Error: Ran out of memory

[thossain]

Hello Everyone! I am trying to run my code to solve an MILP with optmodel procedure. I am using SAS enterprise Guide 7.1. I was trying to locate optimal number of Depots for storing supplies from fields. My two location sets for Depot and Field are the same, using the county centroids. When I used one state (North Carolina) which has 100 counties, the code ran fine and gave me results. But just when I increased the number of states, my log showed me the error of "Ran out of memory". I am attaching my code here and also attaching the log. What can I do to resolve this issue? Thank you in advance!

/*creating macro variables*/

%let NumFields  = 50;
%let NumDepots      = 10;
%let DepotCapacity  = 25000;
%let MaxDemand     = 1000;
%let xmax          = 200;
%let ymax          = 100;
%let seed          = 423;



data fdata(Rename=(County=name));
	set UScounties;

	if state in ("North Carolina", "South Carolina", "Virgina") then
		do;
			x=Long;
			demand=rand('UNIFORM') * &MaxDemand;
			Y=Lat;
			output fdata;
			keep county x demand y;
		end;
run;



data pdata(Rename=(county=name));
	set UScounties;
	if state in ("North Carolina", "South Carolina", "Virgina") then
		do;
			x=Long;
			y=Lat;
			fixed_cost=275000;
			output;
			keep county x y fixed_cost;
		end;
run;


/*Solving the MILP*/
proc optmodel;
	set <str> Fields;

	/*declares set of fields*/
	set <str> Depots init {};

	/*declares set of depots*/
	num x{Fields union Depots};

	/*creating an array of x cooordinate with all the field and depot location, union combines both field and depot*/
	num y{Fields union Depots};

	/*creating an array of y cooordinate with all the field and depot location*/
	num demand{Fields};
	num fixed_cost{Depots};
	num distance {i in Fields, j in Depots}=sqrt((x[i] - x[j])^2 + (y[i] 
		- y[j])^2);

	/* linear distance between fields and depots*/
	read data fdata into Fields=[name] x y demand;
	read data pdata into Depots=[name] x y fixed_cost;
	var Assign {Fields, Depots} binary;

	/* binary value to assign specific fields to specific depots*/
	var Build {Depots} binary;

	/*objective function*/
	/* binary variable to determine which depots will be established*/
	min cost=sum{i in Fields, j in Depots} Distance[i, j]*Assign[i, j] + sum{j in 
		Depots}Fixed_cost[j]*Build[j];

	/*Constraints*/
	con Assign_fields{i in Fields}: sum{j in Depots}Assign[i, j]=1;

	/*each field assigned to one depot only*/
	con Build_depot{i in Fields, j in Depots}: Assign[i, j] <=Build[j];

	/* if a field is assigned to a depot, it has to be build*/
	con Depot_capacity{j in Depots}: sum {i in Fields}Demand[i]*Assign[i, 
		j]<=&DepotCapacity*Build[j];

	/*ensuring total field supply to a depot is within its capacity*/
	solve obj Cost with MILP/Primalin;
	num varcost=sum {i in FIELDS, j in DEPOTS} distance[i, j] * Assign[i, j].sol;
	num fixcost=sum {j in DEPOTS} fixed_cost[j] * Build[j].sol;
 	for {s in 1.._NSOL_} do; 

	/*clean up the solution*/
	for {i in FIELDS, j in DEPOTS} Assign[i, j]=round(Assign[i, j].sol[s]);
	for {j in DEPOTS} Build[j]=round(Build[j].sol[s]);
	call symput('varcost', put(varcost, 6.1));
	call symput('fixcost', put(fixcost, 5.1));
	call symput('totalcost', put(Cost, 6.1));

	/*create a data set for use by PROC SGPLOT*/
	create data CostFixedCharge_Data from
        [FIELD DEPOT]={i in FIELDS, j in DEPOTS: Assign[i, j]=1} 
		x1=x[i] y1=y[i] x2=x[j] y2=y[j] function='line' drawspace='datavalue' 
		linethickness=1 linecolor='black';
 	submit s; 
 	endsubmit; 
 end; 
quit;

[RobPratt]

Can you please attach the UScounties data set or provide code to generate it?

[thossain]

Thank you so much for your reply. Although I am using the county names now as [name] but later I will use the unique FIPS code as there are duplicate county names within the US. I am attaching the US Counites dataset here. 

[RobPratt]

One suggestion is to omit the Build_depot constraints, which are not strictly necessary.  They tighten the formulation but also make it bigger, requiring more memory.  The logical implication "if Assign[i,j] = 1 then Build[j]" is already enforced via the Depot_capacity constraints.

You might also try increasing the MEMSIZE option value, as described here.

Note also that Virgina should instead be Virginia.

[RobPratt]

Two additional suggestions:

1. Consider heuristically reducing the allowed field-to-depot assignments based on a distance threshold.  This documentation example shows how to do that efficiently, by omitting variables from the formulation.

2. Use a Benders decomposition approach, as shown in this SAS Communities thread.

[thossain]

Thank you so much for all your great suggestions!