This presentation is made to represent the basic transportation model. The aim of this presentation is to implement the transportation model in solving transportation problem.
The transportation problem is a special type of linear programming problem where the objective is to minimize the cost of distributing a product from a number of sources or origins to a number of destinations.
Because of its special structure, the usual simplex method is not suitable for solving transportation problems. These problems require a special method of solution.
This presentation is made to represent the basic transportation model. The aim of this presentation is to implement the transportation model in solving transportation problem.
The transportation problem is a special type of linear programming problem where the objective is to minimize the cost of distributing a product from a number of sources or origins to a number of destinations.
Because of its special structure, the usual simplex method is not suitable for solving transportation problems. These problems require a special method of solution.
The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized.
This is a special type of LPP in which the objective function is to find the optimum allocation of a number of tasks (jobs) to an equal number of facilities (persons). Here we make the assumption that each person can perform each job but with varying degree of efficiency. For example, a departmental head may have 4 persons available for assignment and 4 jobs to fill. Then his interest is to find the best assignment which will be in the best interest of the department.
What is Transportation model?
deals with a special class of linear programming problem in which the objective is to transport a homogenous commodity from various origins or factories to different destinations or markets at a total minimum cost.
Concept - addresses the concept of moving a thing from one place to another, without change
- used to analyze transportation systems and find the most efficient route
This presentation is trying to explain the Linear Programming in operations research. There is a software called "Gipels" available on the internet which easily solves the LPP Problems along with the transportation problems. This presentation is co-developed with Sankeerth P & Aakansha Bajpai.
By:-
Aniruddh Tiwari
Linkedin :- http://in.linkedin.com/in/aniruddhtiwari
The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized.
This is a special type of LPP in which the objective function is to find the optimum allocation of a number of tasks (jobs) to an equal number of facilities (persons). Here we make the assumption that each person can perform each job but with varying degree of efficiency. For example, a departmental head may have 4 persons available for assignment and 4 jobs to fill. Then his interest is to find the best assignment which will be in the best interest of the department.
What is Transportation model?
deals with a special class of linear programming problem in which the objective is to transport a homogenous commodity from various origins or factories to different destinations or markets at a total minimum cost.
Concept - addresses the concept of moving a thing from one place to another, without change
- used to analyze transportation systems and find the most efficient route
This presentation is trying to explain the Linear Programming in operations research. There is a software called "Gipels" available on the internet which easily solves the LPP Problems along with the transportation problems. This presentation is co-developed with Sankeerth P & Aakansha Bajpai.
By:-
Aniruddh Tiwari
Linkedin :- http://in.linkedin.com/in/aniruddhtiwari
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
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.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
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.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
2. Outline
• Introduction
• Solution Procedure for Transportation Problem
• Finding an Initial Feasible Solution
• Finding the Optimal Solution
• Special Cases in Transportation Problems
• Maximisation in Transportation Problems
• Exercises
3. The main typical issues in OR :
Formulate the problem
Build a mathematical model
Decision Variable
Objective Function
Constraints
Optimize the model
Operation Research
4. Transportation problem are one of the linear Programming
Problem
The objective is to minimize the cost of distribution a product
from a no of sources or origin to a no of destination in such a
manner to minimize the total transportation cost.
For example
Manufacturer has three plants P1, P2, P3 producing same
products.
From these plants, the product is transported to three
warehouses W1, W2 and W3.
Introduction
5. Each plant has a limited capacity, and each warehouse has
specific demand. Each plant transport to each warehouse, but
transportation cost vary for different combinations.
6. Steps to solve a transportation problem
Formulate the problem and setup in the matrix form.
Obtain the initial basic feasible solution.
Test the solution for optimality.
Updating the solution if required.
For example:
7. Finding an Initial Feasible Solution
There are a number of methods for generating an initial feasible
solution for a transportation problem.
