1. McGraw-Hill/Irwin 6.1 P&T Company Distribution Problem

2. McGraw-Hill/Irwin 6.2 Shipping Data CanneryOutputWarehouseAllocation Bellingham75 truckloadsSacramento80 truckloads Eugene125 truckloadsSalt Lake City65 truckloads Albert Lea100 truckloadsRapid City70 truckloads Total300 truckloadsAlbuquerque85 truckloads Total300 truckloads

3. McGraw-Hill/Irwin 6.3 Current Shipping Plan Warehouse From \ To SacramentoSalt Lake CityRapid CityAlbuquerque Cannery Bellingham75000 Eugene565550 Albert Lea001585

4. McGraw-Hill/Irwin 6.4 Shipping Cost per Truckload Warehouse From \ To SacramentoSalt Lake CityRapid CityAlbuquerque Cannery Bellingham$464$513$654$867 Eugene352416690791 Albert Lea995682388685 Total shipping cost= 75($464) + 5($352) + 65($416) + 55($690) + 15($388) + 85($685) = $165,595

5. McGraw-Hill/Irwin 6.5 Terminology for a Transportation Problem P&T Company Problem Truckloads of canned peas Canneries Warehouses Output from a cannery Allocation to a warehouse Shipping cost per truckload from a cannery to a warehouse General Model Units of a commodity Sources Destinations Supply from a source Demand at a destination Cost per unit distributed from a source to a destination

6. McGraw-Hill/Irwin 6.6 Characteristics of Transportation Problems The Requirements Assumption –Each source has a fixed supply of units, where this entire supply must be distributed to the destinations. –Each destination has a fixed demand for units, where this entire demand must be received from the sources. The Feasible Solutions Property –A transportation problem will have feasible solutions if and only if the sum of its supplies equals the sum of its demands. The Cost Assumption –The cost of distributing units from any particular source to any particular destination is directly proportional to the number of units distributed. –This cost is just the unit cost of distribution times the number of units distributed.

7. McGraw-Hill/Irwin 6.7 The Transportation Model Any problem (whether involving transportation or not) fits the model for a transportation problem if 1.It can be described completely in terms of a table like Table 6.5 that identifies all the sources, destinations, supplies, demands, and unit costs, and 2.satisfies both the requirements assumption and the cost assumption. The objective is to minimize the total cost of distributing the units.

8. McGraw-Hill/Irwin 6.8 The P&T Co. Transportation Problem Unit Cost Destination (Warehouse):SacramentoSalt Lake CityRapid CityAlbuquerqueSupply Source (Cannery) Bellingham$464$513$654$86775 Eugene352416690791125 Albert Lea995682388685100 Demand80657085

9. McGraw-Hill/Irwin 6.9 Spreadsheet Formulation

10. McGraw-Hill/Irwin 6.10 Network Representation

11. McGraw-Hill/Irwin 6.11 The Transportation Problem is an LP Let x ij = the number of truckloads to ship from cannery i to warehouse j (i = 1, 2, 3; j = 1, 2, 3, 4) Minimize Cost = $464x 11 + $513x 12 + $654x 13 + $867x 14 + $352x 21 + $416x 22 + $690x 23 + $791x 24 + $995x 31 + $682x 32 + $388x 33 + $685x 34 subject to Cannery 1:x 11 + x 12 + x 13 + x 14 = 75 Cannery 2:x 21 + x 22 + x 23 + x 24 = 125 Cannery 3:x 31 + x 32 + x 33 + x 34 = 100 Warehouse 1:x 11 + x 21 + x 31 = 80 Warehouse 2:x 12 + x 22 + x 32 = 65 Warehouse 3:x 13 + x 23 + x 33 = 70 Warehouse 4:x 14 + x 24 + x 34 = 85 and x ij ≥ 0 (i = 1, 2, 3; j = 1, 2, 3, 4)

12. McGraw-Hill/Irwin 6.12 Integer Solutions Property As long as all its supplies and demands have integer values, any transportation problem with feasible solutions is guaranteed to have an optimal solution with integer values for all its decision variables. Therefore, it is not necessary to add constraints to the model that restrict these variables to only have integer values.

13. McGraw-Hill/Irwin 6.13 Location of Texago’s Facilities Type of FacilityLocations Oil fields1. Several in Texas 2. Several in California 3. Several in Alaska Refineries1. Near New Orleans, Louisiana 2. Near Charleston, South Carolina 3. Near Seattle, Washington Distribution Centers1. Pittsburgh, Pennsylvania 2. Atlanta, Georgia 3. Kansas City, Missouri 4. San Francisco, California

14. McGraw-Hill/Irwin 6.14 Potential Sites for Texago’s New Refinery Potential SiteMain Advantages Near Los Angeles, California1. Near California oil fields. 2. Ready access from Alaska oil fields. 3. Fairly near San Francisco distribution center. Near Galveston, Texas1. Near Texas oil fields. 2. Ready access from Middle East imports. 3. Near corporate headquarters. Near St. Louis, Missouri1. Low operating costs. 2. Centrally located for distribution centers. 3. Ready access to crude oil via the Mississippi River.

15. McGraw-Hill/Irwin 6.15 Production Data for Texago Refinery Crude Oil Needed Annually (Million Barrels)Oil Fields Crude Oil Produced Annually (Million Barrels) New Orleans100Texas80 Charleston60California60 Seattle80Alaska100 New site120Total240 Total360Needed imports = 360 – 240 = 120

16. McGraw-Hill/Irwin 6.16 Cost Data for Shipping to Refineries Cost per Unit Shipped to Refinery or Potential Refinery (Millions of Dollars per Million Barrels) New OrleansCharlestonSeattle Los AngelesGalvestonSt. Louis Source Texas245311 California553134 Alaska573457 Middle East235434

17. McGraw-Hill/Irwin 6.17 Cost Data for Shipping to Distribution Centers Cost per Unit Shipped to Distribution Center (Millions of Dollars) PittsburghAtlantaKansas CitySan Francisco Refinery New Orleans6.55.568 Charleston7547 Seattle7843 Potential Refinery Los Angeles8632 Galveston5436 St. Louis4315 Number of units needed10080 100

18. McGraw-Hill/Irwin 6.18 Estimated Operating Costs for Refineries SiteAnnual Operating Cost (Millions of Dollars) Los Angeles Galveston St. Louis 620 570 530

19. McGraw-Hill/Irwin 6.19 Basic Spreadsheet for Shipping to Refineries

20. McGraw-Hill/Irwin 6.20 Shipping to Refineries, Including Los Angeles

21. McGraw-Hill/Irwin 6.21 Shipping to Refineries, Including Galveston

22. McGraw-Hill/Irwin 6.22 Shipping to Refineries, Including St. Louis

23. McGraw-Hill/Irwin 6.23 Basic Spreadsheet for Shipping to D.C.’s

24. McGraw-Hill/Irwin 6.24 Shipping to D.C.’s When Choose Los Angeles

25. McGraw-Hill/Irwin 6.25 Shipping to D.C.’s When Choose Galveston

26. McGraw-Hill/Irwin 6.26 Shipping to D.C.’s When Choose St. Louis

27. McGraw-Hill/Irwin 6.27 Annual Variable Costs Site Total Cost of Shipping Crude Oil Total Cost of Shipping Finished Product Operating Cost for New Refinery Total Variable Cost Los Angeles$880 million$1.57 billion$620 million$3.07 billion Galveston920 million1.63 billion570 million3.12 billion St. Louis960 million1.43 billion530 million2.92 billion