Optimizing the Use of Resources: Linear Programming

This paper aims at the problems of professional structure and hierarchical structure in college admission plans, uses linear programming methods to establish mathematical models, maximizes the use of resources on the basis of completing the national enrollment plan, determines the reasonable enrollment structure and enrollment scale, and makes the enrollment plan more scientific and reasonable. In actual situations, the number of students enrolled in the school, the consumption of students, and the number of teachers are constantly changing. Therefore, the concept of fuzzy linear programming is introduced, and the constraints of the linear programming model are fuzzy optimized to obtain more reasonable results, which inspires some reasonable suggestions for colleges in formulating enrollment plans.

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Implementation of a Mathematical Model to Improve Sustainability in the Handling of Transport Costs in a Distribution Network

Sustainability ◽

10.3390/su12010063 ◽

2019 ◽

Vol 12 (1) ◽

pp. 63

Author(s):

José Manuel Velarde ◽

Susana García ◽

Mauricio López ◽

Alfredo Bueno-Solano

Keyword(s):

Mathematical Model ◽

Linear Programming ◽

Integer Linear Programming ◽

Mixed Integer Linear Programming ◽

Numerical Study ◽

Distribution Network ◽

Transport Cost ◽

Mixed Integer ◽

Distribution Area ◽

Use Of Resources

This work considers the application of a mathematical model using mixed-integer linear programming for the vehicle routing problem. The model aims at establishing the distribution routes departing from a distribution center to each customer in order to reduce the transport cost associated with these routes. The study considers the use of a fleet of different capacities in the distribution network, which presents the special characteristic of a star network and which must meet different efficiency criteria, such as the fulfillment of each customer’s demand, the vehicle carrying capacity, work schedule, and sustainable use of resources. The intention is to find the amount of equipment suitable to satisfy the demand, thus improving the level of customer service, optimizing the use of both human and economic resources in the distribution area, and leveraging maximum vehicle capacity usage. The MILP mixed-integer linear programming mathematical model of the case study is presented, as well as the corresponding numerical study.

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PENERAPAN LINEAR PROGRAMMING DALAM PENENTUAN KOMBINASI PRODUK GUNA MEMAKSIMALKAN LABA PADA UD PUTERA SROEDJI JEMBER

BISMA ◽

10.19184/bisma.v12i3.9000 ◽

2018 ◽

Vol 12 (3) ◽

pp. 300

Author(s):

Lutfi Hakim ◽

Hadi Paramu ◽

Eka Bambang Gusminto

Keyword(s):

Linear Programming ◽

Production Process ◽

Limited Resources ◽

Use Of Resources ◽

Maximum Profit

Abstract: The purpose of this study is to analyze the constraints and the optimalproduct combinations in the production process to obtain maximum profit at UDPutera Sroedji. UD Putera Sroedji is one of the trading companies selling packagedrice that consisted of the 2.5 kg, 5 kg, and 25 kg packaging. In its productionprocess, the company experienced the problem or constraints regarding the lessoptimal use of resources to reach maximum profit. Linear programming can beused to allocate the limited resources in the production process in order to obtainmaximum profit. This research used forecasting and linear programming methodsto determine the optimal product combination at UD Putera Sroedji. Resultsshowed that UD Putera Sroedji should produce 200 units of 2.5 kg packaged rice,600 units of 5 kg packaged rice, and 148 units of 25 kg packaged rice in order toachieve a maximum profit of Rp 7,960,977 per month.Keywords: packaged rice, maximum profit, linear programming, and simplexmethod.Abstrak: Tujuan penelitian ini adalah untuk menganalisis kendal-kendala(constraints) dan kombinasi produk yang optimal dalam proses produksi untukmemperoleh laba atau keuntungan maksimal pada UD Putera Sroedji. UD PuteraSroedji merupakan salah satu perusahaan dagang yang bergerak dalamperdagangan beras kemasan, dalam kemasan 2,5 kg, 5 kg, dan 25 kg. Dalamproses produksinya, perusahaan menghadapi beberapa masalah atau kendalayang berhubungan dengan penggunaan sumber daya yang belum optimalsehingga laba yang didapatkan belum maksimal. Linear programming dapatdigunakan untuk mengalokasikan sumber daya yang terbatas untuk memperolehlaba maksimal. Metode analisis yang digunakan dalam penelitian ini adalahforecasting dan linear programming untuk menentukan kombinasi produk yangoptimal. Hasil analisis menunjukkan bahwa UD Putera Sroedji harus memproduksi200 unit beras kemasan 2,5 kg; 600 unit beras kemasan 5 kg; dan 148 unit beraskemasan 25 kg untuk mendapatkan laba maksimal sebesar Rp 7.960.977 perbulan.Kata Kunci: beras kemasan, laba maksimal, linear programming, metodesimpleks.

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Determination of the optimal production volume of the industrial enterprise

E3S Web of Conferences ◽

10.1051/e3sconf/20199108069 ◽

2019 ◽

Vol 91 ◽

pp. 08069

Author(s):

Elena Marys ◽

Natalia Meller ◽

Inna Nekrasova ◽

Elena Rechapova

Keyword(s):

Linear Programming ◽

Industrial Enterprise ◽

Limited Resources ◽

Maximum Efficiency ◽

Production Volume ◽

Effective Management ◽

Optimal Plan ◽

Optimal Production ◽

Use Of Resources

The article observes the methodology and practices of formulating and solving the problem of resource distribution for the industrial enterprise effective management. Methods and models of linear programming are widely used when solving problems of economical and efficient use of resources. One of the tasks solved by the method of linear programming is to determine the optimal production volume having limited resources. The implementation of the found optimal plan will ensure the achievement of the company’s goal of maximum efficiency. Secondly, the mobilization of surplus resources within the identified reserves will increase the efficiency of the industrial enterprise, and thus stabilize its market positions.