Consider three of the following
(i) North West Corner Method
(ii) Least Cost Method
(iii) Vogel’s Approximation Method
8. North West Corner Method (NWCM)
The simplest of the procedures used to generate an initial feasible
solution is NWCM. It is so called because we begin with the North
West or upper left corner cell of our transportation table. Various
steps are given
Step 1
Select the North West (upper left-hand) corner cell of the
transportation table and allocate as many units as possible equal to
the minimum between available supply and demand requirement
i.e., min (S1, D1).
Step 2
Adjust the supply and demand numbers in the respective rows
And columns allocation.
9. Step 3
(a) If the supply for the first row is exhausted, then move down to
the first cell in t he second row and first column and go to step
2.
(b) If the demand for the first column is satisfied, then move
horizontally to the next cell in the second column and first
row and go to step 2.
If for any cell, supply equals demand, then the next allocation can
be made in cell either in the next row or column.
Step 4
10. Remark 1: The quantities so allocated are circled to indicated,
the value of the corresponding variable.
Remark 2: Empty cells indicate the value of the corresponding
variable as zero, I.e., no unit is shipped to this cell.
Continue the procedure until the total available quantity id fully
allocated to the cells as required.
Step 5
11. To illustrate the NWCM,
As stated in this method, we start with the cell (P1 W1) and Allocate the min (S1,
D1) = min (20,21)=20. Therefore we allocate 20 Units this cell which completely
exhausts the supply of Plant P1 and leaves a balance of (21-20) =1 unit of
demand at warehouse W1
12. The allocation according to this method is very useful as it takes into
consideration the lowest cost and therefore, reduce the computation
as well as the amount of time necessary to arrive at the optimal
solution.
Step 1
(a) Select the cell with the lowest transportation cost among all the rows
or columns of the transportation table.
(b) If the minimum cost is not unique, then select arbitrarily any cell
with this minimum cost.
Step 2
Allocate as many units as possible to the cell determined in Step 1
and eliminate that row (column) in which either supply is exhausted
or demand is satisfied.
Least Cost Method
13. Repeat Steps 1 and 2 for the reduced table until the entire supply at
different plants is exhausted to satisfied the demand at different
warehouses.
14. This method is preferred over the other two methods because the
initial feasible solution obtained is either optimal or very close to the
optimal solution.
Step 1:
Compute a penalty for each row and column in the transportation
table.
Step 2:
Identify the row or column with the largest penalty.
Step 3:
Repeat steps 1 and 2 for the reduced table until entire supply at plants
are exhausted to satisfy the demand as different warehouses.
Vogel’s Approximation Method
(VAM)
15.
16. Once an initial solution has been found, the next step is to test that
solution for optimality. The following two methods are widely used
for testing the solutions:
Stepping Stone Method
Modified Distribution Method
Necessary condition
1. Make sure that the number of occupied cells is exactly equal to m+n-
1, where m=number of rows and n=number of columns.
2. Each occupied cell will be at independent position.
Finding the Optimal Solution
17. In this method we calculate the net cost change that can be obtained
by introducing any of the unoccupied cells into the solution.
Steps
1. Check the optimality test necessary condition
2. Evaluate each unoccupied cells by following its closed path and
determine its net cost change.
3. Determine the quality to be shipped to the selected unoccupied
cell. Trace the closed path for the unoccupied cell and identify
the minimum quality by considering the minus sign in the closed
path.
Stepping-Stone Method
18. The MODI method is a more efficient procedure of evaluating the
unoccupied cells. The modified transportation table of the initial
solution is shown below
Steps
1.Determine the initial basic feasible solution by using any method.
2.Determine the value of dual variable ui , vj by using cij = ui + vj
for occupied cell . Associate a number, ui, with each row and vj
with each column.
3.Compute opportunity cost for unoccupied cell by dij = cij - ui - vj.
Modified Distribution (MODI) Method
19. Contd..
4. Check the sign for each opportunity cost. If the opportunity
cost for each unoccupied cell is positive or zero then the
solution is optimum. Otherwise
5. Select the unoccupied cell with largest negative opportunity
cost draw a close loop.
