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A Multi-Item Approach to Repairable Stocking and Expediting in a Fluctuating Demand Environment
Abstract
We consider a single inventory location where multiple types of repairable spare parts are kept for service and maintenance of several different fleets of assets. Demand for each part is a Markov modulated Poisson process (MMPP). Each fleet has a target for the maximum expected number of assets down for lack of a spare part. The inventory manager can meet this target by stocking repairables and by expediting the repair of parts. Expedited repairs have a shorter lead time. There are multiple repair shops (or departments) that handle the repair of parts and the load imposed on repair shops by expedited repairs is constrained. A dual-index policy makes stocking and expediting decisions that depend on demand fluctuations for each spare part type. We formulate the above problem as a non-linear non-convex integer programming problem and provide an algorithm based on column generation to compute feasible near optimal solutions and tight lower bounds. We show how to use the MMPP to model demand fluctuations in maintenance and other settings, including a moment fitting algorithm. We quantify the value of lead time flexibility and show that effective use of this flexibility can yield cost reductions of around 25%.
... Performance Evaluation Optimization [16], [17], [21], [25], [27], [28], [30], [31], [33], [35] [8], [11], [20], [23], [29], [46], [51], [8] [15], [18], [19], [41], [45] [2], [14], [34], [36], [53] [3], [6], [50], [52] [5], [22], [37], [44] [26], [40], [49] [32], [42], [43] [4] ...
... Economy [2], [3], [4], [9], [15], [20], [28], [33], [47] International Journal Of Production Economics • [8], [14], [19], [23], [35] European Journal Of Operational Research [22], [32], [43] Annals Of Operations Research [36], [42], [45] Computers & Operations Research [21], [39] Asia-pacific Journal Of Operational Research • [18], [46] Or Spectrum [16], [41] Journal Of The Operational Research Society [30], [50] International Journal Of Production Research [31], [52] Omega [6], [17] Reliability Engineering & System Safety ...
... Third, various inventory strategies such as lateral and emergency transshipments were not considered even though these strategies may improve RL performance. Big data analytics (BA) is the study of practices, technologies and skills to evaluate operations and strategies to obtain insights and offer guidance to the business planning of an organization [21]. Such evaluation is done for product development, strategic management, and customer services by utilizing evidence-based data, statistical and operations analysis, predictive modeling, forecasting, and optimization techniques [55]. ...
The development of new technological and business contexts has led to the natural evolution of the basic concepts of a production system. The concept of LCC-Life Cycle Cost of production equipment has led to a reflection on the importance of the nature and purpose of the investments to be made. [Luis Andrade Ferreira] Effective management of the equipment, especially in capital intensive organizations, implies not only a vision that encompasses aspects of economic and financial nature, but involves in a definitive way the technical management of the operations of physical assets, since they represent the most important share of the investments. This should be part of every company global strategy, in order to guarantee the company's production capacity throughout the life cycle of the equipment, as well as the margins of capital gains generated, which means keeping the company competitive. [Ferreira 2009] Assessment methods which can vary also according to level of detail needed: from general (the whole building, if need be, split in macro groups) to particular. In the latter case, each component has a specific and detailed evaluation method, like in [1] for facades evaluation, in [2] for roofs, in [3] for rendering facades predictive maintenance, in [4] for ETICS, and in [5] for the entire envelope, and last but not least relating to the spare parts contained in the project, which are the most critical part to manage. Evaluation techniques should give as output an index, a rate, or a mark to enable decision makers to create a building ranking inside the portfolio, to prioritize maintenance works, and to evaluate refurbishment scenarios [6,7].One of the main problems when we faced with maintenance is related to the number and variety of spare parts, the intermittent demand patterns, and are difficult to predict. the consumption of spare parts is related to the product usage, damage, and maintenance [8]. 