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Lecture5eve-new - MBAC6080 Decision Modeling and...

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1 MBAC6080 Thomas Vossen Assistant professor of Operations Management Leeds School of Business University of Colorado Boulder, CO 80309-0419 Decision Modeling and Applications
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Lecture 5, 2-13-2008 2 MBAC6080 Today’s Agenda Network Models Transshipment Models Shortest Path, Max Flow, Spanning Tree Models Integer Programming Formulating IPs Examples Application Study Two-sided Matching
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Lecture 5, 2-13-2008 3 MBAC6080 So Far … Maximize 2H + 4C Subject to C ≤ 10 4H + 6C ≤ 120 2H + 6C ≤ 72 A,C ≥ 0 Linear Programming Models Objective function Constraints Decision Variables
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Lecture 5, 2-13-2008 4 MBAC6080 But Now … Maximize 2H + 4C Subject to C ≤ 10 4H + 6C ≤ 120 2H + 6C ≤ 72 A,C ≥ 0 A,C Integer Linear Programming Models Objective function Constraints Decision Variables Integer Integrality Constraint Some (or all) of the variables are restricted to integer values
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Lecture 5, 2-13-2008 5 MBAC6080 The Key …
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Lecture 5, 2-13-2008 6 MBAC6080 A General Classification Network Models Class of “Specially Structured” Linear Programs Integrality constraint is redundant LP solutions will automatically take on integer values Many applications, Specialized Solution procedures General (Mixed) Integer Programming Models More flexible, many more applications More difficult to model (Usually) Much more difficult to solve !!
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Lecture 5, 2-13-2008 7 MBAC6080 Network Models
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Lecture 5, 2-13-2008 8 MBAC6080 Network Models A number of business problems can be represented graphically as networks. This chapter focuses on several such problems: - Transshipment Problems - Shortest Path Problems - Maximal Flow Problems - Transportation/Assignment Problems - Generalized Network Flow Problems - The Minimum Spanning Tree Problem
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Lecture 5, 2-13-2008 9 MBAC6080 Network Flow Problem Characteristics Network flow problems can be represented as a collection of nodes connected by arcs. There are three types of nodes: Supply Demand Transshipment We’ll use negative numbers to represent supplies and positive numbers to represent demand.
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Lecture 5, 2-13-2008 10 MBAC6080 Transshipment Problems
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Lecture 5, 2-13-2008 11 MBAC6080 Distribution Unlimited Co. The Distribution Unlimited Co. has two factories producing a product that needs to be shipped to two warehouses Factory 1 produces 80 units. Factory 2 produces 70 units. Warehouse 1 needs 60 units. Warehouse 2 needs 90 units. There are rail links directly from Factory 1 to Warehouse 1 and Factory 2 to Warehouse 2. Independent truckers are available to ship up to 50 units from each factory to the distribution center, and then 50 units from the distribution center to each warehouse. Question: How many units (truckloads) should be shipped along each shipping lane?
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Lecture 5, 2-13-2008 12 MBAC6080 The Distribution Network   F1 DC F2 W2 W1 80 units produced 70 units  produced 60 units needed 90 units  needed
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Lecture 5, 2-13-2008 13 MBAC6080 Data for Distribution Network   F1 DC F2 W2 W1 80 un its produced 70 un its produced 60 un its needed 90 un its needed $700 /un it $900 /un it $300
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