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Joachim Arts

Université du Luxembourg, Luxembourg Centre for Logistics and Supply Chain Management, Faculty Member

Massachusetts Institute of Technology (MIT), Center for Transportation and Logistics, Visiting Scholar

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I am professor at the university of Luxembourg within the Luxembourg Center for Logistics and Supply Chain Management which is part of the MIT Scale network. I also hold a visiting appointments at the MIT Centre for Transportation and Logistics. Previously, I was a visiting scholar at MIT Sloan school of management and an assistant professor at Eindhoven University of Technology, where I also received my PhD. My research interests are operations research defined broadly, especially applications in supply chain, logistics, maintenance and inventory. My PhD research received the EDDA award from the European federation of Operations Research societies, and it was funded by NedTrain, a division of the Dutch railways that maintains rolling stock. In current research, I work with NedTrain, ASML, and Philips. I am a veni laureate, recipient of the VvS+OR master thesis award and a Prins Bernhard Cultuurfonds Fellow.
Phone: 0031402474983
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Papers by Joachim Arts

Projected Inventory-Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes

Operations Research

We consider the canonical periodic review lost sales inventory system with positive lead times an... more We consider the canonical periodic review lost sales inventory system with positive lead times and stochastic i.i.d. demand under the average cost criterion. We introduce a new policy that places orders such that the expected inventory level at the time of arrival of an order is at a fixed level and call it the projected inventory-level policy. We prove that this policy has a cost rate superior to the equivalent system where excess demand is backordered instead of lost and therefore, is asymptotically optimal as the cost of losing a sale approaches infinity under mild distributional assumptions. We further show that this policy dominates the constant-order policy for any finite lead time and therefore, is asymptotically optimal as the lead time approaches infinity for the case of exponentially distributed demand per period. Numerical results show that this policy also performs superior relative to other policies.

The profitability-sustainability trade-off in complex chemical value chains

by Joachim Arts and Matteo Cosmi

Annals of Operations Research, 2024

The industry and transportation sectors account for more than 35% of global CO 2 emissions and th... more The industry and transportation sectors account for more than 35% of global CO 2 emissions and there is increasing pressure on industry to reduce emissions. To remain competitive in their markets while reducing their emissions, companies need to re-optimise their entire value chain focusing not only on traditional costs, related to manufacturing and transport, but also on emission reduction targets. In this work, we propose a linear program to optimise a deterministic multi-objective value-chain problem aimed at minimising CO 2 emissions and maximising a company's total contribution margin. We test the model on a real-world dataset, provided by a multinational chemical company, to determine the main sources of emissions and their geographical distribution. Moreover, we analyse how much emissions can be reduced at a negligible impact on the total contribution margin and describe what the best strategies are to achieve the targeted emission reduction. We find that it is beneficial to move production to less polluting production sites, even when that increases the transportation in our setting. It is therefore advisable to jointly address the reduction of production-and transportation-related emissions, rather than separately.

Optimal design of line replaceable units

Naval Research Logistics (NRL)

A line replaceable unit (LRU) is a collection of connected parts in a system that is replaced whe... more A line replaceable unit (LRU) is a collection of connected parts in a system that is replaced when any part of the LRU fails. Companies use LRUs as a mechanism to reduce downtime of systems following a failure. The design of LRUs determines how fast a replacement is performed, so a smart design reduces replacement and downtime cost. A firm must purchase/repair a LRU upon failure, and large LRUs are more expensive to purchase/repair. Hence, a firm seeks to design LRUs such that the average costs per time unit are minimized. We formalize this problem in a new model that captures how parts in a system are connected, and how they are disassembled from the system. Our model optimizes the design of LRUs such that the replacement (and downtime) costs and LRU purchase/repair costs are minimized. We present a set partitioning formulation for which we prove a rare result: the optimal solution is integer, despite a nonintegral feasible polyhedron. Second, we formulate our problem as a binary l...

