Supplement The Transportation Model McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc All Rights Reserved Supplement 8: Learning Objectives • You should be able to: – Describe the nature of a transportation problem – Set up transportation problems in the general linear programming format – Interpret computer solutions 8S-2 Transportation Problem • Involves finding the lowest-cost plan for distributing stocks of goods or supplies from multiple origins to multiple destinations that demand the goods Demand Supply Demand Supply Demand Supply Demand 8S-3 Transportation Model: Applications • The transportation model has numerous applications: – Location decisions • Compare location alternatives in terms of their impact cost on the total distribution costs for the system • Involves working through a separate model for each location being considered – Production planning – Capacity planning – Transshipment 8S-4 Transportation Problem • Shipping (supply) points – Any place from which good are sent • Factories • Warehouses • Departments • Destinations – Any point that receives goods • Factories • Warehouses • Departments 8S-5 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 8S-6 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 8S-7 Transportation Table 8S-8 Transportation Table 8S-9 Transportation Problem: Formulation xij = the number of units to ship from factory i to warehouse j Decision Variables Minimize where i = 1, 2, and and j = A, B, C, and D x1 A + x1B + x1C + 1x1D + 12 x2 A + 3x2 B + x2C + x2 D + x3 A + 10 x3 B + 16 x3C + x3 D Subject to Supply (rows) x1 A + x1B + x1C + x1D = 100 x2 A + x2 B + x2C + x2 D = 200 x3 A + x3 B + x3C + x3 D = 150 Demand (columns) x1 A + x2 A + x3 A = 80 x1B + x2 B + x3 B = 90 x1C + x2C + x3C = 120 x1D + x2 D + x3 D = 160 xij ≥ for all i and j 8S-10 Transportation: Computer Solution • 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 8S-11 Transportation Problem: Excel Template 8S-12 ... mode of transportation being used between each origin and destination 8S-7 Transportation Table 8S -8 Transportation Table 8S-9 Transportation Problem: Formulation xij = the number of units to.. .Supplement 8: Learning Objectives • You should be able to: – Describe the nature of a transportation... x3 D = 150 Demand (columns) x1 A + x2 A + x3 A = 80 x1B + x2 B + x3 B = 90 x1C + x2C + x3C = 120 x1D + x2 D + x3 D = 160 xij ≥ for all i and j 8S-10 Transportation: Computer Solution • Transportation