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Column Minima Method

  • OPERATIONS-RESEARCH
Column Minima Method Step 1 Select the smallest cost in the first column of the transportation table. Let it be $c_{i1}$. Allocate as much as possible amount $x_{i1} = min_i(a_i, b_1)$ in the cell $(i,1)$, so that either the capacity of origin $O_i$ is exhausted or the requirement at destination $D_1$ is satisfied or both. Step 2 If $x_{i1} = b_1$, the requirement at destination $D_1$ is completely exhausted, cross-out the first column of the table and move down to the second column.
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Least Cost Entry Method

  • OPERATIONS-RESEARCH
Least Cost Entry Method This method is also known as Matrix Minima Method. Step 1 Select the smallest cost in the cost matrix of the transportation table. Let it be $c_{ij}$. Allocate $x_{ij} = min_{i,j}(a_i, b_j)$ in the cell $(i,j)$. Step 2 If $x_{ij} = a_i$, then cross-out the $i^{th}$ row of the transportation table and decrease $b_j$ by $a_i$ and goto Step 3. If $x_{ij} = b_j$, then cross-out the $j^{th}$ column of the transportation table and decrease $a_i$ by $b_j$ and goto Step 3.
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North West Corner Method

  • OPERATIONS-RESEARCH
North-West Corner Method The North-West cornet method starts at the northwest corner cell of the transportation problem table. Step 1 Allocate as much as possible to the selected cell, and adjust the associated amounts of supply and demand by subtracting the allocated amount. The maximum possible amount is allocated in in (1,1) cell, i.e., $x_{11} = \min(a_1, b_1)$. Step 2 If $b_1 > a_1$, move vertically downwards to the second row and make the second allocation of amount $x_{21} = \min(a_2,b_1-x_{11})$ in the cell (2,1).
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Row Minima Method

  • OPERATIONS-RESEARCH
Row Minima Method Step 1 Select the smallest cost in the first row of the transportation table. Let it be $c_{1j}$. Allocate as much as possible amount $x_{1j} = min_j(a_1, b_j)$ in the cell $(1,j)$, so that either the capacity of origin $O_1$ is exhausted or the requirement at destination $D_j$ is satisfied or both. Step 2 If $x_{1j} = a_1$, the availability at origin $O_1$ is completely exhausted, cross-out the first row of the table and move down to the second row.
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Transhipment Problem

  • OPERATIONS-RESEARCH
Transhipment Problem The transhipment problem is more general than that of regular transportation problem, where direct shipments only are allowed between a source and destination. In transhipment problem available commodity frequently moves from one source to another source or destination before reaching its actual destination. In Transhipment Network, the nodes of the network that acts as both source and destination are called transhipment nodes. The nodes of the network which acts as source only are called pure supply nodes and the nodes which acts as destination only are called pure demand nodes.
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Transportation Problem

  • OPERATIONS-RESEARCH
Transportation Problem Transportation problem is a special class of linear programming problem that deals with transporting (or shipping) a commodity from various origins or sources (e.g. factories) to various destinations or sinks (e.g., warehouses). In this type of problem the objective is to determine the transportation schedule that minimizes the total transportation cost while satisfying supply and demand conditions. The general Transportation Problem (TP) can be defined as follows: Suppose that there are $m$ origins $O_1, O_2, \ldots, O_m$ and $n$ destinations $D_1, D_2, \ldots, D_n$.
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UV Method for Optimal Solution

  • OPERATIONS-RESEARCH
UV Method For Finding Optimal Solution of TP Step 1 First, construct a transportation table entering the origin capacities $a_i$, the destination requirements $b_j$ and the cost $c_{ij}$. (If the TP is unbalanced convert it into a balanced TP by adding a dummy row or dummy column as per the requirement taking zero costs). Step 2 Find an initial basic feasible solution by any one method (preferably Vogel’s Approximation Method).
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Vogels Approximation Method

  • OPERATIONS-RESEARCH
Vogel’s Approximation Method (VAM) Vogel’s approximation method is an improved version of the least cost entry method. It gives better starting solution as compared to any other method. Step 1 For each row (column), determine the penalty measure by subtracting the smallest unit cost element in the row (column) from the next smallest unit cost element in the same row (column). Step 2 Select the row or column with the largest penalty.
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