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

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

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

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

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

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

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

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