An Introduction to Management Science 13th Edition (Chap 4 Case Problem 4 - \"Wo

Question

An Introduction to Management Science 13th Edition (Chap 4 Case Problem 4 - "Workforce Scheduling")

Davis Instruments has two manufacturing plants located in Atlanta, Georgia. Product demand varies considerably from month to month, causing Davis extreme difculty in workforce scheduling. Recently Davis started hiring temporary workers supplied by WorkForce Unlimited, a company that specializes in providing temporary employees for rms in the greater Atlanta area. WorkForce Unlimited 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 $2000

2 Two months $4800

3 Three months $7500

The longer contract periods are more expensive because WorkForce Unlimited experiences greater difculty nding temporary workers who are willing to commit to longer work assignments. Over the next six months, Davis projects 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 ve employees in January under Option 2, WorkForce Unlimited will supply Davis with ve temporary workers who will work two months: January and February. For these workers, Davis will have to pay 5($4800) !$24,000. Because of some merger negotiations under way, Davis does not want to commit to any contractual obligations for temporary employees that extend beyond June.

Davis’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 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.

Find the decision variables, constraints, objective function, general/standard solution, and excel solver solution.

Develop a 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. 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.

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 temporaryemployees hired,total contract costs,and total training costs.

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 costs would be required to change the hiring plan based on a training cost of $875 per temporary employee?

4. Suppose that Davis hired 10 full-time employees at the beginning of January in order to satisfy part of the labor requirements over the next six months. If Davis can hire full-time employees for $16.50 per hour, including fringe benets, what effect would it have on total labor and training costs over the six-month 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.

Explanation / Answer

The objective function is Minimized

Decision variables = 2000+4500+7500

Minimized H = 2000x1+4500x2+7500x3

Constraints :

x<10

y<23

z=19

a=26

b=20

c=14

x,y,z,a,b,c<0

1)

Month::::::::::Number of Employees      

Jan:::::::::::::::::::10

Feb::::::::::::::::::: 23:

Mar:::::::::::::::::::19:

Aprr:::::::::::::::::::26

May:::::::::::::::::::20

June::::::::::::::::::14

____________________________________________________________________________

2)

Month::::::::::Number of Employees : $2,000::::::::::::$4,800::::::::::::$7500         

Jan:::::::::::::::::::10::::::::::::::::::::::::::::::::::$20,000:::::::$48,000:::::::::$75,000

Feb::::::::::::::::::: 23:::::::::::::::::::::::::::::::::$46,000:::::::$110,400:::::::$172,500

Mar:::::::::::::::::::19::::::::::::::::::::::::::::::::::$38,000:::::::$91,200:::::::::$142,500

Aprr:::::::::::::::::::26::::::::::::::::::::::::::::::::::$52,000:::::::$124,800:::::::::$195,000

May:::::::::::::::::::20:::::::::::::::::::::::::::::::::::$40,000::::::::$96,000::::::::::$150,000

June::::::::::::::::::14::::::::::::::::::::::::::::::::::$28,000::::::::$67,200:::::::::::$$105,000

Training cost

Jan$875*10=$8750 +$20,000=$28750for first month + second month =$20,000+Third month=$20,000

for month contract= $28750

For second contract::$28750 + $28750=$57,500

For third month=-$28750 +$28750 + $28750=$86,250

Feb =$875*23= $20,125+$46,000=$66,125 first month +second month =$66,125+third month=$66,125

one month=$66,125

Second month =$66,125+$66,125=$132,250

Third month =$66,125+$66,125 +$66,125=$198,375

March=$875*19=$16,625+$38,000=$54,625 first month+second month =$54,625+third month =$54,625

First month =$54,625

second Month =$54,625 +=$54,625=$109,250

Third Month =$54,625+$54,625 +=$54,625=$163,875

April=$875*26=      $22,750+$52,000=$74,750+$74,750+$74,750

first month =$74,750

Second month=$74,750 +$74,750=$149,500

Third Month=$74,750+$74,750 +$74,750=$224,250

May =$875 *20=   $17,500+$40,000=$57,500+$57,500+$57,500

First month =$57,500

Second month=$57,500+$57,500=$115,000

Third Month =$57,500$57,500+$57,500=$172,500

June=$875*14=$12,250+$28,000=40,250+40,250+40,250

First month =$12,250+$28,000=40,250

Second Month =40,250 +40,250=$80,500

Third Month =40,250+ 40,250 +40,250=$120,750

So it is recommend use contract one One month $2000 it is minimum cost

____________________________________________________________________________________

3)if it is reduced training cost is $700 -$875=$175 will considered as income for organization by each employee, now also One month $2,000 contract is recommended.

________________________________________________________________________________

4) permanent employee =160 hours * 16.50=$2640

Temporary employee =2,000 per month + $875 training cost=$2875

so,it is stated that permanent employee is better than temporary employee, so use more permanent employee.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.