Transportation Problem - 3 North-West Corner Method (NWCM)

Operations Research - OR MBA - MCA - CA - CS - CWA - BBA - BCA - BCom - MCom - GRE - GMAT - IAS - CAIIB - FIII - IBPS - BANK PO - UPSC - CPA - CMA Obtaining Initial Solution of a Transportation Problem by North-West Corner Method (NWCM) We begin in the upper left corner of the transportation tableau and set x11 as large as possible (clearly, x11 can be no larger than the smaller of s1 and d1, i.e "demand or supply, whichever is lower" will be the quantity of allocation to the cell). • If x11=s1, cross out the first row of the tableau. Also change d1 to d1-s1. • If x11=d1, cross out the first column of the tableau. Change s1 to s1-d1. • If x11=s1=d1, cross out either row 1 or column 1 (but not both!). o If you cross out row, change d1 to 0. o If you cross out column, change s1 to 0. Continue applying this procedure to the most northwest cell in the tableau that does not lie in a crossed out row or column. Eventually, you will come to a point where there is only one cell that can be assigned a value. Assign this cell a value equal to its row or column demand, and cross out both the cell’s row and column. A ‘bfs’ has now been obtained. Example: Determine an initial basic feasible solution to the following transportation problem using NWCM, if the objective is to minimize the transportation cost: Source Destination D1 D2 D3 D4 Supply S1 1 2 1 4 30 S2 3 3 2 1 50 S3 4 2 5 9 20 D 20 40 30 10 100 www.prashantpuaar.com