Application Of Linear Programming Research Articles

Applications of Linear Programming on Diet Problem for Subways’ Sets Menu in Malaysia

Consuming a proper and balanced diet is necessary for each and every individual. It makes them fit, healthy, and keep them safe from chronic diseases. However, in today's world, many individuals frequently buy fast food without realising that the food may not provide all the daily nutrients that the body needs. Therefore, this study aims to propose a mathematical modelling on diet problem for the subways sets menu in Malaysia. The proposed mathematical model will be solved by using the Microsoft Excel Solver in order to produce optimal solution, which mean that the chosen menu from the Subway fulfil the daily requirements of calories, protein, carbohydrates, and fats for both men and women.

Application of linear programming in employee allocation: A case study in emerging economy

Linear programming is widely used in numerous industries for allocating scarce resources to fulfill customers’ demands. In this study, we use this mathematical technique in an automobile industry located in an emerging economy (Bangladesh). Given that, the emerging economy faces problems in implementing sophisticated technologies. Therefore, the key objective of this study is to show how linear programming applications are possible without sophisticated technologies, just by using a software, named GAM. Moreover, this study shows that the application of linear programming in the automobile industry in the emerging economy is also cost-effective and efficient in employee management. Based on the outcome of this study, we find that the company can save $26,174 in employee costs in eight weeks by implementing linear programming in the allocation of its employees. This study will contribute in many ways such as realizing policymakers, employees, and management how linear programming is beneficial for them in providing small efforts. Furthermore, this will add value to the existing literature that linear programming is also applicable in a specific industry in the emerging economy.

Application Of Linear Programming in the Minimization of Transportation Cost in Dangote Cement, Port Harcourt

This study delved into the optimization of transportation expenses for Dangote Cement in Port Harcourt, Rivers State. It aligned the quantities of products required by national distributors with the supply available from their depots, employing linear programming techniques to achieve cost minimization. Three sources (depots) - Onne, Rumuodumaya and Trans Amadi as well as six destinations (national distributors) - Aluu, Bori, Elelewon, Omagwa, Oyibo and Rumuola were examined. The secondary data was obtained from a field survey and it contained the unit cost (in Naira) of transporting the products per bag from their various sources to various destinations as at October, 2023. Also, the data obtained from Dangote Cement National Consumer Promotion 2020 (Redemption Centres Detail) contained the list of eleven national distributors in Port Harcourt; however, only six of the national distributors were used in this research. Initial feasible solutions for the secondary data collected were determined through the application of the North-West Corner Method, the Least Cost Method, and the Vogel Approximation Method resulting in values of ₦452,000, ₦380,750, and ₦370,500, respectively. Upon analyzing the outcomes, it was established that the allocation strategy proposed by the Vogel Approximation Method is the most advantageous for optimizing the company's transportation costs. As such, it is recommended to the company as it offers the potential to reduce transportation expenses to a minimum of ₦370,500.

A Comparative Study of Time and Cost Optimization in Project Management: Primavera P6 & Linear Programming with Lingo Solver

In an effort to boost efficiency and reduce costs, computer-based solutions have become more popular for project management. Although Primavera P6 and other traditional tools have proved essential for project planning and control, difficulties still arise with complicated projects. An innovative approach is provided by the development of mathematical optimization techniques, especially Linear Programming (LP) with programmes like Lingo Solver. The purpose of this study is to compare the time and cost optimization of Primavera P6 and Lingo Solver's LP. The goals are to analyse the advantages and disadvantages, evaluate the effectiveness and adaptability, and offer useful information to decision-makers. Application of Lingo Solver's LP is found to significantly reduce project duration, with a significant impact on cost trends. On the other hand, Primavera P6 shows that project duration can be reduced while maintaining the same level of cost. The study highlights how the duration of the project, additional indirect expenses, and costs interplay dynamically throughout the duration of the project. This research provides useful insights to the continuing discussion on project management methodologies by bridging the gap between conventional project management tools and advanced optimization techniques. This will help decision-makers overcome the complexities of project optimization for optimal results in practical applications. Key Words: Optimization, Construction project, Linear programming, Primavera p6, Lingo, Project management, Mathematical model, Time-cost trade-off.