The Profitability-Sustainability Trade-Off in Complex Chemical Value Chains

Data-driven preventive maintenance for a heterogeneous machine portfolio

Operations Research Letters

We describe a data-driven approach to optimize periodic maintenance policies for a heterogeneous ... more We describe a data-driven approach to optimize periodic maintenance policies for a heterogeneous portfolio with different machine profiles. When insufficient data are available per profile to assess failure intensities and costs accurately, we pool the data of all machine profiles and evaluate the effect of (observable) machine characteristics by calibrating appropriate statistical models. This reduces maintenance costs compared to a stratified approach that splits the data into subsets per profile and a uniform approach that treats all profiles the same.

Effective Dual-Sourcing Through Inventory Projection

Cornell University - arXiv, Jul 22, 2022

We consider a single-echelon inventory system under periodic review with two suppliers facing sto... more We consider a single-echelon inventory system under periodic review with two suppliers facing stochastic demand, where excess demand is backlogged. The expedited supplier has a shorter lead time than the regular supplier but charges a higher unit price. We introduce the Projected Expedited Inventory Position (PEIP) policy, and we show that the relative difference between the long run average cost per period of this policy and the optimal policy converges to zero when both the shortage cost and the cost premium for expedited units become large, with their ratio held constant. A corollary of this result is that several existing heuristics are also asymptotically optimal in this non-trivial regime. We show through an extensive numerical investigation that the PEIP policy outperforms the current best performing heuristic policies in literature.

Real-Time Integrated Learning and Decision Making for Cumulative Shock Degradation

Manufacturing & Service Operations Management

Problem definition: Unexpected failures of equipment can have severe consequences and costs. Such... more Problem definition: Unexpected failures of equipment can have severe consequences and costs. Such unexpected failures can be prevented by performing preventive replacement based on real-time degradation data. We study a component that degrades according to a compound Poisson process and fails when the degradation exceeds the failure threshold. An online sensor measures the degradation in real time, but interventions are only possible during planned downtime. Academic/practical relevance: We characterize the optimal replacement policy that integrates real-time learning from the online sensor. We demonstrate the effectiveness in practice with a case study on interventional x-ray machines. The data set of this case study is available in the online companion. As such, it can serve as a benchmark data set for future studies on stochastically deteriorating systems. Methodology: The degradation parameters vary from one component to the next but cannot be observed directly; the component po...

Efficient Emission Reduction Through Dynamic Supply Mode Selection

European Journal of Operational Research, Jul 22, 2023

Reducing the carbon footprint of global supply chains is a challenge for many companies in differ... more Reducing the carbon footprint of global supply chains is a challenge for many companies in different industries. Not only are governmental emission regulations increasingly stringent, consumers are also becoming more and more environmentally conscious. Companies should therefore integrate carbon emissions explicitly in their supply chain decision making. In this paper, we study the inbound supply mode and inventory management decision making for a company that sells an assortment of products. Stochastic demand for each product arrives periodically and unmet demand is backlogged. Each product has two distinct supply modes that may be different suppliers or different transport modes from the same supplier. These supply modes differ in terms of their carbon emissions, speed, and costs. The company needs to decide when to ship how much using which supply mode such that total holding, backlog, and procurement costs are minimized while the emissions associated with different supply modes across the assortment remains below a certain target level. Such assortment-wide constraints will be increasingly prevalent, either voluntarily or enforced by government regulation. Since the optimal policy for this inventory system is highly complex, we assume that shipment decisions for each product are governed by a dual-index policy. This policy dynamically prescribes shipment quantities with both supply modes based on the on-hand inventory, the backlog, and the products that are still in-transit. We formulate this decision problem as a mixed integer linear program that we solve through Dantzig-wolfe decomposition. We benchmark our decision model against two stateof-the-art approaches in a large test-bed based on real-life carbon emissions data. Relative to our decision model, the first benchmark lacks the flexibility to dynamically ship products with two supply modes while the second benchmark makes supply mode decisions for each product individually rather than holistically for the entire assortment. Our computational experiment shows that our decision model can outperform the first and second benchmark by up to 15 and 40 percent, respectively, for realistic targets for carbon emission reduction.

