scholarly journals Program for Solving Assignment Problems and Its Application in Lecturer Resources Allocation

2021 ◽  
Vol 2070 (1) ◽  
pp. 012003
Author(s):  
N Wattanasiripong ◽  
N W Sangwaranatee
Keyword(s):  
Linear Programming ◽  
Combinatorial Optimization ◽  
Optimal Solution ◽  
Resources Allocation ◽  
Assignment Problems ◽  
Preparation Time ◽  
Total Cost ◽  
Implementation Tool ◽  
The Right ◽  
Manual Calculation

Abstract This paper proposes program for solving assignment problems by Hungarian method. Assignment problem is one of the most famous problems in linear programming and in combinatorial optimization. It can be solved by using an efficient method which is called Hangarian method. In this problem, commonly, there are a number of agents and a number of tasks. Any agent can be assigned to perform any task. The objective of this problem is to decide the right agent to perform the right task and also the total cost of the assignment is minimized. The manual calculation is time-consuming and prone to mistake. Therefore, this program can help to find the optimal solution with less time. In this approach, computer programming is used as an implementation tool to get the accurate solutions. The program can also be applied with the lecturer allocation for each subject to minimize lecturer’s preparation time and to match the lecturer per individual expertise.

Linear Programming Based on Piece-Wise Linearization for Solving the Economic Load Dispatch Problem

2019 ◽  
pp. 20-50
Author(s):  
Ahmad Al-Subhi ◽  
Hesham K. Alfares
Keyword(s):  
Linear Programming ◽  
Optimal Solution ◽  
Linearization Method ◽  
Solution Time ◽  
Test Problems ◽  
Economic Load Dispatch ◽  
Total Cost ◽  
Generation Cost ◽  
Cubic Function ◽  
Lp Solutions

This chapter discusses the application of linear programming (LP) techniques to find the optimal solution of the economic dispatch (ED) problem without considering transmission losses. The ED problem is concerned with optimizing the power generated by several generating units. The objective is to find the optimal power produced by each unit to supply the required load at minimum total cost. The generation cost associated with each unit is usually in the form of a quadratic or cubic function of the power produced. To apply LP, these nonlinear cost functions have to be linearized. The optimal solution is then determined by LP based on the approximate linear model. Piece-wise linearization methodology is adopted in this chapter. To evaluate the performance of the linearization method, a comprehensive set of benchmark test problems is used. LP solutions of linearized ED problems are compared with several other techniques from the literature. The LP technique with piece-wise linearization shows an overall competitive advantage in terms of total cost, solution time, and load satisfaction.

scholarly journals Integer linear programming application in production results optimization using cutting plane method

2021 ◽  
Vol 4 (1) ◽  
pp. 57-66
Author(s):  
Fery Firmansah ◽  
Fitriana Wulandari
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Raw Materials ◽  
Optimal Solution ◽  
Cutting Plane ◽  
Cutting Plane Method ◽  
Daily Production ◽  
Plane Method ◽  
Decision Variables ◽  
The Right

Integer Linear Programming is a special form of linear programming which the decision variables are in integer form. Berkah Rasa is a home industry business in the form of Jenang Ayu and Jenang Krasikan processed food.  The daily production that carried out by Berkah Rasa is based on the availability of raw materials and the number of requests. So far, Berkah Rasa has not had the right strategy in producing Jenang to get maximum profit. The purpose of this research is to apply integer linear programming to the optimization of Jenang Ayu and Jenang Krasikan production. The method used to solve this problem is the cutting plane method. The results of the research obtained is the optimal solution for Berkah Rasa, that is by producing 25 kg of Jenang Ayu and 22 kg of Jenang Krasikan every day. So that the benefits obtained by Berkah Rasa every day are IDR 727,000.00.

scholarly journals Team Teaching Load using Linear Programming

2019 ◽  
Vol 4 (1) ◽  
pp. 8-15
Author(s):  
Syadatul Syaeda binti Mat Saleh ◽  
Nurul Husna Jamian ◽  
Najihan Awang@Ali
Keyword(s):  
Linear Programming ◽  
Programming Model ◽  
Academic Staff ◽  
Optimal Solution ◽  
Teaching Quality ◽  
Primary Data ◽  
Allocation Model ◽  
Teaching Load ◽  
The Right ◽  
Head Of Department

Assignment of teaching loads refers to the allocation of teaching hours among academic staff. It will be the ideal way to assign the right courses to the right staff based on their expertise, preference and experience. The common practice in this department to allocate the teaching load is done manually through trial-and-error using Microsoft Excel which is inefficient and time consuming. Moreover, the manual allocation may lead to bias judgement and get unfavourable courses among academic staff. Thus, this study aims to propose a teaching load allocation model which able to optimize the teaching quality. A primary data has been collected using google form among 25 lecturers with 13 courses considered. Then, a linear programming model was applied based on department policies as constraints in order to find an optimal solution. A feasible solution will be solved using LINGO optimization software and the model serves as a best tool to assist head of department to allocate teaching loads. It found that the model proposed is suitable to be employed for teaching load allocation in this department .

