Unit 4 : Assignment Model

What is the value assigned to each node in an assignment mode?

1

A transportation company pays its drivers according to the following chart using its buses. BY............ R1............ R2........ R3........ R4 Allen ....$450.... $300.... $450.... $300 Joe ........$450.... $250.... $500.... $350 Mike .....$500.... $520.... $510.... $400 1. What is the flow balance equation for Mike? 2. Which driver was assigned to route 1? 3. Which driver was assigned to route 3? 4. What is the objective function? 5. How many more drivers does the transportation company need to hire to make the application a balance assignment model? 6. How many possible solutions does the transportation company need to consider if it had 6 drivers?

1. XM1 + XM2 + XM3 + XM4 = 1 2. Mike 3. The road assignment was not covered for route 3 4. Minimize cost = $450XA1 + $300XA2 + $450XA3 + $300XA4 + $450XJ1 + $250XJ2 + $500XJ3 + $350XJ4 + $500XM1 + $520XM2 + $510XM3 + $400XM4 5. 1 6. 720

A new agent has been added, so you have a total of six agents and five tasks. The costs are listed in the following: Agent...T1............T2...................T3................T4................T5 A1........0.39........-0.065........-0.066........-0.417.........0.308 A2......-0.736.....-0.089..........0.978...........0.641.......-0.822 A3.......0.549.........0.052........-0.83...........-0.141...........0.118 A4.......0.415........-0.339........-0.369........-0.531......-0.488 A5.....-0.669........0.329..........0.718...........0.707..........-0.55 A6.......0.751.........-0.002..........0.016.........-0.996.......0.859 It turns out that your researcher was confused, and the data refer to profit, not cost. If the assignment is made to maximize profit, which tasks are agents A1 and A2 assigned to?

2, 3

A new agent has been added, so you have a total of six agents and five tasks. The costs are listed in the following: Agent...T1............T2...................T3................T4................T5 A1........2.39........1.935..............1.914............1.583..........2.308 A2......1.264.......1.911...............2.978...........2.641............1.178 A3......2.549......2.052...............1.17.............1.859............2.118 A4......2.415......1.661................1.631............1.469............1.512 A5......1.341......2.329..............2.718............2.707............1.45 A6......2.751......1.998..............2.016..............1.004..........2.859 If the optimal assignment is made to reduce the total cost, what is the total cost?

6.354

Which of the following is correct in an assignment model?

A person is assigned to a job A job is assigned to a person

Which of the following is correct in an unbalanced assignment model?

Number of jobs can be greater than or less than the number of people

Which of the following is correct in a balanced assignment model?

Number of people is same as the number of jobs

A transportation company pays its drivers according to the following chart using its buses. BY............ R1............ R2........ R3........ R4 Allen ....$500.... $600.... $450.... $500 Joe ........$450.... $550.... $500.... $550 Mike .....$400.... $650.... $400.... $550 1. How many more drivers does the transportation company need to hire to make the application a balance assignment model? 2. What is the numerical value of the objective function?

1. 1 2. $1,050

Agent........T1........ T2........ T3........ T4........ T5 A1.............. 26........ 38........ 11 ........37........ 36 A2 ............37......... 36........ 25.......49 ........11 A3............ 21.......... 36........ 23...... 15........ 12 A4 ...........40 ..........29........44...... 42........ 35 A5 ............46 .........44 ......28 ........27 ........14 1. Find the minimum cost assignment. To what tasks are Agents 4 and 5 assigned? 2. Find the minimum cost assignment. The total cost is 3. Suppose that it turns out that Agent 3 cannot be assigned to either T1 or T2. How would you change the spreadsheet to represent this constraint? 4. Suppose that it turns out that Agent 3 cannot be assigned to either T1 or T2. Find the minimum cost assignment. What is the total cost? 5. It has been discovered that these are actually the profits made from each possible assignment. What is the maximum profit?

1. 2,4 2. 99 3. Raise the cost of assigning Agent 3 to T1 or T2 to some very high value. OR Add an additional constraint saying that the assignment A2→T1 or A3→T2 had to be 0. 4. 106 5. 211