D a i Penalty S b j Penalty — — The Allocation is D D a i S ( ) ( ) / / b j / / Thus we have the following allocations: D D D D a i S ( ) ( ) S ( ) ( ) S ( ) ( ) b j XII Std - Business Maths & Stat EM Chapter - - Operations Research Transportation schedule : S à D , S à D , S à D , S à D , S à D , S à D This initial transportation cost = ` , Example . Obtain an initial basic feasible solution to the following transportation problem using Vogel’s approximation method. Ware houses Stores I II III IV Availability ( a i ) Requirement ( b j ) Here i j (i.e) Total Availability =Total Requirement ∴ The given problem is balanced transportation problem. Hence there exists a feasible solution to the given problem.
First Allocation: I II III IV a i Penalty ( ) / b j / Penalty Second Allocation: I II III IV a i Penalty ( ) / b j / Penalty Third Allocation: I III IV a i Penalty ( ) / b j / Penalty Fourth Allocation: I IV a i Penalty ( ) / b j / Penalty Fifth Allocation: I IV a i Penalty ( ) / b j / Penalty Sixth Allocation: I Penalty ( ) / — ( ) / — / Penalty XII Std - Business Maths & Stat EM Chapter - - Thus we have the following allocations: I II III IV a i ( ) ( ) ( ) ( ) ( ) ( ) ( ) b j Transportation schedule : A à I,