uimp.gms : UIMP - Production Scheduling Problem
A company manufactures nuts, bolts and washers using three different machines
that can be operated in normal or overtime production mode. The company
needs to plan operations for the next two periods.
Reference:
- Ellison, E F D, and Mitra, P, UIMP - User Interface for Mathematical Programming. ACM Transactions on Mathematical Software 8, 2 (1982).
Small Model of Type: LP
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$Title UIMP - Production Scheduling Problem (UIMP,SEQ=11)
$ontext
A company manufactures nuts, bolts and washers using three different machines
that can be operated in normal or overtime production mode. The company
needs to plan operations for the next two periods.
Ellison, E F D, and Mitra, P, UIMP - User Interface for Mathematical
Programming. ACM Transactions on Mathematical Software 8, 2 (1982).
$Offtext
Sets i time periods / summer, winter /
j production mode / normal, overtime /
k products / nuts, bolts, washers /
l machines / m1, m2, m3 /
Table mh(l,k) machine hours (hours per unit)
nuts bolts washers
m1 4 4 6
m2 7 6 6
m3 3
Table mhadd(i,j) addfactors for mh
normal overtime
summer -1
winter +1
Table av(l,j) availability (hours)
normal overtime
m1 100 80
m2 100 90
m3 40 30
Parameter t(i,j,k,l) machine hours required
a(i,j,l) machine hours available;
t(i,j,k,l) = mh(l,k) + mhadd(i,j)$mh(l,k) ;
t("winter","overtime","washers","m1") = 5;
a("summer",j,l) = av(l,j); a("winter",j,l) = av(l,j) + 10;
Display mh, mhadd, av, t, a;
Table tc(l,k) production cost data
nuts bolts washers
m1 2 3 4
m2 4 3 2
m3 1
Table tcadd(i,j) addfactors for tc
normal overtime
summer 1
winter 1 2
Parameter c(i,j,k,l) production cost ;
c(i,j,k,l) = tc(l,k) + tcadd(i,j)$tc(l,k); display c;
Table p(i,k) selling price
nuts bolts washers
summer 10 10 9
winter 11 11 10
Table d(i,k) demand
nuts bolts washers
summer 25 30 30
winter 30 25 25
Parameter s(k) storage cost / (nuts,bolts,washers) = 1 /
h(k) storage capacity / (nuts,bolts) = 20 /
Variables x(i,j,k,l) production
y(i,k) products stored
z(i,k) products sold
cost, revenue, profit
Positive Variables x, y ;
Equations pdef profit definition
cdef cost definition
rdef revenue definition
ma(i,j,l) machine availability
ib(i,k) inventory balance ;
pdef.. profit =e= revenue - cost ;
cdef.. cost =e= sum((i,k), s(k)*y(i,k) + sum((j,l), c(i,j,k,l)*x(i,j,k,l))) ;
rdef.. revenue =e= sum((i,k), p(i,k)*z(i,k));
ma(i,j,l).. sum(k, t(i,j,k,l)*x(i,j,k,l)) =l= a(i,j,l) ;
ib(i,k).. sum((j,l)$mh(l,k), x(i,j,k,l)) + y(i-1,k) =e= z(i,k) + y(i,k) ;
z.lo(i,k) = d(i,k) ; y.up(i,k) = h(k) ;
Model uimp ellison mitra / all / ;
Solve uimp maximizing revenue using lp ;
Solve uimp maximizing profit using lp ;
Parameter rep summary report ;
rep(l,i,k) = sum(j, x.l(i,j,k,l));
rep("demand",i,k) = d(i,k);
rep("supply",i,k) = sum(l, rep(l,i,k));
Display rep;
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