From Cost Sharing Mechanisms to Online Selection Problems

Abstract

We consider a general class of online optimization problems, called online selection problems, where customers arrive sequentially, and one has to decide upon arrival whether to accept or reject each customer. If a customer is rejected, then a rejection cost is incurred. The accepted customers are served with minimum possible cost, either online or after all customers have arrived. The goal is to minimize the total production costs for the accepted customers plus the rejection costs for the rejected customers. These selection problems are related to online variants of offline prize collecting combinatorial optimization problems that have been widely studied in the computer science literature. In this paper, we provide a general framework to develop online algorithms for this class of selection problems. In essence the algorithmic framework leverages any cost sharing mechanism with certain properties into a poly-logarithmic competitive online algorithm for the respective problem; the competitive ratios are shown to be near-optimal. We believe that the general and transparent connection we establish between cost sharing mechanisms and online algorithms could lead to additional online algorithms for problems beyond the ones studied in this paper.

A review of revenue management: Recent generalizations and advances in industry applications

“…In future research, the linkage of RM in attended home delivery to other existing streams should be made more transparent and eventually exploited, e.g., to online customer selection in supply chain management (e.g., Levi 2015, Elmachtoub andLevi 2016) or to dynamic vehicle routing (e.g., Bent andVan Hentenryck 2004,Ulmer et al 2018). For example, as a result of such an integrated study, research in same-day delivery could be pushed and streamlined.…”

Supply Chain Management with Online Customer Selection

“…Note that we assume the per unit rejection cost is uniform among customers. In Elmachtoub and Levi (2014), it is shown that if there are customer-specific rejection costs per unit, then no deterministic nor randomized online algorithm can have a constant competitive ratio.…”

The Costs and Benefits of Sharing: Sequential Individual Rationality and Sequential Fairness

“…We now outline some of the related work in cost sharing in a dynamic shared resource allocation setting, in which our contributions can potentially discover alternate solutions with different desiderata. For instance, Elmachtoub and Levi (2014) study online allocation problems where customers arrive sequentially, and decisions regarding whether to accept or reject customers must be made upon their arrival, with the goal of minimizing the sum of production costs (for accepted customers) and rejection costs.…”