Linear programming help

[tjn8240]

Hello,
I'm having a bit of trouble with what my professor classified as a transportation problem.


Please see the problem below.

I have found that the The variables are D1, D2, D3, L1, L2, L3, G1, G2, G3.. The objective is to minimize total operating time (D + L + G)..The Constraints are as follows: D1 + D2 + D3 >=1, L1 + L2 + L3 >=1, G1 + G2 + G3 >= 1, D1 + L2 + G3 <= 1, D2 + L2 + G2 <= 1, D3 + L3 + G3 <= 1


My issue with this problem are the basics of this problem..I don't really understand what the constraints mean. (What does the <= 1 or >= 1 in each constraint mean?) (If it is supply and demand.. which is supply and which is demand? Also, how do I relate that to the data table of information I'm provided-- which provides the time it takes for operators to use machinery?)
Also, I'm unsure as to what I'm exactly inputting in solver. I know I cannot ask someone to give me the answer to this-- but I'm hoping someone's explanation as to what the constraints mean will help me determine this myself.


Thank You!

 

[Deleted member 4993]

Hello,
I'm having a bit of trouble with what my professor classified as a transportation problem.


Please see the problem below.

I have found that the The variables are D1, D2, D3, L1, L2, L3, G1, G2, G3.. The objective is to minimize total operating time (D + L + G)..The Constraints are as follows: D1 + D2 + D3 >=1, L1 + L2 + L3 >=1, G1 + G2 + G3 >= 1, D1 + L2 + G3 <= 1, D2 + L2 + G2 <= 1, D3 + L3 + G3 <= 1


My issue with this problem are the basics of this problem..I don't really understand what the constraints mean. (What does the <= 1 or >= 1 in each constraint mean?) (If it is supply and demand.. which is supply and which is demand? Also, how do I relate that to the data table of information I'm provided-- which provides the time it takes for operators to use machinery?)
Also, I'm unsure as to what I'm exactly inputting in solver. I know I cannot ask someone to give me the answer to this-- but I'm hoping someone's explanation as to what the constraints mean will help me determine this myself.


Thank You!

To understand the constraint D1 + D2 + D3 ≤ 1 - you have to first define those variables.

What are D1, D2 & D3?

Once you correctly define those variables, those constraints will become clear.

 

[tjn8240]

D1 is the variable that represents how long it takes the first operator to operate the drill press
D2 is the variable that represents how long it takes the second operator to operate the drill press
D3 is the variable that represents how long it takes the third operator to operate the drill press

And so on for G and L.. So D1+D2+D3 would represent the total time it took the operators to use the drill press..I just do not understand what the greater than or equal to 1 refers to.

 

[tjn8240]

Still don't know it means or refers to.. but thanks anyway. Got the answer by playing with the problem on Excel..

 

[Deleted member 4993]

D1 is the variable that represents how long it takes the first operator to operate the drill press
D2 is the variable that represents how long it takes the second operator to operate the drill press
D3 is the variable that represents how long it takes the third operator to operate the drill press

And so on for G and L.. So D1+D2+D3 would represent the total time it took the operators to use the drill press..I just do not understand what the greater than or equal to 1 refers to.

Now look at the hints → If D1 = 1, then D2 and D3 must be 0 [That is if the operator 1 is on the drill (D1 = 1), other operators cannot be on the drill. So D2 & D3 = 0]