King's Landing is a large amusement theme park located in Virginia. The park hires high school and college students to work during the summer months of May, June, July, August, and September. The student employees operate virtually all the highly mechanized, computerized rides; perform as entertainers; perform most of the custodial work during park hours; make up the workforce for restaurants, food services, retail shops, and stores; drive trams; and park cars.
Park management has assessed the park's monthly needs based on previous summers' attendance at the park and the expected available workforce. Park attendance is relatively low in May, until public schools are out, and then it increases through June, July, and August, and decreases dramatically in September, when schools reopen after Labor Day. The park is open 7 days a week through the summer, until September, when it cuts back to weekends only. Management estimates that it will require 22,000 hours of labor in each of the first 2 weeks of May, 25,000 hours during the third week of May, and 30,000 hours during the last week in May. During the first 2 weeks of June, it will require at least 35,000 hours of labor and 40,000 hours during the last 2 weeks in June. In July 45,000 hours will be required each week, and in August 45,000 hours will be needed each week. In September the park will need only 12,000 hours in the first week, 10,000 hours in each of the second and third weeks, and 8,000 hours the last week of the month.
The park hires new employees each week from the first week in May through August. A new employee mostly trains the first week by observing and helping more experienced employees; however, he or she works approximately 10 hours under the supervision of an experienced employee. An employee is considered experienced after completing 1 week on the job. Experienced employees are considered part-time and are scheduled to work 30 hours per week in order to eliminate overtime and reduce the cost of benefits, and to give more students the opportunity to work. However, no one is ever laid off or will be scheduled for fewer (or more) than 30 hours, even if more employees are available than needed. Management believes this is a necessary condition of employment because many of the student employees move to the area during the summer just to work in the park and live near the beach nearby. If these employees were sporadically laid off and were stuck with lease payments and other expenses, it would be bad public relations and hurt employment efforts in future summers. Although no one is laid off, 15% of all experienced employees quit each week for a variety of reasons, including homesickness, illness, and other personal reasons, plus some are asked to leave because of very poor job performance.
Park management is able to start the first week in May with 700 experienced employees who worked in the park in previous summers and live in the area. These employees are generally able to work a lot of hours on the weekends and then some during the week; however, in May attendance is much heavier on the weekends, so most of the labor hours are needed then. The park expects to have a pool of 1,500 available applicants to hire for the first week in May. After the first week, the pool is diminished by the number of new employees hired the previous week, but each week through June the park gets 200 new job applicants, which decreases to 100 new applicants each week for the rest of the summer.
For example, the available applicant pool in the second week in May would be the previous week's pool, which in week 1 is 1,500, minus the number of new employees hired in week 1 plus 200 new applicants. At the end of the last week in August, 75% of all the experienced employees will quit to go back to school, and the park will not hire any new employees in September. The park must operate in September, using experienced employees who live in the area, but the weekly attrition rate for these employees in September drops to 10%.
Formulate and solve a linear programming model to assist the park's management to plan and schedule the number of new employees it hires each week in order to minimize the total number of new employees it must hire during the summer.