Unbounded or badly scaled problem

[msaqib]

Hello everyone
My optimization problem is the following scenario:
1- Raw material (cotton) is needed at different locations to meet a minimum production workload
2- Production units are available at different locations.
3- Raw material costs vary every day, and are possibly different at each location.
4- Production machines consume cotton at two different rates (idle and peak).
5- Production time unit (say, shifts or days) may or may not be the same as the procurement time units. For instance, you can buy cotton once every day. You can do futures purchases based on projected future cost.
6- Our inventory may already have some cotton procured for a certain production intervals.
7- If I have excesss cotton at some unit, I can dispose of it in the market
I've implemented the model in AMPL and tried to solve it using minos solver, and I get the following error: "Unbounded or badly scaled problem." If I get rid of the selling option (point 7 above, by removing the Sell_Cotton term in the objective function, the solver finds and optimal solution.
Could you kindly take a look at the attached model and data file and suggest why this is a badly scaled problem?
Thanks and best regards

MyProblem.txtMyProblem-Data.txt

[msaqib]

The last message missed the model file

msaqib wrote:

Hello everyone
My optimization problem is the following scenario:
1- Raw material (cotton) is needed at different locations to meet a minimum production workload
2- Production units are available at different locations.
3- Raw material costs vary every day, and are possibly different at each location.
4- Production machines consume cotton at two different rates (idle and peak).
5- Production time unit (say, shifts or days) may or may not be the same as the procurement time units. For instance, you can buy cotton once every day. You can do futures purchases based on projected future cost.
6- Our inventory may already have some cotton procured for a certain production intervals.
7- If I have excesss cotton at some unit, I can dispose of it in the market
I've implemented the model in AMPL and tried to solve it using minos solver, and I get the following error: "Unbounded or badly scaled problem." If I get rid of the selling option (point 7 above, by removing the Sell_Cotton term in the objective function, the solver finds and optimal solution.
Could you kindly take a look at the attached model and data file and suggest why this is a badly scaled problem?
Thanks and best regards

MyProblem.txtMyProblem-Data.txt

MyProblem.txt

[Robert Fourer-2]

This does not appear to be a badly scaled problem, but rather an unbounded
problem.  To see that, I added a constraint that places a lower bound of
-100000000 on the objective function:

subj to obj_lower_bound:
  sum{i in LOCATIONS, j in PROC_TIMES, k in PROC_TIMES}
    exp((j - k)*interest_rate/tyr)*(cotton_price[i,k]*
    (Buy_Cotton[i,j,k] - Sell_Cotton[i,j,k])) >= -1000000000;

Then MINOS returned the solution copied below, in which the objective value
is exactly equal to -100000000.  To prevent this behavior you would need to
add some constraints or bounds, or otherwise fix your model, so that such
solutions would no longer be possible.

Bob Fourer
4er@...


ampl: display {j in 1.._nvars: _var[j] > 0} (_varname[j],_var[j]);

:                _varname[j]                    _var[j]         :=
1     "Machines['Lahore',1]"                   100
2     "Machines['Lahore',2]"                  1000
3     "Machines['Lahore',3]"                  1000
4     "Machines['Lahore',4]"                  1000
5     "Machines['Lahore',5]"                  1000
6     "Machines['Lahore',6]"                  1000
7     "Machines['Lahore',7]"                  1000
15    "Buy_Cotton['Lahore',1,1]"            574860
16    "Buy_Cotton['Lahore',1,2]"           5748500
19    "Buy_Cotton['Lahore',1,5]"           5748600
24    "Buy_Cotton['Lahore',2,3]"           5748600
32    "Buy_Cotton['Lahore',3,4]"           5748600
47    "Buy_Cotton['Lahore',5,5]"                 9.31323e-10
48    "Buy_Cotton['Lahore',5,6]"                 0.000243824
55    "Buy_Cotton['Lahore',6,6]"           5748600
56    "Buy_Cotton['Lahore',6,7]"           5748600
69    "Buy_Cotton['Karachi',1,6]"                7.27119e+11
113   "Ut['Lahore',1]"                           0.001
114   "Ut['Lahore',2]"                           0.001
115   "Ut['Lahore',3]"                           0.001
116   "Ut['Lahore',4]"                           0.001
117   "Ut['Lahore',5]"                           0.001
118   "Ut['Lahore',6]"                           0.001
119   "Ut['Lahore',7]"                           0.001
127   "temp_Required_Cotton['Lahore',1]"    574860
128   "temp_Required_Cotton['Lahore',2]"   5748600
129   "temp_Required_Cotton['Lahore',3]"   5748600
130   "temp_Required_Cotton['Lahore',4]"   5748600
131   "temp_Required_Cotton['Lahore',5]"   5748600
132   "temp_Required_Cotton['Lahore',6]"   5748600
133   "temp_Required_Cotton['Lahore',7]"   5748600
141   "Required_Cotton['Lahore',1]"         574860
142   "Required_Cotton['Lahore',2]"        5748600
143   "Required_Cotton['Lahore',3]"        5748600
144   "Required_Cotton['Lahore',4]"        5748600
145   "Required_Cotton['Lahore',5]"        5748600
146   "Required_Cotton['Lahore',6]"        5748600
147   "Required_Cotton['Lahore',7]"        5748600
163   "Sell_Cotton['Lahore',2,2]"          5748600
166   "Sell_Cotton['Lahore',2,5]"          5748600
171   "Sell_Cotton['Lahore',3,3]"          5748600
179   "Sell_Cotton['Lahore',4,4]"          5748600
195   "Sell_Cotton['Lahore',6,6]"                0.000243824
203   "Sell_Cotton['Lahore',7,7]"          5748600
244   "Sell_Cotton['Karachi',6,6]"               7.27119e+11

