Understanding the interaction between different combinatorial optimization problems is a challenging task of high relevance for numerous real-world applications including modern computer and memory architectures as well as high performance computing. Recently, the Traveling Thief ProblemÂ (TTP), as a combination of the classical traveling salesperson problem and the knapsack problem, has been introduced to study these interactions in a systematic way. We investigate the underlying non-linear Packing While Traveling Problem (PWTP) of the TTP where items have to be selected along a fixed route. We give an exact dynamic programming approach for this problem and a fully polynomial time approximation schemeÂ (FPTAS) when maximizing the benefit that can be gained over the baseline travel cost. Our experimental investigations show that our new approaches outperform current state-of-the-art approaches on a wide range of benchmark instances.