4120_lecture-20-F10 - Computational Methods for Management...

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Computational Methods for Management and Economics Carla Gomes The transportation model Lecture 20 Reading: 8.1 of text book.
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Special IP Problems Transportation Problem Assignment Problem Min. Cost Flow Problems Shortest Path Problem
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Special Types of Integer Programming problems Special types of integer programming problems. (lp solves them) The structure of these problems leads to algorithms – streamlined versions of the simplex method - more efficient than the standard simplex method.
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The transportation problem
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3 canneries 4 distribution centers Shipping costs – major expense in management GOAL – minimize shipping costs
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CANNERY 1 Bellingham CANNERY 2 Eugene WAREHOUSE 1 Sacramento WAREHOUSE 2 Salt Lake City WAREHOUSE 3 Rapid City WAREHOUSE 4 Albuquerque CANNERY 3 Albert Lea
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Shipping Data Cannery Output Warehouse Allocation Bellingham 75 truckloads Sacramento 80 truckloads Eugene 125 truckloads Salt Lake City 65 truckloads Albert Lea 100 truckloads Rapid City 70 truckloads Total 300 truckloads Albuquerque 85 truckloads Total 300 truckloads
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Current Shipping Plan Warehouse From \ To Sacramento Salt Lake City Rapid City Albuquerque Cannery Bellingham 75 0 0 0 Eugene 5 65 55 0 Albert Lea 0 0 15 85
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Shipping Cost per Truckload Warehouse From \ To Sacramento Salt Lake City Rapid City Albuquerque Cannery Bellingham $464 $513 $654 $867 Eugene 352 416 690 791 Albert Lea 995 682 388 685 Total shipping cost = 75($464) + 5($352) + 65($416) + 55($690) + 15($388) + 85($685) = $165,595
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Terminology for a Transportation Problem Truckloads of canned peas Canneries Warehouses Output from a cannery Allocation to a warehouse Shipping cost per truckload from a cannery to a warehouse General Model Units of a commodity Sources Destinations Supply from a source Demand at a destination Cost per unit distributed from a source to a destination
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Characteristics of Transportation Problems The Requirements Assumption Each source has a fixed supply of units, where this entire supply must be distributed to the destinations. Each destination has a fixed demand for units, where this entire demand must be received from the sources. The Feasible Solutions Property A transportation problem will have feasible solutions if and only if the sum of its supplies equals the sum of its demands. The Cost Assumption The cost of distributing units from any particular source to any particular destination is directly proportional to the number of units distributed. This cost is just the unit cost of distribution times the number of units distributed.
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The Transportation Model Any problem (whether involving transportation or not) fits the model for a transportation problem if: 1. It can be described completely in terms of a table that identifies all the sources, destinations, supplies, demands, and unit costs, and
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4120_lecture-20-F10 - Computational Methods for Management...

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