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Lecture Operations management: Chapter 8S - William J. Stevenson

Chapter 8S - The transportation model. After completing this chapter, students will be able to: Describe the nature of a transportation problem, solve transportation problems manually and interpret the results, set up transportation problems in the general linear programming format, interpret computer solutions. | The Transportation Model Supplement 8 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 1 Supplement 8: Learning Objectives You should be able to: LO 8s.1 Describe the nature of a transportation problem LO 8s.2 Solve transportation problems manually and interpret the results LO 8s.3 Set up transportation problems in the general linear programming format LO 8s.4 Interpret computer solutions 2 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 Transportation Problem LO 8s.1 3 Model: Information Requirements Information requirements A list of the origins and each one’s capacity or supply quantity per period A list of the destinations and each one’s demand per period The unit cost of shipping items from each origin to each destination LO 8s.2 4 Model: Assumptions Transportation | The Transportation Model Supplement 8 Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. 1 Supplement 8: Learning Objectives You should be able to: LO 8s.1 Describe the nature of a transportation problem LO 8s.2 Solve transportation problems manually and interpret the results LO 8s.3 Set up transportation problems in the general linear programming format LO 8s.4 Interpret computer solutions 2 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 Transportation Problem LO 8s.1 3 Model: Information Requirements Information requirements A list of the origins and each one’s capacity or supply quantity per period A list of the destinations and each one’s demand per period The unit cost of shipping items from each origin to each destination LO 8s.2 4 Model: Assumptions Transportation model assumptions The items to be shipped are homogeneous Shipping cost per unit is the same regardless of the number of units shipped There is only one route or mode of transportation being used between each origin and destination LO 8s.2 5 4 7 7 1 100 12 3 8 8 200 8 10 16 5 150 80 90 120 160 A B C D Supply Demand 1 2 3 Warehouse Factory 450 450 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 6 Intuitive Lowest-Cost Approach Identify the cell with the lowest cost Allocate as many units as possible to that cell, and cross out the row or column (or both) Find the cells with the next lowest cost from among the feasible cells Repeat steps (2) and (3) until all units have been allocated Initial Solution LO 8s.2 7 Table 6 – Initial Solution 4 7 7 100 1 100 12 90 3 110 8 8 200 80 8 10 10 16 60 5 150 80 90 120 160 A B C D Supply Demand 1 2 3 Warehouse