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Quantitative Methods Problems Set

1. Davis Instruments Davis Instruments 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…

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1.
Davis
Instruments
Davis Instruments 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 workforce unlimited, a company that
specializes in providing temporary employees for firms 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

$2,000

2

Two months

$4,800

3

Three

$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 six months,
David 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 five employees in January under Option2,
WorkForce Unlimited will supply Davis with five 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.
DavisҀ™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.
Managerial
Report
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:
a) A
schedule that shows the number of temporary employees that Davis should hire
each month for each contract option.
b) If
the cost to train each temporary employee could be reduce 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?

2.
Carlson
Department Store (Forecasting)
The Carlson Department Store suffered heavy damage when a
hurricane struck on August 31. The store
was closed for four months (September through December), and Carson is now
involved in a dispute with its insurance company about the amount of lost sales
during the time the store was closed.
Two key issues must be resolved: (1) the amount of sales Carlson would
have made if the hurricane had not struck, and (2) whether Carlson is entitled
to any compensation for excess sales due to increased business activity after
the storm. More than $8 billion in
federal disaster relief and insurance money came into the county, resulting in
increased sales at department stores and numerous other businesses.
The
attached excel file give CarlsonҀ™s sales data for the 48 months preceding the
storm. Tale 15.20 reports total sales
for the 48 months preceding the storm for all department stores in the county,
as well as the total sales in the county for the four months the Carlson
Department Store was closed. CarlsonҀ™s
managers asked you to analyze these data and develop estimates of the lost
sales at the Carlson Department Store for the months of September through
December. They also asked you to
determine whether a case can be made, Carlson is entitled to compensation for
excess sales it would have earned in addition to ordinary sales.
Carlson Department Store
.png”>

County Sales

Month

Year 1

Year 2

Year 3

Year 4

Year 5

January

46.8

46.8

43.8

58

February

48

48.6

45.6

51.6

March

60

59.4

57.6

57.6

April

57.6

58.2

53.4

58.2

May

61.8

60.6

56.4

60

June

58.2

55.2

52.8

57

July

56.4

51

54

57.6

August

63

58.8

60.6

61.8

September

55.8

57.6

49.8

47.4

69

October

56.4

53.4

54.6

54.6

75

November

71.4

71.4

65.4

67.8

85.2

December

117.6

114

102

100.2

121.8

Managerial
Report
Prepare a report for the managers of the Carlson Department
Store that summarizes your findings, forecast, and recommendations. Include the following:
a)
An
estimate of sales for Carlson Department Store had there been no hurricane
b)
An
estimate of countywide department store sales had there been no hurricane
c)
An
estimate of lost sales for the Carlson Department Store for September through
December
d)
In
addition, use the countywide actual department stores sales for September
through December and the estimate in part (2) to make a case for or against
excess storm-related sales.
e)
How
accurate are the above models?

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