12 Transportation Model LP

# 12 Transportation Model LP - Lesson 12 The Transportation...

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12 - 1 An Application of Linear Programming Lesson 12 The Transportation Model

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12 - 2 Minimize transportation costs between Supplying Locations (Factories) and Demand Locations (Warehouses). Demand Location C Demand Location A Demand Location D Supply Location 1 Supply Location 3 The Problem
12 - 3 The transportation cost per unit between Factory and Warehouse are shown in the cost matrix table below: The Cost Matrix Warehouse Factory A B C D 1 4 7 7 1 2 12 3 8 8 3 8 10 16 5 The transportation cost to ship 1 unit of product between Factory 1 and Warehouse A is 4.

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12 - 4 The factory capacity (supply units per period) and the warehouse demand (units per period that can be handled) are shown in the following tables: Factory Capacity & Warehouse Demand Factory Supply 1 100 2 200 3 150 Total 450 Warehouse A B C D Total Demand 80 90 120 160 450
12 - 5 The three previous tables can be summarized in one matrix as follows: Summary Matrix Warehouse Factory A B C D Supply 1 4 7 7 1 100 2 12 3 8 8 200 Total 3 8 10 16 5 150 Supply Demand 80 90 120 160 450 Total Demand 450

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12 - 6 Once the initial allocation is made, there are methods for obtaining an optimal solution which involve still further steps - these are discussed in the section “ Testing for Optimality”pages 393 though 405. Although, the manual solution to the transportation model is relatively straightforward, it is time consuming. The transportation model can also be optimally solved by Linear Programming. An Optimal Solution
12 - 7 let x i, j be the quantity shipped from factory i to warehouse j minimize 4x 1,A x 1,B x 1,C x 1,D 12x 2,A x 2,B x 2,C x 2,D 8x 3,A x 3,B x 3,C x 3,D + + + + + + + + + + + 7 7 1 3 8 8 10 16 5 The LP Formulation Warehouse Factory A B C D Supply 1 4 7 7 1 100 2 12 3 8 8 200 Total 3 8 10 16 5 150 Supply Demand 80 90 120 160 450 Total Demand 450

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12 - 8 . Supply Constraints (rows) . Demand Constraints (columns) subject to x x x x 100 x x x x 200 x x x x 150 1,A 1,B 1,C 1,D 2,A 2,B 2,C 2,D 3,A 3,B 3,C 3,D + + + = + + + = + + + = subject to x x x 80 x x x 90 x x x 120 x x x 1,A 2,A 3,A 1,B 2,B 3,B 1,C 2,C 3,C 1,D 2,D 3,D + + = + + = + + = + + = 160 The LP Formulation
12 - 9

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12 - 10 Transportation LP Enter Transportation LP formulation in green cells
12 - 11 The total cost of the optimum solution is 2,300. Shipments are: from supplier 1 send 10 to receiver C, 90 to receiver D from supplier 2 send 90 to receiver B, 110 to receiver C from supplier 3 send 80 to receiver A Transportation LP Tools, Solver, Solve Calculates the LP solution.

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12 - 12 Unequal Supply & Demand Consider the following situation showing cost per unit between supply and demand (receiving) location where the supply and the demand are unequal.
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## This note was uploaded on 09/10/2011 for the course ECON 101 taught by Professor Halcrow,b during the Spring '08 term at Antelope Valley College.

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12 Transportation Model LP - Lesson 12 The Transportation...

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