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Optimization of the integrated fleet-level imperfect selective maintenance and repairpersons assignment problem

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Abstract

Industrial environments such as manufacturing and transportation industries usually involve fleets of identical systems that must carry out several missions interspersed with scheduled finite breaks. Given the limited amount of maintenance resources and time available, only a restricted number of maintenance actions can be performed on selected components to ensure a pre-specified performance level of the fleet for the next mission. Such a maintenance strategy is known as fleet-level selective maintenance (FSM). The FSM is more complex than the selective maintenance problem as it adds the total number of systems in the fleet as another level of combinations to be explored during the optimization process. Most FSM models consider the replacement or perfect repair of system components as the only maintenance option. Furthermore, they consider a single repair channel and disregard the assignment of repairpersons and the impact of their variable skillsets on the maintenance costs and duration. In this paper, an approach is proposed to help in more realistic decision making for FSM where several imperfect maintenance levels and multiple repair channels are available. A novel integrated non-linear programming formulation of the FSM problem where maintenance and repairpersons assignment decisions are made jointly is proposed. All relevant parameters and terms of this non-linear optimization problem are developed and discussed. A two-phase modeling approach is then used to transform the original nonlinear problem into a binary integer optimization model. To demonstrate the validity and the added value of the proposed approach, multiple sets of numerical experiments are investigated and managerial implications are provided.

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Abbreviations

\(\mathrm{CM}\) :

Corrective maintenance

\(\mathrm{IM}\) :

Imperfect maintenance

\(\mathrm{PM}\) :

Preventive maintenance

\(\mathrm{SM}\) :

Selective maintenance

\(\mathrm{SMP}\) :

Selective maintenance problem

\(\mathrm{SMOP}\) :

SM optimization problem

\(\mathrm{RBD}\) :

Reliability block diagram

\(\mathrm{FSM}\) :

Fleet-level SM

\(\mathrm{FSMP}\) :

Fleet-level SMP

\(\mathrm{FSMOP}\) :

FSM optimization problem

\({\mathcal {F}}\) :

Fleet composed of several systems

f :

Number of systems in the fleet

s :

Index of systems in the fleet (\(s=1,\ldots ,f\))

m :

Number of subsystems per system

i :

Index of subsystems (\(i=1,\ldots ,m\))

\(n_{i}\) :

Number of components in the ith subsystem

j :

Index of component in subsystems

\(E_{sij}\) :

The jth component in the ith subsystem of the sth system (\(j=1,\ldots ,n_{i}\))

\(h_{sij}(t)\) :

Failure rate of component \(E_{sij}\) when new

\(L_{ij}\) :

The highest maintenance level available for component \(E_{sij}\)

l :

Index of maintenance level \(l\in \{0,\ldots ,L_{ij}\}\)

\(\theta _{ijl}\) :

Age reduction coefficient of CM of level l performed on \(E_{sij}\)

\(\varphi _{ijl}\) :

Age reduction coefficient of PM of level l performed on \(E_{sij}\)

K :

Number of repairpersons

k :

Index of repairpersons (\(k=1,\ldots ,K\))

Q :

Set {T, S, P} of repairpersons qualification levels: Trainee (T), Standard (S) and Pro (P)

q :

Function of repairpersons qualification levels: \(q:\{1,\ldots ,K\}\rightarrow Q\)

\(t_{sijkl}^c\) :

Duration of CM of level l performed on \(E_{sij}\) by repairperson k of qualification level q(k)

\(t_{sijkl}^p\) :

Duration of PM of level l performed on \(E_{sij}\) by repairperson k of qualification level q(k)

\(c_k\) :

Fixed cost of hiring/using repairperson k of qualification level q(k)

\(c_k^v\) :

Variable cost rate of using repairperson k of qualification level q(k)

\(B_{sij} (A_{sij})\) :

Age of component \(E_{sij}\) at the start (the end) of the break

\(U_{sij} (V_{sij})\) :

Binary status variable of \(E_{sij}\) at the start (the end) of the break

\({\mathcal {T}}_0\) :

Limited break duration

\({\mathcal {R}}_{0}\) :

Minimum required fleet reliability level for the next mission

D :

Duration of the next mission

\(R_{sij}^c\left( D|_{A_{sij}}\right) \) :

Conditional reliability of \(E_{sij}\) during the next mission

\({\mathcal {R}}_s^c\) :

Conditional reliability of the sth system during the next mission

\({\mathcal {R}}_{{\mathcal {F}}}^c\) :

Conditional fleet reliability during the next mission

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Authors and Affiliations

  1. Laboratory of Industrial Engineering, Production and Maintenance, Lorraine University, Metz, France

    A. Khatab

  2. Department of Industrial Engineering, Dalhousie University, Halifax, Canada

    A. Khatab, C. Diallo & U. Venkatadri

  3. Department of Industrial Systems Engineering and Product Design, Faculty of Engineering and Architecture, Ghent University, Ghent, Belgium

    E.-H. Aghezzaf

  4. Industrial Systems Engineering (ISyE), Flanders Make, Kortrijk, Belgium

    E.-H. Aghezzaf

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  1. A. Khatab
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Khatab, A., Diallo, C., Aghezzaf, EH. et al. Optimization of the integrated fleet-level imperfect selective maintenance and repairpersons assignment problem. J Intell Manuf 33, 703–718 (2022). https://doi.org/10.1007/s10845-020-01672-0

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