SENSITIVITY ANALYSIS OF OBJECTIVE FUNCTION COEFFICIENTS OF THE ASSIGNMENT PROBLEM

2007 ◽  
Vol 24 (02) ◽  
pp. 203-221 ◽  
Author(s):  
CHI-JEN LIN ◽  
UE-PYNG WEN
Keyword(s):  
Sensitivity Analysis ◽  
Assignment Problem ◽  
Optimal Solution ◽  
The Other ◽  
Sensitivity Analyses ◽  
Basic Solution ◽  
Optimal Assignment ◽  
Cost Matrix ◽  
Sensitivity Range ◽  
Optimal Basic Solution

Information of sensitivity analysis, in a linear programming problem, is usually more important than the optimal solution itself. However, traditional sensitivity analysis, which perturbs exactly one coefficient and then determines the range preserving the optimality of the current optimal base, is impractical for the assignment problem. An optimal basic solution of the assignment problem is inherently degenerate, so it may be that the optimal base has changed but the optimal assignment remains unchanged. Furthermore, elements of a column (or row) in a cost matrix of assignment problem are usually closely related and change simultaneously, not uniquely. This paper focuses on two kinds of sensitivity analyses for the assignment problem. One is to determine the sensitivity range, over which the current optimal assignment or all the optimal assignments remain optimal, while perturbing the elements of one column (or row) in a cost matrix of the assignment problem simultaneously but dependently. The other is to perturb elements of one column (or row) in a cost matrix of the assignment problem simultaneously but independently. Numerical illustrations are presented to demonstrate that the approaches are useful in practice.

scholarly journals PENDEKATAN DIAGONAL UNTUK MASALAH PENUGASAN

2019 ◽  
Vol 13 (2) ◽  
pp. 16
Author(s):  
Zahrotun Mu’alifah ◽  
Pardi Affandi ◽  
Akhmad Yusuf
Keyword(s):  
Assignment Problem ◽  
Optimal Solution ◽  
Optimal Assignment ◽  
Transportation Model ◽  
Cost Matrix ◽  
Diagonal Approach ◽  
Optimal Approach ◽  
Different Levels

The assignment problem is a problem related to the optimal assignment of different productive sources that have different levels of efficiency for different tasks. The assignment problem has only one optimization goal, is maximizing or minimizing the resource that use to complete a task. The purpose of this reaserch is to solve the assignment problem with the goal of maximizing or minimizing resource using the steps in the optimal diagonal approach. The steps used in this research with the goal of maximizing resources are looking for two different entries from the assignment cost matrix that has the greatest value of each row and column, whereash the goal of minimizing resource is looking for two different entries from the assignment cost matrix that has value the smallest of each row and column. The results obtained to resolve the assignment problem using an optimal diagonal approach with the goal of maximizing resource, reach the optimal solution if the sum of all diagonal cells is less than zero. While the results to solve the assignment problem with the goal of minimizing resources, reach the optimal solution if the sum of all diagonal cells more than zero. Keywords: Assignment Problem, Transportation Model, Diagonal Optimal Approach

scholarly journals ANALISIS SENSIVITAS MODEL PENUGASAN DENGAN METODE HUNGARIAN

2021 ◽  
Vol 10 (1) ◽  
pp. 41
Author(s):  
ELFRIDA RIANI TSANI ◽  
NI KETUT TARI TASTRAWATI ◽  
KARTIKA SARI
Keyword(s):  
Sensitivity Analysis ◽  
Linear Programming ◽  
Assignment Problem ◽  
Optimal Solution ◽  
Working Time ◽  
Optimal Decision ◽  
Optimal Decisions ◽  
Hungarian Method

In linear programming the assignment problem can be solved by the Hungarian method. This method produces an optimal solution for the placement of employees on their assignments. The purpose of this research is to determine the sensitivity analysis of the optimal results from the assignment that has been obtained by the Hungarian Method. Sensitivity analysis is used to determine the extent to which changes can occur without changing the optimal decisions that have been obtained. The results of this research obtain interval working time that can be tolerated without changing the optimal decision that has been obtained. So, no matter how much working time of the Employee changes, as long as the change is still within the interval, it does not interfere with the optimal solution that has been obtained previously.

