A Joint Optimization of Strategic Workforce Planning and Preventive Maintenance Scheduling: A Simulation–Optimization Approach
Introduction
Assets’ maintenance has been getting wide-spread attention among researcher and practitioners, mostly due to its importance in several industries and governmental sectors to keep their assets working condition. The increased need of assets’ operations lead to an increase in their corresponding maintenance actions. However, to design an effective assets’ maintenance plan, tuned decisions between the maintenance sub-processes (e.g., decisions for spares’ stock level and facilities management, tasks scheduling and workforce planning) are essential to reach the best performance of the overall system [1]. In other words, an isolated decision for one sub-process/module, while ignoring its reflection on others, will not represent the real-system interactions and subsequently will distract the overall system performance. Thus, this fact paved the way for several techniques of the Operations Research domain to be adopted in a combined format to handle this problem, for instance the simulation–optimization (Sim-Opt) mixture [2], [3].
Along with this growth, the major maintenance process itself is classified into two types: (i) Corrective Maintenance (CM), which occurs when an asset or one of its components fails to perform its task, and requires maintenance to return to its working condition as fast as possible [1], (ii) Preventive Maintenance (PM), that is scheduled frequently, in attempt to prevent the failure from occurrence, or preserve the working condition of the asset [4]. However, a well-established preventive strategy will be a strong element to reduce the number of CM. Thus, a balanced strategy is important to achieve the minimum cost while preserving a high quality of asset operations [1]. The actions corresponding to PM are further classified as ’predetermined/scheduled maintenance’ which is based on calendar, age or usage clock and the ’condition-based maintenance’, which is based on the condition of an asset. The PM schedule is commonly based on multiple indicators of each asset, e.g., the Mean Time Between Failure (MTBF), Mean time to repair (MTTR), Mean Time Between Repairs (MTBR) [4]. Among all those indicators, this work has considered the MTBF.
The assets’ maintenance problem is commonly devoted to handle the maintenance modules’ decisions one at a time. For instance, multiple optimization techniques have been proposed to optimize the PM frequency decision exclusively [5], [6]. Concurrently, research over the workforce planning and training has evolved independently through the literature as reviewed in [7], where they introduced a generic mathematical formulation of an optimization problem by representing the task’s restrictions and skill-based performance measure. Notably, they recorded that a very few research on workforce has applied in the maintenance application area. Also, they indicated there is a lack of research that models the link between the skill level and the consequences of it, and even if exists, it forms a complex problem to solve. Some applications of workforce training problems in real-world are: call centres [8], healthcare systems [9], and manufacturing [10]. Only few articles addressed the cross-training and multi-skilled workforce issues in the maintenance planning problem [11], [12], [13], [14]. Nevertheless, the majority of the previous work ignored the optimum utilization of maintenance-workforce resource, given the consideration of their career progression.
These developments have heightened the need for modelling and solving a holistic assets’ maintenance planning framework, Considering all its joint modules’ decisions inside a single model, i.e. the optimal maintenance schedule and its related maintenance-workforce capacity, training and progression, spares inventory levels and facilities. Therefore, to overcome these challenges and to contribute to the literature, we present and solve an integrated optimization problem that is aimed at helping decision makers in order to find answers to the following maintenance planning questions with harmony between each others:
- (a)
What is the optimal scheduled maintenance frequency for every asset?
- (b)
What is the optimal recruitment rates of new skilled workforce?
- (c)
What is the optimal promotion rates and career progression of existing skilled workforce?
- (d)
what is the link/relationship between all previous points?
The modelling and solving such a holistic maintenance-workforce framework suffers from number of complexities, due to the stochastic and complex nature of the system, that lead to non-linear or non-traceable mathematical models in common [15]. Consequently, the presence of the simulation models from one side and the meta-heuristic optimization algorithms from the other side is remarkable in multiple proposed approaches, primarily for their ability to handle and solve complex problems. Further, the coupling between both algorithms fosters the ability of the combined framework to handle the problems effectively, as reported in [16]. This coupling is known in the literature as the Simulation–Optimization (Sim-Opt) approach, that is dedicated to solve large-scale, complex and optimization problems with uncertainty. This coupled approach benefits from both algorithms advantages to overcome each other’s drawbacks. For example, the optimization algorithm provides optimal decision, which the simulation model cannot reach, while the simulation model provide evaluation for the non-traceable models for such complex systems. Several systematic reviews in the literature show different ways of hybridizing the simulation and optimization methods, i.e., simulation-based optimization, optimization-based simulation, sequential simulation and optimization, and alternate simulation and optimization, as reviewed by Amaran et al. [16]. In this research, we adopt the Simulation-based Optimization. The Sim-Opt has been utilized in several maintenance planning and management applications [2], [3], [17]. Thus, this solution domain is recently in the lead for the maintenance applications [18], [19]. For more detailed discussion about the application of simulation-based optimization in maintenance, the reader is referred to Alrabghi and Tiwari [20].
