Deliver or hold: Approximation Algorithms for the Periodic Inventory Routing Problem
The inventory routing problem involves trading off inventory holding
costs at client locations with vehicle routing costs to deliver
frequently from a single central depot to meet deterministic client demands over a finite planing horizon. In this paper, we consider periodic solutions that visit clients in one of several specified frequencies, and focus on the case when the frequencies of visiting nodes are nested. We give the first constant-factor approximation algorithms for designing optimum nested periodic schedules for the problem with no limit on vehicle capacities by simple reductions to prize-collecting network design problems. For instance, we present a 2.55-approximation algorithm for the minimum-cost nested periodic
schedule where the vehicle routes are modeled as minimum Steiner trees. We also show a general reduction from the capacitated
problem where all vehicles have the same capacity to the uncapacitated
version with a slight loss in performance. This reduction gives a
4.55-approximation for the capacitated problem. In addition, we prove several structural results relating the values of optimal policies of various types.
Inventry Routing Problem
Approximation algorithm
Prize-collecting Steiner Tree
209-225
Regular Paper
Takuro
Fukunaga
Takuro Fukunaga
Afshin
Nikzad
Afshin Nikzad
R.
Ravi
R. Ravi
10.4230/LIPIcs.APPROX-RANDOM.2014.209
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