> -----Original Message-----
> From: ampl@... [mailto:ampl@...]
> On Behalf Of msaqib [msaqib@...]
> Sent: Thursday, July 09, 2009 11:19 AM
> To: ampl@...
> Subject: [AMPL 2633] Re: Unbounded or badly scaled problem
>
>
>
> The last message missed the model file
>
>
>
> Hello everyone
> My optimization problem is the following scenario:
> 1- Raw material (cotton) is needed at different locations to meet a
> minimum
> production workload
> 2- Production units are available at different locations.
> 3- Raw material costs vary every day, and are possibly different at each
> location.
> 4- Production machines consume cotton at two different rates (idle and
> peak).
> 5- Production time unit (say, shifts or days) may or may not be the same
> as
> the procurement time units. For instance, you can buy cotton once every
> day.
> You can do futures purchases based on projected future cost.
> 6- Our inventory may already have some cotton procured for a certain
> production intervals.
> 7- If I have excesss cotton at some unit, I can dispose of it in the
> market
> I've implemented the model in AMPL and tried to solve it using minos
> solver,
> and I get the following error: "Unbounded or badly scaled problem." If I
> get
> rid of the selling option (point 7 above, by removing the Sell_Cotton term
> in the objective function, the solver finds and optimal solution.
> Could you kindly take a look at the attached model and data file and
> suggest
> why this is a badly scaled problem?
> Thanks and best regards

> > http://www.nabble.com/file/p24413197/MyProblem.txt MyProblem.txt
> > http://www.nabble.com/file/p24413197/MyProblem-Data.txt MyProblem-
> Data.txt
> >
> http://www.nabble.com/file/p24413207/MyProblem.txt MyProblem.txt
> --



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[msaqib]

Thanks Robert. That was very helpful. I also only just decided to change the last constraint, so that I allow selling of pre-existing cotton, only. Because otherwise, the solver may try to look for solutions where it buys cotton during low cost periods and later sells it. Unnecessary buying for anticipated profit is against the spirit of the problem. Selling cotton should only be done if it is surplus and even after selling at a loss you can buy as much or more cotton at a different location, at a lower price.
Thanks again.

Robert Fourer-2 wrote:

This does not appear to be a badly scaled problem, but rather an unbounded
problem.  To see that, I added a constraint that places a lower bound of
-100000000 on the objective function:

subj to obj_lower_bound:
  sum{i in LOCATIONS, j in PROC_TIMES, k in PROC_TIMES}
    exp((j - k)*interest_rate/tyr)*(cotton_price[i,k]*
    (Buy_Cotton[i,j,k] - Sell_Cotton[i,j,k])) >= -1000000000;

Then MINOS returned the solution copied below, in which the objective value
is exactly equal to -100000000.  To prevent this behavior you would need to
add some constraints or bounds, or otherwise fix your model, so that such
solutions would no longer be possible.