Optimal commonality and reliability : a life cycle costs perspective

Competitive Original equipment manufacturers (OEMs) do not only sell equipment, but also service ... more Competitive Original equipment manufacturers (OEMs) do not only sell equipment, but also service contracts that ensure proper functioning and uptime of equipment after the sale. It then becomes the concern of OEMs to minimize equipment downtime by providing after-sales services such as repairs and spare parts over the lifetime of equipment. OEMs will therefore aim to minimize the total Life Cycle Costs (LCC) of their equipment by deciding for each component (1) whether to use a common component (one-for-all-systems) or a dedicated component (one-for-each-system), (2) the reliability and (3) the spare parts stock levels. We present life cycle cost functions in case of both dedicated and common components. These original life cycle cost functions can only be analyzed numerically. Therefore, we prove that there is a simpler expression that is asymptotically equivalent to the LCC in the regime where downtime of equipment is expensive. These asymptotics allow us to show that commonality ...

Design of multi-component periodic maintenance programs with single-component models

IISE Transactions, 2018

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

The asymptotic hazard rate of sums of discrete random variables

Statistics & Probability Letters, 2017

We show that the asymptotic hazard rate of the sum of discrete random variables is dominated by t... more

Fleet readiness: Stocking spare parts and high-tech assets

IISE Transactions, 2017

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

A multi-item approach to repairable stocking and expediting in a fluctuating demand environment

European Journal of Operational Research, 2017

We consider a single inventory location where multiple types of repairable spare parts are kept t... more We consider a single inventory location where multiple types of repairable spare parts are kept to service several different fleets of assets. Demand for each part is modeled by a Markov modulated Poisson process (MMPP). Each fleet has a target for the maximum expected mean 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 mean number of expedited repairs that can be requested per time unit is constrained per repair shop. 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 solutions and tight lower bounds. We show how to use the MMPP to model demand fluctuations in this 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%.

Repairable Stocking and Expediting in a Fluctuating Demand Environment: Optimal Policy and Heuristics

Operations Research, 2016

Both service and manufacturing industries depend on the availability of expensive equipment to de... more Both service and manufacturing industries depend on the availability of expensive equipment to deliver their products. Examples of such equipment include aircraft, rolling stock and manufacturing equipment. When this equipment is not working, the primary processes of their owners come to an immediate stop. To reduce the downtime of equipment, companies stock critical components such that the equipment can be returned to an operational state quickly by replacing a defective component with a ready-for-use component. Many components represent a significant financial investment and so they are repaired rather than discarded after a defect occurs. Consider for example, jet engines, bogies, or lens units for wafer steppers; these are components of aircraft, rolling stock, and integrated circuit manufacturing equipment, respectively, and their prices range from several hundreds of thousands up to millions of dollars. The best time for companies to buy these components is early in the lifecycle of the original equipment, because, at this time, it is possible to negotiate reasonable prices. In the literature, this is often referred to as the initial spare parts supply problem and it occurs in many different environments (e.g. Rustenburg et al., 2001; Pérès and Grenouilleau, 2002). Also note that since such components are repairable, there is no natural inventory depletion that can reduce stock levels in case a company buys too many components. Later in the life cycle of a technical system, components often have to be custom made and prices are very steep, if the component can be purchased at all. An aggravating factor is that demand intensity for these components typically fluctuates over time, reflecting the fluctuating need for maintenance over time. Companies anticipate these demand fluctuations by leveraging the possibility of expediting the repair of defective components, rather than buying new components. Expediting a repair comes at a price, either because an external repair shop charges more for expedited repairs or because an internal repair shop can only handle a limited amount of expedited repairs.

Spare parts planning and control for maintenance operations

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Optimal and heuristic repairable stocking and expediting in a fluctuating demand environment

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Aggregate overhaul and supply chain planning for rotables

Annals of Operations Research, 2013

We consider the problem of planning preventive maintenance and overhaul for modules that occur in... more We consider the problem of planning preventive maintenance and overhaul for modules that occur in a fleet of assets such as trains or airplanes. Each type of module, or rotable, has its own maintenance program in which a maximum amount of time between overhauls of a module is stipulated. Overhauls are performed in an overhaul workshop with limited capacity. The problem we study is to determine aggregate workforce levels, turnaround stock levels of modules, and overhaul and replacement quantities per period so as to minimize to sum of labor costs, material costs of overhaul, and turnaround stock investments over the entire life-cycle of the system to be maintained. We prove that this planning problem is strongly N P-hard, but we also provide computational evidence that the mixed integer programming formulation can be solved within reasonable time for real-life instances. Furthermore, we show that the linear programming relaxation can also be used to aid decision making. We apply the model in a case study.