scholarly journals Implementation of Modified Best Candidate Method in Fuzzy Assignment Problem

YMER Digital ◽  
2021 ◽  
Vol 20 (11) ◽  
pp. 196-207
Author(s):  
M Maragatham ◽  
◽  
Suzane Raj L ◽  
Keyword(s):  
Assignment Problem ◽  
Fuzzy Numbers ◽  
Optimal Solution ◽  
The Other ◽  
Limited Time ◽  
Assignment Problems ◽  
Trapezoidal Fuzzy Numbers ◽  
Ranking Of Fuzzy Numbers ◽  
Ranking Technique

To meet the demands of every customer by supplying the products at the limited time by maximizing the profit is a dream for many companies. By choosing the best candidate among the other candidates and effectively reaching the optimal solution with a new modified approach using Best Candidate Method in Fuzzy assignment problems. In this paper the author solve Fuzzy assignment problem in which Triangular and Trapezoidal fuzzy numbers are used. Robust Ranking Technique is used for the ranking of fuzzy numbers.

scholarly journals Application Of Hungarian Method In Optimizing The Scheduling Of Employee Assignment And Profit Of Home Industry Production

2019 ◽  
Vol 1 (1) ◽  
pp. 27-37
Author(s):  
Siti Rusdiana ◽  
Rini Oktavia ◽  
Empya Charlie
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Optimal Scheduling ◽  
Total Work ◽  
Optimal Assignment ◽  
Work Time ◽  
Hungarian Method ◽  
Total Work Time

This research has a purpose to optimize the scheduling of employees in an embroidery company for doing certain tasks using Hungarian method, as well as analyzing the sensitivity of the optimal solution if there is a reduction on the employees’ time to finish the tasks. The Hungarian method was applied on the assignment of workers in embroidery process involving 11 employees and 10 tasks. The optimal scheduling result minimizes the time of the embroidery production of the company. The optimal scheduling result found the optimal assignment of each worker to the tasks with the total work time is 13,7 hours. After the Hungarian method was applied, the company got the increasing revenue as much as 9,09 %. The sensitivity analysis was conducted by reducing the time of the employees take in embroidery the bags. The results of the sensitivity analysis are some boundaries for basis and non basis variables to maintain the optimal solution.

Aplikasi Metode Hungarian Dalam Optimalisasi Waktu Penugasan Karyawan dan Keuntungan Produksi Home Industry

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Empya Charlie ◽  
Siti Rusdiana ◽  
Rini Oktavia
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Optimal Scheduling ◽  
Total Work ◽  
Work Time ◽  
Hungarian Method ◽  
Total Work Time

Penelitian ini bertujuan untuk mengoptimalkan penjadwalan karyawan di CV. Karya Indah Bordir dalam melakukan tugas-tugas tertentu menggunakan metode Hungaria, serta menganalisis sensitivitas solusi optimal jika ada pengurangan waktu karyawan untuk menyelesaikan tugas-tugas. Metode Hongaria diterapkan pada proses bordir yang melibatkan 11 karyawan dan 10 tugas. Hasil penjadwalan yang optimal meminimalkan waktu produksi bordir perusahaan. Hasil penjadwalan optimal yang ditemukan adalah: karyawan 1 mengerjakan tas Mambo, karyawan 2 mengerjakan tas Elli, karyawan 3 mengerjakan tas Lonjong, karyawan 4 mengerjakan tas Tampang bunga, karyawan 6 mengerjakan tas Ransel, karyawan 7 mengerjakan tas Tima, karyawan 8 mengerjakan tas Keong, karyawan 9 mengerjakan tas Alexa, karyawan 10 mengerjakan tas Luna, dan karyawan 11 mengerjakan tas Mikha, dengan total waktu kerja adalah 13,7 jam. Setelah metode Hongaria diterapkan, CV. Karya Indah Bordir mendapat peningkatan pendapatan sebanyak 9,09%. Analisis sensitivitas dilakukan dengan mengurangi waktu karyawan dalam menyulam tas. Hasil analisis sensitivitas adalah beberapa batasan untuk variabel basis dan non basis untuk mempertahankan solusi optimal.   This research has a purpose to optimize the scheduling of employees in CV. Karya Indah Bordir in doing certain tasks using Hungarian method, as well as analyzing the sensitivity of the optimal solution if there is a reduction on the employees time to finish the tasks. The Hungarian method was applied on the embroidery process involving 11 employees and 10 tasks. The optimal scheduling result minimize the time of the embroidery production of the company. The optimal scheduling result found is: employee 1 does the Mambo bag, employee 2 does the Elli bag, employee 3 does the Lonjong bag, employee 4 does the Tampang bunga bag, employee 6 does the Ransel, employee 7 does the Tima bag, employee 8 does the Keong bag, employee 9 does the Alexa bag, employees 10 does the Luna bag, and employee 11 does the Mikha bag, with the total work time is 13,7 hours. After the Hungarian method was applied, CV. Karya Indah Bordir got the increasing revenue as much as 9,09 %. The sensitivity analysis was conducted by reducing the time of the employees take in embroidery the bags. The results of the sensitivity analysis are some boundaries for basis and non basis variables to maintain the optimal solution. 