Bob Fourer
[e-mail]


ampl: display {j in 1.._nvars: _var[j] > 0} (_varname[j],_var[j]);

:                _varname[j]                    _var[j]         :=
1     "Machines['Lahore',1]"                   100
2     "Machines['Lahore',2]"                  1000
3     "Machines['Lahore',3]"                  1000
4     "Machines['Lahore',4]"                  1000
5     "Machines['Lahore',5]"                  1000
6     "Machines['Lahore',6]"                  1000
7     "Machines['Lahore',7]"                  1000
15    "Buy_Cotton['Lahore',1,1]"            574860
16    "Buy_Cotton['Lahore',1,2]"           5748500
19    "Buy_Cotton['Lahore',1,5]"           5748600
24    "Buy_Cotton['Lahore',2,3]"           5748600
32    "Buy_Cotton['Lahore',3,4]"           5748600
47    "Buy_Cotton['Lahore',5,5]"                 9.31323e-10
48    "Buy_Cotton['Lahore',5,6]"                 0.000243824
55    "Buy_Cotton['Lahore',6,6]"           5748600
56    "Buy_Cotton['Lahore',6,7]"           5748600
69    "Buy_Cotton['Karachi',1,6]"                7.27119e+11
113   "Ut['Lahore',1]"                           0.001
114   "Ut['Lahore',2]"                           0.001
115   "Ut['Lahore',3]"                           0.001
116   "Ut['Lahore',4]"                           0.001
117   "Ut['Lahore',5]"                           0.001
118   "Ut['Lahore',6]"                           0.001
119   "Ut['Lahore',7]"                           0.001
127   "temp_Required_Cotton['Lahore',1]"    574860
128   "temp_Required_Cotton['Lahore',2]"   5748600
129   "temp_Required_Cotton['Lahore',3]"   5748600
130   "temp_Required_Cotton['Lahore',4]"   5748600
131   "temp_Required_Cotton['Lahore',5]"   5748600
132   "temp_Required_Cotton['Lahore',6]"   5748600
133   "temp_Required_Cotton['Lahore',7]"   5748600
141   "Required_Cotton['Lahore',1]"         574860
142   "Required_Cotton['Lahore',2]"        5748600
143   "Required_Cotton['Lahore',3]"        5748600
144   "Required_Cotton['Lahore',4]"        5748600
145   "Required_Cotton['Lahore',5]"        5748600
146   "Required_Cotton['Lahore',6]"        5748600
147   "Required_Cotton['Lahore',7]"        5748600
163   "Sell_Cotton['Lahore',2,2]"          5748600
166   "Sell_Cotton['Lahore',2,5]"          5748600
171   "Sell_Cotton['Lahore',3,3]"          5748600
179   "Sell_Cotton['Lahore',4,4]"          5748600
195   "Sell_Cotton['Lahore',6,6]"                0.000243824
203   "Sell_Cotton['Lahore',7,7]"          5748600
244   "Sell_Cotton['Karachi',6,6]"               7.27119e+11



> -----Original Message-----
> From: [e-mail] [mailto:[e-mail]]
> On Behalf Of msaqib [[e-mail]]
> Sent: Thursday, July 09, 2009 11:19 AM
> To: [e-mail]
> Subject: [AMPL 2633] Re: Unbounded or badly scaled problem
>
>
>
> The last message missed the model file
>
>
>
> Hello everyone
> My optimization problem is the following scenario:
> 1- Raw material (cotton) is needed at different locations to meet a
> minimum
> production workload
> 2- Production units are available at different locations.
> 3- Raw material costs vary every day, and are possibly different at each
> location.
> 4- Production machines consume cotton at two different rates (idle and
> peak).
> 5- Production time unit (say, shifts or days) may or may not be the same
> as
> the procurement time units. For instance, you can buy cotton once every
> day.
> You can do futures purchases based on projected future cost.
> 6- Our inventory may already have some cotton procured for a certain
> production intervals.
> 7- If I have excesss cotton at some unit, I can dispose of it in the
> market
> I've implemented the model in AMPL and tried to solve it using minos
> solver,
> and I get the following error: "Unbounded or badly scaled problem." If I
> get
> rid of the selling option (point 7 above, by removing the Sell_Cotton term
> in the objective function, the solver finds and optimal solution.
> Could you kindly take a look at the attached model and data file and
> suggest
> why this is a badly scaled problem?
> Thanks and best regards

> > http://www.nabble.com/file/p24413197/MyProblem.txt MyProblem.txt
> > http://www.nabble.com/file/p24413197/MyProblem-Data.txt MyProblem-
> Data.txt
> >
> http://www.nabble.com/file/p24413207/MyProblem.txt MyProblem.txt
> --



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