Maintenance spare parts planning and control: a framework for control and agenda for future research

Production Planning & Control, 2014

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Real-Time Integrated Learning and Decision Making for Deteriorating Systems

Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes

We consider the canonical periodic review lost sales inventory system with positive lead-times an... more We consider the canonical periodic review lost sales inventory system with positive lead-times and stochastic i.i.d. demand under the average cost criterion. We introduce a new policy that places orders such that the expected inventory level at the time of arrival of an order is at a fixed level and call it the Projected Inventory Level (PIL) policy. We prove that this policy has a cost-rate superior to the equivalent system where excess demand is back-ordered instead of lost and is therefore asymptotically optimal as the cost of losing a sale approaches infinity under mild distributional assumptions. We further show that this policy dominates the constant order policy for any finite lead-time and is therefore asymptotically optimal as the lead-time approaches infinity for the case of exponentially distributed demand per period. Numerical results show this policy also performs superior relative to other policies.

Projected Inventory-Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes

Operations Research

We consider the canonical periodic review lost sales inventory system with positive lead times an... more We consider the canonical periodic review lost sales inventory system with positive lead times and stochastic i.i.d. demand under the average cost criterion. We introduce a new policy that places orders such that the expected inventory level at the time of arrival of an order is at a fixed level and call it the projected inventory-level policy. We prove that this policy has a cost rate superior to the equivalent system where excess demand is backordered instead of lost and therefore, is asymptotically optimal as the cost of losing a sale approaches infinity under mild distributional assumptions. We further show that this policy dominates the constant-order policy for any finite lead time and therefore, is asymptotically optimal as the lead time approaches infinity for the case of exponentially distributed demand per period. Numerical results show that this policy also performs superior relative to other policies.

The profitability-sustainability trade-off in complex chemical value chains

by Joachim Arts and Matteo Cosmi

Annals of Operations Research, 2024

The industry and transportation sectors account for more than 35% of global CO 2 emissions and th... more The industry and transportation sectors account for more than 35% of global CO 2 emissions and there is increasing pressure on industry to reduce emissions. To remain competitive in their markets while reducing their emissions, companies need to re-optimise their entire value chain focusing not only on traditional costs, related to manufacturing and transport, but also on emission reduction targets. In this work, we propose a linear program to optimise a deterministic multi-objective value-chain problem aimed at minimising CO 2 emissions and maximising a company's total contribution margin. We test the model on a real-world dataset, provided by a multinational chemical company, to determine the main sources of emissions and their geographical distribution. Moreover, we analyse how much emissions can be reduced at a negligible impact on the total contribution margin and describe what the best strategies are to achieve the targeted emission reduction. We find that it is beneficial to move production to less polluting production sites, even when that increases the transportation in our setting. It is therefore advisable to jointly address the reduction of production-and transportation-related emissions, rather than separately.

Optimal design of line replaceable units

Naval Research Logistics (NRL)

A line replaceable unit (LRU) is a collection of connected parts in a system that is replaced whe... more A line replaceable unit (LRU) is a collection of connected parts in a system that is replaced when any part of the LRU fails. Companies use LRUs as a mechanism to reduce downtime of systems following a failure. The design of LRUs determines how fast a replacement is performed, so a smart design reduces replacement and downtime cost. A firm must purchase/repair a LRU upon failure, and large LRUs are more expensive to purchase/repair. Hence, a firm seeks to design LRUs such that the average costs per time unit are minimized. We formalize this problem in a new model that captures how parts in a system are connected, and how they are disassembled from the system. Our model optimizes the design of LRUs such that the replacement (and downtime) costs and LRU purchase/repair costs are minimized. We present a set partitioning formulation for which we prove a rare result: the optimal solution is integer, despite a nonintegral feasible polyhedron. Second, we formulate our problem as a binary l...

