8S The Transportation Model McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc All Learning Objective Describe the nature of a transportation problem Set up transportation problems in the general linear programming format Interpret computer solutions 8S-2 Requirements for Transportation Model List of origins and each one’s capacity List of destinations and each one’s demand Unit cost of shipping Note: The DVD that accompanies this book contains a module that provides detailed instruction on the transportation model 8S-3 Transportation Model Assumptions Items to be shipped are homogeneous Shipping cost per unit is the same Only one route between origin and destination 8S-4 The Transportation Problem Figure 8S.1 D (demand) D (demand) S (supply) S (supply) D (demand) S (supply) D (demand) 8S-5 A Transportation Table Table 8S.1 A Factory Warehouse C B D 7 100 12 8 200 10 16 150 Demand Factory can supply 100 units per period 80 90 120 Warehouse B can use 90 units per period 160 Total supply 450 capacity per 450 period Total demand per period 8S-6 Special Problems Unequal supply and demand Dummy: Imaginary number added equal to the difference between supply and demand when these are unequal Degeneracy: The condition of too few completed cells to allow all necessary paths to be constructed 8S-7 Summary of Procedure Make certain that supply and demand are equal Develop an initial solution using intuitive, low-cost approach Check that completed cells = R+C-1 Evaluate each empty cell Repeat until all cells are zero or positive 8S-8 Excel Template Figure 8S.2 8S-9