This document describes an optimization problem involving the production of three types of overalls (work overalls, pilot overalls, competitor overalls) by a factory to maximize profits. The problem is modeled using linear programming with production quantities as decision variables and machine hours in three departments (marking, cutting, sewing) as constraints. The optimal solution is found to be producing 9 units of pilot overalls for a maximum profit of $2070. Sensitivity analysis shows the optimal solution remains unchanged within certain ranges when production or profit parameters are varied.
I am Enamul Haque, presented this paper for the course: CS885 Spring 2020 offered by Prof. Pascal Poupart.
https://cs.uwaterloo.ca/~ppoupart/teaching/cs885-spring20/schedule.html
The link to the paper: https://arxiv.org/pdf/1808.03196.pdf
Hansraj sir sharing SSC-CGL Mains Test Paper With Solutions. Which will helps you in Maths SSC-CGL and Others Maths Classes for Common Competitive Preparation Test Series.
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I am Enamul Haque, presented this paper for the course: CS885 Spring 2020 offered by Prof. Pascal Poupart.
https://cs.uwaterloo.ca/~ppoupart/teaching/cs885-spring20/schedule.html
The link to the paper: https://arxiv.org/pdf/1808.03196.pdf
Hansraj sir sharing SSC-CGL Mains Test Paper With Solutions. Which will helps you in Maths SSC-CGL and Others Maths Classes for Common Competitive Preparation Test Series.
Get update with all Govt. Exams visit at sschansrajacademy.com
This PowerPoint was created to help out graduating seniors who are taking the TAKS Mathematics Exit-Level test. It includes formulas, rules & things that they need to remember to pass the test.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
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Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
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Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
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When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
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using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
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Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
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Optimización de recursos en la confección de overoles
1. UNIVERSIDAD AUTÓNOMA
“GABRIEL RENE MORENO”
FACULTAD DE TECNOLOGIA Y CIENCIAS EXACTAS
OPTIMIZACION DE RECURSOS EN LA
CONFECCION DE OVEROLES
INTEGRANTES :
ANTONIO CHOQUE ALEJO
CLAUDIA GABRIELA MAMANI MAMANI
MARIA DEL CARMEN MONTAÑO TORRICO
SHIRLEY ROELLY QUIROZ ARTEAGA
ROSSMERY ZARATE AGUILAR
MATERIA : INVESTIGACION DE OPERACIONES I
DOCENTE : JHONNY CASTRO MARISCAL
FECHA : 16/12/2017
Santa Cruz – Bolivia
2. “OPTIMIZACION DE RECURSOS EN LA CONFECCION DE
OVEROLES”
OBJETIVO GENERAL
Nuestro principal objetivo es aplicar los conocimientos obtenidos en la materia de
investigación operativa para poder solucionar problemas reales ya sea
maximizando ganancias o minimizar costos.
OBJETIVOS ESPECIFICOS
Obtener la maximización de ganancias de un problema real mediante la
programación lineal hallando la solución óptima.
Realizar un correcto análisis de post-optimalidad del problema.
Analizar las variaciones las contribuciones económicas unitarias de las
variables de decisión para mantener óptima la solución del problema y si se
puede aumentar ganancias.
Analizar los cambios en los requerimientos unitarios del problema para
verificar si la solución permanece siendo óptima.
Interpretar los resultados de las variaciones realizadas en los recursos
disponibles.
PLANEAMIENTO DEL PROBLEMA
Incolit es una industria que tiene suscrito un contrato en la provisión de overoles
hacia distintas empresas, con el fin de maximizar sus ganancias y satisfacer la
demanda de los clientes.
Para ello la empresa tiene 3 tipos de overoles:
Overol de trabajo
3. Overol de piloto
Overol de competidor
Para elaborar los overoles se requiere necesariamente que pase por tres
departamentos:
Marcado: Se encarga de diseñar los diferentes modelos de overoles.
Cortado: Es el cual se encarga de cortar el diseño.
Costura: Realiza la costura de los overoles.
TABLA DE REQUERIMIENTOS
Departamentos
Overoles Disponibilidad
Hrs-maq/mes
Trabajador Piloto Competidor
Marcado 1 1 12 40
Cortado 1 2 2 60
Costura 12 12 30 108
La ganancia unitaria es de bs 150, bs 230 y bs 350 respectivamente por unidad, la
industria desea elaborar un plan de producción para maximizar sus ganancias.
