1. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-1 Operations Management Transportation Models Module C

2. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-2 Outline  Transportation Modeling  Developing an Initial Solution  The Northwest-Corner Rule  The Intuitive Lowest Cost Method  The Stepping-Stone Method  Special Issues in Modeling  Demand Not Equal to Supply  Degeneracy

3. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-3 Learning Objectives When you complete this chapter, you should be able to :  Identify or Define :  Transportation modeling  Facility location analysis  Explain or be able to use:  Northwest-corner rule  Stepping-stone method

4. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-4 Transportation Problem DesMoines (100 unit capacity) Fort Lauderdale (300 units capacity) Boston (200 units required) Cleveland (200 units required) Evansville (300 units capacity) Albuquerque (300 units required)

5. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-5  How much should be shipped from several sources to several destinations  Sources: Factories, warehouses, etc.  Destinations: Warehouses, stores, etc.  Transportation models  Find lowest cost shipping arrangement  Used primarily for existing distribution systems Transportation Problem

6. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-6 A Transportation Model Requires  The origin points, and the capacity or supply per period at each  The destination points and the demand per period at each  The cost of shipping one unit from each origin to each destination

7. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-7 2 2 n Supply Quantity Source Quantity Shipped Destination aiaiaiaiix mn j bjbjbjbj a1a1a1a11 b1b1b1b1 x 11 a2a2a2a2 x 22 b2b2b2b2: :x2n :: amamamam x mn bnbnbnbn x 1n x 12 x 21 Demand Quantity m x m2 1 x m1 Transportation Problem Graphical Solution

8. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-8  Define problem  Set up transportation table (matrix)  Summarizes all data  Keeps track of computations  Develop initial solution  Northwest corner rule  Find optimal solution  Stepping stone method Transportation Problem Solution Steps

9. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-9 Transportation Costs From To (Destination) (Sources)AlbuquerqueBostonCleveland Des Moines$5$4$3 Evansville$8$4$3 Fort Lauderdale $9$7$5

10. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-10 Transportation Table

11. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-11 Transportation Table

12. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-12 Transportation Table

13. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-13 Transportation Table To From Albuquerque (A) Boston (B) Cleveland (C) Factory Capacity Des Moines (D) 100 Evansville (E) 300 Fort Lauderdale (F) 300 Warehouse Requirements 300200 700 5 8 97 4 43 3 5

14. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-14 Initial Solution Using the Northwest Corner Rule To From Albuquerque (A) Boston (B) Cleveland (C) Factory Capacity Des Moines (D) 100 Evansville (E) 200100300 Fort Lauderdale (F) 100200300 Warehouse Requirements 300200 700 5 8 97 4 43 3 5

15. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-15 The Stepping Stone Method ¬ Select any unused square to evaluate ­ Begin at this square. Trace a closed path back to the original square via squares that are currently being used (only horizontal or vertical moves allowed) ® Place + in unused square; alternate - and + on each corner square of the closed path ¯ Calculate improvement index: add together the unit cost figures found in each square containing a +; subtract the unit cost figure in each square containing a -. ° Repeat steps 1-4 for each unused square

16. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-16 Stepping-Stone Method: Tracing a Closed Path - Des Moines to Cleveland To From Albuquerque (A) Boston (B) Cleveland (C) Factory Capacity Des Moines (D) 100 Evansville (E) 200 100300 Fort Lauderdale (F) 100200300 Warehouse Requirements 300200 700 5 8 97 4 43 3 5 Start + + + - - -

17. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-17 The Intuitive Lowest Cost Method À Identify the cell with the lowest cost. Arbitrarily break any ties for the lowest cost. Á Allocate as many units as possible to that cell without exceeding the supply or demand. Then cross out that row or column (or both) that is exhausted by this assignment. Â Find the cell with the lowest cost from the remaining cells. Ã Repeat steps 2 & 3 until all units have been allocated.

18. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-18 Initial Solution Using the Intuitive Lowest- Cost Method To From Albuquerque (A) Boston (B) Cleveland (C) Factory Capacity Des Moines (D) 100 Evansville (E) 200 100 300 Fort Lauderdale (F) 300 Warehouse Requirements 300200 700 5 8 97 4 43 3 5 First, cross out top row Second, cross out column C Third, cross out row E

19. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-19  Linear programming model is difficult to formulate & solve  Special purpose methods  Are easier to formulate  Are faster to compute  Give integer solutions  Methods  Stepping-stone  MODI © 1995 Corel Corp. Specialized Methods

20. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-20  Demand not equal to supply  Called ‘unbalanced’ problem  Add dummy source if demand > supply  Add dummy destination if supply > demand  Degeneracy in Stepping Stone Method  Too few shipping routes (cells) used  Number of occupied cells should be: m + n - 1  Create artificially occupied cell (0 value)  Represents fake shipment Special Issues in the Transportation Model

21. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-21 Transportation Table Demand Not Equal Supply To From Albuquerque (A) Boston (B) Cleveland (C) Factory Capacity Des Moines (D) 250 Evansville (E) 300 Fort Lauderdale (F) 300 Warehouse Requirements 300200 700 5 8 97 4 43 3 5 0 0 0 Dummy 150 New Des Moines capacity

22. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-22 Degeneracy To From Albuquerque (A) Boston (B) Cleveland (C) Factory Capacity Des Moines (D) 100 Evansville (E) 200100300 Fort Lauderdale (F) 200 Warehouse Requirements 300100200700 5 8 97 4 43 3 5

23. PowerPoint presentation to accompany Operations Management, 6E (Heizer & Render) © 2001 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 C-23 Degeneracy - continued To From Albuquerque (A) Boston (B) Cleveland (C) Factory Capacity Des Moines (D) 100 Evansville (E) 200100300 Fort Lauderdale (F) 200 Warehouse Requirements 300100200700 5 8 97 4 43 3 5 0