Sequoia Airlines is a well-established regional airline serving California, Nevada, Arizona, and Utah. Sequoia competes against much larger carriers in this regional market, and its management feels that the price, frequency of flight service, ability to meet schedules, baggage handling, and image projected by its flight attendants are the most important marketing factors that airline passengers consider when deciding to use a particular carrier.

In each of these areas, Sequoia is attaining its desired objectives. Maintaining its flight-attendant staff at desired levels has been difficult in the past, however, and many times, it has had to ask flight attendants to work overtime because of worker shortages. This has resulted in excessive personnel costs and some morale problems among the attendants. One reason for these worker shortages is a higher-than-industry-average turnover rate resulting from experienced attendants being hired away by other airlines. This is not totally due to morale problems; that cause seems to become important only during seasonal peak-demand periods, when shortages are particularly bad. By interviewing the existing personnel, Sequoia has discovered that competing regional carriers (whose training programs are not as highly developed) have been hiring away from Sequoia a significant proportion of its staff by offering slightly higher direct salaries, attractive indirect benefit packages, and guarantees of a minimum number of flying hours in off-peak demand periods.

As a beginning, Sequoia's management has asked for a 6-month hiring and training analysis of the flight attendant staff requirements beginning next month (July). An investigation of the operations schedule indicates that 14,000 attendant-hours are needed in July, 16,000 in August, 13,000 in September, 12,000 in October, 18,000 in November, and 20,000 in December. Sequoia's training program for new personnel requires an entire month of classroom preparation before they are assigned to regular flight service. As junior flight attendants, they remain on probationary status for 1 additional month. Periodically, there is some personnel movement from the working flight attendant staff to the staff that supervises the training of new employees. Figure 11.16 shows the relationships and percentages of interstaff movements.
When no personnel shortages occur, each junior flight attendant normally works an average of 140 hours per month and is paid a salary of $1,050 during the probationary period. During the training period, each new employee is paid $750. Experienced flight attendants receive an average salary of $1,400 per month and work an average of 125 hours per month. Each instructor receives a salary of $1,500 per month.

The poorly kept secret of Sequoia's personalized training program is that the number of trainees is limited to no more than five per instructor. Instructors not needed in a particular month (i.e., surplus) may be used as flight attendants. To ensure a high level of quality in flight service, Sequoia requires that the proportion of junior flight attendant hours not exceed 25 percent of any month's total (i.e., junior plus experienced) attendant hours.

In May, Sequoia hired 10 new employees to enter the training program, and this month, it hired 10 more. At the beginning of June, there were 120 experienced flight attendants and six instructors on Sequoia's staff.

Questions

1. For the forecast period (i.e., July-December), determine the number of new trainees who must be hired at the beginning of each month so that total personnel costs for the flight-attendant staff and training program are minimized. Formulate the problem as an LP model and solve

2. How would you deal with noninteger results?

3. Discuss how you would use the LP model to make your hiring decision for the next six months.