Date:         Wed, 14 Apr 2010 22:56:11 -0400
Reply-To:     Sigurd Hermansen <HERMANS1@WESTAT.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Sigurd Hermansen <HERMANS1@WESTAT.COM>
Subject:      Re: PROC OPTMODEL in SAS 9.1.3
Comments: To: Ban Cheah <BanCheah@WESTAT.com>
In-Reply-To:  <201004121545.o3CFetoo022076@malibu.cc.uga.edu>
Content-Type: text/plain; charset="us-ascii"

The omission of "number rate = 0.08;" in the second specification of the problem likely has more of an impact than the small change in add_amt. The first specification of the problem likely leads to an empty solution set. The second specification may solve for the minimum interest rate given the other parameter values.
S

-----Original Message-----
From: SAS(r) Discussion [mailto:SAS-L@LISTSERV.UGA.EDU] On Behalf Of Ban Cheah
Sent: Monday, April 12, 2010 11:46 AM
To: SAS-L@LISTSERV.UGA.EDU
Subject: PROC OPTMODEL in SAS 9.1.3

The problem is the following: I plan to retire in year 5 and expect to live
8 years. For each of those 8 years, I plan to spend 30,000 per year. How
much must I put into my savings account from years 0 to 4 if my return from
saving is 8 percent?

The code is as follows:
proc optmodel;
   number rate = 0.08;
   number life = 13;
   number year;
   number cf{1..life} init -30000;
   var add_amt init 30000;

   do year = 0 to 4;
     cf[year+1]=add_amt;
   end;

   min z = sum {i in 0..12} (cf[i+1]/((1+rate)**(i)));
   con add_amt>=0, z=0;
   solve ;
   print add_amt;

quit;

OPTMODEL is unable to solve this problem - the note in the log is:
The constraint '_ACON_[2]' is empty and infeasible.  Constraint _ACON_[2]
causes the problem to be infeasible.

The solution (using Excel's Solver) is add_amt = 29386.55

If I rephrase the problem as the following: If I save 29,386.55 per year,
what must my return be? The code is as follows:

proc optmodel;
   number life = 13;
   number year;
   number cf{1..life} init -30000;
   number add_amt init 29386.55;
   var rate;

   do year = 0 to 4;
     cf[year+1]=add_amt;
   end;

   min z = sum {i in 0..12} (cf[i+1]/((1+rate)**(i)));
   con add_amt>=0, z=0;
   solve ;
   print rate;

quit;

OPTMODEL returns the correct answer as 0.08.

I'm running OPTMODEL in 9.1.3 SP4 which is experimental. Perhaps this is
the problem? Or is the first code incorrectly specified?

Thanks.