A new algorithm for finding CRM-model coefficients

2019 ◽  
Vol 5 (3) ◽  
pp. 164-185 ◽  
Author(s):  
Alexander D. Bekman ◽  
Sergey V. Stepanov ◽  
Alexander A. Ruchkin ◽  
Dmitry V. Zelenin
Keyword(s):  
Approximate Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Complex Form ◽  
Approximate Solutions ◽  
The Other ◽  
Programming Algorithm ◽  
Stochastic Algorithms ◽  
Large Set ◽  
Flow Rates

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example&nbsp;— the ambiguity of the solution as the result of data inaccuracy.<br> The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

scholarly journals IMMU-04. IMMUNE-RELATED ADVERSE EVENTS STRONGLY PREDICT SUPERIOR OUTCOMES IN BRAIN METASTASES PATIENTS RECEIVING LOCAL TREATMENT AND IMMUNE CHECKPOINT INHIBITORS

2020 ◽  
Vol 22 (Supplement_2) ◽  
pp. ii105-ii105
Author(s):  
Alexander Hulsbergen ◽  
Asad Lak ◽  
Yu Tung Lo ◽  
Nayan Lamba ◽  
Steven Nagtegaal ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Adverse Events ◽  
Brain Metastases ◽  
Immune Checkpoint ◽  
Immune Checkpoint Inhibitors ◽  
Checkpoint Inhibitors ◽  
Local Treatment ◽  
Sensitivity Analyses ◽  
Immortal Time Bias ◽  
The Brain

Abstract INTRODUCTION In several cancers treated with immune checkpoint inhibitors (ICIs), a remarkable association between the occurrence of immune-related adverse events (irAEs) and superior oncological outcomes has been reported. This effect has hitherto not been reported in the brain. This study aimed to investigate the relation between irAEs and outcomes in brain metastases (BM) patients treated with both local treatment to the brain (LT; i.e. surgery and/or radiation) and ICIs. METHODS This study is a retrospective cohort analysis of patients treated for non-small cell lung cancer (NSCLC) BMs in a tertiary institution in Boston, MA. Outcomes of interest were overall survival (OS) and intracranial progression-free survival (IC-PFS), measured from the time of LT. Sensitivity analyses were performed to account for immortal time bias (i.e., patients who live longer receive more cycles of ICIs and thus have more opportunity to develop an irAE). RESULTS A total of 184 patients were included; 62 (33.7%) were treated with neurosurgical resection and 122 (66.3%) with upfront brain radiation. irAEs occurred in 62 patients (33.7%). After adjusting for lung-Graded Prognostic Assessment, type of LT, type of ICI, newly diagnosed vs. recurrent BM, BM size and number, targetable mutations, and smoking status, irAEs were strongly associated with better OS (HR 0.33, 95% CI 0.19 – 0.58, p &lt; 0.0001) and IC-PFS (HR 0.41; 95% CI 0.26 – 0.65; p = 0.0001). Landmark analysis including only patients who received more than 3 cycles of ICI (n = 133) demonstrated similar results for OS and IC-PFS, as did sensitivity analysis adjusting for the number of cycles administered (HR range 0.36 – 0.51, all p-values &lt; 0.02). CONCLUSIONS After adjusting for known prognostic factors, irAEs strongly predict superior outcomes after LT in NSCLC BM patients. Sensitivity analysis suggests that this is unlikely due to immortal time bias.

