Operations Management Transportation Models Module C Power Point

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

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 Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) 2 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

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 Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) 3 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

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

Transportation Problem ¨ 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 ¨ Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) 5 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

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

Transportation Problem Solution Steps ¨ 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 Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) 8 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

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

Transportation Table Destination Source 1 2 . . n Supply 1 a 1 2 a 2 : : Quantity demanded or required m Demand b 1 Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) b 2 am bn 10 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Transportation Table Source Destination 2. . 1 n Supply 1 x 11 c 11 x 12 c 12. . 2 supplying. . of x 21 c 21 x 22 c 22 Cost x 2 n c 2 n a 2 : m Demand : : Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) . . b 2 11 a 1 1 unit from sources : : : to destinations xm 1 cm 1 xm 2 cm 2. . b 1 x 1 n c 1 n xmn cmn am bn © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Transportation Table Destination 1 2 1 x 12 2 x 21 x 22 : : m x m 1 x m 2 b 1 b 2 Source Demand : : Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) . . n x 1 n . . supplied Quantity x 2 n from sources to : : : destinations. . x mn Supply a 1 a 2 : am bn 12 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Transportation Table To Albuquerque Boston From (A) (B) 4 5 Des Moines (D) 8 4 Evansville (E) 9 7 Fort Lauderdale (F) Warehouse 300 200 Requirements Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) 13 Cleveland Factory (C) Capacity 3 3 5 200 100 300 700 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Initial Solution Using the Northwest Corner Rule From To Albuquerque Boston (A) (B) Des Moines (D) Evansville (E) 100 200 Fort Lauderdale (F) Warehouse Requirements 5 4 3 8 4 3 7 5 100 9 100 300 Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) Cleveland Factory (C) Capacity 200 14 200 100 300 700 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

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 -. 15 each unused square Repeat steps 1 -4 for Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) ° © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Stepping-Stone Method: Tracing a Closed Path - Des Moines to Cleveland From To Albuquerque Boston (A) (B) Des Moines (D) Evansville (E) + 100 200 8 - 100 9 Fort Lauderdale (F) Warehouse Requirements 4 5 + 300 Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) 100 200 16 4 7 Cleveland Factory (C) Capacity Start + -200 3 3 5 100 300 700 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

The Intuitive Lowest Cost Method ÀIdentify the cell with the lowest cost. Arbitrarily break any ties for the lowest cost. ÁAllocate 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. Find the cell with the lowest cost from the remaining cells. ÃRepeat steps 2 & 317 until all units have been allocated. Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Initial Solution Using the Intuitive Lowest-Cost Method Second, cross out column To. Albuquerque. Boston Cleveland Factory From (A) (B) (C)C Capacity First, 4 3 5 Des Moines 100 cross out (D) Evansville 3 8 4 top row 100 Third, cross 300 200 (E) out row E Fort Lauderdale 9 7 5 (F) Warehouse Requirements 300 300 Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) 200 18 200 700 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Specialized Methods ¨ 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. ¨ Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) 19 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Special Issues in the Transportation Model ¨ 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 Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) 20 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Transportation Table Demand Not Equal Supply To Albuquerque Boston Cleveland. Dumm Factory From (A) (B) (C) Capacity y 5 4 3 0 Des Moines 250 (D) 3 8 4 0 Evansville 300 (E) 5 9 7 0 Fort Lauderdale 300 (F) Warehouse 15 200 700 Requirements 300 0 New Des Moines capacity Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) 21 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Degeneracy From To Albuquerque Boston (A) (B) Des Moines (D) Evansville (E) 100 200 Fort Lauderdale (F) Warehouse Requirements 5 4 3 8 4 3 7 5 100 9 300 Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) Cleveland Factory (C) Capacity 100 22 200 100 300 200 700 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458

Degeneracy - continued From To Albuquerque Boston (A) (B) Des Moines (D) Evansville (E) 100 200 Fort Lauderdale (F) Warehouse Requirements 5 4 8 4 3 7 5 100 9 300 Power. Point presentation to accompany Operations Management, 6 E (Heizer & Render) Cleveland Factory (C) Capacity 100 23 0 200 3 100 300 200 700 © 2001 by Prentice Hall, Inc. , Upper Saddle River, N. J. 07458