A framework for window design in delivery schedules
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917225280045056 |
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| author | Bharti, Bharti Bekker, René Levering, Nikki Mandjes, Michel |
| author_facet | Bharti, Bharti Bekker, René Levering, Nikki Mandjes, Michel |
| contents | This paper develops a structured framework for the design and dynamic updating of service time windows in delivery and appointment-based systems. We consider a single-server setting with stochastic service and travel times, where customers are promised a time window in which the provider will arrive. The first part of the paper introduces a static window construction method based on a probabilistic threshold criterion, using an analytical approximation of residual travel and service time distributions. Building on this, we develop a dynamic update mechanism that monitors residual system uncertainty, where time windows are revised during execution only when the remaining time until the window's start falls below a predefined threshold. This threshold-based approach enables communication-efficient scheduling while substantially improving delivery accuracy. Numerical experiments demonstrate significant performance gains of the dynamic approach in both stylized and real-world settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19601 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A framework for window design in delivery schedules Bharti, Bharti Bekker, René Levering, Nikki Mandjes, Michel Optimization and Control This paper develops a structured framework for the design and dynamic updating of service time windows in delivery and appointment-based systems. We consider a single-server setting with stochastic service and travel times, where customers are promised a time window in which the provider will arrive. The first part of the paper introduces a static window construction method based on a probabilistic threshold criterion, using an analytical approximation of residual travel and service time distributions. Building on this, we develop a dynamic update mechanism that monitors residual system uncertainty, where time windows are revised during execution only when the remaining time until the window's start falls below a predefined threshold. This threshold-based approach enables communication-efficient scheduling while substantially improving delivery accuracy. Numerical experiments demonstrate significant performance gains of the dynamic approach in both stylized and real-world settings. |
| title | A framework for window design in delivery schedules |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.19601 |