AMPL: Syntax for sets? - set

Question

I'm spinning up on high level language for mixed integer linear programs (MILPs). The language is A Modeling Language for A Mathematical Programming Language (AMPL).
Chapter 4, page 65, Figure 4-7 shows the following syntax:
set PROD := bands coils plate ;
However, Chapter 5, page 74, shows the following syntax:
set PROD = {"bands", "coils", "plate"};
Can anyone please explain this difference in syntax?
I put the latter into a *.dat file, and AMPL complains expected ; ( : or symbol where the { is. Wondering if it is just a mistake in the manual.
Thanks.

Answer 1

The syntax in Chapter 4 --
set PROD := bands coils plate;
-- is used in data files, while the syntax in Chapter 5 --
set PROD = {"bands", "coils", "plate"};
-- is used in model files. It's a little weird (IMO) that the syntax for sets is different in model and data files, but it is. For another example of this difference, see this question and answer.
Complete working example code modified from AMPL manual
Added by the original poster of the question.
dietu.mod:
# dietu.mod
#----------
# set MINREQ; # nutrients with minimum requirements
# set MAXREQ; # nutrients with maximum requirements
set MINREQ = {"A", "B1", "B2", "C", "CAL"};
set MAXREQ = {"A", "NA", "CAL"};
set NUTR = MINREQ union MAXREQ; # nutrients
set FOOD; # foods
param cost {FOOD} > 0;
param f_min {FOOD} >= 0;
param f_max {j in FOOD} >= f_min[j];
param n_min {MINREQ} >= 0;
param n_max {MAXREQ} >= 0;
param amt {NUTR,FOOD} >= 0;
var Buy {j in FOOD} >= f_min[j], <= f_max[j];
minimize Total_Cost: sum {j in FOOD} cost[j] * Buy[j];
subject to Diet_Min {i in MINREQ}:
sum {j in FOOD} amt[i,j] * Buy[j] >= n_min[i];
subject to Diet_Max {i in MAXREQ}:
sum {j in FOOD} amt[i,j] * Buy[j] <= n_max[i];
The explicit definitions of setes MINREQ and MAXREQ and their members is taken from the *.dat file below (where their definitions have been commented out). Matlab users, observe above & beware that you need commas between members in a set.
dietu.dat:
# dietu.dat
#----------
data;
# set MINREQ := A B1 B2 C CAL ;
# set MAXREQ := A NA CAL ;
set FOOD := BEEF CHK FISH HAM MCH MTL SPG TUR ;
param: cost f_min f_max :=
BEEF 3.19 2 10
CHK 2.59 2 10
FISH 2.29 2 10
HAM 2.89 2 10
MCH 1.89 2 10
MTL 1.99 2 10
SPG 1.99 2 10
TUR 2.49 2 10 ;
param: n_min n_max :=
A 700 20000
C 700 .
B1 0 .
B2 0 .
NA . 50000
CAL 16000 24000 ;
param amt (tr): A C B1 B2 NA CAL :=
BEEF 60 20 10 15 938 295
CHK 8 0 20 20 2180 770
FISH 8 10 15 10 945 440
HAM 40 40 35 10 278 430
MCH 15 35 15 15 1182 315
MTL 70 30 15 15 896 400
SPG 25 50 25 15 1329 370
TUR 60 20 15 10 1397 450 ;
Solve the model using the following at the AMPL prompt:
reset data;
reset;
model dietu.mod;
data dietu.dat;
solve;