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Geraldine Shawhan is president of a firm that manufactures two types of metal file cabinets. Demand for her 2-drawer model is up to 600 weekly, while demand.

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Presentation on theme: "Geraldine Shawhan is president of a firm that manufactures two types of metal file cabinets. Demand for her 2-drawer model is up to 600 weekly, while demand."— Presentation transcript:

1 Geraldine Shawhan is president of a firm that manufactures two types of metal file cabinets. Demand for her 2-drawer model is up to 600 weekly, while demand for her 3-drawer model is limited to 400 weekly. The firm has a weekly operating capacity of 1,300 hours, with the 2-drawer cabinet taking 1 hour to produce and the 3-drawer cabin- et requiring 2 hours. Each 2-drawer model yields a $10.00 profit, while the profit for the large model is $ MGMT E-5050 Homework Solution SHAWHAN FILE WORKS GOAL PROGRAMMING

2 Shawhan has listed the following goals in order of importance: 1.Attain a profit as close to $11, as possible each week. 2.Avoid underutilization of the firm’s production capacity. 3.Sell as many 2-drawer cabinets and 3-drawer cabinets as the demand indicates. REQUIREMENT: A.Formulate the goal programming model. B.Solve this problem on QM for WINDOWS. Homework Solution GOAL PROGRAMMING SHAWHAN FILE WORKS

3 Let : X 1 = number of 2-drawer cabinets produced weekly X 2 = number of 3-drawer cabinets produced weekly d 1 = underachievement of profit goal d 1 = overachievement of profit goal d 2 = idle time in production capacity d 3 = underachievement of sales goal for 2-drawer cabinets d 4 = underachievement of sales goal for 3-drawer cabinets Homework Solution GOAL PROGRAMMING SHAWHAN FILE WORKS

4 Minimize deviations = P 1 d 1 + P 1 d 1 + P 2 d 2 + P 3 d 3 + P 3 d 4 subject to : 10X X 2 + d 1 – d 1 = $11, ( profit target ) 1X 1 + 2X 2 + d 2 - d 2 = 1,300 hours ( production limit ) 1X 1 + d 3 - d 3 = 600 ( 2-drawer sales limit ) 1X 2 + d 4 - d 4 = 400 ( 3-drawer sales limit ) All Xi, di variables => Homework Solution GOAL PROGRAMMING + + +

5 Goal Programming with QM for WINDOWS Shawhan File Works

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8 1 st Goal, 1 st Priority : Profit should be as close to $11,000. as possible 2 nd Goal, 2 nd Priority : Avoid underutilization of production capacity 3 rd Goal, 3 rd Priority : Sell as many 2-draw cabinets as demand states 3 rd Goal, 3 rd Priority : Sell as many 3-draw cabinets as demand states

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13 The campaign manager for a politician who is running for reelection is currently engaged in the planning process. Four ways to advertise have been selected: television ads, radio ads, billboards, and newspa- per ads. The costs are as follows: - $ for each television ad - $ for each radio ad - $ for a billboard for one month - $ for each newspaper ad The audience reached by each type of advertising has been estimated at: - 40,000 for each television ad - 32,000 for each radio ad - 34,000 for each billboard - 17,000 for each newspaper ad The total monthly advertising budget is $16, THE CAMPAIGN MANAGER GOAL PROGRAMMING Homework Solution

14 THE CAMPAIGN MANAGER The following goals have been established and ranked: 1.The number of people reached should be at least 1,500, The total monthly advertising budget should not be exceeded. 3.Together, the number of ads on either television or radio should be at least six (6). 4.No more than ten (10) ads of any type of advertising should be used. REQUIREMENT: 1.Formulate this as a goal programming problem. 2.Solve this problem via QM for WINDOWS. 3.Which goals are completely met and which of them are not? Homework Solution

15 THE CAMPAIGN MANAGER Let : X 1 = the number of television ads X 2 = the number of radio ads X 3 = the number of billboard ads X 4 = the number of newspaper ads Subject to : (1) the number of people reached. (2) the budget. (3) the number of TV or radio ads. (4) restriction on the number of each individual type of ad. Homework Solution GOAL PROGRAMMING

16 THE CAMPAIGN MANAGER Minimize deviations = P 1 d P 2 d P 3 d P 4 d P 4 d 5 + P 4 d P 4 d 7 + subject to : The number of people reached: 40,000 X ,000 X ,000 X ,000 X 4 –d d 1 - = 1,500,000 The budget: 900 X X X X 4 –d d 2 - = 16,000 The number of television or radio ads: X 1 + X 2 –d d 3 - = 6 Restriction on the number of each individual type of ad: X 1 – d d 4 - = 10 X 3 –d d 6 - = 10 X 2 – d d 5 - = 10 X 4 –d d 7 - = 10 X 1, X 2, X 3, X 4, and all d i => 0 non-negativity constraint Homework Solution

17 THE CAMPAIGN MANAGER SUMMARY  The number of television ads = 0  The number of radio ads =.73 ≈ 0  The number of billboard ads = 0  The number of newspaper ads =  The number of newspaper ads was exceeded by Goal #1 – the number of people reached was met exactly. Goal #2 – the budget of $16, was met ($15,994.80) Goals #3 and #4 – not met ; the number of television, radio, and billboard ads are each less than 10. Homework Solution

18 Goal Programming with QM for WINDOWS The Campaign Manager

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24 newspaper $ = $15, newspaper 17,000 people reached = 1,510,620 people Audience exposure and budget are met completely. The number of TV, radio, and billboard ads are each less than 10. The other goals are not met.


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