robert.gms : Elementary Production and Inventory Model
A manufacturer can produce three different products requiring the
storage of two raw materials. Expected profits change over time and
remaining raw materials are valued.
Reference:
- Fourer, R, Modeling Languages Versus Matrix Generators for Linear Programming. ACM Transaction on Mathematical Software 9, 2 (1983), 143-183.
Small Model of Type: LP
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$Title Elementary Production and Inventory Model (ROBERT,SEQ=37)
$Ontext
A manufacturer can produce three different products requiring the
storage of two raw materials. Expected profits change over time and
remaining raw materials are valued.
Fourer, R, Modeling Languages versus Matrix Generators For Linear
Programming. ACM Transaction of Mathematical Software 9, 2 (1983),
143-183.
$Offtext
Sets p products / low, medium, high /
r raw materials / scrap, new /
tt long horizon / 1*4 /
t(tt) short horizon / 1*3 /
Table a(r,p) input coefficients
low medium high
scrap 5 3 1
new 1 2 3
Table c(p,t) expected profits
1 2 3
low 25 20 10
medium 50 50 50
high 75 80 100
Table misc(*,r) other data
scrap new
max-stock 400 275
storage-c .5 2
res-value 15 25
Scalar m maximum production / 40 /;
Variables x(p,tt) production and sales
s(r,tt) opening stocks
profit
Positive variables x, s;
Equations cc(t) capacity constraint
sb(r,tt) stock balance
pd profit definition ;
cc(t).. sum(p, x(p,t)) =l= m;
sb(r,tt+1).. s(r,tt+1) =e= s(r,tt) - sum(p, a(r,p)*x(p,tt));
pd.. profit =e= sum(t, sum(p, c(p,t)*x(p,t))-sum(r, misc("storage-c",r)*s(r,t)))
+ sum(r, misc("res-value",r)*s(r,"4"));
s.up(r,"1") = misc("max-stock",r);
Model robert / all /
Solve robert maximizing profit using lp;
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