lecture2-4up

lecture2-4up - ISyE 323 Lecture #2 Prof. Jeff Linderoth...

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Unformatted text preview: ISyE 323 Lecture #2 Prof. Jeff Linderoth September 8, 2009 ISyE Lecture #2 Outline Outline Wyndor Glass Case Study (Section 3.1) A More General Model (Section 3.2) Assumptions of Linear Programming (Section 3.3) ISyE Lecture #2 2 ISyE Lecture #2 Wyndor Glass Case Study (Section 3.1) Outline Wyndor Glass Case Study (Section 3.1) Problem Statement Formulating the Model Graphical Method for Solving the Model A More General Model (Section 3.2) Assumptions of Linear Programming (Section 3.3) ISyE Lecture #2 3 ISyE Lecture #2 Wyndor Glass Case Study (Section 3.1) Problem Statement Case Study I Wyndor Glass Co. I Produces windows and doors I Three plants I Plant 1: aluminum frames and hardware I Plant 2: wood frames I Plant 3: glass and assembly I Two new products to be introduced I Product 1: 8-foot glass door with aluminum frame I Product 2: 4 6-foot double-hung wood-framed window I Product 1 requires plants 1 and 3 I Product 2 requires plants 2 and 3 I Demand is unlimited I Capacity is limited ISyE Lecture #2 4 ISyE Lecture #2 Wyndor Glass Case Study (Section 3.1) Problem Statement Problem Definition The problem: I Choose production quantity of each product I To maximize total profit I Subject to capacity restrictions at each plant We might find: I It is optimal to produce both products I It is optimal to max out capacity with one product and not produce the other I It is optimal to produce neither product (cant turn a profit) I There is not enough capacity to produce either product (the problem is infeasible ) ISyE Lecture #2 5 ISyE Lecture #2 Wyndor Glass Case Study (Section 3.1) Problem Statement Data Requirements We need to know: I Number of hours of production time available at each plant per week (the available capacity) I Number of hours of production time required for one batch of each product at each plant I Profit per batch of each product produced ISyE Lecture #2 6 ISyE Lecture #2 Wyndor Glass Case Study (Section 3.1) Problem Statement Data Requirements, contd After months of meetings with Wyndor Glass managers, we find: Production Time (hrs/batch) Plant Product 1 Product 2 Available Hours 1 1 4 2 2 12 3 3 2 18 Profit per Batch $3000 $5000 ISyE Lecture #2 7 ISyE Lecture #2 Wyndor Glass Case Study (Section 3.1) Formulating the Model Decision Variables I Let I x 1 = number of batches of product 1 produced per week I x 2 = number of batches of product 2 produced per week I We dont know the values of x 1 and x 2 yetthe model is supposed to decide I These are called decision variables ISyE Lecture #2 8 ISyE Lecture #2 Wyndor Glass Case Study (Section 3.1) Formulating the Model Objective Function I We want to maximize total profit I Total profit (in $1000s) is given by 3 x 1 + 5 x 2 (recall: product 1 earns $3000/batch, product 2 earns $5000/batch) I So we want to maximize 3 x 1 + 5 x 2 I This is called the objective function ISyE Lecture #2 9 ISyE Lecture #2 Wyndor Glass Case Study (Section 3.1) Formulating the Model Constraints I...
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lecture2-4up - ISyE 323 Lecture #2 Prof. Jeff Linderoth...

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