Faaliyetler İş Araştırma ve İktisat Goal Programming Applications (Questions) I' /1 I GOAL PROGRAMMING_APPLICATIONS Man 203 A Non Pre Emptive Goal Programming 1_ THE firm ABC produces three items (xl, x2, and x3). The management consider ..... ee goals in the long run. The unit profit of xl is 12, x2 is 9 and x3 is 15 To produce the items: 5 workers for xl, 3 workers for x2, and 4 workers for x3 are needed The investment cost values are: 5 for xl, 7 for x2, and 8 for x3. GOALS: A - The profit should be at least 125 (thousand $) in the long run B -The current manpower should be set at exactly 40 (xlOO) workers C -The investment for buying new equipment should not exceeds 55 (thousands $) These three goals are equilly important there is no priority among the goals, If the profit goal would not be established, there will be 5 (thousand$) penalty (loss) if the manpower goal is exceeded the penalty value is 2 (thousand$ for every 100 workers) if the manpower goal is behind the goal, the penalty value is 4 (thousand$ for evert 100 workers) if the investment goal is exceeded the penalty value is 3 'Ithousan d$ ) , Wr, ite a goal prog'ramming model for the fiven problem (Tip:·there is no functional constrainfs in this question) . . ' , ". ONCELlKLI HEDEF PROGRAM lAMA 2_ (RElATED TO THE QUESTION U) The firm ABC found out that the given problem with the non-preemtive solution resulted in . S33 manpower loss(exceeds ,the goal), Therefore they prioritize the problem The first goal: P1)the manpower should not be more than 40 P2) the cost of investment should not be more than 55 The second Goal: P3)the profit shaul be more than 125 in the long run , P4) the the balance of manpoer( should be <= 40) should be obtained Re formiJlaize the goal programming model for the given priorities P1>p2>p3>p4 3_ the firm-XY2 is produc;ing two type. of computer: type-A--and-type S, For both of the types, they are using the same tower and same floppy disk(disket surucu), In type A, there are hard disk and 35-lloppy disk, In type B, there are hard disk, floppy and,cd driver. The tower and the floppys are'imported from another finns, XY2 can obtain (up to) 1000 pcs of floppys, 500 pcs hard disks, 500 pcs CD drives, and 600 pcs towers per week, It takes 1hr to produce type A and the unit profit of type A is $200, also, it ta kes 15hrs to produce type S and the unit profit of it is $500, The management of XY2 are trying to establish the given goals below PI) produce at least 200 pcs of type A per week P2) produce at least a total of 500 pcs of computers per week P3) make at least profit of $250,000 in sum per week P4) do not overpass the 400hrs of working time" a) ForrT'!ulize the given problem as non-preemtive.goa.! programming b) Formulize the given problem as a preemtive goal programming. The priorities of the given goals are p1>p2>p3>p4 1 4_ for the election ca m paign of mr X,there are lobo people are working as volunteer'S. There is only 1 week before the election. The workkers will be working 12 hou rs a da y during this 7 days of campaign There are three strategies for the campaign Media channel Face to face introduction (visiting houses) C alling people by telephone Each phone call takes 4 min in average and vis iting people takes 7 min in average. ~OI" the media publicity. there should be 3 people to work together. Mr X's advisors reccommend to have at least 30,000 phone calls, 20,000 vi sits to home, and also at least 3 media publicity should be done to have a successful campaign. Mr X 's wants to have (his Goals are): PI) at least 50,000 phone calls P2) 50,000 visits P3) 5 media publicities The advisors found that P3 is 50 times more important than P2. also P2 is 2 times more important than Pl. Write th goal programming model of this given problem. ' - 5~Alfa Industry. will advertise the n~w produced item A. Each ad in a TV channel is-50,OOOll, while it is ;5,OOOTlof" radio ad. To pr,epare a lV ad, 3 marketing personnel is y!o~king, and for the Radio ad only 1 work~r is wprking to prepare the ad. There are o~ly 24 people in ma.rketi(lg department. The management wants at least 6 ads in a montry. They also . have the given goals to establish. Goals 1. .the ad budget of 250,000 should not be exceeded 2. the number of workers for preparation of advertisement should not exceed (less than) the the half of the workers in the department of marketing 3. ~Jt least 4 TV ads in a month ..;. 4. at least 4 radio ads in a month a) write t . he model of the given problem by using the. non-preemtive goal program' ming b) 3 th and the 4 th goals are more important than the 1st and the 2nd goals. At the same time 3th goal is 2 times . more important than the 4th goal. Write the mate'matical model by considering the priorities in terms of pceemetive goal programming. 6_ X_Charity institution donate 20 (million Tl) for scholarship out of which 200( th0u5andTl) for the earthquake victim students, 100(thousand TL) for the athletic students, and SO(thousand Tl) lor the needs and the successful students are given. The management of X_Charity Institution wants to give at least 20 student~ to the "" - rthquake victim st~dents. Other than this the management sets certain goals to achieve PI) at least 80 scholarships in total should be given P2) more than 50% of the scholarship should be given to the earthquake victim students P3) at least 50 scholarships to earhquake victim students, P4) at least 30 scholarships to athlatic students and P5) at least 20 scholarships to the-needy and the successful students should be given P3 is 3 times more important than the goals of P4 and P5 Write the preemtive goal programming model for the given question. 2