The selection of the suitable simulation and optimization approaches to be coupled is a vital step to build an efficient framework. The selection depends on the problem’s level of complexity, such as the problem and variables’ nature (e.g. stochastic or deterministic and discrete or continuous), mathematical model characteristics (e.g. the analytical tractability and model linearity) [16]. From the simulation side, multiple researches demonstrated the efficiency of the Discrete Event Simulation (DES) to model/capture the dynamics of the maintenance system modules and the interactions between them, as reported in [15], [20], [21], [22], [23]. From the optimization side, it is reported that Sim-Opt approach commonly uses population-based meta-heuristics optimization algorithms as they are well known for solving complex optimization problems [16], [20]. For instance, Genetic Algorithms [24], [25], [26] and Simulated Annealing [27] meta-heuristics are widely used meta-heuristics optimization methods in the simulation–optimization framework to address maintenance optimization problems. These evidences, besides the complex nature of the problem under study, motivated us to utilize other meta-heuristic population based optimization algorithm, that is rarely explored in the maintenance Sim-Opt framework, such as Differential Evolution (DE) to solve the assets’ maintenance problem. DE is one of the rising meta-heuristics approaches which has shown excellent performance for solving complex constrained optimization problems in the continuous domain [28], [29], but has not been fully exploited in the assets’ maintenance problem. In the meanwhile, enhancing the performance of the classical DE for better manipulation of the problem is an ongoing research area. Therefore, we chose to contribute to this area and enhance the classical DE performance by a proposed k-means mutation scheme, that uses the K-means clustering method Wu [30], merged with the evolutionary mutation process to boost the algorithm’s performance. Given the hypothesis that k-means mutation scheme can be used to represent all clusters of individuals during the evolution process, which will lead to wider exploration of the decision space, hence better convergence.
The hybrid framework of the DES and the optimization fosters the planning for joint decisions of the maintenance processes (i.e. workforce planning, maintenance and inventory management), which might have various planning horizons [15], [22], [23]. As from the simulation side, the DES model represents these processes by modules, where each is governed by its predefined simulation rules, and then integrates them by the main DES model rules. Also, the DES features handling a series of events over a main planning horizon, while each event requires series of decisions through the modules at multiple points of time, or multiple horizons within the main simulation horizon. While from the optimization side, the optimization model generates and tests multiple key decision variables for the simulation modules and optimizes the corresponding overall system performance. Eventually, the overall system performance is the sum up of these modules’ performances. Therefore, the DES integrated modules structure along their joint decisions and optimization process, is the key behind the planning for multiple horizons.
In this study, we focus on finding an appropriate scheduled preventive maintenance planning strategies, with their corresponding decisions regarding optimal workforce plan arrangements and career progression. To achieve this, we propose a novel mathematical optimization model to minimize the total system cost and determine the optimum frequency of the scheduled maintenance, the workforce capacity, and their cross-training policies. In particular, a novel formulation is proposed of the relationship between the scheduled maintenance and its related workforce promotions, based on the number of their authorized tasks, and the new technicians’ recruitment. This integrated model enables decision makers to trade-off between investing in workforce capacity or workforce training given the required scheduled maintenance. The system’s performance is measured by the maintenance cost objective function, including multiple cost categories (e.g. maintenance tasks cost, workforce cost and tasks’ backlog cost). We develop a simulation-based optimization approach to solve the proposed mathematical model formulation of maintenance-workforce planning optimization problem. The proposed approach includes a holistic DES model, that captures the maintenance system dynamics through multiple modules, while the overall system performance is evaluated by its total cost. The DES is coupled with an improved DE optimization algorithm assisted with k-means clustering method. The interaction between those Sim-Opt models is as follows: the decision variables are generated by the optimization algorithm to minimize the maintenance cost objective function. The objective function is evaluated by the DES model, that takes the decision variables as input. Subsequently, the objective value is used to feedback the optimization algorithm to search for its optimal value. This is an iterative process between the two algorithms, until the predetermined termination conditions are met.
