Spare Parts Inventory Control under a Fixed-Term Contract with a Long-Down Constraint

DOI: 10.1016/j.ijpe.2019.05.023

Posted: 8 Mar 2019 Last revised: 7 Jun 2019

See all articles by Douniel Lamghari-Idrissi

Douniel Lamghari-Idrissi

Eindhoven University of Technology (TUE) - Department of Industrial Engineering and Innovation Sciences

Rob J.I. Basten

Eindhoven University of Technology (TUE)

Geert-Jan van Houtum

Eindhoven University of Technology (TUE)

Date Written: May 31, 2019

Abstract

We are interested in service contracts for spare parts. We introduce a new performance measure, XLD (extreme long down), that limits the number of deliveries that are later than an agreed threshold during the contract period. We consider a single item, single location stockpoint serving multiple systems where demand is satisfied in an alternative way if the stockpoint is out of stock. Using a finite horizon Markov decision process, we derive the optimal spare parts inventory policy for meeting the contract at minimum costs. We prove that a state-dependent and time-dependent base stock policy is optimal. We also prove that the optimal base stock level is non-increasing in the number of allowed extreme long downs in the remaining contract period and that the optimal base stock level decreases at most by one unit per step. We formulate three heuristics for our finite horizon problem. These heuristics are a translation of heuristics commonly used for other service measures than the XLD measure. We assess their performance in comparison to the optimal policy. The results of our numerical study show that Heuristic 3, a myopic heuristic, is the best performing with an average optimality gap of 4.5% and an optimality gap lower than 5% in 81% of the instances. The maximum optimality gap is very high for all three heuristics, showing that important savings can be made by taking into account the actual contract performance and the remaining contract duration in stocking decisions.

Keywords: Spare parts inventory; Service measure; Markov decision process; Optimal policies; Discrete convexity

Suggested Citation

Lamghari-Idrissi, Douniel and Basten, Rob J.I. and van Houtum, Geert-Jan, Spare Parts Inventory Control under a Fixed-Term Contract with a Long-Down Constraint (May 31, 2019). DOI: 10.1016/j.ijpe.2019.05.023 . Available at SSRN: https://ssrn.com/abstract=3341439 or http://dx.doi.org/10.2139/ssrn.3341439

Douniel Lamghari-Idrissi (Contact Author)

Eindhoven University of Technology (TUE) - Department of Industrial Engineering and Innovation Sciences ( email )

Den Dolech 2
Eindhoven
Netherlands

Rob J.I. Basten

Eindhoven University of Technology (TUE) ( email )

PO Box 513
Den Dolech 2
Eindhoven, 5600 MB
Netherlands

Geert-Jan Van Houtum

Eindhoven University of Technology (TUE) ( email )

PO Box 513
Eindhoven, 5600 MB
Netherlands

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