The Transportation Model Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.

8S-2 You should be able to: LO 8s.1Describe the nature of a transportation problem LO 8s.2Solve transportation problems manually and interpret the results LO 8s.3Set up transportation problems in the general linear programming format LO 8s.4Interpret computer solutions

8S-3 Involves finding the lowest-cost plan for distributing a stock of goods or supplies from multiple points of origin to multiple destinations that demand the goods LO 8s.1

8S-4 Information requirements 1. A list of the origins and each one’s capacity or supply quantity per period 2. A list of the destinations and each one’s demand per period 3. The unit cost of shipping items from each origin to each destination LO 8s.2

8S-5 Transportation model assumptions 1. The items to be shipped are homogeneous 2. Shipping cost per unit is the same regardless of the number of units shipped 3. There is only one route or mode of transportation being used between each origin and destination LO 8s.2

8S ABCD Supply Demand Warehouse Factory 450 Factory 1 can supply 100 units per period Total capacity per period Cost to ship one unit from factory 1 to warehouse A Total Demand per period Warehouse B can use 90 units per period LO 8s.2

8S-7 Intuitive Lowest-Cost Approach 1. Identify the cell with the lowest cost 2. Allocate as many units as possible to that cell, and cross out the row or column (or both) 3. Find the cells with the next lowest cost from among the feasible cells 4. Repeat steps (2) and (3) until all units have been allocated LO 8s.2

8S ABCD Supply Demand Warehouse Factory 450 LO 8s.2

8S-9 Evaluating Stepping Stone Paths: 1. Start by placing a + sign in the cell you wish to evaluate. 2. Move horizontally (or vertically) to a cell that has units assigned to it. Assign a minus sign (-) to it. It is OK to pass through an empty cell or a completed cell without stopping. Choose a cell that will permit your next move to another completed cell. Change direction and move to another completed cell. Assign a plus sign (+) to the cell. 3. Continue the process until a closed path back to the original cell can be completed. LO 8s.2

8S ABCD Supply Demand Warehouse Factory 450 (+) (-) (+) (-) 4 – – 8 = 0 LO 8s.2

8S ABCD Supply Demand Warehouse Factory 450 LO 8s.2

8S ABCD Supply Demand Warehouse Factory LO 8s.2

8S-13 LO 8s.3

8S-14 Transportation problems can be solved manually in a straightforward manner Except for very small problems, solving the problem manually can be very time consuming For medium to large problems, computer solution techniques are more practical A variety of software packages are available for solving the transportation model Some require formulating the problem as a general LP model Others allow data entry in a more simple, tabular format LO 8s.4

8S-15 LO 8s.4