1 State of the art A National Institute of Standards and Technology (NIST) study shows that all stakeholders in the capital facilities industry waste a huge amount of money looking for, validating, and/or recreating facility information that should be readily available. The total cost of these activities within the capital facilities industries in the United States was conservatively estimated at $15.8 billion in 2002, with two-thirds of that cost occurring during the facilities' operations and maintenance phase. This is confirmed by the International Facility Management Association (IFMA) Maintenance Survey in 2009, which states that the loss of information generates an added cost of 12.4% of total annual mean O&M costs. Nowadays, standards and specifications have been developed about availability, integrity, and transfer of data and information during the operational phase of an asset life. Managing an asset (or a portfolio) means making decisions, more or less important, to meet the objectives given by the asset strategy, as defined in the ISO 55000:2013 [9]. As we know organization''. There are three types of decisions, from complex to simple: (a) strategic: long-term, complex decisions made by senior management;(b) tactical: medium-term, less complex decisions made by middle managers; and (c) operational: day-today decisions made by junior managers that are simple and routine. Strategic decisions, in
... Chang et al. (2011) priced catastrophe equity put options under the MMPP's framework modelling catastrophic events. Economic demand was modelled by an MMPP in Arts (2017) for which each part of a single inventory location with multiple types of repairable spare parts are kept for service and maintenance of several different fleets of assets. Avanzi et al. (2021) used the MMNPP to describe the auto-insurance claim arrivals. ...
Data breaches have been increasing noticeably after 2021 notwithstanding the efforts of regulatory bodies to strengthen cybersecurity measures to protect health information. We provide a modelling framework that assesses the risk of private health data breaches focusing on the data sets compiled by the Privacy Rights Clearinghouse and the US Department of Health and Human Services. We show that the counting process of the data-breach incidents is adequately modelled by the Markov-modulated non-homogeneous Poisson process (MMNPP) whilst the logarithm of the breach sizes is well-captured by the generalised Pareto distribution. The cyber insurance premium per institution and two risk measures Value-at-Risk (VaR) and Average VaR are obtained. The computed results indicate that cyber insurance policies with longer maturity are more cost effective. A comprehensive analysis, parameter estimation and implementation of the MMNPP to model cyber risks are underscored as the principal contributions of this research. Some implications to practitioners in handling the modelling of data breaches for a group of institutions are given.
... near here[/t] Considering the optimization of the performance indicators of the repair shops, it could be observed that Linear or Non-linear Programming (16 papers) are the algorithms most commonly used, accounting for 30% of all papers. The objective is to minimize either the expected waiting time in repair shops(Safaei et al. 2011;Liang et al. 2013;Aramon and Beck 2014;Dreyfuss et al. 2018;Al-Refaie et al. 2020;Driessen et al. 2020) or the spare parts inventory(Adan et al. 2009;Basten and van Houtum 2014;Jaber et al. 2014;van Jaarsveld et al. 2015;Taleizadeh et al. 2016;Arts 2017;Sleptchenko et al. 2019) or the maintenance costs(van Ommeren et al. 2006;Simeu-Abazi and Ahmad 2011;Shivasankaran et al. 2013;Turan et al. 2018;Sanchez et al. 2020). The advantage of both methods is that they are exact, even though the repair shop model needs to be simplified as much as possible to reduce calculation complexity. ...
Maintenance activities are crucial for all manufacturing industries. To ensure availability and lifetime of production equipment, operations management and logistics support for maintenance need to evolve year after year. Besides, Centralised Maintenance Workshops are one of the most interesting approaches to reduce the cost and time required to repair faulty equipment. Generally known in the research community as ‘repair shops’, they aim to pool all the resources needed to repair defective equipment provided by different production sites. This paper aims to provide a comprehensive overview of repair shops and to present opportunities for future research with a focus on the circular economy context. The most relevant papers have been rigorously selected and analyzed, providing interesting reference materials on the subject. Repair shops are a set of workstations, operators, and spare parts inventories required to restore a group of failed production equipment. After detecting the origin of the failures, there are two options: either repair the equipment by restoring its defective components or replace the defective components with others in good working order. In the case of non-repairable components/equipment, circular strategies allow identification of components/equipment that could be restored and used to supply the spare parts warehouse.
