Cost Optimization for Workforce Scheduling Iet4405

COST OPTIMIZATION FOR WORKFORCE SCHEDULING

An Operations Research Report
IET4405
Submitted to Gregory Wiles

By
Group 3:
Amanda Bathe
Eminue Eminue
Danielle Harmon
Theophilus Holley
Coltan Palmer
Abigale Vining

April 24, 2013

EXECUTIVE SUMMARY This report presents a recommendation for a hiring schedule that would allow Davis Instruments to hire temporary employees based on the product demand that varies from month to month for the six months of January to June, at the lowest cost.
Figure 2
Full-time and Temporary Employee Suggested Schedule
Figure 2
Full-time and Temporary Employee Suggested Schedule
Temporary Employee Suggested Schedule
Figure 1
Temporary Employee Suggested Schedule
Figure 1 In order to find the hiring schedule that would result in the least incremental training and salary costs, a linear programming model was formulated and solved. Temporary employees can be hired under three options. Option one allows the temporary employee to work for one month, Option two for two months, and Option three for three months. The training for all temporary employees occurs once, each time they are hired, even if they have worked for Davis before. The recommended hiring schedules for temporary workers is displayed below, next to a recommended hiring schedule for temporary workers assuming Davis first hired 10 full-time positions.

Figure 1 suggests 43 temporary workers for the 112 available positions. The total cost of this 6 month option is $313,525.00. Figure 2 suggests 10 fulltime positions and 23 temporary positions at a 6 month cost of $313,175.00. In the course of the 6 months, the full-time, part-time mix will save Davis $350.00.

PROBLEM DESCRIPTION
Davis Instruments (Davis) has manufacturing plants in Atlanta, Georgia. The customer demand for Davis’s products fluctuates considerably each month. The constant change in product demand makes it difficult for Davis to schedule its workforce. Davis started hiring temporary workers to help fill in the needs of the fluctuating product demand. Ultimately, Davis would like to simplify its workforce scheduling in relation to its expenses. Davis is currently hiring temporary workers from WorkForce Unlimited. WorkForce Unlimited offers Davis three options: Option | Length of Employment | Cost | 1 | One month | $2000 | 2 | Two months | $4800 | Figure 3
Figure 3
3 | Three months | $7500 |

Davis Instruments needs a profitable solution. Based on Davis’s projected employee needs for the six month period from January to June, a hiring schedule that minimizes cost is needed. Davis requires all employees, even if previously hired by the company to first go through the company’s $875.00 training course. Option | Length of Employment | Cost | Training | Cost per Month | 1 | One month | $2000 | $875 | $2875.00 | 2 | Two months | $4800 | $875 | $2837.50 | Figure 4
Figure 4
3 | Three months | $7500 | $875 | $2791.67 |

Because this part of Davis’s hiring expenses is a deciding factor in minimizing cost, as displayed in Figure 4, Davis would also like to know whether or not reducing training costs, and by how much, would greatly impact the hiring schedule. Finally, Davis is considering hiring ten full-time employees. These full-time employees would reduce the need for temporary positions over the six month period from 112 positions to 52 positions. Davis also needs a hiring schedule that minimizes costs for the 52 position potential. Ultimately, the hiring schedules associated with each of the two possible hiring strategies need to be evaluated based on their costs to help further suggest ways to minimize the cost of hiring at Davis.
ANALYSIS
MIN 2875(T11 + T12 + T13 + T14 + T15 + T16) + 5675(T21 + T22 + T23 + T24 + T25) + 8375(T31 + T32 + T33 + T34)
MIN 2875(T11 + T12 + T13 + T14 + T15 + T16) + 5675(T21 + T22 + T23 + T24 + T25) + 8375(T31 + T32 + T33 + T34)
In order to discover the optimal solution for reducing Davis’s costs while hiring temporary employees to fill each of the 112 needed positions, the following objective function was created:

T11+T21+T31=10
T21+T31+T12+T22+T32=23
T31+T22+T32+T13+T23+T33=19
T32+T23+T33+T14+T24+T34=26
T33+T24+T34+T15+T25=20
T34+T25+T16=14

T11+T21+T31=10
T21+T31+T12+T22+T32=23
T31+T22+T32+T13+T23+T33=19
T32+T23+T33+T14+T24+T34=26
T33+T24+T34+T15+T25=20
T34+T25+T16=14

With the use of LINDO- an optimization modeling program- and the following constraints,

Temporary Employee Suggested Schedule
Figure 5
Temporary Employee Suggested Schedule
Figure 5 optimal hiring strategy was discovered (see Appendix A and Figure 5). The hiring schedule according to each month and per each of the three options is mapped out in Figure 5.

