Industrial Control Systems

247Chapter eight: Mathematical modeling and control

availability by adding information into constraints. Thus, we perturbed

the third mapping constraint which was previously set to prohibit map-

ping of resource units at time t

c

which are in use by activities in progress

at that time. The constraint was originally dened as

u y i t j J

t

j k

i

j k

k

R

c

c

j

, ,

( ) , ,⋅ = ∈ = …

=

∑

0

1

for for 1Ω

To now further prevent mapping of resource units whose

a

i

j k

c

t

,

( )

equals

zero at t

c

, we modify the aforementioned constraint as follows:

u t y i t j J

t

j k

i

j k

c

i

j k

k

R

c

c

j

, , ,

( ) ( ) , ,+ −

( )

( )

⋅ = ∈ = …

=

∑

1 0

1

a for for 1Ω

This modied constraint now not only lters out those resource units that

are engaged in activities in progress at t

c

, but also those units whic