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[AMPL 2659] Re: Unbounded or badly scaled problem

by Robert Fourer-2 :: Rate this Message:

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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