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Linear Model for Brand Portfolio Optimization

Economics and Culture ◽

10.2478/jec-2019-0004 ◽

2019 ◽

Vol 16 (1) ◽

pp. 32-39

Author(s):

Pavol Kral ◽

Katarina Janoskova ◽

Pavol Durana

Keyword(s):

Linear Programming ◽

Portfolio Optimization ◽

Portfolio Management ◽

Risk Level ◽

Portfolio Optimisation ◽

Use Of Resources ◽

Business Goals ◽

Brand Portfolio Management ◽

Brand Portfolio ◽

Selection Of

Abstract Research purpose. The aim of the paper is to create a model that allows building an optimal brand portfolio, allowing an organisation to achieve its goals. The created model is based on the bivalent programming theory. A mathematical model of optimum brand portfolio is created based on linear programming with restricting conditions being the maximum acceptable risk level and budget. The basic types of resources and basic types of relations between brands are explained, which are part of the process of brand portfolio optimization. Design / Methodology / Approach. Knowledge and many years of experience of mainly economic disciplines were used for the selection of characteristics for brand portfolio specified in this article. Our assumptions were based mainly on project portfolio management, operational analysis and linear programming as well as tools and methods of graph theory. Findings. Brand portfolio management such as creating, planning, organising and then maintaining a successful brand is a costly and long-term process involving effective marketing strategies and decisions. The prerequisite for brand portfolio creation is deciding on the number and type of brands. A properly constructed brand portfolio is a prerequisite for achieving business goals. Originality / Value / Practical implications. Brand portfolio optimisation requires sufficient attention; however, rather than the selection of the highest number of brands, it should be based on compilation of a set, according to pre-defined priorities, which would provide the best possible means to meet the company’s goals for the current limitations. It should be implemented upon objective rules (in our case maximum allowable risk level and available budget). Frequent changes in the brand portfolio structure are not beneficial since they reduce the ability for the company to achieve its targets and represent excessive use of resources. In addition, qualitative brand characteristics have to be respected in the brand portfolio management, but this was not covered in our research.

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Multi Crop Optimization Using Linear Programming Model for Maximum Net Benefit

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i3.12.16504 ◽

2018 ◽

Vol 7 (3.12) ◽

pp. 797

Author(s):

Shreedhar R

Keyword(s):

Linear Programming ◽

Water Resources ◽

Water Availability ◽

Programming Model ◽

Optimization Techniques ◽

Cropping Pattern ◽

Economic Returns ◽

Net Benefit ◽

Use Of Resources ◽

Optimal Cropping

The water used for agriculture is 70% globally. This has resulted in new methods of saving water. Hence water saving techniques has to be practiced. In water resources planning and management, optimization techniques is used for limited use of resources such as such as water, land, production cost, manpower, fertilizers, seeds, and pesticides. For cultivating each crop, the land area needs to be planned properly. Hence the crop pattern has to be decided optimally depending on available water resources and on economic basis. Therefore farmer needs to be educated to adopt optimum cropping pattern which maximises the economic returns. Hence the study is taken up to optimize the allocation of land areas to crops. The objective function for multi crop model were formulated using linear programming for maximizing the net benefits. The study resulted in optimal cropping pattern for different water availabilities ranging from 2000 Ha-m to 5500 Ha-m. The maximum net benefit for the study area varied from Rs. 53.2 Crores for 2000 Ha-m water availability to Rs.78 Crores at 5000 Ha-m water availability.

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The Optimization Problem of Product Mix and Linear Programming Applications: Case Study in the Apparel Industry

Open Science Journal ◽

10.23954/osj.v2i2.853 ◽

2017 ◽

Vol 2 (2) ◽

Cited By ~ 1

Author(s):

Gera Workie Woubante

Keyword(s):

Decision Making ◽

Linear Programming ◽

Inventory Management ◽

Industrial Development ◽

Optimization Problem ◽

Management Decision ◽

Product Mix ◽

Use Of Resources ◽

Customer Orders

Industrial development strategy is characterized by the efficient use of resources at every production stage. The analysis and efficient utilization of resources are made sustainable by effective management decision making techniques employed in the industry. A quantitative decision making tool called linear programming can be used for the optimization problem of product mix. Understanding the concept behind the optimization problem of product mix is essential to the success of the industry for meeting customer needs, determining its image, focusing on its core business, and inventory management. Apparel manufacturing firms profit mainly depends on the proper allocation and usage of available production time, material, and labor resources. This paper considers an apparel industrial unit in Ethiopia as a case study. The monthly held resources, product volume, and amount of resources used to produce each unit of product and profit per unit for each product have been collected from the company. The data gathered was used to estimate the parameters of the linear programming model. The model was solved using LINGO 16.0 software. The findings of the study show that the profit of the company can be improved by 59.84%, that is, the total profit of Birr 465,456 per month can be increased to Birr 777,877.3 per month by applying linear programming models if customer orders have to be satisfied. The profit of the company can be improved by 7.22% if the linear programming formulation does not need to consider customer orders.

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