PM Computer Services Paulette Smith and Maureen Becker are seniors in engineerin

Question

PM Computer Services
Paulette Smith and Maureen Becker are seniors in engineering
and business, respectively, at State University.
They have set up a company, PM Computer Services, to
assemble and sell their own brand of personal computers.
They buy component parts on the open market from a variety
of sources in the United States and overseas, and they
assemble their computers, mostly at night, in their threebedroom
apartment. They sell their computers primarily to
departments at State University and to other students. They
hire other students to perform the assembly operations
and to test and package the computers. In addition to managing
the operations, Paulette and Maureen help with all
other tasks, including sales and accounting.
They pay the students who work for them $8 per hour
for a 40-hour week, or $1,280 per month. They hire students
on a monthly basis, and their delivery schedule is also on a
monthly (i.e., end-of-the-month) basis. PM currently has
five employees. PM Computers has determined that each of
its employees is able to produce 12.7 computers, on average,
per month. When the monthly demand for its computers exceeds
its regular production capacity, PM employs limited
overtime. Each computer produced on an overtime basis
adds $12 to the labor cost of a computer. A PM employee
can produce 0.6 computer per month on an overtime basis.
Paulette and Maureen have received the following
computer orders for the next 6 months:
Month I Computer Orders
1 63
2 74
3 95
4 57
5 68
6 86
In the past, PM has met its demand strictly from regular
and overtime production. To meet demand in some
months when it did not have sufficient regular and overtime
production, the company would plan ahead and produce
computers in previous months with available
capacity. However, Paulette and Maureen’s apartment was
completely filled with components and workspace, so they
could not store completed computers. Instead, they leased
warehouse space in town to store their completed computers
for delivery in future months. They had to transport the
computers across town to the warehouse and pay for all
handling; also, the warehouse had to be climate controlled.
The cost of holding a computer in storage at the warehouse
is $15 per month.
Paulette and Maureen are considering an alternative
production strategy wherein they would hire new workers
on a monthly basis as needed and lay off workers when
they are not needed. They estimate the cost of hiring new
workers to be $200, primarily for related paperwork and
training. The cost of laying off a worker is $320, or approximately
1 week’s wages. They may want to rehire
some of the workers they lay off at a later date, so they
want them to leave with a good feeling about PM.
Determine a planning schedule for PM Computer
Services, indicating the number of employees working
each month, including the number hired and the number
laid off, the number of computers produced each month
in both regular time and overtime, and the number of
computers carried over in inventory each month. There
should be no inventory left over after month 6. Provide
integer solution values for these different variables. Compare
this solution with the one you would obtain without
integer restrictions

Explanation / Answer

opening +produced -sold =closing stock

0+produced - (63+74+95+57+68+86) = 0

produced = 443

co. can make without over time

5*12.7*6=63.5*6=381 computers

needed 443

difference 62 computers

1 worker can make 12.7 then we need 62/ 12.7 =4.88 workers

but either we took 5 or 4 workers but as per the condition we need no closing stock

so 4 workers and overtime combination will work

so 4 workers + overtime by( 18 workers + 1 worker* .66%)

we have used overtime work in last 3 mnths in increasing order bcoz warehousing cost will occur.

0

month opening produced sold closing 1 0 63.5 63 .5 2 .5 63.5+12.7 74 2.7 3 2.7 63.5+25.4+3.6 95 0.2 4 0.2 63.5+1.2 57 7.9 5 7.9 63.5+3 68 6.4 6 6.4 63.5+12.7+3.4 86 0

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