Optimal tuned direct adaptive controller for seismic protecting of structures

2021 ◽  
pp. 1045389X2098878
Author(s):  
Amin Hosseini ◽  
Touraj Taghikhany ◽  
Milad Jahangiri
Keyword(s):  
Sensitivity Analysis ◽  
Adaptive Control ◽  
Optimization Problem ◽  
Adaptive Controller ◽  
Sensitivity Analyses ◽  
Building Structures ◽  
Building Structure ◽  
The Past ◽  
Innovative Method ◽  
Story Building

In the past few years, many studies have proved the efficiency of Simple Adaptive Control (SAC) in mitigating earthquakes’ damages to building structures. Nevertheless, the weighting matrices of this controller should be selected after a large number of sensitivity analyses. This step is time-consuming and it will not necessarily yield a controller with optimum performance. In the current study, an innovative method is introduced to tuning the SAC’s weighting matrices, which dispenses with excessive sensitivity analysis. In this regard, we try to define an optimization problem using intelligent evolutionary algorithm and utilized control indices in an objective function. The efficiency of the introduced method is investigated in 6-story building structure equipped with magnetorheological dampers under different seismic actions with and without uncertainty in the model of the proposed structure. The results indicate that the controller designed by the introduced method has a desirable performance under different conditions of uncertainty in the model. Furthermore, it improves the seismic performance of structure as compared to controllers designed through sensitivity analysis.

Ixazomib (IXA), carfilzomib (CAR), elotuzumab (ELO) or daratumumab (DAR) with lenalidomide and dexamethasone (LEN+DEX) versus LEN+DEX only in relapsed/refractory multiple myeloma (R/R MM): A comparative cost-effectiveness analysis.

2021 ◽  
Vol 39 (15_suppl) ◽  
pp. 8043-8043
Author(s):  
Mavis Obeng-Kusi ◽  
Daniel Arku ◽  
Neda Alrawashdh ◽  
Briana Choi ◽  
Nimer S. Alkhatib ◽  
...  
Keyword(s):  
Cost Effectiveness ◽  
Cost Effective ◽  
Cost Utility ◽  
Cost Effectiveness Analysis ◽  
The Other ◽  
Sensitivity Analyses ◽  
Treatment Comparison ◽  
Comparative Cost ◽  
Effectiveness Analysis ◽  
Life Years

8043 Background: IXA, CAR, ELO and DARin combination with LEN+DEXhave been found superior in efficacy compared to LEN+DEX in the management of R/R MM. Applying indirect treatment comparisons from a network meta-analysis (NMA), this economic evaluation aimed to estimate the comparative cost-effectiveness and cost-utility of these four triplet regimens in terms of progression-free survival (PFS). Methods: In the absence of direct treatment comparison from a single clinical trial, NMA was used to indirectly estimate the comparative PFS benefit of each regimen. A 2-state Markov model simulating the health outcomes and costs was used to evaluate PFS life years (LY) and quality-adjusted life years (QALY) with the triplet regimens over LEN+DEX and expressed as the incremental cost-effectiveness (ICER) and cost-utility ratios (ICUR). Probability sensitivity analyses were conducted to assess the influence of parameter uncertainty on the model. Results: The NMA revealed that DAR+LEN+DEX was superior to the other triplet therapies, which did not differ statistically amongst them. As detailed in the Table, in our cost-effectiveness analysis, all 4 triplet regimens were associated with increased PFSLY and PFSQALY gained (g) over LEN+DEX at an additional cost. DAR+LEN+DEX emerged the most cost-effective with ICER and ICUR of $667,652/PFSLYg and $813,322/PFSQALYg, respectively. The highest probability of cost-effectiveness occurred at a willingness-to-pay threshold of $1,040,000/QALYg. Conclusions: Our economic analysis shows that all the triplet regimens were more expensive than LEN +DEX only but were also more effective with respect to PFSLY and PFSQALY gained. Relative to the other regimens, the daratumumab regimen was the most cost-effective.[Table: see text]

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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