The Packing While Traveling Problem

Sergey Polyakovskiy; Frank Neumann

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arXiv · 1512.08831

The Packing While Traveling Problem

Sergey Polyakovskiy·Frank Neumann

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Abstract

This paper introduces the Packing While Traveling problem as a new non-linear knapsack problem. Given are a set of cities that have a set of items of distinct profits and weights and a vehicle that may collect the items when visiting all the cities in a fixed order. Each selected item contributes its profit, but produces a transportation cost relative to its weight. The problem asks to find a subset of the items such that the total gain is maximized. We investigate constrained and unconstrained versions of the problem and show that both are NP-hard. We propose a pre-processing scheme that decreases the size of instances making them easier for computation. We provide lower and upper bounds based on mixed-integer programming (MIP) adopting the ideas of piecewise linear approximation. Furthermore, we introduce two exact approaches: one is based on MIP employing linearization technique, and another is a branch-infer-and-bound (BIB) hybrid approach that compounds the upper bound procedure with a constraint programming model strengthened with customized constraints. Our experimental results show the effectiveness of our exact and approximate solutions in terms of solution quality and computational time.

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BibTeX RIS

Sergey Polyakovskiy, Frank Neumann. 2017-03-21. The Packing While Traveling Problem. https://arxiv.org/abs/1512.08831

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