Efficient continuous piecewise linear regression for linearising univariate non-linear functions

Due to their flexibility and ability to incorporate non-linear relationships, Mixed-Integer Non-Linear Programming (MINLP) approaches for optimization are commonly presented as a solution tool for real-world problems. Within this context, piecewise linear (PWL) approximations of non-linear continuous functions are useful, as opposed to non-linear machine learning-based approaches, since they enable the application of Mixed-Integer Linear Programming techniques in the MINLP framework, as well as retaining important features of the approximated non-linear functions, such as convexity. In this work, we extend upon fast algorithmic approaches for modeling discrete data using PWL regression by tuning them to allow the modeling of continuous functions. We show that if the input function is convex, then the convexity of the resulting PWL function is guaranteed. An analysis of the runtime of the presented algorithm shows which function characteristics affect the efficiency of the model, and which classes of functions can be modeled very quickly. Experimental results show that the presented approach is significantly faster than five existing approaches for modeling non-linear functions from the literature, at least 11 times faster on the tested functions, and up to a maximum speedup of more than 328,000. The presented approach also solves six benchmark problems for the first time.

Minimization of transportation costs using linear programming

This paper intricately explores the utilization of Linear Programming (LP), a distinguished mathematical optimization technique, within the logistics and transportation sector, a domain persistently pursuing methods to bolster efficiency and curtail expenses. LP, characterized by its adeptness in optimizing a linear objective function subject to linear constraints, emerges as a pragmatic solution. This exposition elucidates how LP can be harnessed to ascertain the most economically viable transportation routes and quantities of goods transported from warehouses to consumers. A case study is introduced to spotlight the pragmatic applicability of LP in authentic scenarios, and the potential fiscal savings corporations can realize through its adoption. While recognizing the merits of LP, such as clarity, versatility, and computational efficacy, the paper also sheds light on its limitations, involving its dependency on certain presumptions, a necessity for precise data, and its concentration on single-objective optimization. The discourse concludes by prospecting the future of LP in transportation, exploring its amalgamation with artificial intelligence, machine learning, multi-objective optimization, and green logistics, intending to underscore the significance of LP in transportation and furnish insights for ensuing research and application.

Application of Linear Programming to Optimize Sugarcane Production and Sugarcane Farming Income at HGU Jengkol PT. Perkebunan Nusantara X

Sugar production in Indonesia is currently unable to meet domestic needs, even though the potential demand for domestic sugar is still relatively high. Therefore, targeted efforts are needed to predict the decline in sugar production. One of the efforts in that direction is to optimize sugarcane production of HGU Djengkol PT Perkebunaan Nusantara X. This research aims to maximize income and increase sugarcane production by optimizing the area per crop category/ This research was carried out at HGU Djengkol PT Perkebunan Nusantara X. This research will take place from October 2023 to November 2023. The data collected is in the form of secondary data, namely sugarcane production data and income for the 2022 growing season, climate/weather data, and area per crop category. The data analysis method used is Linear Programming using POM software for Windows. The results showed that optimization of the broad composition per plant category can increase the income of HGU Djengkol by 107%, with actual income of Rp. 26,974,475,108, - after being optimized to Rp. 28,817,240,000,-, to get maximum income, by eliminating the category of ratoon 2 plants with a combination of area per category of plants Pure PC 30%, PC BR, 5%, RT 1 35% and Lahan Bero 30%. can increase HGU Djengkol sugarcane production by 102% with actual sugarcane production of 100,488 tons after being optimized to 102,432 tons.

“The Application of Linear Programming for Profit Maximization in a Bakery”

“The Application of Linear Programming for Profit Maximization in a Bakery”

Application of linear programming in two-player zero-sum games

Linear programming is a useful optimization tool that has been utilized since the 1940s. It has been studied for a long time, and it can be applied to many different areas and fields. One of these applications is the two-player zero-sum game. In this game, each player has a set of possible strategies that is finite. While one player tries to maximize the net payoff, the other player tries to minimize this payoff. Since the problem involves optimizations, linear programming can be involved. This paper analyzes a famous and classic example of the game the Colonel Blotto Game. This game is a military planning problem. Indeed, Linear programming was first developed to solve complex military and planning problems during wartime. This paper utilizes a payoff matrix and some mathematical models to build the mathematical problem of the Colonel Blotto Game. Then the results can be obtained by converting the mathematical problem into a Python Linprog problem. The paper finds the best strategy for Colonel Blotto to maximize the net payoff and how eliminating certain possible strategies will or will not affect the results. Moreover, the paper provides an understanding of the combination of the two-player zero-sum game and linear programming.