1er
PASO. Identificar las variables de decisión
X1 = cantidad de unidades de overoles tipo trabajador
X2 = cantidad de unidades de overoles tipo piloto
X3 = cantidad de unidades de overoles tipo competidor
2do
PASO. Identificar la función objetivo
4. Max (z) = 150x1+230x2+350x3
3er
PASO. Identificar las restricciones del problema
Departamento de marcado: x1+x2+12x3 ≤ 40
Departamento de cortado: x1+x2+2x3 ≤ 60
Departamento de costura: 12x1+12x2+30x3 ≤ 108
4to
PASO. Transformar las restricciones de desigualdades en igualdades
x1+x2+12x3 +h1 = 40
x1+x2+2x3 +h2 = 60
12x1+12x2+30x3 + h3 = 108
5to
PASO. Replantear la función objetivo
Max (z) = 150x1+230x2+350x3+0h1+0h2+0h3
Z= 0
Z - 150x1 - 230x2 - 350x3
5. 4to
PASO. Hallar la solución optima
Utilizamos el método simplex tabular simplificado
Mezcla X1 X2 X3 H1 H2 H3 solución
z -150 -230 -350 0 0 0 0
vs→H1 1 1 12 1 0 0 40
H2 1 1 2 0 1 0 60
H3 12 12 30 0 0 1 108
z -725/6 -1205/6 0 175/6 0 0 3500/3
X3 1/12 1/12 1 1/12 0 0 10/3
H2 5/6 5/6 0 -1/6 1 0 160/3
H3 19/2 19/2 0 -5/2 0 1 8
z 80 0 0 -450/19 0 1205/57 25380/19
X3 0 0 1 2/19 0 -1/114 62/19
H2 0 0 0 1/19 1 -5/57 1000/19
X2 1 1 0 -5/19 0 2/19 16/19
z 80 0 225 0 0 115/6 2070
H1 0 0 19/2 1 0 -1/12 31
H2 0 0 -1/2 0 1 -1/12 51
X2 1 1 5/2 0 0 1/12 9
DECISION
La industria de confecciones deberá producir 9 unidades de overoles tipo piloto y
ninguna unidad de overoles tipo trabajador y competidor para obtener una
ganancia de bs 2070.
Existe 31 horas maquinas en el departamento de marcado y 51 horas-maquinas
en el departamento de cortado.
6. Análisis De Recursos
DEPARTAMENTO
DE
FABRICACION
RECURSOS
DISPONIBLES
bi
RECURSOS
SOBRANTES
SITUACION
DEL
RECURSO
Marcado 40 b1 31 ABUNDANTE
Cortado 60 b2 51 ABUNDANTE
Costura 108 B3 0 ESCASO
1.- Si se quiere aumentar las ganancias, ¿en qué área de la fábrica se debe
incrementar recursos ?¿en cuánto? ¿Cuál es la nueva solución?
R.- Se debe incrementar recurso en el departamento de costura, porque tiene
mayor precio sombra, habrá mayores ganancias.
B-1
( b3+ ) ≥ 0
[ ] [ ] ≥ 0
1(40) + 0(60) - 1/12(108 + ) ≥ 0
40 + 10 – 9 -1/12 ≥ 0 (-1)
≥ 372
(0)(40) +1(60) -1/12 (108 + ) ≥ 0
0 + 60 - 9 - 1/12 ≥ 0
0(40) + 60(0) + 1/12 (108 + ≥ 0
7. Análisis de intervalo
-108 ≤ ≤ 372
-108 + 108 ≤ b3 ≤ 372 + 108
0 ≤ b3 ≤ 480
Como se quiere aumentar ganancias entonces elegimos el mayor valor
b3 = 480
xb = B-1
×b = [ ] ×[ ]
xb = [ ]
z = [ 0 0 230 ] [ ] = $US 9200
0
0
612
372
0
h1
h2
x2
8. DECISION: La nueva orden será:
X1 = 0 trajes de overoles tipo trabajador
X2 = 90 trajes de overoles tipo piloto
X3 = 0 trajes de overoles tipo competidor
H1 = 0 no existe recursos sobrantes
H2 = 20 hrs. – maq en el departamento de cortado
H3 = 0 no existe recursos sobrantes
Max (z) = $US. 9200
2.- ¿entre que valores puede variar la ganancia de los overoles tipo piloto?
