Optimisasi Model Analisa Sensitivitas Primal–Dual dalam Management Produksi Dodol

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Iin Maulina ◽  
Siti Rusdiana ◽  
Rini Oktavia
Keyword(s):  
Sensitivity Analysis ◽  
Objective Function ◽  
Operation Research ◽  
Raw Materials ◽  
Applied Mathematics ◽  
Optimal Solution ◽  
Optimal Level ◽  
Research Problems ◽  
Dual Analysis ◽  
Primal Dual

Optimalisasi adalah cabang matematika terapan yang mempelajari masalah-masalah operasi riset dengan tujuan untuk memaksimalkan atau meminimalkan besaran tertentu. Dalam penelitian ini, kami akan menerapkan konsep optimasi pada mengoptimalkan kegiatan produksi di CV. Sentra Halia Sabang yang merupakan industri rumah tangga yang memproduksi dodol dalam kotak kemasan. Dengan melakukan penelitian tentang kegiatan produksi di CV. Sentra Halia Sabang, ditentukan bahwa fungsi tujuan adalah untuk memaksimalkan keuntungan perusahaan, yang dimodelkan sebagai Z=7537x1+5871x2+7887x3+6151x4+7987x5+6231x6+7909x7+6171x8+8037x9+6271x10+8629x11, di mana xi mewakili jumlah produksi untuk setiap jenis dodol. Selanjutnya, juga ditinjau sumber daya terbatas yang digunakan oleh perusahaan seperti jumlah bahan baku, waktu, maksimum dan batas minimum produksi. Pemrosesan data dilakukan dengan menggunakan perangkat lunak LINDO. Analisis yang digunakan adalah analisis dual primal yang dilanjutkan dengan analisis sensitivitas. Hasil penelitian ini menunjukkan bahwa produksi CV. Sentra Halia Sabang hampir mencapai level optimal. Jika perusahaan berproduksi dalam kondisi optimal, laba yang bisa diperoleh adalah Rp 195.330. Analisis dual primal menunjukkan bahwa ada sumber daya yang belum digunakan secara optimal, yang bisa dilihat dari nilai slack / surplus pada beberapa sumber daya. Dalam analisis sensitivitas, beberapa variasi penambahan pada masing-masing koefisien fungsi tujuan diterapkan. Hasil analisis sensitivitas menunjukkan bahwa penambahan koefisien fungsi tujuan sebesar Rp 150 tidak akan mempengaruhi solusi optimal awal.   Optimization is a part of applied mathematics that studies operation research problems with the aim to maximize or minimize a certain magnitude. In this research, we will apply the optimization concepts on optimizing production activities in CV. Sentra Halia Sabang which is a home industry producing dodol in a packing box. By doing research on production activities at CV. Sentra Halia Sabang, it was determined that the objective function is to maximize the profits of the company, which is modeled as Z=7537x1+5871x2+7887x3+6151x4+7987x5+6231x6+7909x7+6171x8+8037x9+6271x10+8629x11, where xi represents the amount of productions for each type of dodol. Next, it is also reviewed the limited resources used by the company such as the amount of raw materials, the time, the maximum and the minimum limit of production. Data processing is performed using software LINDO. The analyses applied were the primal dual analysis that was continued with the sensitivity analysis. The results of this study indicate that the production of CV. Sentra Halia Sabang almost reached the optimal level. If the company produces in optimal conditions, the profit that can be obtained is Rp 195 430. The primal dual analyses show that there are resources that have not been used optimally, that can be seen from the value of slack / surplus on some resources. In the sensitivity analysis, some various addition on each of the coefficients of the objective function were applied. The result of the sensitivity analysis show that the addition of the coefficients of the objective function as much as Rp 150 will not affect the initial optimal solution.

scholarly journals Optimalisasi Keuntungan pada Usaha Komoditi Bunga Krisan di Kecamatan Cipanas, Kabupaten Cianjur (Optimizing the Profits of Chrysanthemum Commodities in Cipanas, Cianjur)

1970 ◽  
Vol 3 (1) ◽  
pp. 21-26
Author(s):  
Wien Kuntari ◽  
Uding Sastrawan
Keyword(s):  
Sensitivity Analysis ◽  
Optimum Condition ◽  
Environmental Changes ◽  
Raw Materials ◽  
Growing Season ◽  
Land Resources ◽  
Optimal Conditions ◽  
Standard Type ◽  
Use Of Resources ◽  
Dual Analysis

Many farmers are interested in planting chrysanthemums because of its beautiful colors. The allocation of land resources, raw materials, machinery, capital and labor which is now done by farmers, is relatively not able to meet the desired target. It demonstrates that the use of resources is not optimal and it will have an impact on the level of benefits received. The result of the data processing was: the Chrysanthemum production rate, based on the optimization results, illustrated that the recommended type of chrysanthemum to be produced was only the standard type, because it increased the revenue for companies. Company A produced 486.11 bunches of chrysanthemum for Rp 1,701,389 per growing season, company B produced 277.77 bunches for Rp 972,222 per growing season, company C produced 150 bunches for Rp 450,000 per growing season, and company D produced 250 bunches for Rp 750,000 per growing season. The resource or factor of production that was totally applied on the optimum condition was the green house land resources, which is a limiting resource; but other resources was excessive or not a limiting resource. The usage or availability of limiting resource could be improved to increase the profit of the company. The environmental changes can affect the company's revenue, to see how big the changes which didn’t change the optimal conditions were. It was generated by looking at the results of the sensitivity analysis. Sensitivity analysis of the objective coefficient value which was obtained for the standard type of chrysanthemum, the allowed increase in gross profit was infinity, while the allowed decrease in gross profit was when it approached the value of the gross profit.Keyword: chrysanthemum, primal analysis, dual analysis, sensitivity analysis

