Page 129 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Self Assessment

Multiple Choice Questions:
1. When total supply is equal to the total demand in a transportation problem, the problem
is said to be

(a) Balanced (b) Unbalanced
(c) Degenerate (d) All of the above
2. Which of the following methods is used to verify the optimality of the current solution of
the transportation problem?
(a) Least Cost Method (b) Vogel’s Approximation Method
(c) MODI method (d) All of the above

3. MODI method and stepping stone method is used for this purpose
(a) To find out initial basic feasible solution
(b) Optimal solution
(c) Multiple solution
(d) All of the above

6.3 Modified Distribution Method (MODI)

Another method to check optimality is that of MODI.

Steps Involved:

Step 1: Row 1, row 2,…, row i of the cost matrix are assigned with variables U , U , …, U and the
1 2 i
column 1, column 2,…, column j are assigned with variables V , V , …,V respectively.
1 2 j
Step 2: Initially, assume any one of U values as zero and compute the values for U , U , …,U and
i 1 2 i
V , V , …,V by applying the formula for occupied cell.
1 2 j
For occupied cells,
,
C ij + U i + V j = 0
C ij
U i
A
V j

Step 3: Obtain all the values of C for unoccupied cells by applying the formula for unoccupied
ij
cell. For unoccupied cells,
Opportunity Cost, = C + U + V
ij i j
U i
C ij

C
i
V j

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