We consider a variant of the vehicle routing problem (VRP) where each customer has a unit demand and the goal is to minimize the total cost of routing a fleet of capacitated vehicles from one or multiple depots to visit all customers. We propose two parallel algorithms to efficiently solve the columngenerationbased linearprogramming relaxation for this VRP. Specifically, we focus on algorithms for the “pricing problem,” which corresponds to the resourceconstrained elementary shortest path problem. The first algorithm extends the pulse algorithm for which we derive a new bounding scheme on the maximum load of any route. The second algorithm is based on random coloring from parameterized complexity which can be also combined with other techniques in the literature for improving VRPs, including cutting planes and column enumeration. We conduct numerical studies using VRP benchmarks (with 50–957 nodes) and instances of a medical home care delivery problem using census data in Wayne County, Michigan. Using parallel computing, both pulse and random coloring can significantly improve column generation for solving the linear programming relaxations and we can obtain heuristic integer solutions with small optimality gaps. Combining random coloring with column enumeration, we can obtain improved integer solutions having less than 2%more »
This content will become publicly available on July 11, 2023
Brief Announcement: A Parallel (Δ, Γ)Stepping Algorithm for the Constrained Shortest Path Problem
We design a parallel algorithm for the Constrained Shortest Path (CSP) problem. The CSP problem is known to be NPhard and there exists a pseudopolynomial time sequential algorithm that solves it. To design the parallel algorithm, we extend the techniques used in the design of the Δstepping algorithm for the singlesource shortest paths problem.
 Award ID(s):
 1724227
 Publication Date:
 NSFPAR ID:
 10349904
 Journal Name:
 SPAA '22: Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures
 Page Range or eLocationID:
 287 to 289
 Sponsoring Org:
 National Science Foundation
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