Davis Instruments has two manufacturing plants in Atlanta, Georgia. Project demand varies considerably from month to month, causing Davis extreme difficulty in workforce scheduling. Recently Davis started hiring temporary workers supplied by WorkForce Unlimited, a company that specializes in providing temporary employees for firms in the greater Atlanta area. WorkForce Unlimited has offered to provide temporary employees under three contract options that differ in terms of the length of employment and the cost. The three options are summarized:
Option Length of Employment Cost
1 One month $2,000
2 Two months $4,800
3 Three months $7,500
The longer contract periods are more expensive because WorkForce Unlimited has greater difficulty finding temporary workers who are willing to commit to longer work assignments.
During the next six months, Davis has projected the following needs for additional employees.
Month__________________January February March April May June
Employees Needed 10 23 19 26 20 14
Each month, Davis can hire as many temporary employees as needed under each of the three options. For instance, if Davis hires five employees in January under Option 2, WorkForce Unlimited will supply Davis with five temporary workers who will work two months: January and February. For this, Davis must pay 5($4,800)=$24,000. Due to merger negotiations underway, Davis does not want to commit to any contractual obligations for temporary employees that extend beyond June.
Davis has a quality control program that requires each temporary employee to receive training at the time of hire. The training program is required even if the person has worked for Davis Instruments in the past. Davis estimates that the cost of training is $875 each time a temporary employee is hired. Thus, if a temporary employee is hired for one month, Davis will incur a training cost of $875, but will incur no additional training cost if the employee is on a two- or three-month contract.
Develop a linear programming model that can be used to determine the number of temporary employees Davis should hire each month under each contract plan in order to meet the projected needs at a minimum total cost. Define your variables.