A study of the application of linear programming to material transportation problems

With the quick development of the world logistics industry, the transportation cost of Chinese enterprises is still very high. There is still a lot of room for development compared with other developed countries. Reducing transportation costs, especially transportation costs, is one of the effective ways for enterprises to improve their income. Due to the rapid development of China's industry, the demand for various materials is increasing day by day. Therefore, China's material transportation is also getting more and more attention. Operations Research is a subject of establishing mathematical models to solve practical problems. It is very necessary to use the relevant theories of operations research to solve material transportation problems. By reading the related literature at home and abroad and analysing the characteristics of material transportation problems and the application of operations research in this field, it is found that the on-table operation method is unable to effectively solve the complex material transportation problems. In order to reduce the transportation cost of enterprises, by conducting theoretical and practical research on the material transportation problem in the field of logistics management, this paper aims to simulate and calculate it by establishing a mathematical model and using Lingo software.

Evaluation of the effectiveness of the functioning of production and consumption waste management systems in the Arctic regions of Russia based on Data Envelopment Analysis

Subject of research: is the functioning of the production and consumption waste management systems of the regions (RSOO) of the Arctic zone of the Russian Federation for the period from 2016 to 2020.
 Purpose of research: is to quantify production efficiency production efficiency coefficients (СEP) of the functioning of these systems based on shell data analysis (Data Envelopment Analysis, DEA). This method is based on the repeated application of linear programming to a set of input and output indicators recorded by the current system of state statistics and characterizing the activities of sets of similar specialized enterprises in the regions for waste management (production facility, software).
 Methods and objects of research: to assess the СEP of the software functioning by the DEA method, the "time slice" and "time window" schemes were used. Based on the calculated СEP values, stable subgroups of software with low, medium and high СEP values were identified. For insufficiently effective software, target values of input indicators were calculated, the achievement of which allows them to maximize СEP values. At the same time, for these software, a recommendatory choice of a leader/landmark object was carried out, which can be considered as a carrier of best practices and successful experience in organizing work, which is relevant for the development of the RSOO.
 Main results of research: the formed classification of RSOO was compared with the normative indicators of waste processing given in the State Program of the Russian Federation "Environmental Protection" for 20122020.

Linear Programming in a Restaurant Setup

The restaurant industry is a dynamic and pretty competitive zone that calls for powerful aid management and efficient choice-making to thrive inside the marketplace. Linear programming, a mathematical technique that optimizes aid allocation, has emerged as a powerful tool for boosting eating place operations. This paper delves into the application of linear programming inside the context of restaurant management and its profound impact on streamlining various facets of the enterprise, from menu making plans and personnel scheduling to inventory control and pricing strategies. This observe makes a speciality of elucidating how linear programming models can be developed and implemented to restaurant control, enabling owners and executives to make facts-driven decisions that improve efficiency, decrease charges, and ultimately raise profitability whilst retaining client pleasure and provider great. By integrating mathematical optimization strategies, restaurants can navigate the complicated balance between useful resource allocation and customer support, ensuring a harmonious and profitable operation. The paper attracts on actual-international examples and case studies to demonstrate the sensible implementation of linear programming inside the eating place enterprise. It underscores the effectiveness of this approach in real situations, showing how it may deal with common challenges confronted by means of eating place companies and lead to tangible upgrades in diverse domain names.

The Application of Linear Programming into Production Schedule at Electrical Panel Company

The Application of Linear Programming into Production Schedule at Electrical Panel Company

Application of Linear Programming on Cost Minimization of Pig Feeds (A Case Study of MOV Farms)

This paper discusses cost minimization for pig diet formulation. A linear programming model was formulated for minimum cost and maximum shelf life feed quality. Linear programming technique via MATLAB was employed to obtain solution using real life data collected from MOV Farms, Ilorin. The results, attained at the $7^{th}$ iteration gave an optimal value of the objective function obtained as $ \#94,226$ per 100 kg, with the corresponding values 1.5714, 0.6929, 2.8929, 0 and 0 for $x_{1}$(pig weaner), $x_{2}$(pig growers), $x_{3}$(pig finishers), $x_{4}$(pregnant sow), $x_{5}$(lactating sow) recorded respectively. Hence, the cost of pig feeds formulation can be optimized effectively.

