clever or smart: Strategies for the online target date assignment problem

Abstract

In this paper, we consider the Online Target Date Assignment Problem (OnlineTDAP) with deferral time one and unsplittable requests for general downstream problems, where the downstream cost are nonnegative, additive and satisfy the triangle inequality.We show that the lower bound on the competitive ratio of any online algorithm for this problem is greater than 3/2 − ε. The first online algorithm analyzed is smart, which was introduced by Angelelli et al. [3]. We prove that its competitive ratio is at most 2 √ 2 − 1 ≈ 1.8284 for this setting. This result answers the question posed in Angelelli et al. [4], if smart has a competitive ratio strictly less than 2 for the Dynamic Multi-Period Routing Problem (Dmprp) with customers located on the Euclidean plane, provided splitting of request sets is prohibited.Finally, we present the online algorithm clever and show that this strategy is asymptotically optimal with a competitive ratio of 3/2.