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Hi I would like to know which algorithm is best suited to solve this Cost Minimisation problem:

Total Cost =

                      FC1           if  0 < W < 30                       FC2           if  30 < W < 150                       FC3           if  W > 150               +             W* ECL                     if q(e,b,W) ≤ BOD                           W* ECH                     if q(e,b,W) > BOD              + Price*Labor + Price*Capital + Price*Water + Price*Abatement 

FC1, FC2, FC3 are constants while BOD is pollution standard, ECL and ECH are also constants

q is like the pollution concentration like BOD/liters of wastewater, I defined it as a function of e (emission), b (the firm's pollution abatement efforts) and W (water).

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    I'm not a programmer, and I don't know what `q(e,b,W)` is anyway. :(2011-08-24
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    I know what BOD is, sure, but like anon, I wonder about q. Do give some background, please.2011-08-24
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    i have updated my query. thanks anon and J.M. :)2011-08-24
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    @Joseph: What's missing is not so much the real-world interpretation of the quantities but the mathematical structure. You haven't told us which are the variables to be determined by the cost minimisation. Since you call some of the quantities "constants", are we to assume that everything else is a variable? Are the variables unrestricted? For instance, if the answer to both of those questions is "yes", then the cost function is unbounded and the problem has no solution. Also, I suspect that we might need to know the function $q$ in order to say anything useful.2011-08-24
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    @joriki: I think the cost function is a piecewise constant function from the first three lines plus a piecewise linear (in $W$) function depending on $q(e,b,W)$ in the next two lines plus a generic linear function from the last line. That should mean $e,b,W$ (from whatever bounds they are allowed to take values in) are the degrees of freedom and the only thing we're missing is what the function $q$ actually is. (And how big all of the constants are relative to each other.)2011-08-24
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    Just setup three different (constrained) optimization problems (to get rid of the step function), then use your preferred optimization problem solver for each problem separately, and then select the optimum from these three solutions.2011-08-24
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    @Thomas: I think there may be 6 problems, given the different values of `ECL` and `ECH`.2011-08-24

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