6. Assign alternative positive and negative sign at corner points
of the closed loop(start from unoccupied cell with positive
sign)
7. Determine the maximum number of units that should be
allocated to this unoccupied cell. This should be added to
cells with positive sign and subtracted from negative sign
8. Repeat procedure till an optimal solution is obtained
20. Multiple Optimal Solutions
Unbalanced Transportation Problems
Degeneracy in Transportation Problem
Maximization In Transport Problems
Special Cases in Transportation Problem
21. Objective function
Model to be optimized
cij = variable cost
xij = number of unit transported from supply point i
to demand j
24. i = number of sources
j = number of demands
Decision variable
Number of millions energy (kWh) produced from sources
and sent to demands
x (i,j) = number of sources
26. x (i,j) > 0 (i = 1,2,3) and j=1,2,3,4)
j = number of demands
Constraints
Constraints of Demands
Constraints of Supply
Constraints of number of Supply and demand
29. Introduction
The Assignment problem deals in allocating the various
items (resources) to various receivers (activities) on a one to one
basis in such a way that the resultant effectiveness is optimised.
Assignment Models
This is a special case of transportation problem. In this
problem, supply in each now represents the availability of a
resource such as man, vehicle, produce, etc.
30. Hungarian Method of Assignment problem
An efficient method for solving an assignment problem, known as
Hungarian method of assignment based on the following properties
1. In an assignment problem, if a constant quantity is added or subtracted
from every element of any row or column in the given cost matrix, an
assignment that minimizes the total cost in the matrix also minimize the
total cost in the other.
2. In an assignment problem, a solution having zero total cost is an
optimum solution. It can be summarized as follows.
Step 1:- In the given matrix, subtract the smallest element in each row
from every element of the row.
Step 2:- Reduced matrix obtained from step1, subtract the smallest
element in each column from every element of that column.
Step 3:- Make the assignment for the reduced matrix obtained from
steps 1 and 2.
Continued ….
31. Step 4:- Draw the minimum number of horizontal and vertical lines to cover all
zeros in the reduced matrix obtained from 3 in the following way.
a) Mark (√) all rows that do not have assignments.
b) Mark (√) all column that have zeros in marked rows (step 4 (a)).
c) Mark (√) all rows that have assignments in marked columns (step 4 (b))
d) Repeat steps 4 (a) to 4 ( c ) until no more rows or columns can be marked.
e) Draw straight lines through all unmarked rows and marked columns.
Step 5:- If the number of lines drawn ( step 4 ( c ) are equal to the number
of columns or rows, then it is an optimal solution, otherwise go to step 6.
Step 6:- Select the smallest elements among all the uncovered elements.
Step 7:- Go to step 3 and repeat the procedure until the number of
assignments become equal to the number of rows or column.
32. Example
A company faced with problem of assigning 5 jobs to 5 machines.
Each job must be done on only machine. The cost of processing is as
shown
33. Solution
Now, select the minimum cost (element) in each row and
subtract this element form each element of that row.
34. Special Cases in Assignment Problems
1. Maximization Cases.
2. Multiple Optimal Solution
1. Maximization Cases :-
The Hungarian method explained earlier can be used for maximization
case. The problem of maximization can be converted into a minimization
case by selecting the largest element among all the element of the profit
matrix and then subtracting it from all the elements of the matrix. We Can
then proceed as usual and obtain the optimal solution by adding original
values to the cells to which assignment have been made.
35. Multiple Optimal Solution:
Sometimes, it is possible to have two or more ways to cross out
all zero elements in the final reduced matrix for a given problem. This
implies that there are more than required number of independent zero
elements. In such cases, there will be multiple optimal solutions with the
same total cost of assignment. In such type of situation, management
may exercise their judgment or preference and select that set of optimal
assignment which is more suited for their requirement.
….
36. Summary
Assignment problem is a special case of
transportation problem. It deals with allocating the various
items to various activities on a one to one basis in such a
way that the resultant effectiveness is optimised. In this
unit, we have solved assignment problem using Hungarian
Method. We have also disscussed the special cases in
assignment problems.