An Integer Linear Programming Model for Project Portfolio Selection in a Community

2011 ◽  
Vol 4 ◽  
pp. 67-74
Author(s):  
C.O. Anyaeche ◽  
R.A. Okwara
Keyword(s):  
Linear Programming ◽  
Portfolio Selection ◽  
Integer Linear Programming ◽  
Programming Model ◽  
Project Selection ◽  
Linear Programming Model ◽  
Project Portfolio ◽  
Integer Linear Programming Model ◽  
Total Cost ◽  
The Right

Project portfolio selection involves decision making and it plays a crucial role in any organization. Therefore selecting not just the right projects but also the right mix of projects for the portfolio is considered as one of the most important tasks for organisations to ensure the achievement of the corporate strategy within limited resources and capabilities of the organization. Prioritizing and selecting optimal project portfolio can be very challenging especially with a large number of projects with multiple constraints and interdependences. In an ideal world with unlimited budget the project selection process would be very straightforward. However, this is not the case in life situations. In this work, an attempt is made to address this challenge. An integer linear programming model for project selection was developed and applied in a selected organization in Nigeria. The model seeks to optimize the mix of the projects to be undertaken while keeping the total cost and project interdependency as constraints. The analysis of the results showed that a total of 11 projects out of 16 were eligible for selection in the period under review. The total cost of the selected project was 92,840,000 Naira, which was about 90% of the total budget. Ordinarily, apart from not prioritizing and obtaining an optimal project mix, the community would have spread its entire resources on the 16 projects with some of them being abandoned later. The model can also be used to plan an optimal mix of project portfolio for a future date within the limitations of a given set of constraints and interdependence.

scholarly journals Solving fully fuzzy linear programming problems by controlling the variation range of variables

2021 ◽  
Vol 103 (3) ◽  
pp. 13-24
Author(s):  
S.M. Davoodi ◽  
◽  
N.A. Abdul Rahman ◽  
Keyword(s):  
Linear Programming ◽  
Optimal Solution ◽  
Fuzzy Linear Programming ◽  
Ranking Functions ◽  
Fuzzy Variables ◽  
Decision Variables ◽  
Proposed Model ◽  
Linear Programming Problems ◽  
Left And Right ◽  
The Right

This paper deals with a fully fuzzy linear programming problem (FFLP) in which the coefficients of decision variables, the right-hand coefficients and variables are characterized by fuzzy numbers. A method of obtaining optimal fuzzy solutions is proposed by controlling the left and right sides of the fuzzy variables according to the fuzzy parameters. By using fuzzy controlled solutions, we avoid unexpected answers. Finally, two numerical examples are solved to demonstrate how the proposed model can provide a better optimal solution than that of other methods using several ranking functions.

A Class of Collocating Problem in Production and its Optimization Models

2014 ◽  
Vol 513-517 ◽  
pp. 1215-1220
Author(s):  
Dai Lun Tan ◽  
Hong Xia Chen ◽  
Ze Jian Cui
Keyword(s):  
Linear Programming ◽  
Combinatorial Optimization ◽  
Integer Linear Programming ◽  
Programming Model ◽  
Optimal Solution ◽  
Linear Programming Model ◽  
Optimization Models ◽  
General Description ◽  
Integer Linear Programming Model ◽  
Model Based

The paper gives a general description of a typical combinatorial optimization problem-the collocation problem of production, and respectively establish the integer linear programming model based on the collocation ways and the integer linear programming model based on the optimal collocation amounts and the integer nonlinear programming model based on the local optimum. In the solving methods of the models, we have mainly analyzed the enumeration method and the method by using LINGO optimization software to solve the model. The instance shows that the models and solutions are all effective. The first model reflects the mechanism of the collocation problem better and gets the global optimal solution most likely, but more difficult to solve large-scale; the second model can quickly obtain the optimal the numbers of the finished products and all kinds of materials consumptions, but still need to enumerate the collocation ways step by step; the third model can gets the local optimal solution and the specific collocation ways through solving the model circularly. The optimization models and solution methods in this paper can be extended to the similar sub-problems of the combinatorial optimization problems, such as assembly problem, packing problem, the cutting problem, etc.