... In the dual sourcing literature, studies on continuous review repair expediting are the closest to our repair expediting model as they consider the repair expediting using a threshold on the ''initial'' part of the repair process. Our study employs this control heuristic within a larger repairable inventory system which includes random inspection and condemnation processes and is optimized with respect to service level and expediting frequency constraints, which are also mentioned by Arts (2017). However, they focus on unconstrained cost optimization problem with no condemnation. ...
Stockouts of repairable spares usually lead to significant downtime costs. Managers of Maintenance Repair Organizations (MROs) seek advance indicators of future stockouts which might allow them to take proactive actions that are beneficial for achieving target service levels with reasonable costs. Among such (proactive) actions, the most common, and the cheapest one is expediting existing repair processes.
In this study, we develop an advance stockout risk estimation system for repairable spare parts. To the best of our knowledge, this is the first study to estimate the future stockout risk of a repairable part. The method considers different statistics, e.g. the number of ongoing repair processes, demand rate, repair time, etc. to estimate stockout risk of a repairable part for a given planning horizon. In our field tests with empirical data, the suggested method overperforms two heuristic approaches and achieves accuracy rates of 63% for 15 day-planning horizon and 83% for 45 days.
We also suggest a repairable inventory control system including repair expediting, inspection and condemnation processes. To optimize the control parameters we suggest a simple algorithm considering two constraints: Target service level and maximum fraction of expedited demand. The algorithm is proved to be efficient for finding the optimum policy parameter in our tests with empirical data. Tests with empirical data suggest savings up to 8%. Both systems are implemented at an MRO as building blocks of a inventory control tower. The impact of the implementation is assessed with empirical simulations and verified from the financial indicators of the company.
... The work in Sethi and Cheng (1997) also addresses the optimality of re-ordering policies with an MMPP fluctuating demand, and considers extensions to the model of Song and Zipkin (1993) to account for cyclic demand (non-stationarity), ordering periods and service level constraints. Recent formulations of mathematical models that capture fluctuation in the demand process via an MMPP include Bhat and Krishnamurthy (2015), Nasr and Maddah (2015), Arts et al. (2016), Arts (2017), Chen et al. (2017), and Avci et al. (2019). ...
Modeling the behavior of customer demand is a key challenge in inventory control, where an accurate characterization of the demand process often involves accounting for a wide range of statistical descriptors. This motivates the use of Markovian processes, due to their proven versatility in matching key components of point processes, to capture the behavior of customer demand. Accordingly, this work presents computational frameworks for continuous inventory models with a batch Markovian demand. A Markovian formulation of the system state-space is presented along with computational approaches to obtain key inventory performance measures. Compact matrix representations are considered for the steady-state solution of the system performance measures. The transient and non-stationary behavior of the inventory system is calculated by numerically integrating the corresponding set of Kolmogorov forward equations. A byproduct of this work is explicitly expressing the solution of the moments of the batch Markovian counting process by a compact matrix exponential equation. Numerical examples illustrate the computational efficiency of the mathematical frameworks when evaluating and comparing the performance of different re-ordering policies.
... Optimization model types Note that a model with a stochastic setting does not necessarily lead to a stochastic optimization problem. For example, [35] considered a repairable spare parts inventory problem with a stochastic setting, i.e., the demand for each part is a Markov-modulated Poisson process, but the problem is formulated as a non-linear integer programming optimization problem. In the third column of Table 8, we classify the studies based on optimization model types. ...
Spare parts are held as inventory to support product maintenance in order to reduce downtime and extend the lifetime of products. Recently, spare parts inventory management has been attracting more attention due to the “right-to-repair” movement which requires that manufacturers provide sufficient spare parts throughout the life-cyle of their products to reduce waste so as to achieve sustainability. In this review, 148 papers regarding spare parts inventory management published from 2010 to 2020 are examined. The studies are classified based on two groups of perspectives. The first group includes the characteristics of spare parts, products, inventory systems, and supply chains, while the second group focuses on the characteristics of research methodologies and topics in the reviewed studies. The novelty of this literature review is three-fold. Firstly, we focus on analyzing the supply chain structure of different inventory networks for managing spare parts. Secondly, we classify the current literature based on analytics techniques, i.e., descriptive analytics, predictive analytics, and prescriptive analytics. Finally, the research gaps in this field are discussed from the perspective of reverse logistics, consumer durable goods, inventory network structure and policy, spare parts demand pattern modeling, and big data analytics.
