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Route feasibility testing and forward time slack for the Synchronized Pickup and Delivery Problem

  • Timo GschwindEmail author
Regular Article


The Synchronized Pickup and Delivery Problem (SPDP) consists of finding a set of minimum-cost routes servicing user-specified transportation requests from pickup to delivery locations subject to pairing and precedence, capacity, time-window, and minimum and maximum time-lag constraints. The temporal constraints of the SPDP impose a complex scheduling problem for the service times at the customer locations which makes the efficient feasibility checking of routes intricate. We present different route feasibility tests for the SPDP and compare their practical runtime on a huge number of randomly generated routes. Furthermore, we generalize to the SPDP the concept of forward time slack, which has proven a versatile tool for feasibility testing of customer or request insertions into a given (feasible) route for many VRP variants.


Vehicle routing Temporal synchronization Feasibility testing Forward time slack 



This research was partially funded by the Deutsche Forschungsgemeinschaft (DFG) under Grant No. IR 122/5-2.

Supplementary material

291_2018_544_MOESM1_ESM.pdf (127 kb)
Supplementary material 1 (pdf 126 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chair of Logistics Management, Gutenberg School of Management and EconomicsJohannes Gutenberg University MainzMainzGermany

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