Modified Distribution Method
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A Linear Programming Method to optimize delivery of goods from different sources to different destinations.
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Vogel's Approximation Method & Modified Distribution Method
Vogel's Approximation Method (VAM) and Modified Distribution Method (MODI) are used to solve transportation problems. VAM computes penalties for each row and column to select the cell with the lowest cost to allocate units until constraints are satisfied, producing an initial basic feasible solution. MODI determines if the solution is optimal and identifies non-basic variables to consider, allowing it to find the true optimal solution. It is applied after VAM to a manufacturing company's transportation problem of supplying raw materials across plants and destinations.
transporation problem - stepping stone method
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This document presents a transportation problem involving 3 production facilities and 4 warehouses. The facilities have weekly production capacities of 7, 10, and 18 units. The warehouses have weekly demands of 5, 8, 7, and 15 units. The transportation costs between each facility-warehouse pair are given.
Using the Vogel's Approximation Method, an initial basic feasible solution is found allocating specific facilities to meet warehouse demands. The MODI method is then used to test for optimality. Some reallocations are made to improve the solution.
The optimal solution allocates production from the facilities to warehouses to meet demands at a total transportation cost of Rs. 900.
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MODI Method- Optimization of transportation problem
The document discusses MODI, a method for optimizing transportation problems. MODI stands for Modified Distribution Method and is used to find the optimal solution for transportation problems by looping through iterations to distribute quantities in a way that minimizes costs.
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Transportation Problem in Operational Research
The document discusses the transportation problem and methods for finding its optimal solution. It begins by defining key terminology used in transportation models like feasible solution, basic feasible solution, and optimal solution. It then outlines the basic steps to obtain an initial basic feasible solution and subsequently improve it to reach the optimal solution. Three common methods for obtaining the initial solution are described: the Northwest Corner Method, Least Cost Entry Method, and Vogel's Approximation Method. The document also addresses how to solve unbalanced transportation problems and provides examples applying the methods.
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This document presents a transportation problem involving 3 production facilities and 4 warehouses. The facilities have weekly production capacities of 7, 10, and 18 units. The warehouses have weekly demands of 5, 8, 7, and 15 units. The transportation costs between each facility-warehouse pair are given.
Using the Vogel's Approximation Method, an initial basic feasible solution is found allocating specific facilities to meet warehouse demands. The MODI method is then used to test for optimality. Some reallocations are made to improve the solution.
The optimal solution allocates production from the facilities to warehouses to meet demands at a total transportation cost of Rs. 900.
Transportation Problem- Stepping Stone Method
The stepping stone method is used to find the optimal feasible solution to a transportation problem after an initial basic feasible solution is found. It involves systematically checking each unused cell to see if shipping one additional unit to that cell would lower total transportation costs. This is done by forming closed loops around the cell and calculating the net change in cost. If a cell is found that lowers costs, units are reallocated until no further improvements can be made. The document provides an example problem that is solved step-by-step using this method, ultimately arriving at a lower optimal transportation cost than the initial basic feasible solution.
MODI Method- Optimization of transportation problem
The document discusses MODI, a method for optimizing transportation problems. MODI stands for Modified Distribution Method and is used to find the optimal solution for transportation problems by looping through iterations to distribute quantities in a way that minimizes costs.
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The document outlines the presentation topic of Modified Distribution Method (MODI Method) for solving transportation problems. It first discusses the prerequisite methods of Least Cost Method, Vogel's Approximation Method and North-West Corner Method. It then explains the steps of MODI Method which involves setting up cost matrices for unallocated cells and introducing dual variables to find the implicit cost and evaluate unoccupied cells to determine if the initial solution can be improved. The document provides an example problem and solution to demonstrate the application of MODI Method.
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The document discusses transportation problems and their optimization using linear programming. It begins by explaining that transportation problems aim to optimally transport goods from supply origins to demand destinations at minimum cost while satisfying supply and demand constraints. The document then discusses how balanced transportation problems have equal total supply and demand, while unbalanced problems introduce dummy variables to balance totals. It provides examples of unbalanced problems where supply exceeds demand and vice versa, and how dummy columns/rows are added to balance the problems and find optimal solutions.
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(2) The Intuitive Lowest-Cost Method which assigns units to the lowest cost cell, exhausting rows and columns, until all units are allocated.
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(E) Evansville
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(2) The Intuitive Lowest-Cost Method which assigns units to the lowest cost cell, exhausting rows and columns, until all units are allocated.
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Testing the assumption of normality
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Advantages of non-parametric tests
Limitations
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This document provides an overview of nonparametric tests. It defines nonparametric tests as techniques that do not rely on assumptions about the underlying data distribution. Some key points made in the document include:
- Nonparametric tests are used when the sample distribution is unknown or when there are too many variables to assume a normal distribution.
- Common nonparametric tests include the chi-square test, Kruskal-Wallis test, Wilcoxon signed-rank test, median test, and sign test.
- The main difference between parametric and nonparametric tests is that parametric tests make assumptions about the population distribution, while nonparametric tests do not require these assumptions and are distribution-
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