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Quantitative Methods for Managerial Decision-Making ACN 309-5 Operations Management Transportation Models

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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

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Quantitative Methods for Managerial Decision-Making ACN 309-5 Learning Objectives After you read these notes, 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

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Quantitative Methods for Managerial Decision-Making ACN 309-5 Transportation Problem DesMoines (100 unit capacity) Fort Lauderdale (300 units capacity) Cleveland (200 units required) Evansville (300 units capacity) Albuquerque (300 units required) Boston (200 units required)

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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

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Quantitative Methods for Managerial Decision-Making ACN 309-5 2 2 n Supply Quantity Source Quantity Shipped Destination aiai ix mn jbjbj a1a1 1 b1b1 x 11 a2a2 x 22 b2b2 : : x 2n :: amam x mn bnbn x 1n x 12 x 21 Demand Quantity m x m2 1 x m1 Transportation Problem Graphical Solution

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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

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Quantitative Methods for Managerial Decision-Making ACN 309-5 Transportation Costs From To (Destination) (Sources)AlbuquerqueBostonCleveland Des Moines$5$4$3 Evansville$8$4$3 Fort Lauderdale $9$7$5

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Quantitative Methods for Managerial Decision-Making ACN 309-5 Transportation Table

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Quantitative Methods for Managerial Decision-Making ACN 309-5 Transportation Table

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Quantitative Methods for Managerial Decision-Making ACN 309-5 Transportation Table

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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 + + + - - -

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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. ÂFind the cell with the lowest cost from the remaining cells. ÃRepeat steps 2 & 3 until all units have been allocated.

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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 Initial Solution Using the Intuitive Lowest- Cost Method

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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 See your CD Tutorial © 1995 Corel Corp. Specialized Methods

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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

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Quantitative Methods for Managerial Decision-Making ACN 309-5 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

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