Neural Network For Optimization
An artificial neural network is an information or signal processing system composed of a large number of simple processing elements, called artificial neurons or simply nodes, which are interconnected by direct links called connections and which cooperate to perform parallel distributed processing in order to solve a desired computational task. The potential benefits of neural networks extend beyond the high computation rates provided by massive parallelism. The neural network models are specified by the net topology, node characteristics, and training or learning rules. These rules specify an initial set of weights and indicate how weights should be adapted during use to improve performance. Roughly speaking, these computations fall into two categories: natural problems and optimization problems. Natural problems, such as pattern recognition, are typically implemented on a feed-forward neural network. Optimization problems are typically implemented on a feedback network. These networks interconnect the neurons with a feedback path. A typical feedback neural network is the Hopfield neural network [Hop85]. Figure 4 shows the circuit structure of the neuron and its functional structure. This differential equation describes the neuron: [pic] (1)

where [pic](j=1,2..., n), and g( ) is the sigmoid activation function. It is shown in [Hop85] how to choose the values of synapse [pic]so that (1) represents the dynamics corresponding to a given energy function. If the energy function corresponds to an optimization objective, the initialization of the [pic]'s to an initial configuration will result in an equilibration which settles to a local minimum of the objective function. One famous example using the neural networks is the Traveling Salesman Problem (TSP) [Wil88], in which a salesman is supposed to tour a number of cities (visiting each exactly once, then returning to where he started) and desires to minimize the total distance of the...

...Report- Hard Copy
ASSIGNMENT METHOD
The assignmentproblem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics. It consists of finding a maximum weight matching in a weighted bipartite graph.
In its most general form, the problem is as follows:
There are a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. It is required to perform all tasks by assigning exactly one agent to each task in such a way that the total cost of the assignment is minimized.
If the numbers of agents and tasks are equal and the total cost of the assignment for all tasks is equal to the sum of the costs for each agent (or the sum of the costs for each task, which is the same thing in this case), then the problem is called the linear assignmentproblem. Commonly, when speaking of the assignmentproblem without any additional qualification, then the linear assignmentproblem is meant.
Example:
A machine shop currently has three jobs A,B,C to be done on three machines W,X,Y. Any one of the jobs can be processed completely on any one of the machines, and the assignment of jobs to...

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Briefing:
Industrial management is a dynamic field of study, always developing and adapting to the need of the global market.
Industrial management holds solutions for many problems the market offers with many tools, including the 'Hungarian Algorithm'.
The Hungarian method is a combinatorial optimization algorithm which solves the assignmentproblem in polynomial time that's anticipated later primal-dual methods. The algorithm was developed and published by Harold Kuhn in 1955, who gave the name 'Hungarian Method' because the algorithm was largely based on earlier works of two Hungarian mathematicians: Dénes Kőnig and Jenő Egerváry.
A modern industrial engineer needs to cope the ever growing needs of the organization, our times requires him to do it fast and efficient.
We based our work on the 2010 project by: Michal Cohen, Asher Halili, Itay Levi, Guy Bar Sheshet, Bilga Damir and Barak Goldkorn, which developed a Windows-environment solver.
The reason we chose to focus our project on the selected topic is the desire to improve and to provide powerful tools to the everyday industrial engineer.
Today's organizations are more demanding, requiring more outcomes for less time. That is why we chose developing this tool for the 'here and now' industrial engineer.
We accomplished our goal by editing and modifying the source code to mobile phones and tablets based on Android® platform.
A few reasons for...

...CHAPTER 6:
TRANSPORTATION, TRANSSHIPMENT AND ASSIGNMENTPROBLEMS
Transportation Problem
- A distribution-type problem in which supplies of goods that are held at various locations are to be distributed to other receiving locations.
- The solution of a transportation problem will indicate to a manager the quantities and costs of various routes and the resulting minimum cost
- Used to compare location alternatives in deciding where to locate factories and warehouses to achieve the minimum cost distribution configuration
Formulating the model
Transportation
-Typically involves a set of locations which referred to as origins, and a set of receiving locations which referred to as destinations
-To develop a model of transportation problem, following information are needed:
1. Supply quantity (capacity) of each origin
2. Demand quantity of each destination
3. Unit transportation cost for each origin-destination route
Special Cases of Transportation Problems:
Maximization Problems
- A transportation-type problems that concern profits or revenues rather than costs.
-objective to maximize profits rather than to minimize costs.
Unacceptable Routes
-Certain origin-destination combinations may be unacceptable due to weather factors, equipment breakdowns, labor problems, or skill requirements that either prohibit, or make...

