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May 14th, 2010, 08:07 AM   #1
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Integer Programming

hello guys, kindly help me with this problem..

Case Problem - PM Computer Services, P.237
Paulette Smith and Maureen Becker are senior in engineering and business, respectively, at State University. They have set up a company, PM Computer Services, to assemble and see their own brand of personal computers. They buy component parts on the open market from a variety of sources domestic and overseas, and they assemble their computers, mostly at night, in their three bedroom 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 40 hour week, or $1280 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 order 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 work apace, 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 $15per month.
Paulette and Maureen are considering an alternative production strategy wherein they would hire new workers on monthly basis as needed and fire 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 firing a worker is $320, or approximately 1 week's wages. They may want to rehire some of the workers they fire at later date, so they want them to leave with 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 fired, 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 restriction.


just give the formulations that will do.. >.<
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May 14th, 2010, 08:22 AM   #2
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Re: Integer Programming

So what's the problem? Show us your work so far so we can help you where you get stuck.

This has been posted all over the 'net -- has anyone helped you yet?

Introduction to Management Science 9th Edition, Bernard W. Taylor III
Chapter 5 --- Integer Linear Programming Models
http://www.expertbee.com/auction-query_i14300.html
http://www.brainmass.com/homework-help/ ... ics/275766
http://answers.yahoo.com/question/index ... 352AAil50p
http://www.physicsforums.com/showthread.php?p=2716693
http://www.coursehero.com/homework-help ... aylor-III/
http://ca.answers.yahoo.com/question/in ... 252AA48Y19
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May 14th, 2010, 08:43 AM   #3
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Re: Integer Programming

No one has helped me yet.. Still trying to figure out those contraints.. Will post my attempt constraints tom. I hope you could guide me.. For now I need to sleep..
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May 16th, 2010, 11:47 PM   #4
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Re: Integer Programming

http://www.mediafire.com/?yjmdme51zmj

This is the constraints obtain. what to do next?
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May 17th, 2010, 09:30 AM   #5
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Re: Integer Programming



What's next? Branch and bound? Cutting-Plane? Kindly guide me please..
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May 17th, 2010, 10:12 AM   #6
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Re: Integer Programming

I don't think that your objective function is right -- $12 is the additional cost of an overtime computer, not the total overtime cost of a computer. I think the total overtime cost of a computer is $1280/12.7 + $12 or about $112.78.
You also missed the constraint that Inv_6 = 0, though that doesn't change anything (the optimal solution would have this in any case).

Your constraint #1 should use 12.7, not 12.6, unless I misread your problem (or you mistyped it).

It looks like the problem can almost be cut in half: the first three months and the last three months. Inv_3 should be 0, so the only thing connecting the two segments is the number of workers. Presumably, some will need to be fired between the two segments.
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May 17th, 2010, 09:02 PM   #7
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Re: Integer Programming

ahh.. It's a typo I think.. It should be 12.7^_^

So the MInimization now is

Min TC=1280/12.7+$12 + 200 + 320 + 15 right?

So Inv_3=0 and Inv_6=0 right? Can you explain it briefly?

Which method will I use? Branch and bound or Gomory?
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May 17th, 2010, 09:48 PM   #8
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Re: Integer Programming

Quote:
Originally Posted by aspirare21a
So the MInimization now is

Min TC=1280/12.7+$12 + 200 + 320 + 15 right?
No, I don't think so, unless you're changing the order of the (unwritten) variables.

Quote:
Originally Posted by aspirare21a
So Inv_3=0 and Inv_6=0 right? Can you explain it briefly?
Inv_3 = 0 is just my mathematical intuition. Inv_6 = 0 is required in the problem: "There should be no inventory left over after month 6".
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May 18th, 2010, 04:34 PM   #9
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Re: Integer Programming

So the Min TC= 1280 +112.78+200+320+15?
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September 25th, 2010, 01:03 PM   #10
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Re: Integer Programming

HI,

I am also working on this problem.

So the objective function should be this?

Minimise Z = 100.78( r1 + r2+ r3+r4+r5 +r6) + 112.78(o1+o2+o3+o4+o5+o6) + 15(i1 + i2+ i3+i4+i5) + 200(h1+h2 +h3+ h4+h5+h6) + 320(f2+f3+f4+f5+f6) + 1280(x1 +x2+x3+x4+x5)?

r= total no of PC produced under regular time
o= total no of PC produced under OT
i= total inventory carried over
h= total no of employees hired
f= total no of employees fired
x= total no of full time employees...

Correct?
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