I have prepared and run a Linear Programming model in SAS. I have some questions about the output that I can’t find answers to, and am hoping that someone can help.
My model contains the decision variables X1, X2 …………..X12, and all are binary. The model minimizes cost of inputs on a weekly basis over a period of 7 weeks.
There are constraints that restrict use of specific inputs to no m ore than in 2 consecutive weeks, for minimum levels of effectiveness, and others. An example constraint for week 1 was
0.598X1-1 +0.585X2-1+0.435 X3-1+0.372X4-1 +0.479X5-1+0.63X6-1+0.678X7-1+0.648X8-1+0.631X9-1 +0.48X10-1+0.144X11-1+0.207X12-1 ≥ 0.5
Same as constraints for week2 …..week 7. X1-1 indicates pesticide 1 applied in week 1.
The objective function: MinCost= C ∑(i=1)^12▒∑(j=1)^7 X(i-j)
In the solution, the variable summary from the SAS output is
Variable name Status type pric Activity Reduced cost
X1-1 Binary 6.98 1 1.12
X1-6 Binary 6.98 1 5.69
X7-7 Binary 17.01 1 11.15
X8-3 Binary 12.95 1 7.09
X8-4 Binary 12.95 1 7.09
X9-2 Binary 1.44 1 4.57
X9-5 Basi Binary 1.44 1 0
I picked the variables from the summary output that had the value ‘1' in the “activity column”. Only one of the variables has status of ‘basic’, the others apparently being non-basic by default. When a variable is a basic variable, it is in the optimal solution, and its reduced cost is o. However, only one of these reduced costs is 0.
My question is
does this output suggest an error in the program?
if no, is this just the way that SAS presents output from the LP model?
how do I explain and interpret these non-zero reduced costs for what appear to be basic variables?
Thanks for the help!