To summarize, the contributions of this paper are:
- 1.
development of a simulation–optimization framework that integrates a discrete event simulation (DES) and an improved differential evolution with novel k-means mutation scheme (K-DE) algorithm, that seeks the optimal maintenance frequencies for assets and its associated workforce planning and progression decisions
- 2.
development of a large scale simulation (i.e., a holistic approach) model that has the ability to address different aspects of maintenance planning with multiple decisions for repair and storage facilities, spare parts’ inventory system and workforce modules.
- 3.
formulation of a mixed integer nonlinear (MINLP) constrained mathematical model to jointly optimize the scheduled maintenance frequencies and workforce recruitment and promotion policies, inside the simulation–optimization framework.
- 4.
comparison of the developed approach with a classical DE method in terms of total cost of multiple scenarios via extensive computational study.
- 5.
propose a comprehensive maintenance cost break-up study and sensitivity analysis for well-informed decisions.
The remainder of this paper is organized as follows. In Section 2, a review of related literature is provided. In Section 3, a detailed description of the problem is provided. Section 4 presents the proposed simulation–optimization algorithm, while Section 5 outlines the computational experiment design and presents obtained results. Conclusions and future research directions are discussed in Section 6.
Section snippets
Literature review
This paper contributes to both (i) the modelling of a joint optimization problem in the assets’ maintenance planning domain, and (ii) the development of a simulation-based optimization approach to solve the modelled problem. In Section 2.1, we first provide a summary of the existing optimization problems that considers separate and joint decision making in maintenance planning, in order to emphasize the lack of joint decision making research from some aspects, versus the separate decision
Problem description and formulation
Consider a maintenance facility for assets, where each requires multiple tasks and resources to be maintained, i.e. facilities, workforce and spare parts, in addition to the inevitable need for a preventive maintenance schedule to hedge against expected failure. In this research, we propose a sim-opt model, where the simulation component imitates the holistic process of the assets’ maintenance, illustrated in Section 4, while the optimization component emphasizes some of the key variables that
Simulation-based solution algorithm
In this section, we discuss the details of coupling between a simulation model and an optimization algorithm. This coupling is known as the simulation–optimization,1
Numerical study
In this section, we perform a numerical study to investigate the performance of the proposed Sim-Opt model with the novel k-mean mutation scheme in solving the maintenance-workforce problem. In this first subsection, we describe the design of experiments (DoE) for different DE parameters’ settings, also called parameters’ tuning, by Taguchi method [57]. Subsequently, we adopt the best parameters combination in the following subsection, to perform the scenario analysis and test the impact of
Conclusions and future research
A holistic simulation–optimization framework has been proposed for solving asset maintenance and its corresponding workforce requirements problem. A novel mathematical model has been formulated for this problem to optimize the simulation model’s key policies and minimize the total maintenance, workforce and backlogs costs. The optimization model has been solved by an enhanced meta-heuristic Differential Evolution optimization algorithm with k-means mutation scheme, named K-DE. The k-means
CRediT authorship contribution statement
Amany M. Akl: Wrote the manuscript, Carried out the experiment, Conceived the original idea, Developed the mathematical formulation, Performed the analytic calculation, Performed the numerical simulations, Contributed to the final version of the manuscript. Sondoss El Sawah: Conceived the original idea, Designed the simulation model, Supervised the project, Contributed to the final version of the manuscript. Ripon K. Chakrabortty: Conceived the original idea, Supervised the project, Contributed
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
All authors provided critical feedback and helped shape the research, analysis and manuscript.
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2023, Engineering Applications of Artificial IntelligenceCitation Excerpt :The main contributions to this study can be summarised as follows: The presented work is a continuation of our previous research (Bocewicz et al., 2021; Szwarc et al., 2021; Szwarc and Wikarek, 2020) and falls within the trend of the dynamically explored area of personalised and robust human resources management (Akl et al., 2022; Porto et al., 2022; Małachowski and Korytkowski, 2016; Chen et al., 2020; Tian et al., 2022; Henao et al., 2015). The remainder of the paper is organised as follows.