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This project report is part of degree completion in computer science at Ambedkar University, Delhi. Its main points are: Dynamic, Programming, Research, Proposal, Assembly, Line, Graph, Theory, Divide-and-conquer, Algorithm
Typology: Study Guides, Projects, Research
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The Research Proposal is one of the critical documents since it identifies the aims and goals of the research. This is important to the success of the research project since it clearly outlines what the team must achieve in order to classify the research project to be complete. A strict definition of this type also enables the team to outline the necessary means to achieve these goals. If this step is not carried out correctly the research can encounter delays.
An assembly line is used in such manufacturing process in which interchangeable parts are added to a product in a sequence to get a final product. The best known form of the assembly line, the moving assembly line, was created by Henry Ford. We need to find the solution of assembly line problem (using Graph Theory), based on the problem, which can be described as: A company produces automobiles in a factory that has two assembly lines. An chassis enters each assembly line, has parts added to it at a number of stations, and a finished auto exits at the end of the line. Each assembly line has n stations.
Figure 1: A manufacturing problem to find the fastest way through assembly line
In this project we are first going to generalize the typical 2-assembly- line algorithm for n-assembly-line problem. After generalization of the algorithm using the graph theory, we will get the possible optimized solution of the n-assembly-line problem. It will be basically a scheduling algorithm which could be used in industry for rapid assembling of the products in the production line. At first brute force approach algorithm will be proposed for the particular problem. Then an efficient algorithm will be designed using dynamic programming.
Graph theory is the study of graphs, graphs are basically structures used to model relations between objects from a certain collection. A graph consists of a collection of vertices and a collection of edges that connect pairs of vertices (e.g. stations). Applications of graph theory are mostly concerned with labeled graphs and various specializations of these. Structures that can be represented as graphs are ubiquitous, and many problems of practical interest can be represented by graphs. Graphs with weights, or weighted graphs, are used to represent structures in which pair wise connections have some numerical values. For example if a graph represents a LAN network, the weights could represent the cost of each connection. A digraph with weighted edges in the context of graph theory is called a network. So we can say that our problem is based on a network in context of the graph theory in which the stations are the nodes and the paths between them as edges with time as weight on them. As in the network the edges must have directions and here the only possible direction of the edge is from (j-1) th station towards jth station. Our concern is with minimum time possible for a product (to be assembled) to go through the assembly line.
Dynamic programming usually takes one of two approaches: Top-down approach: The problem is broken into sub problems, and these sub problems are solved and the solutions remembered, in case they need to be solved again. This is recursion and memorization combined together. Bottom-up approach: All sub problems that might be needed are solved in advance and then used to build up solutions to larger problems. In this project we will use the bottom-up-approach of dynamic programming to get the optimized solution.
The main steps that are to be followed in this research are as follows: Understanding the 2-line assembly problem. Study of existing algorithm for the problem. Learning of Graph theory. Generalizing the algorithm for n-line assembly problem. Using dynamic programming to optimize the solution. Validation and verification of the algorithm.
The research plan will be followed as below: 6 th^ Semester: In this semester, mostly the necessary background study for the research will be carried out that includes understanding the assembly line problem and study of the existing algorithm for the problem. Summer vacations: During this period of time, the understating of the existing algorithm and the learning of the graph theory and Brute force approach will be done.
7 th^ semester: In this interval generalization of the existing algorithm for the n-line-assembly problem and study of dynamic programming will be done. 8 th^ Semester: Generalized algorithm will be optimized using the dynamic programming. Verification and validation of the proposed algorithm will also be carried out. The remaining time will be consumed in the thesis writing.
Dynamic programming is a technique for finding optimal solution/algorithms of a complex type of problems. We will introduce this technique in solution of complex and critical assembly line problem. As the use of divide and conquer approach is not useful for solving such complex problems especially where the time is an important factor. The use of formal methods technology (involving graph theory) has several advantages over other technologies such as, quality assurance, requirement capturing, removing ambiguities, validation and verification.
