Linear Programming Applications

EMP 504 Quantitative methods in Management
Name: Yi-Chun Kuo
Student id: 106357165
HW #7: Linear Programming Applications
Due Date: 11pm on Nov 6, 2008

Davis Instrument has two manufacturing plants located in Atlanta, Georgia. Product demand varies considerably from month to month, causing Davis extreme difficulty in workforce scheduling. Recently Davis started hiring temporary workers supplied by Workers Unlimited, a company that specializes in providing temporary employees for firms in the grater Atlanta area. Workforce Unlimited offered to provide temporary employees under three contract opinions that differ in terms of the length of employment and the cost. The three options are summarized:
|options |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 experiences greater difficulty finding temporary workers who are willing to commit to longer work assignments.
Over the next 6 months, Davis projects the following needs for additional employees.
|Months |Jan |Feb |Mar |Apr |May |Jun |
|Employees needed |10 |23 |19 |26 |20 |14 |

Each month, Davis can hire as many temporary employees as needed under each of the 3 options. For instance, if Davis hires 5 employees in Jan under Option2, Workforce Unlimited will apply Davis with 5 temporary workers who will work 2 months: January and February. For these workers, Davis will have to pay
5($4800)=$24000. Because of some merger negotiations under way, Davis does not want to commit any contractual obligations for temporary employees that extend beyond June.
David’s quality control program requires each temporary employee to receive training at the time of hire. The training program is required even if the person worked for Davis Instrument 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.
Managerial Report
Develop a model that can be used to determine the number of temporary employees Davis should hire each month under contract plan in order to meet the projected needs at a minimum total cost. Include the following items in your report.
1. A schedule that shows the number of temporary employees that Davis should hire each month for each contract option

| |OPT 1 |OPT 2 |OPT 3 |
|Jan. |0 |10 |13 |
|Feb. |0 |10 |13 |
|Mar. |0 |0 |13 |
|Apr. |0 |0 |20 |
|May |0 |13 |20 |
|Jun. |0 |13 |20 |

2. A summary table that shows the number of temporary employees that Davis should hire under each contract option, the associated contract cost for each option, and the associated training cost for each option. Provide summary totals showing the total number of temporary employees hired, total contract costs, and total training costs.

Total number of temporary employees hired: 49 Total contract costs: $324,300 Total training costs: $42,875

3. If the cost to train each temporary employee could be reduced to $700 per month, what effect would this change have on the hiring plan? Explain. Discuss the implications that this effect on the hiring plan has for identifying methods for reducing training costs. How much of a reduction in training cost would be required to change the hiring plan based on a training cost of $875 per temporary employee?

Total training cost on $875 is $42875. Total training cost on $700 will be $34300, there is a big gap between two. If a training fee cost down to $700, we will hire more opt1 workers instead of opt3 workers. Because of opt1 worker has lower pay.

4. Suppose that Davis hired 10 full-time employees at the beginning of January in order to satisfy part of the labor requirement over the next 6 months. If Davis can hire full-time employees for $16.5 per hour, including fringe benefits, what effect would it have on total labor and training costs over the 6 months period as compared to hiring only temporary employees? Assume that full-time and temporary employees both work approximately 160 hours per month. Provide a recommendation regarding the decision to hire additional full-time employees.

When hiring full-time workers, total cost=$158400
When hiring temporary employees, total cost= $324300(Cost) + $42875(Training)
Comparing to hire temporary employees, it is cheaper hiring full-time employees.