State Dependent Maintenance Scheduling

• Applicants: Professor Dr. Dirk Briskorn; Professor Dr. Florian Jaehn
• Subject Area: Accounting and Finance
• Term: from 2021 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 452470135

• Final Report Year: 2025

Final Report Abstract

Machine deterioration and preventive and predictive maintenance operation have been considered in the scheduling literature for quite a while. Most models assume that machine deterioration is time dependent in the sense that a machine deteriorates by age or by the time being in use. Moreover, a maintenance operation is classically assumed to be of a fixed duration, leading to a full recovery of the machine. These models neglect the fact that a machine’s deterioration may depend on factors such as the number of setups for a job or, more generally, can be expressed by a machine’s state, which might be influenced by each job individually. For example, in aviation, an aircraft’s state can be defined by flying hours, flying distance, and the number of flights. In preliminary work, the applicants developed three basic models. In the first one, maintenance has to be scheduled at fixed positions (with respect to the job sequence). The second considers a situation with maintenance scheduling in which the deterioration only depends on the number of jobs. The third model allows for variable maintenance duration, giving more flexible control over a machine’s state. These very basic models will be further developed in the course of the project so that they can better reflect real life situations. To do so, we will combine characteristics of the different models, analyze situations in which preemption of jobs is allowed, and introduce processing times depending on the machine’s state (e.g., learning effects, deterioration). In a final stage, which certainly reflects real life situations best, we will consider multidimensional machine’s states. Here, each state dimension might be of a different type, e.g., a classical time dependent state, the number of jobs, or a fuel level.

Publications

• Minimizing the makespan on a single machine subject to modular setups. Journal of Scheduling, 25(1), 125-137.
  Briskorn, Dirk; Stephan, Konrad & Boysen, Nils
  
• A Greedy heuristic for solving scheduling problems with bounded rejection cost. Computers & Operations Research, 144, 105827.
  Atsmony, Matan & Mosheiov, Gur
  
• A note on batch scheduling on a two-machine flowshop with machine-dependent processing times. 4OR, 21(3), 457-469.
  Mosheiov, Gur & Oron, Daniel
  
• How to charge while driving: scheduling point-to-point deliveries of an electric vehicle under overhead wiring. Journal of Scheduling, 26(1), 19-41.
  Boysen, Nils; Briskorn, Dirk & Schwerdfeger, Stefan
  
• Minimizing total completion time with linear deterioration: A new lower bound. Computers & Industrial Engineering, 163, 107867.
  Atsmony, Matan & Mosheiov, Gur
  
• On the tractability of hard scheduling problems with generalized due-dates with respect to the number of different due-dates. Journal of Scheduling, 25(5), 577-587.
  Mosheiov, Gur; Oron, Daniel & Shabtay, Dvir
  
• Scheduling to maximize the weighted number of on-time jobs on parallel machines with bounded job-rejection. Journal of Scheduling, 26(2), 193-207.
  Atsmony, Matan & Mosheiov, Gur
  
• Single machine scheduling with common assignable due date/due window to minimize total weighted early and late work. European Journal of Operational Research, 303(1), 66-77.
  Shabtay, Dvir; Mosheiov, Gur & Oron, Daniel
  
• Single machine scheduling with step-learning. Journal of Scheduling, 27(3), 227-237.
  Atsmony, Matan; Mor, Baruch & Mosheiov, Gur
  
• The LPT heuristic for minimizing total load on a proportionate openshop. Discrete Applied Mathematics, 338, 190-198.
  Gerstl, Enrique & Mosheiov, Gur
  
• Scheduling maintenance activities subject to stochastic job-dependent machine deterioration. European Journal of Operational Research, 319(1), 62-78.
  Briskorn, Dirk; Gönsch, Jochen & Thiemeyer, Antonia
  
• Scheduling with jobs at fixed positions. European Journal of Operational Research, 318(2), 388-397.
  Jaehn, Florian
  
• Single machine scheduling to minimize maximum earliness/tardiness cost with job rejection. Optimization Letters, 18(3), 751-766.
  Atsmony, Matan & Mosheiov, Gur
  
• A note: on the two-stage flowshop with dedicated machines to minimize total load. Optimization Letters, 19(9), 1871-1882.
  Agnetis, Alessandro & Mosheiov, Gur
  
• Scheduling Position-Dependent Maintenance Operations in Single Machine Layouts. Lecture Notes in Operations Research, 25-31. Springer Nature Switzerland.
  Hipp, Andreas