The Profitability-Sustainability Trade-Off in Complex Chemical Value Chains

Data-driven preventive maintenance for a heterogeneous machine portfolio

Operations Research Letters

We describe a data-driven approach to optimize periodic maintenance policies for a heterogeneous ... more We describe a data-driven approach to optimize periodic maintenance policies for a heterogeneous portfolio with different machine profiles. When insufficient data are available per profile to assess failure intensities and costs accurately, we pool the data of all machine profiles and evaluate the effect of (observable) machine characteristics by calibrating appropriate statistical models. This reduces maintenance costs compared to a stratified approach that splits the data into subsets per profile and a uniform approach that treats all profiles the same.

Effective Dual-Sourcing Through Inventory Projection

Cornell University - arXiv, Jul 22, 2022

We consider a single-echelon inventory system under periodic review with two suppliers facing sto... more We consider a single-echelon inventory system under periodic review with two suppliers facing stochastic demand, where excess demand is backlogged. The expedited supplier has a shorter lead time than the regular supplier but charges a higher unit price. We introduce the Projected Expedited Inventory Position (PEIP) policy, and we show that the relative difference between the long run average cost per period of this policy and the optimal policy converges to zero when both the shortage cost and the cost premium for expedited units become large, with their ratio held constant. A corollary of this result is that several existing heuristics are also asymptotically optimal in this non-trivial regime. We show through an extensive numerical investigation that the PEIP policy outperforms the current best performing heuristic policies in literature.

Real-Time Integrated Learning and Decision Making for Cumulative Shock Degradation

Manufacturing & Service Operations Management

Problem definition: Unexpected failures of equipment can have severe consequences and costs. Such... more Problem definition: Unexpected failures of equipment can have severe consequences and costs. Such unexpected failures can be prevented by performing preventive replacement based on real-time degradation data. We study a component that degrades according to a compound Poisson process and fails when the degradation exceeds the failure threshold. An online sensor measures the degradation in real time, but interventions are only possible during planned downtime. Academic/practical relevance: We characterize the optimal replacement policy that integrates real-time learning from the online sensor. We demonstrate the effectiveness in practice with a case study on interventional x-ray machines. The data set of this case study is available in the online companion. As such, it can serve as a benchmark data set for future studies on stochastically deteriorating systems. Methodology: The degradation parameters vary from one component to the next but cannot be observed directly; the component po...

Efficient Emission Reduction Through Dynamic Supply Mode Selection

European Journal of Operational Research, Jul 22, 2023

Reducing the carbon footprint of global supply chains is a challenge for many companies in differ... more Reducing the carbon footprint of global supply chains is a challenge for many companies in different industries. Not only are governmental emission regulations increasingly stringent, consumers are also becoming more and more environmentally conscious. Companies should therefore integrate carbon emissions explicitly in their supply chain decision making. In this paper, we study the inbound supply mode and inventory management decision making for a company that sells an assortment of products. Stochastic demand for each product arrives periodically and unmet demand is backlogged. Each product has two distinct supply modes that may be different suppliers or different transport modes from the same supplier. These supply modes differ in terms of their carbon emissions, speed, and costs. The company needs to decide when to ship how much using which supply mode such that total holding, backlog, and procurement costs are minimized while the emissions associated with different supply modes across the assortment remains below a certain target level. Such assortment-wide constraints will be increasingly prevalent, either voluntarily or enforced by government regulation. Since the optimal policy for this inventory system is highly complex, we assume that shipment decisions for each product are governed by a dual-index policy. This policy dynamically prescribes shipment quantities with both supply modes based on the on-hand inventory, the backlog, and the products that are still in-transit. We formulate this decision problem as a mixed integer linear program that we solve through Dantzig-wolfe decomposition. We benchmark our decision model against two stateof-the-art approaches in a large test-bed based on real-life carbon emissions data. Relative to our decision model, the first benchmark lacks the flexibility to dynamically ship products with two supply modes while the second benchmark makes supply mode decisions for each product individually rather than holistically for the entire assortment. Our computational experiment shows that our decision model can outperform the first and second benchmark by up to 15 and 40 percent, respectively, for realistic targets for carbon emission reduction.

