A worst-case analysis for the split delivery vehicle routing problem with minimum delivery amounts

In the vehicle routing problem (VRP), a fleet of vehicles must service the demands of customers in a least-cost way. In the split delivery vehicle routing problem (SDVRP), multiple vehicles can service the same customer by splitting the deliveries. By allowing split deliveries, savings in travel costs of up to 50 % are possible, and this bound is tight. Recently, a variant of the SDVRP, the split delivery vehicle routing problem with minimum delivery amounts (SDVRP-MDA), has been introduced. In the SDVRP-MDA, split deliveries are allowed only if at least a minimum fraction of a customer’s demand is delivered by each visiting vehicle. We perform a worst-case analysis on the SDVRP-MDA to determine tight bounds on the maximum possible savings.

We thank Claudia Archetti for her input on an early version of this paper.

Authors and Affiliations

1. Mercury Systems, Inc., Princeton, NJ, 08540, USA

   Yupei Xiong

2. RouteSmart Technologies, Inc., Columbia, MD, 21045, USA

   Damon Gulczynski

3. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

   Daniel Kleitman

4. Robert H. Smith School of Business, University of Maryland, College Park, MD, 20742, USA

   Bruce Golden

5. Kogod School of Business, American University, Washington, DC, 20016, USA

   Edward Wasil

Corresponding author

Correspondence to Damon Gulczynski.

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