CASE: The King’s Landing Amusement Park
King’s Landingis a large amusement theme park locatedin Virginia. The park hires highschool and college studentsto work during the summer months of May, June,July, August, and September. The student employeesoperatevirtuallyallthehighlymechanized,computerizedrides;performasentertainers;perform most of the custodial workduring park hours; make up the workforce for restaurants,food services, retail shops, and stores; drive trams; and parkcars. Park management has assessed the park’s monthlyneeds based on previous summers’attendance at the parkand the expected available workforce. Park attendance isrelatively low in May, until publicschools are out, and thenit increases through June, July, and August, and decreasesdramatically in September, when schools reopen afterLabor Day. The park is open 7 days a week through thesummer, until September, when itcuts back to weekendsonly. Management estimates that it will require 22,000hours of labor in each of the first 2 weeks of May, 25,000hours during the third week of May, and 30,000 hours duringthelast weekinMay. Duringthe first 2 weeks of June,it will require at least 35,000 hours of labor and 40,000hours during the last 2 weeks in June. In July 45,000 hourswill be required each week, and in August 45,000 hourswill be needed each week. In September the park will needonly 12,000 hours in the first week, 10,000 hours in each ofthe second and third weeks, and 8,000 hours the last weekof the month. The park hires new employees each week from the firstweek in May through August. A new employee mostly trainsthe first week by observing and helping more experiencedemployees; however, he or she works approximately 10hours under the supervision of an experienced employee. Anemployee is considered experienced after completing 1 weekon the job. Experienced employees are considered part-timeand are scheduled to work 30 hours per week to eliminateovertime and reduce the cost of benefits, and to give morestudents the opportunity to work. However, no one is ever laidoff or will be scheduled for fewer (or more) than 30 hours,even if more employees are available than needed. Managementbelieves thisisanecessaryconditionofemploymentbecausemanyofthestudentemployeesmovetotheareaduring the summer just to work in the park and live near thebeach nearby. If these employees were sporadically laid offand were stuck with lease payments and other expenses, itwould be bad public relations and hurt employment effortsin future summers. Although no one is laid off, 15% of allexperienced employees quit each week for a variety of reasons,including homesickness, illness, and other personalreasons, plus some are asked to leave because of very poorjob performance. Park management is able to start the first week in Maywith 700 experienced employees who worked in the park inprevious summers and live in the area. These employees aregenerally able to work a lot of hours on the weekends andthen some during the week; however, in May attendance ismuch heavier on the weekends, so most of the labor hoursare needed then. The park expects to have a pool of 1,500 available applicants to hire for the first week in May. Afterthe first week, the pool is diminished by the number of newemployees hired the previous week, but each week throughJune the park gets 200 new job applicants, which decreasesto 100 new applicants each week for the rest of the summer.For example, the available applicant pool in the secondweek in May would be the previous week’s pool, which inweek 1 is 1,500, minus the number of new employees hiredin week 1 plus 200 new applicants. At the end of the last week in August, 75% of all the experienced employees willquit to go back toschool, and the park will not hire any newemployeesin September. The park must operate in September,using experienced employees who live in the area, butthe weekly attrition rate for these employees in Septemberdrops to 10%. Formulate and solve a linear programming model toassist the park’s management to plan and schedule thenumber of new employees it hires each week to minimizethe total number of new employees it must hire during thesummer.

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rahima28gh rahima28gh

25-01-2024
Mathematics

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CASE: The King’s Landing Amusement Park
King’s Landingis a large amusement theme park locatedin Virginia. The park hires highschool and college studentsto work during the summer months of May, June,July, August, and September. The student employeesoperatevirtuallyallthehighlymechanized,computerizedrides;performasentertainers;perform most of the custodial workduring park hours; make up the workforce for restaurants,food services, retail shops, and stores; drive trams; and parkcars. Park management has assessed the park’s monthlyneeds based on previous summers’attendance at the parkand the expected available workforce. Park attendance isrelatively low in May, until publicschools are out, and thenit increases through June, July, and August, and decreasesdramatically in September, when schools reopen afterLabor Day. The park is open 7 days a week through thesummer, until September, when itcuts back to weekendsonly. Management estimates that it will require 22,000hours of labor in each of the first 2 weeks of May, 25,000hours during the third week of May, and 30,000 hours duringthelast weekinMay. Duringthe first 2 weeks of June,it will require at least 35,000 hours of labor and 40,000hours during the last 2 weeks in June. In July 45,000 hourswill be required each week, and in August 45,000 hourswill be needed each week. In September the park will needonly 12,000 hours in the first week, 10,000 hours in each ofthe second and third weeks, and 8,000 hours the last weekof the month. The park hires new employees each week from the firstweek in May through August. A new employee mostly trainsthe first week by observing and helping more experiencedemployees; however, he or she works approximately 10hours under the supervision of an experienced employee. Anemployee is considered experienced after completing 1 weekon the job. Experienced employees are considered part-timeand are scheduled to work 30 hours per week to eliminateovertime and reduce the cost of benefits, and to give morestudents the opportunity to work. However, no one is ever laidoff or will be scheduled for fewer (or more) than 30 hours,even if more employees are available than needed. Managementbelieves thisisanecessaryconditionofemploymentbecausemanyofthestudentemployeesmovetotheareaduring the summer just to work in the park and live near thebeach nearby. If these employees were sporadically laid offand were stuck with lease payments and other expenses, itwould be bad public relations and hurt employment effortsin future summers. Although no one is laid off, 15% of allexperienced employees quit each week for a variety of reasons,including homesickness, illness, and other personalreasons, plus some are asked to leave because of very poorjob performance. Park management is able to start the first week in Maywith 700 experienced employees who worked in the park inprevious summers and live in the area. These employees aregenerally able to work a lot of hours on the weekends andthen some during the week; however, in May attendance ismuch heavier on the weekends, so most of the labor hoursare needed then. The park expects to have a pool of 1,500 available applicants to hire for the first week in May. Afterthe first week, the pool is diminished by the number of newemployees hired the previous week, but each week throughJune the park gets 200 new job applicants, which decreasesto 100 new applicants each week for the rest of the summer.For example, the available applicant pool in the secondweek in May would be the previous week’s pool, which inweek 1 is 1,500, minus the number of new employees hiredin week 1 plus 200 new applicants. At the end of the last week in August, 75% of all the experienced employees willquit to go back toschool, and the park will not hire any newemployeesin September. The park must operate in September,using experienced employees who live in the area, butthe weekly attrition rate for these employees in Septemberdrops to 10%. Formulate and solve a linear programming model toassist the park’s management to plan and schedule thenumber of new employees it hires each week to minimizethe total number of new employees it must hire during thesummer.

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