By (5) the number of Production Orders Op
i ðtÞ
for each product i issued
at any time t, is defined as the customer orders remaining in
the Customer Order File (Fi(t)) divided by the order handling time
(toht) (anchor), combined with a fraction Kw (0 6 Kw 6 1) of the discrepancy
between desired WIP W
i ðtÞ
and actual WIP (WIP adjustment),
and a fraction Kl (0 6 Kl 6 1) of the number of tardy jobs
(Ti(t)) (we consider the desired value of tardy jobs equal to zero).
The actual WIP for each product i, is the sum of WIP in all workstations
WiðtÞ ¼
Pmj
¼1WijðtÞ
, while the desired WIP level is defined in
(6) by the expected customer orders (E(Oi(t))) and the average manufacturing
lead time E MLi
ðtÞ
. Expected customer orders and
average manufacturing lead time are defined in (7) and (8) respectively,
as a first-order exponential smoothing of the actual Customer
Orders (Oi(t)) and manufacturing lead time MLi
ðtÞ
of product i at
time t respectively, with smoothing factor a. Manufacturing lead
time is defined in (9) as the time needed to eliminate WIP from
all workstations, based on the current production rate (Pij(t)).