Entropy Maximization and Geometric Programming

1977 ◽  
Vol 9 (4) ◽  
pp. 419-427 ◽  
Author(s):  
J J Dinkel ◽  
G A Kochenberger ◽  
S-N Wong
Keyword(s):  
Sensitivity Analysis ◽  
Convex Function ◽  
Geometric Programming ◽  
Optimal Solution ◽  
Entropy Model ◽  
Entropy Maximization ◽  
Geometric Programs ◽  
Geometric Program

This paper shows the equivalence of entropy-maximization models to geometric programs. As a result we derive a dual geometric program which consists of the minimization of an unconstrained convex function. We develop the necessary duality equivalencies between the two dual programs and show the computational attractiveness of our approach. We also develop some characterizations of the optimal solution of the entropy model which have important implications with regard to postoptimal or sensitivity analysis.

Sensitivity Analysis of Regional Planning Models

1977 ◽  
Vol 9 (1) ◽  
pp. 85-98 ◽  
Author(s):  
J J Dinkel ◽  
G A Kochenberger ◽  
S-N Wong
Keyword(s):  
Sensitivity Analysis ◽  
Nonlinear Programming ◽  
Regional Planning ◽  
Geometric Programming ◽  
Optimal Solution ◽  
Point Of View ◽  
Model Parameters ◽  
Entropy Maximization ◽  
Planning Models ◽  
Recent Developments

This paper exploits recent developments in sensitivity (postoptimal) analysis in nonlinear programming and applies them to regional planning models. In particular the geometric programming point of view is used to develop sensitivity analysis procedures for entropy-maximization and accessibility models. As a result of these developments, we analyze changes in the model parameters with respect to changes in the optimal solution without resolving the model. Several examples are used to illustrate the basic procedures and some error reducing refinements.

scholarly journals Entropy based transportation model: A geometric programming approach

2007 ◽  
Vol 17 (1) ◽  
pp. 43-54 ◽  
Author(s):  
Bablu Samanta ◽  
Kumar Majumder
Keyword(s):  
Regional Planning ◽  
Geometric Programming ◽  
Good Deal ◽  
Programming Approach ◽  
Transportation Model ◽  
Entropy Model ◽  
Entropy Maximization ◽  
Urban And Regional Planning ◽  
Mathematical Programs ◽  
Geometric Programs

The entropy model has attached a good deal of attention in transportation analysis, urban and regional planning as well as in other areas. This paper shows the equivalence of entropy maximization models to geometric programs. To provide a better understanding of this entropy based transportation model they are analyzed by geometric programming. Dual mathematical programs and algorithms are also obtained and are supported by an illustrative example. .

Resizing: Predicting a New Geometric Programming Optimum as Coefficients Vary

1984 ◽  
Vol 106 (1) ◽  
pp. 11-16
Author(s):  
D. J. Wilde
Keyword(s):  
Design Problem ◽  
Geometric Programming ◽  
Optimal Solution ◽  
Matrix Equations ◽  
Dual Variable ◽  
Method Of Least Squares ◽  
Satisfactory Solution ◽  
Geometric Program ◽  
The Matrix ◽  
Dual Variables

Imagine that an optimal solution is available for a constrained geometric program, and suppose one wishes a satisfactory solution for greatly different values of some of the coefficients. An estimate can be constructed by using the values of the dual variables for the old optimum in the invariance conditions for the new problem. Although these are inconsistent except at the precise optimum, a unique primal solution can easily be generated from them by the method of least squares with individual equations weighted by the value of the corresponding dual variable. The matrix equations for these linear operations are derived and applied to a well-known merchant fleet design problem. The predictions are remarkably accurate—1.4 percent error for a 100 percent coefficient change.

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 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 Sensitivity Analysis of Road Freight Transportation of a Mega Non-Alcoholic Beverage Industry

2020 ◽  
Vol 24 (3) ◽  
pp. 449-454
Author(s):  
T. Latunde ◽  
J.O. Richard ◽  
O.O. Esan ◽  
O.O. Dare
Keyword(s):  
Sensitivity Analysis ◽  
Alcoholic Beverage ◽  
Optimal Solution ◽  
Transportation Cost ◽  
Demand And Supply ◽  
North West ◽  
The North ◽  
Beverage Industry ◽  
Road Freight ◽  
Road Freight Transportation

Re-optimization can be very costly for gathering and obtaining more data for a particular problem, to curb this very expensive investment.  Sensitivity analysis has been used in this work to determine the behaviour of input parameters of the formulated problem. The main goal of the study is to respectively provide, derive, observe, compare and discuss the sensitivity analysis of data that has been optimized using different methods of the optimal solution. The best method, saving the highest percentage of transportation cost, for the formulated problem is determined to be the North-West Corner method. This was carried out by arbitrarily assigning values to the available warehouses to determine the best possible demand and supply cases rather than the initial cases. Thus, more cases are advised to be supplied to FID from the Asejire plant for the optimum reduced value of transportation cost. Keywords: Sensitivity, Parameters, Transportation Problem.

scholarly journals Generalized Differentiable -Invex Functions and Their Applications in Optimization

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
S. Jaiswal ◽  
G. Panda
Keyword(s):  
Convex Function ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Invex Functions ◽  
General Optimization Problem

The concept of -convex function and its generalizations is studied with differentiability assumption. Generalized differentiable -convexity and generalized differentiable -invexity are used to derive the existence of optimal solution of a general optimization problem.

scholarly journals EPQ Model for Trended Demand with Rework and Random Preventive Machine Time

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Nita H. Shah ◽  
Dushyantkumar G. Patel ◽  
Digeshkumar B. Shah
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Rate Of Change ◽  
Machine Time ◽  
Economic Production Quantity ◽  
Economic Production ◽  
Model Search ◽  
Demand Rate ◽  
Epq Model ◽  
Production Quantity

Economic production quantity (EPQ) inventory model for trended demand has been analyzed with rework facility and stochastic preventive machine time. Due to the complexity of the model, search method is proposed to determine the best optimal solution. A numerical example and sensitivity analysis are carried out to validate the proposed model. From the sensitivity analysis, it is observed that the rate of change of demand has significant impact on the optimal inventory cost. The model is very sensitive to the production and demand rate.

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