472.21 7 Fall 2011

1. MS 472.21 7 Fall 2011

2. transshipment assignment Chapter 6 • transportation • transshipment • assignment transportation not so hard

3. Transportation transportation transshipment assignment • you’ve seen this before • a quick review • then expand we’re going to concentrate on formulation for a bit

4. Transportation transportation transshipment assignment • shipments • concrete company • from 3 plants • to 3 construction sites • known cost for each option pg 239

5. Transportation • shipments • formulate the lp • Min or max? • then assign variables xij • then write out the objective function Z = • Then the constraints

6. Transportation • shipments • formulate the lp • min Z = $8.00x11 + $5.00x12 + $6.00x13 + $15.00x21 + $10.00x22 + $12.00x23 + $3.00x31 + $9.00x32 + $10.00x33 • s.t. x11 + x12 + x13 <= 120.00 x21 + x22 + x23 <= 80.00 x31 + x32 + x33 <= 80.00 x11 + x21 + x31 >= 150.00 x12 + x22 + x32 >= 70.00 x13 + x23 + x33 >= 100.00 xij >= 0

7. Transportation • problem • ch6pr11 • pg 243

8. transshipment Transshipment transportation assignment

9. Transshipment • same problem as transportation with one little wrinkle: • in addition to starting locations and ending locations • stops along the way • storage options between

10. 6 8 7 Transshipment e.g.: Shipping Wheat pg 230 • rather than start with a table • usually start with a diagram 6 200 3 16 8 10 15 1 300 7 10 11 100 4 14 11 2 5 300 12 17 4 12 300 5

11. Transshipment • formulate the lp • Min or max? • then assign variables xij • then write out the objective function Z = • then the constraints

12. Transshipment • formulate the lp • Min • variables x13, x14, x15 x23, x24, x25 x36, x37, x38 x46, x47, x48 x56, x57, x58

13. Transshipment • formulate the lp • write out the objective function

14. Transshipment • formulate the lp • then the constraints • supply • demand • transshipment points • non-negative

15. Transshipment • formulate the lp • then the constraints • supply x13 + x14 + x15 = 300 x23 + x24 + x25 = 300 • demand x36 + x46 + x56 = 200 x37 + x47 + x57 = 100 x38 + x48 + x58= 300

16. Transshipment • formulate the lp • then the constraints • transshipment points amount in must equal amount out x13 + x23 = x36 + x37+ x38 x14 + x24 = x46 + x47+ x48 x15 + x25 = x56 + x57+ x58

17. Transshipment • formulate the lp • then the constraints • transshipment points amount in must equal amount out x13 + x23 - x36 - x37 - x38 = 0 x14 + x24 - x46 - x47 - x48 = 0 x15 + x25 - x56 - x57- x58 = 0 • non-negative xij >= 0

18. Transshipment

19. Transshipment problem Walsh’s Fruit Company chapter 6 problem 37 9th edition: page 254

20. Transshipment: Walsh’s usually start with a diagram then formulate the lp Min or max? then assign variables xij then write out the objective function Z = then the constraints

21. Transshipment 1 90,000 6 72,000 23 16 21 20 4 15 18 29 105,000 2 7 80,000 16 17 5 22 25 24 8 3 83,000 120,000

22. Transshipment

23. Transshipment general forms

24. Assignment transportation transshipment assignment

25. Assignment back to the transportation structure except the constraint is 1 (each assigned to 1 place) Atlantic Coast Conference assigning officials pg 234

26. Assignment formulate the lp Min variables xij objective function Z = then the constraints

27. Assignment

28. Assignment ch6pr50 pg 261

29. Applications software reviews http://www.lionhrtpub.com/orms/swrindexmain.html A.MAZE Enterprise Optimizer MBAWare http://www.mbaware.com/opsof.html GeneHunter also google: “management science” applications optimization software Bausch, et. al.: Mobilizing Marine Corps Officers

30. Quiz 2 next Mon problems like Transportation ch6pr11 “A Manufacturing Firm” formulation Transshipment ch6pr37 Walsh’s Fruit Company diagram formulation Assignment ch6pr50 Citywide Taxi Company formulation ch6pr54 “A University Department” formulation

31. To Do “reading Assessment” 1 Next Thu Mgmt Sci for Prov