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McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Linear Programming Using the Excel Solver Appendix A.

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Presentation on theme: "McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Linear Programming Using the Excel Solver Appendix A."— Presentation transcript:

1 McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Linear Programming Using the Excel Solver Appendix A

2 A-2 Background  The key to profitable operations is making the best use of available resources of people, material, plant and equipment, and money  Today’s manager has a powerful mathematical modeling tool available for this purpose - linear programming  In this presentation, we will show how the use of the Microsoft Excel Solver to solve LP problems

3 A-3 Introduction  Linear programming (LP) refers to several related mathematical techniques used to allocate limited resources among competing demands in an optimal way  LP is the most popular of the approaches falling under the general heading of mathematical optimization techniques

4 A-4 Linear Programming Applications Finding the minimum-cost production schedule Aggregate sales and operations planning Comparing how efficiently different service and manufacturing outlets are using their resources Service/manufacturing productivity analysis Finding the optimal product mix where several products have different costs and resource requirements Product planning Finding the optimal way to produce a product that must be processed sequentially through several machine centers Product routing Finding the optimal way to use resources such as aircraft, buses, or trucks Vehicle/crew scheduling

5 A-5 Linear Programming Applications Minimizing the amount of scrap material generated Process control Finding the optimal combination of products to stock in a network of warehouses or storage locations Inventory control Finding the optimal shipping schedule for distributing products between factories and warehouses Distribution scheduling Finding the optimal location of a new plant by evaluating shipping costs between alternative locations Plant location studies Finding the minimum-cost routings of material handling devices between departments Material handling

6 A-6 Linear Programming – Essential Conditions There must be limited resources There must be an explicit objective There must be linearity There must be homogeneity There must be divisibility

7 A-7 Linear Programming Model

8 A-8 Graphical Linear Programming  Limited to solving problems with two variables  Steps are: 1. Formulate the problem in mathematical terms 2. Plot constraint equations 3. Determine the area of feasibility 4. Plot the objective function 5. Find the optimal point

9 A-9 Linear Programming Using Microsoft Excel  Spreadsheets can be used to solve linear programming problems  Microsoft Excel has an optimization tool called Solver for this purpose  If the Solver option does not appear in your Data menu, you likely need to install the Solver Add-In  Search Excel help for “Load the Solver Add-In” for detailed instructions specific to your version of Excel

10 A-10 Linear Programming with Excel 1. Define changing cells 2. Calculate total profit 3. Set up resource usage 4. Set up Solver 5. Solve the problem

11 A-11 Step 1 – Define Changing Cells  A convenient starting point is to identify cells to be used for the decision variables in the problem  These are H and C, the number of hockey sticks and number of chess sets to produce  Excel refers to these cells as changing cells in Solver  We have designated B4 as the location for the number of hockey sticks to produce and C4 for the number of chess sets Changing Cells – designate B2 as “H” and B3 as “C”

12 A-12 Step 2 – Calculate Total Profit  This is the objective function  Calculated by multiplying profit associated with each product by the number of units produced  We have placed the profits in cells B5 and D5 so the profit is calculated by the following equation: B2*B5 + B3*D5, which is calculated in cell F5 Objective Function – “=B2*B5+B3*D5”

13 A-13 Step 3 – Resource Usage (Constraints)  Our resources are machine centers A, B, and C  For machine center A, 4 hours of processing time are used for each hockey stick produced and 6 hours for each chess set  For a solution, the total amount of the machine center A resource used is calculated in F7 (=B7*B2 + D7*B3)  We indicate in cell G7 that we want this to be less than the 120-hour capacity of machine center A, in H7  Resource usage for machine centers B and C are set up in the exact same manner in rows 10 and 11 Constraints – Row 7 – Machine Center A Row 8 – Machine Center B Row 9 – Machine Center C

14 A-14 Step 4 – Set Up Solver 1. Set Target Cell: is the location where the value that we want to optimize is calculated This is the profit calculated in F5 2. Equal To: set to Max since maximize profit 3. By Changing Cells: are the cells that Solver can change to maximize profit Cells B2 through B3 are the changing cells 4. Subject to the Constraints: correspond to our machine center capacity Here click on Add and indicate that the total used for a resource is less than or equal to the capacity available

15 A-15 Step 5 – Solve the Problem  Solver has numerous options, but we will need to use only a few  Use the Simplex LP solving method to tell Solver that we want to use the linear programming option for solving the problem  We know our changing cells (decision variables) must be numbers that are greater than or equal to zero since it makes no sense to make a negative number of hockey sticks or chess sets We indicate this by selecting “Make Unconstrained Variables Non-Negative” as an option Click on “Solve” to find the answer

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