Presentation on theme: "Homework Solution GOAL PROGRAMMING"— Presentation transcript:
1 Homework Solution GOAL PROGRAMMING SHAWHAN FILE WORKSMGMT E-5050Geraldine Shawhan is president of a firm that manufactures twotypes of metal file cabinets.Demand for her 2-drawer model is up to 600 weekly, while demandfor her 3-drawer model is limited to 400 weekly.The firm has a weekly operating capacity of 1,300 hours, with the2-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 thelarge model is $
2 Homework Solution GOAL PROGRAMMING SHAWHAN FILE WORKSShawhan has listed the following goals in order of importance:Attain a profit as close to $11, as possible each week.Avoid underutilization of the firm’s production capacity.Sell as many 2-drawer cabinets and 3-drawer cabinets asthe demand indicates.REQUIREMENT:Formulate the goal programming model.Solve this problem on QM for WINDOWS.
3 Homework Solution GOAL PROGRAMMING Let : SHAWHAN FILE WORKSLet :X1 = number of 2-drawer cabinets produced weeklyX2 = number of 3-drawer cabinets produced weeklyd1 = underachievement of profit goald1 = overachievement of profit goald2 = idle time in production capacityd3 = underachievement of sales goal for 2-drawer cabinetsd4 = underachievement of sales goal for 3-drawer cabinets-+---
8 1st Goal, 1st Priority : Profit should be as close to $11,000 1st Goal, 1st Priority : Profit should be as close to $11,000. as possible2nd Goal, 2nd Priority : Avoid underutilization of production capacity3rd Goal, 3rd Priority : Sell as many 2-draw cabinets as demand states3rd Goal, 3rd Priority : Sell as many 3-draw cabinets as demand states
13 Homework Solution THE CAMPAIGN MANAGER GOAL PROGRAMMING The campaign manager for a politician who is running for reelectionis currently engaged in the planning process. Four ways to advertisehave 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 adThe audience reached by each type of advertising has been estimatedat:- 40,000 for each television ad- 32,000 for each radio ad- 34,000 for each billboard- 17,000 for each newspaper adThe total monthly advertising budget is $16,000.00
14 THE CAMPAIGN MANAGERHomework SolutionThe following goals have been established and ranked:The number of people reached should be at least 1,500,000.The total monthly advertising budget should not be exceeded.Together, the number of ads on either television or radio shouldbe at least six (6).No more than ten (10) ads of any type of advertising should beused.REQUIREMENT:Formulate this as a goal programming problem.Solve this problem via QM for WINDOWS.Which goals are completely met and which of them are not?
15 Homework Solution GOAL PROGRAMMING THE CAMPAIGN MANAGERHomework SolutionGOAL PROGRAMMINGLet : X1 = the number of television adsX2 = the number of radio adsX3 = the number of billboard adsX4 = the number of newspaper adsSubject to :(1) the number of people reached.(2) the budget.(3) the number of TV or radio ads.(4) restriction on the number of eachindividual type of ad.
16 THE CAMPAIGN MANAGERHomework SolutionMinimize deviations = P1d1- + P2d2+ + P3d3- + P4d4+ + P4d5+ P4d6+ + P4d7+subject to :The number of people reached:40,000 X1 + 32,000 X2 + 34,000 X3 + 17,000 X4 –d1+ + d1- = 1,500,000The budget:900 X X X X4 –d2+ + d2- = 16,000The number of television or radio ads:X1 + X2 –d3+ + d3- = 6Restriction on the number of each individual type of ad:X1 – d4+ + d4- = X3 –d6+ + d6- = 10X2 – d5+ + d5- = X4 –d7+ + d7- = 10X1 , X2 , X3, X4 , and all di => 0 non-negativity constraint
17 Homework Solution SUMMARY The number of television ads = 0 THE CAMPAIGN MANAGERHomework SolutionSUMMARYThe number of television ads = 0The number of radio ads = .73 ≈ 0The number of billboard ads = 0The number of newspaper ads = 88.86The number of newspaper ads was exceeded by 78.86Goal #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.
18 Goal Programming with QM for WINDOWS The Campaign Manager
24 88.86 newspaper ads @ $180.00 = $15,994.80 88.86 newspaper ads 388.86 newspaper ads@ 17,000 peoplereached= 1,510,620 peopleAudience exposureand budget are metcompletely.The number of TV,radio, and billboardads are each less than10.The other goals arenot met.