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Transportation Problems

Transportation Problems. Tableau Shipping Solutions NorthWest Corner Rule Stepping Stone Algorithm. Transportation Problems. Have suppliers, users, shipping costs. Tableau: displays info with rim conditions . Each cell has two entries: costs and amount to ship.

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Transportation Problems

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  1. Transportation Problems Tableau Shipping Solutions NorthWest Corner Rule Stepping Stone Algorithm Mathematics in Management Science

  2. Transportation Problems Have suppliers, users, shipping costs. Tableau: displays info with rim conditions. Each cell has two entries: costs and amount to ship. Shipping solution: obeys all constraints. NorthWest Corner Rule: an algorthim for obtaining a shipping solution. Indicator Values: Stepping Stone Algorithm.

  3. Bakery Example Chain gets bread deliveries from a bakery chain that does its baking in different places. Each store needs certain number of loaves/day. Supplier bakes enough to exactly meet demands. How many loaves should be to stay within the demands and to minimize the cost?

  4. Mines & Plants Two mines (extract/supply ore) and three plants (process/demand ore). Mine A supplies 7 m tons, B 3 m tons. Plant 1 needs 2 tons, 2&3 each 4 tons. Shipping costs are from A to P1,P2,P3 --- 7, 1, 3 from B to P1,P2,P3 --- 9, 5, 12

  5. Suppliers on left; demanders on top. Next add rim conditions: Supply amounts in last column. Demand amounts in last row. Check that amounts agree!

  6. Next add shipping costs. Cell (m,p) is cost to ship from mine m to plant p.

  7. Need shipping solution to start with.

  8. NorthWest Corner Rule Locate top far-left-hand cell. Ship via this cell with smaller of the two rim cells (call the value s) ; circle entry in tableau. Cross out row or column with rim value s, & reduce other rim value for this cell by s. When a single cell remains, shud be tie for rim conditions of row and column involved; put this amount into cell and circle.

  9. Here!

  10. Cost=14+4+3+36=57

  11. Check Indicator Values

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