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. 

scholarly journals An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics

Pharmaceutics ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 42
Author(s):  
Walter M. Yamada ◽  
Michael N. Neely ◽  
Jay Bartroff ◽  
David S. Bayard ◽  
James V. Burke ◽  
...  
Keyword(s):  
Drug Development ◽  
Population Pharmacokinetics ◽  
Empirical Bayes ◽  
Applied Mathematics ◽  
Grid Method ◽  
Bayes Estimation ◽  
Population Pharmacokinetic ◽  
Support Points ◽  
Primal Dual ◽  
Log Normal

Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing.

Structural Analysis and Optimization Design of Motor Hanging Seat Structural Based on Pro/ENGINEER

2013 ◽  
Vol 380-384 ◽  
pp. 39-42
Author(s):  
Shun Xi Gao ◽  
Shu Guo Zhao ◽  
Li Fang Zhao
Keyword(s):  
Structural Analysis ◽  
Objective Function ◽  
Economic Efficiency ◽  
Mass Production ◽  
Optimization Design ◽  
Raw Materials ◽  
Parametric Model ◽  
Production Costs ◽  
Practical Significance ◽  
Displacement Constraints

This paper establishes a parametric model on the motor hanging seat structure by pro / ENGINEER software, and then optimizes the structure of the hanging seat by the weight of the hanging seat as the objective function. Taking into account the stress and displacement constraints in the optimization process, the weight of the hanging seat is greatly reduced after being optimized. It is practical significance to save a large amount of raw materials for the mass production and to reduce production costs and create higher economic efficiency.

scholarly journals An evolutionary-based optimization algorithm for truss sizing design

2016 ◽  
Vol 38 (4) ◽  
pp. 307-317
Author(s):  
Pham Hoang Anh
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
The Other ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Objective Functions

In this paper, the optimal sizing of truss structures is solved using a novel evolutionary-based optimization algorithm. The efficiency of the proposed method lies in the combination of global search and local search, in which the global move is applied for a set of random solutions whereas the local move is performed on the other solutions in the search population. Three truss sizing benchmark problems with discrete variables are used to examine the performance of the proposed algorithm. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress in members and displacement at nodes. Here, the constraints and objective function are treated separately so that both function and constraint evaluations can be saved. The results show that the new algorithm can find optimal solution effectively and it is competitive with some recent metaheuristic algorithms in terms of number of structural analyses required.

scholarly journals Two – Warehouse Inventory System Model for Deteriorating Items Considering Partial Upstream Trade Credit Financing

2021 ◽  
pp. 69-80
Author(s):  
Z. H. Aliyu ◽  
B. Sani
Keyword(s):  
Sensitivity Analysis ◽  
Credit Risk ◽  
Trade Credit ◽  
Optimal Solution ◽  
Inventory System ◽  
System Model ◽  
Credit Period ◽  
Business Transaction ◽  
Credit Financing ◽  
Relevant Cost

In this study, we developed an inventory system model under two – level trade credit where the supplier considers the retailer as credit risk but the retailer considers the customers as credit worthy. Therefore, the retailer is given a trade credit period on  proportion of the goods ordered whenever he/she pays for proportion of the goods immediately after delivery. In the same vein, the retailer passes the same grace to the customers but without attaching any condition as the customers are assumed credit worthy. This partial upstream trade credit is offered to reduce the risk of failure in payment on the business transaction especially that most retailers are involved in bulk orders. The relevant cost functions are determined and a numerical example is given. Sensitivity analysis was carried out to see the effect of changes in parameters on the optimal solution of the model.

scholarly journals Optimasi OPTIMASI BIAYA TRANSPORTASI PADA UKM DI KOTA BATAM

2021 ◽  
Vol 9 (1) ◽  
pp. 1-19
Author(s):  
Welly Sugianto ◽  
Elva Susanti
Keyword(s):  
Sensitivity Analysis ◽  
Objective Function ◽  
Approximation Method ◽  
Minimum Cost ◽  
Transportation Cost ◽  
Product Distribution ◽  
Mathematical Form ◽  
Total Production ◽  
Calculation Results ◽  
Iteration Methods

This research was conducted at UKM Jovelyn in Batam city. Jovelyn's UKM produces various kinds of cakes and is marketed in markets in Batam City. The UKM opened 4 branches and marketed its products to 7 markets in the city of Batam. Product distribution is still random and not properly regulated. This resulted in a very large transportation cost, up to 1/3 of the total production cost. This shows that product transportation is still not carried out effectively and efficiently. The transportation problem is converted into a mathematical form so that the problem can be solved by the transportation method. The transportation method aims to minimize the objective function which is a function of transportation costs. The transportation method is basically the same as the linear program where at each iteration a selection is made to enter the basic variabel and leave the basic variabel. There are several iteration methods, namely the northwest corner method, minimum cost method, genetic algorithm, Vogel's approximation method, minimum row method, Russell's approximation method and column minimum method. Previous research has shown that the Vogel's approximation method, and Russell's approximation method are more efficient and accurate. This study uses both methods and a sensitivity analysis is performed to optimize the calculation results. The sensitivity analysis aims to determine the extent to which the objective function constants and the constraint function constants can change Keywords: Transportation, Sensitivity, SME  

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