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Maintenance optimization with duration-dependent costs

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Abstract

High levels of availability and reliability are essential in many industries where production is subject to high costs due to downtime. Examples include the mechanical drive in natural gas pipelines and power generation on oil platforms, where gas turbines are commonly used as a power source. To mitigate the effects of service outages and increase overall reliability, it is also possible to use one or more redundant units serving as cold standby backup units. In this paper, we consider preventive maintenance optimization for parallel k-out-of-n multi-unit systems, where production at a reduced level is possible when some of the units are still operational. In such systems, there are both positive and negative effects of grouping activities together. The positive effects come from parallel execution of maintenance activities and shared setup costs, while the negative effects come from the limited number of units which can be maintained at the same time. To show the possible economic effects, we evaluate the approach on models of two production environments under a no-fault assumption. We conclude that savings were substantial in our experiments on preventive maintenance, compared to a traditional preventive maintenance plan. For single-unit systems, costs were on average 39 % lower when using optimization. For multi-unit systems, average savings were 19 %. We also used the optimization models to evaluate the effects of re-planning at breakdown and effects due to modeling of inclusion relations. Breakdown re-planning saved between 0 and 11 % of the maintenance costs, depending on which component failed, while inclusion relation modeling resulted in an 7 % average cost reduction.

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Abbreviations

α :

Minimum availability due to preventive maintenance.

k t :

Maximum duration at occasion t.

d t :

Total production-affecting time at occasion t.

Δ i :

Duration specification for item i. Δ i =〈Δ 1i ,Δ 2i ,…,Δ pi 〉.

Δ pi :

Duration of item i in phase p∈1…P.

C i :

Maintenance cost for item i.

\(r^{N}_{t}\) :

Number of night rests at occasion t.

ϕ pt :

Maintenance duration of phase p at occasion t for a single unit system.

ϕ upt :

Duration of maintenance affecting production in phase p on unit u at occasion t.

T i :

Period time for item i.

D t :

Value of production at occasion t.

N i :

Set of items which include item i.

S t :

Setup cost at occasion t.

δ T :

Time between two consecutive occasions.

O i :

Initially used life of item i in a single-unit system.

O ui :

Initially used life of item i in unit u.

\(r^{W}_{t}\) :

Number of week rests at occasion t.

w t :

Total working time at occasion t for a single unit.

w ut :

Total working time at occasion t for unit u in a multi-unit system.

A :

Working hours per day.

C f (t):

Fuel quality influence on EOH at occasion t.

C w (t):

Water injection influence on EOH at occasion t.

C x (t):

Load influence on EOH at occasion t.

C T7diff (t):

Exhaust temperature influence on EOH at occasion t.

f :

Total cost.

H :

Scheduling horizon.

I :

Number of maintenance items.

i :

Maintenance item.

k :

Units needed for operation.

n :

Total number of available units.

P :

Number of working phases.

p :

Working phase.

t,j :

Maintenance occasion at occasion t or j.

u :

Production unit.

W :

Working days per week.

x it :

Decision variable indicating whether item i is maintained at occasion t or not, for a single unit system.

x uit :

Decision variable indicating whether item i on unit u is maintained at occasion t.

y t :

Decision variable indicating whether maintenance is done at occasion t or not.

z ut :

Service of redundant unit u at occasion t.

CBM:

Condition-Based Maintenance.

EOC:

Equivalent Operating Cycles.

EOH:

Equivalent Operating Hours.

SIT AB:

Siemens Industrial Turbomachinery AB.

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Acknowledgements

This work was funded by VINNOVA and Siemens Industrial Turbomachinery AB.

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Authors and Affiliations

  1. Swedish Institute of Computer Science, Box 1263, 164 29, Kista, Sweden

    Markus Bohlin

  2. Siemens Industrial Turbomachinery AB, 612 83, Finspong, Sweden

    Mathias Wärja

Authors
  1. Markus Bohlin
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  2. Mathias Wärja
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Correspondence to Markus Bohlin.

Additional information

This work was supported by VINNOVA grant P32551-1

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Bohlin, M., Wärja, M. Maintenance optimization with duration-dependent costs. Ann Oper Res 224, 1–23 (2015). https://doi.org/10.1007/s10479-012-1179-1

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