1. Assignment Problem A balanced transportation problem in which
All si = 1 and dj = 1
Therefore xij = 0 or 1
Cost matrix: contains cost, time, or distance
Solve using Hungarian method
IE 416, Chap 7:3, March 99

2. Hungarian Method for Assignment Problem (skip)
Step 1: Find the min element in each row of cost matrix.
Subtract from each cost the min cost in its row.
Find the min element in each column.
Subtract from each cost the min cost in its column.
The new matrix is called reduced cost matrix.
Step 2: Draw the min number of lines to cover all zeros.
If number of lines equal number of rows, optimal solution
can be found among the zeros in the matrix.
Step 3: If number of lines not equal to number of rows,
find smallest nonzero element, k, not covered by the lines.
Subtract k from each uncovered elements and
add k to each element that is covered by two lines.
Return to Step 2.
IE 416, Chap 7:3, July 98

3. Given: Time to perform each job by each person
Problem 1 Page 379
Given: Time to perform each job by each person
Objective: Find assignments so that to Minimize
the total hours
IE 416, Chap 7, July 99

4. Transshipment Problem
A special transportation problem in which, some
points are not a simple supply point or a simple
demand point, but several units will be shipped
to them and shipped from them. i j k
Demand
Point
Supply
Point
Transshipment
Point
IE 416, Chap 7, July 99

5. Transshipment Example 1: Demand 200
600
Supply
Transshipment
300
500 e a 9 7 k 2 8 b f
IE 416, Chap 7, July 99

6. Transshipment Example 2: Demand 200
600
Supply
Transshipment
300
500 e a 9 7 k 1 2 8 b f
IE 416, Chap 7, July 99

7. Transshipment Example 3: Demand 200
600
Supply
Transshipment
300
500 e a 9 7 12 k 2 8 b f
IE 416, Chap 7, July 99

8. Cost of shipment of one unit:
Need to decide about:
Cost of shipment
Capacity of each point
Cost of shipment of one unit:
Cij = 0 if i = j (from a point to itself)
Cij = 0 if j is dummy point (do not ship)
Cij = M if no information available or forbidden
Cij > 0 if given
Cij = penalty cost if i is dummy point
(demand not met)
IE 416, Chap 7, July 99