As you can see in Figure 5, the best hiring plan includes hiring seven employees under option 1, three employees under option 2, and thirty-three employees under option 3. This brings the total of temporary employees to hire, in order to fill the 112 positions, to 43. Using all of the costs associated with each of the three options, previously shown in Figure 4, the total cost associated with hiring 43 temporary employees was calculated to be $313,525.00. All data used in calculations can be reviewed in Appendix B.
T11+T21+T31=0
T21+T31+T12+T22+T32=13
T31+T22+T32+T13+T23+T33=9
T32+T23+T33+T14+T24+T34=16
T33+T24+T34+T15+T25=10
T34+T25+T16=4

T11+T21+T31=0
T21+T31+T12+T22+T32=13
T31+T22+T32+T13+T23+T33=9
T32+T23+T33+T14+T24+T34=16
T33+T24+T34+T15+T25=10
T34+T25+T16=4

Because Davis was interested in hiring ten full-time positions as another option for reducing costs, an additional set of constraints was used with the previously stated objective function.
Figure 6
Full-time and Temporary Employee Suggested Schedule
Figure 6
Full-time and Temporary Employee Suggested Schedule
Running the new program in Lindo gave a new optimal hiring schedule shown in Figure 6 (full results in Appendix C). According to Figure 6, other than hiring ten full-time employees, Davis would need to hire seven employees under option 1, three employees under option 2, and 13 employees under option 3. According to this hiring plan, Davis has now filled 52 needed temporary positions with 23 temporary employees. Both part-time and full-time employees work approximately 160 hours per month. Full-time employees would work for $16.50 per hour. The total cost of the ten full-time employees, over the six month period, comes out at $167,150.00. The total cost of the accompanying 23 temporary employees is $146,025.00. The total combined cost for the six months is $313,175.00. This strategy for hiring would ultimately save Davis $350.00 over the six month period. All data and calculations associated can be viewed in Appendix B.
As seen in Figure 4, the costs of hiring under Options 2 and 3 through WorkForce Unlimited are higher than hiring an employee for just one month under Option1. However, once Davis’s one-time $875.00 training cost is added in, Options 2 and 3 become more affordable than Option 1. Through this information alone, it is evident that the cost of training is an important deciding factor when minimizing cost. For example, dropping the training cost to $700.00 per new employee would significantly change the hiring plan for Davis Instruments. By reducing the training cost this much, the most affordable solution would be for Davis to hire 112 Option 1 employees through WorkForce Unlimited. This would now only cost Davis $302,400.00, which is $10,125 cheaper than the previous optimal solution (see Appendix B). Cutting the cost of training from $875.00 to $700.00 may not actually be feasible. Knowing this, the amount of reduction in training cost necessary to change the optimal hiring schedule was drawn from the output of Lindo (Appendix A and C). If Davis reduced the training cost by $75.00 per new employee, Option 1 and Option 2 would cost the same for the company. Reduction in training cost of more than $75.00 would make hiring under Option 1 always cheaper than Option 2.
RECOMMENDATIONS
Based strictly on the costs for the six month period only, it is most financially favorable for Davis to first hire ten full-time employees and then continue to fill the remaining positions needed with temporary workers. As the chart in Appendix B shows, the full-time employee plan would save the company $350.00 over the six month period. However, it is necessary to review past experiences and projections of employment needs beyond the six month period to know for sure whether or not the ten full time employees will later cost the company extra money because they are not all needed. Additionally, Davis should evaluate its training cost. With a reduction in the cost of training of $75.01 or more, Davis could greatly impact its optimal hiring plan and also further reduce cost over the six months. Because $75.01 is only 8.6% of the total cost of Davis’s training it may be possible to invest in different materials or locations for training that would make the training cost less than $800.00. At that point Davis would be able to further optimize its hiring strategy based on cost.

Appendix A

Appendix B

Appendix C