Optimizing Crop Selection and Production Planning in Agriculture: Applications of Linear Programming for Profit Maximization and Sustainability

Optimizing Crop Selection and Production Planning in Agriculture: Applications of Linear Programming for Profit Maximization and Sustainability

The Application of Linear Programming for the Optimal Profit of Pt. Naruna Using the Simplex Method

Abstract PT. Naruna is a ceramics factory located in Salatiga, Indonesia. In PT. Naruna ceramics, all products are handmade with contemporary designs and have a high artistic value in shape and color. Getting profit is the company’s primary goal, but many companies still need to learn the maximum profit that can be obtained by optimizing their resources, one of which is PT. Naruna. PT. Naruna produces goods based on intuition. As a result, a lot of goods are piled up in warehouses. Meanwhile, with the development of the times, new trends and images will appear more attractive so that consumer tastes and motifs from ceramics will change. In addition, ceramic products that have gone through the combustion process cannot be recycled and must be burned. This research focuses on the production of glasses with three different types according to price. The aim of this paper is to optimize profits by determining the composition of the number of products produced. We used linear programming with a simplex method to solve our problem in PT. Naruna. Linear programming is the most appropriate method for solving problems that exist in PT. Naruna, namely by paying attention to the objective and constraint functions. The objective function is to maximize profit, so it takes the form of a linear equation with the variable X1 being the first type of glass, X2 being the second type of glass, and X3 being the third type of glass. The constraint functions used include the number of products, the number of workers, the amount of clay, and the time for production. The results show that PT. Naruna can achieve maximum profit when producing glass type 1 less than type 3 less than type 2.

A biased random-key genetic algorithm for the chordal completion problem

A graph is chordal if all its cycles of length greater than or equal to four contain a chord, i.e., an edge connecting two nonconsecutive vertices of the cycle. Given a graph G = (V, E), the chordal completion problem consists in finding the minimum set of edges to be added to G to obtain a chordal graph. It has applications in sparse linear systems, database management and computer vision programming. In this article, we developed a biased random-key genetic algorithm (BRKGA) for solving the chordal completion problem, based on the strategy of manipulating permutations that represent perfect elimination orderings of triangulations. Computational results show that the proposed heuristic improve the results of the constructive heuristics fill-in and min-degree. We also developed a strategy for injecting externally constructed feasible solutions coded as random keys into the initial population of the BRKGA that significantly improves the solutions obtained and may benefit other implementations of biased random-key genetic algorithms.

Nonlinear Programming Techniques in Optimization: An exhaustive comparative study understanding Quasi – Newton and Gauss – Newton methods

Non – linear Programming Applications are becoming increasingly important as managers and operations researchers become more sophisticated in implementing decision – oriented mathematical models, as well as computer routines capable of solving large – scale nonlinear problems become more widely available. By means of this paper, we investigate two of the very widely and varied NLP techniques, namely the Gauss – Newton method and the Quasi – Newton method. When computation or iteration is expensive, Quasi –Newton methods are an effective method for function optimization. Even if their precise approaches differ, when the issues are complicated, they can all determine the optimum more quickly and effectively than Newton's Method. Gauss – Newton can be used to locate a single point or, as it is most frequently use, to evaluate how well a theoretical model matches a collection of experimental data points. We get the most accurate estimates of the unknown variables in a theoretical model by solving the system of nonlinear equations. In this review we present an overview of the methods mentioned earlier, discuss the scope of them, and advocate a comparison between the two.

Application of Linear Programming on the Maximum-Profit of Milk Tea Store

The aim of this article is the application of the industrial profit optimization on milk tea store. The linear programming model is used to determine the optimal production structure of amount of raw material purchased. The first part optimizes only the single profit from the sales which are put into the objective function. The second section of the article extends the model by the considering factors of employee. This model will have more constraints. The model aims to meet the maximum cost of raw materials, and meet the situation that the staff will have different abilities on making tea and each tea for each person takes different time to complete. The model will be built based on real data, and then will compare the real data results with the calculated results. Conclusions of the paper demonstrate the applicability of the model and possibilities of its extensions.

A Proposed Method for Finding Initial Solutions to Transportation Problems

The Transportation Model (TM) in the application of Linear Programming (LP) is very useful in optimal distribution of goods. This paper focuses on finding Initial Basic Feasible Solutions (IBFS) to TMs hence, proposing a Demand-Based Allocation Method (DBAM) to solve the problem. This unprecedented proposal goes in contrast to the Cost-Based Resource Allocations (CBRA) associated with existing methods (including North-west Corner Rule, Least Cost Method and Vogel’s Approximation Method) which make cost cell (i.e. decision variable) selections before choosing demand and supply constraints. The proposed ‘DBAM’ on page 4 is implemented in MATLAB and has the ability to solve large-scale transportation problems to meet industrial needs. A sample of five (5) examples are presented to evaluate efficiency of the method. Initial Basic Feasible Solutions drawn from the study (according to DBAM) represent the optimal with higher accuracy, in comparison to the existing methods. Results from the study qualify the DBAM as one of the best methods to solve industrial transportation problems.