Feasibility and Evaluation of Automated Methods for Radiolabeling of Radiopharmaceutical Kits with Gallium-68

2019 ◽  
Vol 12 (3) ◽  
pp. 229-237 ◽  
Author(s):  
Alban Revy ◽  
François Hallouard ◽  
Sandrine Joyeux-Klamber ◽  
Andrea Skanjeti ◽  
Catherine Rioufol ◽  
...  
Keyword(s):  
The European Union ◽  
Preparation Time ◽  
Limit Of Quantification ◽  
Manual Method ◽  
Personnel Costs ◽  
Automated Method ◽  
Gallium 68 ◽  
The Right ◽  
First Time ◽  
Automated Methods

Objective: Recent gallium-68 labeled peptides are of increasing interest in PET imaging in nuclear medicine. Somakit TOC® is a radiopharmaceutical kit registered in the European Union for the preparation of [68Ga]Ga-DOTA-TOC used for the diagnosis of neuroendocrine tumors. Development of a labeling process using a synthesizer is particularly interesting for the quality and reproducibility of the final product although only manual processes are described in the Summary of Product (SmPC) of the registered product. The aim of the present study was therefore to evaluate the feasibility and value of using an automated synthesizer for the preparation of [68Ga]Ga-DOTA-TOC according to the SmPC of the Somakit TOC®. Methods: Three methods of preparation were compared; each followed the SmPC of the Somakit TOC®. Over time, overheads, and overexposure were evaluated for each method. Results: Mean±SD preparation time was 26.2±0.3 minutes for the manual method, 28±0.5 minutes for the semi-automated, and 40.3±0.2 minutes for the automated method. Overcost of the semi-automated method is 0.25€ per preparation for consumables and from 0.58€ to 0.92€ for personnel costs according to the operator (respectively, technician or pharmacist). For the automated method, overcost is 70€ for consumables and from 4.06€ to 6.44€ for personnel. For the manual method, extremity exposure was 0.425mSv for the right finger, and 0.350mSv for the left finger; for both the semi-automated and automated method extremity exposure were below the limit of quantification. Conclusion: The present study reports for the first time both the feasibility of using a [68Ga]- radiopharmaceutical kit with a synthesizer and the limits for the development of a fully automated process.

scholarly journals Data-based polyhedron model for optimization of engineering structures involving uncertainties

2021 ◽  
Vol 2 ◽  
Author(s):  
Zhiping Qiu ◽  
Han Wu ◽  
Isaac Elishakoff ◽  
Dongliang Liu
Keyword(s):  
Linear Programming ◽  
Convex Polyhedron ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Composite Plates ◽  
Convex Polyhedra ◽  
Chebyshev Inequality ◽  
Engineering Structures ◽  
Load Bearing ◽  
Polyhedron Model

Abstract This paper studies the data-based polyhedron model and its application in uncertain linear optimization of engineering structures, especially in the absence of information either on probabilistic properties or about membership functions in the fussy sets-based approach, in which situation it is more appropriate to quantify the uncertainties by convex polyhedra. Firstly, we introduce the uncertainty quantification method of the convex polyhedron approach and the model modification method by Chebyshev inequality. Secondly, the characteristics of the optimal solution of convex polyhedron linear programming are investigated. Then the vertex solution of convex polyhedron linear programming is presented and proven. Next, the application of convex polyhedron linear programming in the static load-bearing capacity problem is introduced. Finally, the effectiveness of the vertex solution is verified by an example of the plane truss bearing problem, and the efficiency is verified by a load-bearing problem of stiffened composite plates.

Computationally Simple and Efficient Method for Solving Real-Life Mixed Intuitionistic Fuzzy 3D Assignment Problems

2022 ◽  
Vol 14 (1) ◽  
pp. 0-0
Keyword(s):  
Assignment Problem ◽  
Graphical Representation ◽  
Real Life ◽  
Optimal Solution ◽  
Future Research ◽  
Assignment Problems ◽  
3 Dimensional ◽  
Intuitionistic Fuzzy ◽  
Comparison Results ◽  
Future Research Directions

This article addresses the 3-dimensional mixed intuitionistic fuzzy assignment problems (3D-MIFAPs). In this article, firstly, the author formulates an assignment problem (AP) and assumes the parameters are in uncertainty with hesitation. Secondly, based on the nature of the parameter the author defines various types of solid assignment problem (SAP) in uncertain environment. Thirdly, to solve 3D-MIFAP the PSK method for finding an optimal solution of fully intuitionistic fuzzy assignment problem (FIFAP) is extended by the author. Fourthly, the author presents the proofs of the proposed theorems and corollary. Fifthly, the proposed approach is illustrated with three numerical examples and the optimal objective value of 3D-MIFAP is obtained in the form of intuitionistic fuzzy number and the solution is checked with MATLAB and their coding are also given by the author. Sixthly, the author presents the comparison results and their graphical representation, merits and demerits of the proposed and existing methods and finally the author presents conclusion and future research directions.

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