This paper reviews the literature on inventory models with multiple sourcing options and presents a typology for classification. By means of the classification, the progression of the literature (policies and modeling assumptions) is illustrated, the main decision trade-offs in multiple sourcing are identified and avenues for future research are pointed out. Multiple sourcing decision models trade off the added costs of backup sourcing against higher inventory or shortage costs under single sourcing. The value of multiple over single sourcing is found to increase in the uncertainty to be buffered, in inventory holding and shortage costs, as well as in the constraints of the primary source. The literature evolved from small, restrictive models to larger problems and more realism. Accordingly, replenishment policies progressed from optimal policies to more heuristic decision rules. Three areas for future research are suggested for moving the field forward and towards more practical applicability. (1) Further integration of model aspects such as the extension of replenishment policies to more than two suppliers and to multi-echelon models. (2) Focusing on supply chain resilience with decision making disruption events or demand spikes under consideration of risk preferences. (3) Utilizing industry data in machine learning and data-driven methodologies.
We consider a single stock-point for a repairable item facing Markov modulated Poisson demand. Repair of failed parts may be expedited at an additional cost to receive a shorter lead time. Demand that cannot be filled immediately is backordered and penalized. The manager decides on the number of spare repairables to purchase and on the expediting policy. We characterize the optimal expediting policy using a Markov decision process formulation and provide closed-form necessary and sufficient conditions that determine whether the optimal policy is a type of threshold policy or a no-expediting policy. We derive further asymptotic results as demand fluctuates arbitrarily slowly. In this regime, the cost of this system can be written as a weighted average of costs for systems facing Poisson demand. These asymptotics are leveraged to show that approximating Markov modulated Poisson demand by stationary Poisson demand can lead to arbitrarily poor results. We propose two heuristics based on our analytical results, and numerical tests show good performance with an average optimality gap of 0.11% and 0.33% respectively. Naive heuristics that ignore demand fluctuations have an average optimality gaps of more than 11%. This shows that there is great value in leveraging knowledge about demand fluctuations in making repairable expediting and stocking decisions.
In this paper, we analyze a repair shop serving several fleets of machines that fail from time to time. To reduce downtime costs, a continuous-review spare machine inventory is kept for each fleet. A spare machine, if available on stock, is installed instantaneously in place of a broken machine. When a repaired machine is returned from the repair shop, it is placed in inventory for future use if the fleet has the required number of machines operating. Since the repair shop is shared by different fleets, choosing which type of broken machine to repair is crucial to minimize downtime and holding costs. The optimal policy of this problem is difficult to characterize, and, therefore, is only formulated as a Markov Decision Process to numerically compute the optimal cost and base-stock level for each spare machine inventory. As an alternative, we propose the dynamic Myopic(R) policy, which is easy to implement, yielding costs very close to the optimal. Most of the time it outperforms the static first-come-first-served, and preemptive-resume priority policies. Additionally, via our numerical study, we demonstrate that repair shop pooling is better than reserving a repair shop for each fleet.
IntroductionThe Erlang Delay ModelLoss ModelsService-system DesignInsensitivityA Phase Method
Queueing NetworksExercisesBibliographic NotesReferences
In this paper, we develop an approximate model of an inventory control system in which there exist two options for resupply, with one having a shorter lead-time. We assume that demand and the fixed ordering costs are small relative to the holding cost so that a one-for-one ordering policy is appropriate. We consider a policy for placing emergency orders that uses information about the age of outstanding orders. We derive the steady-state behavior of this policy and present some computational results.