topic Re: PROC OPTMODEL - Data Envelope Analysis - Return Input and Output Slacks in Mathematical Optimization, Discrete-Event Simulation, and OR

PROC OPTMODEL - Data Envelope Analysis - Return Input and Output Slacks

Sypert — Mon, 29 Jun 2020 22:29:02 GMT

How can I return the input and output slacks using the DEA example from the SAS/OR(R) 12.1 User's Guide?

Here is a link: https://support.sas.com/documentation/cdl/en/ormpex/65555/HTML/default/viewer.htm#ormpex_ex22_sect009.htm

Thanks.

Re: PROC OPTMODEL - Data Envelope Analysis - Return Input and Output Slacks

RobPratt — Mon, 29 Jun 2020 22:37:40 GMT

By slacks, do you mean the differences between the two sides of the inequalities?

input[i,k] - sum {j in GARAGES} input[i,j] * Weight[j]

sum {j in GARAGES} output[i,j] * Weight[j] - output[i,k] * Inefficiency

And do you want to print the values or save them to a data set?

Re: PROC OPTMODEL - Data Envelope Analysis - Return Input and Output Slacks

Sypert — Mon, 29 Jun 2020 23:14:33 GMT

By slacks, I'm trying to get specific potential input and output variable improvements for the inefficient garages. My understanding is the slacks show the further increases in output or reduction in input that could be gained beyond that from the radial projection (equal increase in all outputs, or decrease in all inputs) or a radial efficiency score equal to 1. I'd like to save it to a data set.

I hope this helps. Thanks for your time.

Re: PROC OPTMODEL - Data Envelope Analysis - Return Input and Output Slacks

RobPratt — Tue, 30 Jun 2020 00:51:36 GMT

If I understand correctly, the following changes should do what you want:

   num input_slack  {GARAGES, INPUTS};
   num output_slack {GARAGES, OUTPUTS};
   do k = GARAGES;
      solve;
      efficiency_number[k] = 1 / Inefficiency.sol;
      for {j in GARAGES}
         weight_sol[k,j] = (if Weight[j].sol > 1e-6 then Weight[j].sol else .);
      for {i in INPUTS}
         input_slack[k,i] = round(Input_con[i].ub - Input_con[i].body, 1e-6);
      for {i in OUTPUTS}
         output_slack[k,i] = round(Output_con[i].body - Output_con[i].lb, 1e-6);
   end;

   set EFFICIENT_GARAGES = {j in GARAGES: efficiency_number[j] >= 1 - 1e-6};
   set INEFFICIENT_GARAGES = GARAGES diff EFFICIENT_GARAGES;

   create data slack_data from [garage]=INEFFICIENT_GARAGES garage_name efficiency_number
      {i in INPUTS} <col(i)=input_slack[garage,i]>
      {i in OUTPUTS} <col(i)=output_slack[garage,i]>;

Re: PROC OPTMODEL - Data Envelope Analysis - Return Input and Output Slacks

Sypert — Tue, 30 Jun 2020 22:41:33 GMT

That is exactly what I was after. Thank you so much for your time and the fast response!