[Cmpl] objective function with a percentage (divisor)

[Mike Steglich]

Hi James,

The total demand has to be unequal to the total supply. (You used obviously the expression s[i]*0.8 in your original model to have unequal demands and supplies due to the equal demands and supplies in your Excel sheet):

Thanks,

Mike

> Am 25.11.2017 um 21:51 schrieb James Carlson <jddcarlson at gmail.com>:
> 
> hey Mike,
> 
> Thank you for he prompt reply. As you very accurately stated i am attempting to minimize the under and over delivery (thank you for the clarification).  I have implemented your suggestions and it runs in the Solver.  It appears the u and o arrays are zero could you suggest how i should define the U and O arrays in CMPL so they are non-zero values?  Attached is an updated model ... thank you again for your help!
> 
> James
> 
> 
> On Sat, Nov 25, 2017 at 10:38 AM, Mike Steglich <mike.steglich at berlin.de <mailto:mike.steglich at berlin.de>> wrote:
> Hi James,
> 
> If I am right to assume that you want to minimise the under and over  delivery (beside the transportation costs) then I would like to propose the following model:
> 
>  
> 
> %data : sources set, destinations set, s[sources], d[destinations], c[sources,destinations]
> 
>  
> 
> parameters:
> 
>              { i in sources , j in destinations:
> 
>         costs[i,j]:= c[i,j]*d[j];
> 
>     }       
> 
>             
> 
> variables:
> 
>              x[sources,destinations]: binary;
> 
>              u[sources]:real[0..];
> 
>              o[sources]:real[0..];
> 
> objectives:
> 
>              #Total_cost: sum{i in sources, j in destinations : #costs[i,j] * x[i,j]} +
> 
>              sum{i in sources: u[i]+o[i]} ->min;
> 
>  
> 
> constraints:
> 
>              supplies {i in sources  : sum{j in destinations: d[j]*x[i,j]} +u[i] -o[i] = s[i]*0.8;}
> 
> demands  {j in destinations : sum{i in sources : x[i,j]} =  1;}
> 
>  
> 
> There are to new vectors of non-negative, continues variables (u for under deliveries and o for over deliveries) to be used in the extended supply constraints.
> 
>  
> 
> This absolute differences of the actual quantities to the supplies of the sources are to be minimised in the objective function.
> 
>  
> 
> Cheers,
> 
>  
> 
> Mike
> 
> 
>   <>
> Von: Cmpl [mailto:cmpl-bounces at coin-or.org <mailto:cmpl-bounces at coin-or.org>] Im Auftrag von James Carlson
> Gesendet: Samstag, 25. November 2017 04:10
> An: cmpl at list.coin-or.org <mailto:cmpl at list.coin-or.org>
> Betreff: [Cmpl] objective function with a percentage (divisor)
> 
>  
> 
> good evening, I am new to CMPL.  I took several LP and combination optimization courses in university - in other words I am very new to this!  I have successfully created a model in SolverStudio and the results seem reasonable.  I am now attempting to change the objective function so the that difference between the delivered volume versus the demand is a ratio (or absolute).  Attached is my model:
> ------------------------------------------------------------------------------------------------------------------------------------------
> %data : sources set, destinations set, s[sources], d[destinations], c[sources,destinations] 
> %display nonZeros
> 
> parameters:
>     { i in sources , j in destinations: costs[i,j]:= c[i,j]*d[j]; }    
>     
> variables:
>     x[sources,destinations]: binary;
> 
> objectives:
>     Total_cost: sum{i in sources, j in destinations : costs[i,j] * x[i,j]} +
>                 sum{i in sources  : sum{j in destinations: d[j]*x[i,j]} - s[i]}  ->min;
> 
> constraints:
>     supplies {i in sources  : sum{j in destinations: d[j]*x[i,j]} >= s[i]*0.8;}
>     demands  {j in destinations : sum{i in sources : x[i,j]} =  1;} 
> ------------------------------------------------------------------------------------------------------------------------------------------
> 
> I would like to try something like this for my objectives:
> 
>     Total_cost: sum{i in sources, j in destinations : costs[i,j] * x[i,j]} +
>                 sum{i in sources  : sum{j in destinations: d[j]*x[i,j]} - s[i]}/s[i]  ->min;
> 
> As i mentioned above I am attempting to make the OF minimize the error as a percentage delivered to each destination.  This is meant to overcome the problem of an under or over delivery is offset by an equal (negative or positive) amount so the function is not really minimizing the value (it is always almost zero due to aggregation of offsetting positive and negative values). 
> 
>  
> 
> Attached is an OpenSolver excel model (in a zip file).  Please note I have made all the costs equal to 1 to better diagnose the OF's second term.
> 
>  
> 
> Any suggestions would be appreciated!  thank you.
> 
>  
> 
> 
> <tester-added_Mikes_suggestions.zip>

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