topic Quick Syntax Related Question in Mathematical Optimization, Discrete-Event Simulation, and OR

Quick Syntax Related Question

MikeCarter — Wed, 17 Dec 2014 23:25:59 GMT

Hello all,

This may be an easy question dealing with the syntax or structure of PROC OPTMODEL.

I have simplified my problem here, just to focus what I want to know.

Assume I have pairs of cities, Origin and Destination, my Objective Function Cost is defined as-

Origin Destination Type Cost Distance

A1 B1 One 5 1

A1 B2 One 5 2

A1 B3 One 5 3

B1 C1 Two 8 4

B1 C2 Two 8 5

B2 C1 Two 8 6

B2 C2 Two 8 7

B3 C1 Two 8 8

B3 C2 Two 8 9

min Total_Cost =

(sum{<a, b> in ARCS, p in PRODUCTS} ((Flow[a,b,p] * Distance[a,b] * Cost[a,b]) ;

Data-

ARCS is set of [Origin, Destination].
PRODUCTS is a set containing Product Types.
SET_A is set {A1,A2,A3} ; SET_B is {B1,B2,B3}

This is basic structure- where I just read cost from the data table.

But now, we want to pass Cost as a Macro variable. As you can see, Cost is 5 for Type One and 8 for Type Two Arc. So, I would have %MACRO Name (cost_one, cost_two) at the top of PRO OPTMODEL. Obviously, now with conditional usage of variable Cost- the above Objective Function is not the same. It needs be broken down for type One and Two Arcs, as below.

min Total_Cost =

(sum{<o, d> in ARCS: o in SET_A, p in PRODUCTS} ((Flow[o,d,p] * Distance[o,d] * &cost_one]) + (sum{< o,d > in ARCS: o in SET_B, p in PRODUCTS } ((Flow[o,d,p] * Distance[o,d] * &cost_two]);

o in SET_A represent ARCS in Type One; o in SET_B represent ARCS in Type Two

We know, “{<o, d> in ARCS: o in SET_A “ --- such conditional statement to pick only selected ARCS works in a constraint declaration, but Does NOT in Objective function.

My question is, how can we break down this Objective Function- to use Cost as Macro variable for different types of Arcs ? How would the above function (which is written intuitively) be programmed to fit in syntax of SAS/OR?

Am open to suggestion, alternate or easier way to accomplish the same.

-Thanks,

Re: Quick Syntax Related Question

RobPratt — Wed, 17 Dec 2014 23:34:44 GMT

The logical condition has to appear last, after all index-set-items:

SAS/OR(R) 13.2 User's Guide: Mathematical Programming

Here are two ways to accomplish what you want:

sum{<o, d> in ARCS, p in PRODUCTS: o in SET_A}

sum{<o, d> in ARCS: o in SET_A} sum{p in PRODUCTS}

Re: Quick Syntax Related Question

Ksharp — Thu, 18 Dec 2014 12:51:59 GMT

Can you clarify it more . What is constraint ? What is your object ? Maybe I could get job done by Data Step or IML .

Xia Keshan

Re: Quick Syntax Related Question

LeoLopes — Thu, 18 Dec 2014 13:25:06 GMT

I think I misunderstood something about the data earlier. So here is a better answer. It is still best to define the macro variables early IMHO.

It might be simpler to continue to incorporate the macro variable earlier, and leave the origin-based cost as is. That way the macro references are in one place:

%let cost_one = 5;

%let cost_two = 8;

proc optmodel;

set NODES;

set ARCS init NODES cross NODES;

set SET_A, SET_B;

num cost{<o,d> in ARCS} = if o in SET_A then &cost_one

else if o in SET_B then &cost_two

else .;

quit;

Then if there are any errors they get detected early, and you can still use cost[o,d] to create reports and diagnostics.

Re: Quick Syntax Related Question

MikeCarter — Thu, 18 Dec 2014 14:40:55 GMT

@ All- Thank you so much, this helps and gives me a direction at least to develop on this further.

@Rob- Thanks Rob, I should have thought about it, but this helps. Thanks again.

@Leo- Great approach, sure I will think on this, once the basic one starts working. Thanks for suggestion.