Optimal commonality and reliability : a life cycle costs perspective

Competitive Original equipment manufacturers (OEMs) do not only sell equipment, but also service ... more Competitive Original equipment manufacturers (OEMs) do not only sell equipment, but also service contracts that ensure proper functioning and uptime of equipment after the sale. It then becomes the concern of OEMs to minimize equipment downtime by providing after-sales services such as repairs and spare parts over the lifetime of equipment. OEMs will therefore aim to minimize the total Life Cycle Costs (LCC) of their equipment by deciding for each component (1) whether to use a common component (one-for-all-systems) or a dedicated component (one-for-each-system), (2) the reliability and (3) the spare parts stock levels. We present life cycle cost functions in case of both dedicated and common components. These original life cycle cost functions can only be analyzed numerically. Therefore, we prove that there is a simpler expression that is asymptotically equivalent to the LCC in the regime where downtime of equipment is expensive. These asymptotics allow us to show that commonality ...

Design of multi-component periodic maintenance programs with single-component models

IISE Transactions, 2018

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

The asymptotic hazard rate of sums of discrete random variables

Statistics & Probability Letters, 2017

We show that the asymptotic hazard rate of the sum of discrete random variables is dominated by t... more

Fleet readiness: Stocking spare parts and high-tech assets

IISE Transactions, 2017

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

A multi-item approach to repairable stocking and expediting in a fluctuating demand environment

European Journal of Operational Research, 2017

We consider a single inventory location where multiple types of repairable spare parts are kept t... more We consider a single inventory location where multiple types of repairable spare parts are kept to service several different fleets of assets. Demand for each part is modeled by a Markov modulated Poisson process (MMPP). Each fleet has a target for the maximum expected mean 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 mean number of expedited repairs that can be requested per time unit is constrained per repair shop. 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 solutions and tight lower bounds. We show how to use the MMPP to model demand fluctuations in this 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%.

Repairable Stocking and Expediting in a Fluctuating Demand Environment: Optimal Policy and Heuristics

Operations Research, 2016

Both service and manufacturing industries depend on the availability of expensive equipment to de... more Both service and manufacturing industries depend on the availability of expensive equipment to deliver their products. Examples of such equipment include aircraft, rolling stock and manufacturing equipment. When this equipment is not working, the primary processes of their owners come to an immediate stop. To reduce the downtime of equipment, companies stock critical components such that the equipment can be returned to an operational state quickly by replacing a defective component with a ready-for-use component. Many components represent a significant financial investment and so they are repaired rather than discarded after a defect occurs. Consider for example, jet engines, bogies, or lens units for wafer steppers; these are components of aircraft, rolling stock, and integrated circuit manufacturing equipment, respectively, and their prices range from several hundreds of thousands up to millions of dollars. The best time for companies to buy these components is early in the lifecycle of the original equipment, because, at this time, it is possible to negotiate reasonable prices. In the literature, this is often referred to as the initial spare parts supply problem and it occurs in many different environments (e.g. Rustenburg et al., 2001; Pérès and Grenouilleau, 2002). Also note that since such components are repairable, there is no natural inventory depletion that can reduce stock levels in case a company buys too many components. Later in the life cycle of a technical system, components often have to be custom made and prices are very steep, if the component can be purchased at all. An aggravating factor is that demand intensity for these components typically fluctuates over time, reflecting the fluctuating need for maintenance over time. Companies anticipate these demand fluctuations by leveraging the possibility of expediting the repair of defective components, rather than buying new components. Expediting a repair comes at a price, either because an external repair shop charges more for expedited repairs or because an internal repair shop can only handle a limited amount of expedited repairs.