...MB0048 –Operations Research- 4 CreditsAssignment Set - 1
Q1. a. What do you mean by linear programming problem? Explain the steps involved in linear programming problem formulation? b. A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper in a week. There are 160 production hours in a week. It requires 0.20 and 0.40 hours to produce a ton of grade X and Y papers. The mill earns a profit of Rs. 200 and Rs. 500 per ton of grade X and Y paper respectively. Formulate this as a Linear Programming Problem.
Q2. a. Discuss the methodology of Operations Research. b. Explain in brief the phases of Operations Research.
Q3. Solve the following Linear Programming Problem using Simple method.
Maximize Z= 3x1 + 2X2
Subject to the constraints:
X1+ X2 4
X1+ X2 2
X1, X2 0
Q4. Explain the procedure of MODI method of finding solution through optimality test.
Q5. a. Explain the steps in Hungarian method. b. Solve the following assignmentproblem.
Machine | Operators |
| 1 | 2 | 3 | 4 |
A | 60 | 50 | 45 | 45 |
B | 40 | 45 | 55 | 35 |
C | 55 | 70 | 60 | 50 |
D | 45 | 45 | 40 | 45 |...

...Special Multi-Objective AssignmentProblem Author(s): D. J. White Source: The Journal of the Operational Research Society, Vol. 35, No. 8 (Aug., 1984), pp. 759767 Published by: Palgrave Macmillan Journals on behalf of the Operational Research Society Stable URL: http://www.jstor.org/stable/2581982 . Accessed: 19/04/2013 03:45
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J. OpI Res. Soc. Vol. 35, No. 8, pp. 759-767, Printed in Great Britain. All rights reserved
1984 Copyright
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A Special Multi-Objective AssignmentProblem
D. J. WHITE
University of...

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...PERFORMANCE EXCELLENCE IN THE WOOD PRODUCTS INDUSTRY
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Transportation Problem: A Special Case for Linear Programming Problems
J. Reeb and S. Leavengood
A
key problem managers face is how to allocate scarce resources among various activities or projects. Linear programming, or LP, is a method of allocating resources in an optimal way. It is one of the most widely used operations research tools and has been a decisionmaking aid in almost all manufacturing perations research (OR) is concerned industries and in financial and service with scientifically deciding how to best organizations. design and operate people–machine systems, In the term linear programming, usually under conditions requiring the programming refers to mathematical proallocation of scarce resources.1 gramming. In this context, it refers to a This publication, one of a series, is planning process that allocates resources— offered to supervisors, lead people, middle labor, materials, machines, capital—in the managers, and anyone who has responsibility best possible (optimal) way so that costs are for operations planning in manufacturing minimized or profits are maximized. In LP, facilities or corporate planning over multiple these resources are known as decision facilities. Practical examples are geared to variables. The criterion for selecting the the wood products industry, although best values of the decision variables (e.g.,...

...ACC 290 Week 2 Individual WileyPLUS AssignmentProblem 3-5A
Sunflower Architects incorporated as licensed architects on April 1, 2010. During the first month of the operation of the business, these events and transactions occurred:
April 1
Stockholders invested $15,000 cash in exchange for common stock of the corporation.
1
Hired a secretary-receptionist at a salary of $375 per week, payable monthly.
2
Paid office rent for the month $900.
3
Purchased architectural supplies on account from Spring Green Company $1,000.
10
Completed blueprints on a carport and billed client $1,500 for services.
11
Received $500 cash advance from J. Madison to design a new home.
20
Received $2,300 cash for services completed and delivered to M. Svetlana.
30
Paid secretary-receptionist for the month $1,500.
30
Paid $300 to Spring Green Company for accounts payable due.
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