Method 3:- Vogel s Approximation Method: This methods uses penalty costs. Step 3: Repeat the Step-1 and Step-2 till all requirements are exhausted i.e. Step 2: Make allocation to the second least cost cell depending upon the remaining demand/supply for the column/row containing that cell. In case of tie in the least cost cell, make allocation to the cell by which maximum demand or capacity is exhausted. Method 2:- Least Cost Method : The practical steps involved in the Least Cost are given below: Step 1: Make maximum possible allocation to the least cost cell depending upon the demand/supply for the column/row containing that cell. Step 4: Repeat the Step-1 to Step-3 till all requirements are exhausted i.e. Step 3: Move to the next row and make allocation to the cell below the cell of the preceding row in which the last allocation was made and follow Step-1 and Step-2. Step 2: Move to the next cell of the first row depending upon remaining supply for that Row and the demand requirement for the next column. 1.2ģ The Transportation Problems Method 1: North-West corner method: The practical steps in the North-West Corner cell are given below: Step 1: Make maximum possible allocation to the upper-left corner cell (known as North-West corner cell) in the first row depending upon the availability to supply for that row and demand requirement for the column containing that cell. Stages -5: In case the IBFS solution is not optimal, develop the improved solutions. Modified Distribution (MODI) is the most common method and widely used for test the optimality. Stages -4: Test the IBFS solution for optimality. Stages -3: Develop an initial basic feasible solution (IBFS) by using any of the following methods. In case of unbalanced matrix, a dummy column or dummy row should be introduced with nil transportation cost. In case of Maximization or profit matrix, convert the same in to opportunity loss matrix by subtracting each element from the highest element of the matrix. Stages -2: Do preliminary check consist the following: (i) (ii) Verify Objective = Minimization. A feasible allocation is one in which all demand at the destinations is satisfied and all supply at the origin is allocated. Stages -1: Arrange the data in table format and set up the transportation table to find any feasible allocation. Stages in Transportation Problems: The transportation algorithm has four stages. The total supply must equal the total demand. The requirement of items at each destination must be known.
The supply of items at each origin must be known. (i) (ii) (iii) (iv) The cost per item of each combination of origin and destination must be satisfied. Find minimum cost production schedule that satisfies firm s demand and production limitations (called Production Smoothing ) Conditions: To use the transportation algorithm the following conditions must be satisfied. Applications: (i) (ii) (iii) Minimize shipping costs from factories to warehouses (or from warehouses to retail outlets) Determine lowest cost location for new factory warehouse office or other facility. The objective of the transportation problems is to determine the quantity to be shipped from each source to each destinations so as the transportation cost is lowest to maintain the supply and demand requirements. 1Ģ Advance Management Accounting Transportation: The transportation problem is concerned with the allocation of items between suppliers (called origins) and consumers (called destinations) so that the total cost of the allocation is minimized. 3 (b) 4 (b) 2 (c) 3 (b) 4 (b) 5 (c) 2 (b) 4 (b) 2 (b) 2 (b) Marks * means questions from old syllabus # means theory questions CA.
1 C H A P T E R 11 Transportation Problems Learning Objectives: Understanding the feature of Assignment Problems.