Spare parts planning and control for maintenance operations

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Optimal and heuristic repairable stocking and expediting in a fluctuating demand environment

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Aggregate overhaul and supply chain planning for rotables

Annals of Operations Research, 2013

We consider the problem of planning preventive maintenance and overhaul for modules that occur in... more We consider the problem of planning preventive maintenance and overhaul for modules that occur in a fleet of assets such as trains or airplanes. Each type of module, or rotable, has its own maintenance program in which a maximum amount of time between overhauls of a module is stipulated. Overhauls are performed in an overhaul workshop with limited capacity. The problem we study is to determine aggregate workforce levels, turnaround stock levels of modules, and overhaul and replacement quantities per period so as to minimize to sum of labor costs, material costs of overhaul, and turnaround stock investments over the entire life-cycle of the system to be maintained. We prove that this planning problem is strongly N P-hard, but we also provide computational evidence that the mixed integer programming formulation can be solved within reasonable time for real-life instances. Furthermore, we show that the linear programming relaxation can also be used to aid decision making. We apply the model in a case study.

Maintenance spare parts planning and control: a framework for control and agenda for future research

Production Planning & Control, 2014

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Real-Time Integrated Learning and Decision Making for Deteriorating Systems

Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes

We consider the canonical periodic review lost sales inventory system with positive lead-times an... more We consider the canonical periodic review lost sales inventory system with positive lead-times and stochastic i.i.d. demand under the average cost criterion. We introduce a new policy that places orders such that the expected inventory level at the time of arrival of an order is at a fixed level and call it the Projected Inventory Level (PIL) policy. We prove that this policy has a cost-rate superior to the equivalent system where excess demand is back-ordered instead of lost and is therefore asymptotically optimal as the cost of losing a sale approaches infinity under mild distributional assumptions. We further show that this policy dominates the constant order policy for any finite lead-time and is therefore asymptotically optimal as the lead-time approaches infinity for the case of exponentially distributed demand per period. Numerical results show this policy also performs superior relative to other policies.

Elementary Maintenance Models

Yield in production systems

A common misconception in industry is the notion that quality decreases productivity. In fact, th... more A common misconception in industry is the notion that quality decreases productivity. In fact, the contrary holds: a high-quality and defect-free manufacturing process usually reduces total costs and increases available capacity. As we shall see in this handout, large savings can be accomplished by ensuring that no time and money is wasted on defective items. To enrich our understanding of this, we will formulate and analyze several mathematical models of production systems with uncertain yield.

Spare parts planning and control for maintenance operations

Single-Item Models with Minimal Repair for Multi-Item Maintenance Optimization

by Joachim Arts and Rob Basten

Capital assets, such as wind turbines and ships, require maintenance throughout their long life t... more Capital assets, such as wind turbines and ships, require maintenance throughout their long life times. Assets usually need to go down to perform maintenance and such downs can be either scheduled or unscheduled. Since different components in an asset have different maintenance policies, it is key to have a maintenance program in place that coordinates the maintenance policies of all components, so as to minimize costs associated with maintenance and downtime. Single component maintenance policies have been developed for decades, but such policies do not usually allow coordination between different components within an asset. We study a periodic maintenance policy and a condition based maintenance policy in which the scheduled downs can be coordinated between components. In both policies, we assume that at unscheduled downs, a minimal repair is performed to keep unscheduled downtime as short as possible. Both policies can be evaluated exactly using renewal theory, and we show how these policies can be used as building blocks to design and optimize maintenance programs for multi-component assets.

Single-Item Models with Minimal Repair for Multi-Item Maintenance Optimization Single-Item Models with Minimal Repair for Multi-Item Maintenance Optimization

by Joachim Arts and Rob Basten

Capital assets, such as wind turbines and ships, require maintenance throughout their long life t... more Capital assets, such as wind turbines and ships, require maintenance throughout their long life times. Assets usually need to go down to perform maintenance and such downs can be either scheduled or unscheduled. Since different components in an asset have different maintenance policies, it is key to have a maintenance program in place that coordinates the maintenance policies of all components, so as to minimize costs associated with maintenance and downtime. Single component maintenance policies have been developed for decades, but such policies do not usually allow coordination between different components within an asset. We study a periodic maintenance policy and a condition based maintenance policy in which the scheduled downs can be coordinated between components. In both policies, we assume that at unscheduled downs, a minimal repair is performed to keep unscheduled downtime as short as possible. Both policies can be evaluated exactly using renewal theory, and we show how these policies can be used as building blocks to design and optimize maintenance programs for multi-component assets.