络下的OD重构问题中,利用密度作为观测变量优于流量作为观测变量,同时在求解方法上,利用KKT条件转换为单层模型的求解方法优于上下层交替求解法。