X2 = cantidad de overoles tipo piloto
C2 =$230 →C2 =?
f.o.→max(z) = 150x1+230x2+350x3 *(-1)
Min (z) →max (-z)
f.o.→min (-z)=-150x1 -230x2-350x3
Identificar CB
Cb = [0 0 230]
Ĉb = [0 0 (-230 + λ)]
CB = ĈB – CB = [0 0 λ ]
Luego se hace el análisis de intervalos para las variables .NO BASICAS
Para X1 →C1 - CB 1 ≥ 0
11. -C2 = -230 + (d + 0) -C2 = -230 + ( )
-C2 = -230 + d - C2 = -230 +
-C2 = -230 +d *(1) - C2 = - – d *(1)
C2 = 230 – d - C2 = - + d
C2 + d = 230 C2 – d =
C2 ≤ 230 C2 ≥
$150 ≤ C2 ≤ $ 230
Z= CB. XB
XB = B – B = [ ] . [ ] [ ]
Z max (z) [ ] * [ ] = $us 2070
Z min = [ ] [ ] = $us 1350
Decisión: la ganancia de los overoles tipo piloto puede variar entre $ hasta
$230.
Con una ganancia máxima de $us 2070 y una ganancia mínima de $us 1350
12. 3.- Si la ganancia unitaria del overol tipo piloto se modifica a $ 400 y los,
requerimientos unitarios de hora por cada unidad de overol cambia a 15, 8,
20 ¿Cambia el conjunto solución? ¿es óptima la solución?
Antiguos parámetros Nuevos parámetros
C2 = 230 C2 = 400
a12 = 1 a12 = 15
a22 = 1 a22 = 8
a32 = 12 a32 = 20
Zj = [ ] [ ] - [ ]
Zj = 115/3 – 400
Zj = - cambia la solución
A*j= B-1
. Aj = [ ] [ ]
[ ]
Nueva Tabla Simplex
Mezcla X1 X2 X3 h1 h2 h3 Solución
Z 80 -50/3 225 0 0 115/6 2070
h1 0 40/3 19/2 1 0 -1/12 31
h2 0 19/3 -1/2 0 1 -1/12 51
X2 1 5/3 5/2 0 0 1/12 9
Z 90 0 250 0 0 20 2160
h1 -8 0 -21/2 1 0 -2/5 -41
h2 -19/5 0 -10 0 1 -49/60 84/5
X2 3/5 1 3/2 0 0 1/20 27/5
Luego h1 = -41 hrs – maq. IMPOSIBLE
Significa que no es conveniente realizar los cambios a los parámetros de la
variable X2, por que la solución es infactible.
13. 4.- si la contribución unitaria de los overoles cambia a C1 = y a1 = 10 ; a3 = 20
¿Cambia el conjunto solución? ¿La nueva solución es óptimo?
Solución Primala Solución Dual
X1 = 0 Y1 = 0
X2 = 9 Y2 = 0
X3 = 0 Y3 = 115/6
h1 = 31 (Z1 – C1) = 80
h2 = 51 (Z2 – C1) = 0
h3 = 0 (Z3 – C3) = 225
De la solución Dual
10 Y1 + 3 Y2 + 20 Y3 ≥ 250
10(0) + 3 (0) + 20 ( ) ≥ 250
≥ 250
383,33 ≥ 250
La desigualdad se cumple
La solución final no cambiaria
14. CONCLUCIONES
Mediante este proyecto pudimos poner en la practica la aplicación de la
programación lineal en caso de la vida real, pudiendo así determinar en cuanto
pueden variar los parámetros de los recursos y la disponibilidad que estos pueden
tener sin afectar la solución óptima del problema.
Si se quiere obtener la mayor ganancia se deberá incrementar en el área de
marcado, (mayor precio sombra) hasta 115/6 horas/mes y obtener una
ganancia máxima de $us 9200
La contribución económica de los overoles tipo piloto puede variar desde un
mínimo de $us 3720/19 hasta $460 sin afectar la solución optima.
Si realizamos cambio a los parámetros de los overoles de pilotos y
aumentamos su ganancia a $us 400 la solución final dejaría de ser factible,
por lo tanto no es conveniente hacer cambios.
Si cambiamos los parámetros de los overoles de trabajo como se observa
en el numero 4 la solución no cambiaría y seguiría siendo óptima.