Performance analysis and capacity planning for stochastic systems with cut-off service levels

• Applicants: Professor Dr.-Ing. Kai Furmans; Professor Dr. Raik Stolletz
• Subject Area: Accounting and Finance ; Production Systems, Operations Management, Quality Management and Factory Planning ; Traffic and Transport Systems, Intelligent and Automated Traffic
• Term: from 2018 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 394845127

• Final Report Year: 2024

Final Report Abstract

In practice, distribution centers or e-commerce providers usually communicate cut-off times to their customers, i.e. the latest time customers need to place their orders so that a certain delivery date will be met. For instance, the agreement may state: “If you order until 5:00 PM today, you will receive the ordered goods tomorrow.” However, since both the daily order volume received and the processing capacity available are stochastic variables, order fulfilment centers cannot always guarantee that this promise will be fulfilled. Therfore, this research project aims to assess the influencing factors of stochastic system parameters on the cutoff service level and gain insights into the consequences for personnel demand and staff planning. As the service level definitions found in the literature differ widely, we introduced a morphology to classify and formally describe service levels. Based on the academic papers found, we identified various influencing parameters and investigated their impact on cutoff service level. For this purpose, we modeled the order fulfilment system as a discrete-time Markov chain and conducted extensive numerical studies. The numerical results showed that introducing a late cutoff time significantly improves the system’s performance, compared to a benchmark system without cutoff times. From these findings, we derived managerial insights and key findings to steer stochastic order fulfilment systems and their personnel capacity planning. Based on the numerical results, we analytically derived structural properties of the investigated order fulfilment systems. We showed that the system’s performance can be dircetly derived from the cumulative workload distribution. Based on this conclusion, we derived an efficient design method for personnel resource planning for stochastic order fulfilment systems with cutoff service level. The procedure exploits the fact that, assuming single-period shifts, the optimum capacity lies in the last planning period and the shifts before can be scheduled backwards up to the theoretically required capacity or the maximum possible number of parallel shifts. The proposed method either terminates with the optimum solution or aborts as infeasisable. Furthermore, we extendet the method to an efficient algorithm for scheduling shift plans in single and multi-level as well as for deterministic and stochastic cases.

Publications

• A Machine Learning Approach to the Performance Evaluation of Time-dependent Queues. SMMSO 2022, Grenoble, France.
  Khayyati, S.; Zenouzzadeh, S.M. & Stolletz, R.
  
• Analysis of Time-dependent Queues Using Machine Learning. 9th Workshop on Queueing Theory, Obergurgl, Austria.
  Khayyati, S.; Zenouzzadeh, S.M. & Stolletz, R.
  
• Analysis of Time-dependent Queues Using Machine Learning. EURO conference 2022, Espoo, Finland.
  Khayyati, S.; Zenouzzadeh, S.M. & Stolletz, R.
  
• Cutoff service level – Some insights. XIIIth Conference on Stochastic Models of Manufacturing and Service Operations (SMMSO), Grenoble, France.
  Furmans, K. & Stolletz, R.
  
• Discrete-time Performance Analysis of Stochastic Order Fulfilment Systems with Cutoff Service Level. 2022 OR Konferenz Karlsruhe, Gesellschaft für Operations Research e.V., Karlsruhe, Germany.
  Mohring, U.; Jacobi, C. & Furmans, K.
  
• First thoughts on capacity planning according to Cut-Off service levels. 13th Workshop for Supply Chain Management and Production, Obergurgl, Austria.
  Stolletz, R.
  
• Shift Scheduling in Interdependent Multi-stage Systems with Reallocation of Workforce. EURO Conference 2022, Espoo, Finland.
  Zenouzzadeh, S.M. & Stolletz, R.
  
• Shift Scheduling in Interdependent Multi-stage Systems with Reallocation of Workforce. PATAT 2022, Leuven, Belgium.
  Zenouzzadeh, S.M. & Stolletz, R.
  
• A machine learning approach for the analysis of time-dependent queues: ML4TDQ. 32nd QBWL-Workshop, Bad Windsheim, Germany.
  Khayyati, S.; Zenouzzadeh, S.M. & Stolletz, R.
  
• Managing cutoff-based shipment promises for order fulfilment processes in warehousing. OR Spectrum, 46(2), 513-543.
  Mohring, Uta; Jacobi, Christoph; Furmans, Kai & Stolletz, Raik