Polyakovskiy, S.Neumann, F.2019-07-092019-07-092017European Journal of Operational Research, 2017; 258(2):424-4390377-22171872-6860http://hdl.handle.net/2440/119962This 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 programing (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 programing 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.en© 2016 Elsevier B.V. All rights reserved.Combinatorial optimization; non-linear knapsack problem; linearization technique; piecewise approximation; hybrid optimizationJournal article003004558110.1016/j.ejor.2016.09.0350003927894000032-s2.0-85006063438234088Polyakovskiy, S. [0000-0001-9489-1972]Neumann, F. [0000-0002-2721-3618]