Problem Formulation
As discussed earlier, the model deals with the scheduling of production jobs and preventive
maintenance jobs on multiple production lines. Common production planning models use as
principal decision variables the quantity to be produced in a certain period. The model proposed
below only indicates whether or not to produce a certain product in a certain period on a certain
production line. The assumption is therefore made that the production rate is constant throughout
the planning period. This assumption is very reasonable in the chemical industry, where it is very
hard if not impossible to change the production rate in the short term. The model minimizes total
costs, including preventive maintenance costs, expected breakdown costs or expected corrective
maintenance costs, inventory costs, backorder costs and setup costs. Production costs are not
taken into account, as they are not relevant to the objective function.
The following additional assumptions are made in the model:
- equipment is as good as new after a preventive maintenance service
- when a breakdown occurs, the equipment has to be repaired or replaced immediately
- the expected breakdown costs increase strictly with time elapsed since the last repair
- only one product can be produced on a particular production line in a particular period
- maintenance takes the same time on all production lines
- setup costs are sequence-independent
- demand is deterministic
The Model
The indices:
i: products, i=1,...,N
j: production line, j=1,...,M
t: time, t=0,...,T
Period 0 is included as a dummy period to initialize some of the variables.
The decision variables:
δ ijt: 1 if product i is produced on line j in period t
0 otherwise
φ ijt: 1 if product i is produced on line j in period t but not in period t-1
0 otherwise
mjt: 1 if preventive maintenance is performed on line j in period t
0 otherwise
zjt: 1 if preventive maintenance is done on line j in period t but not in period t-1
0 otherwise
yjmt: 1 if in period t the last preventive maintenance job on line j ended in period m
0 otherwise
αijmt: 1 if yjmt and δijt are 1
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