Online multi-dimensional generalized assignment problem with predictions

Abstract

The Online Multi-Dimensional Generalized Assignment Problem (online MDGAP) can model a large number of applications such as parallel machine scheduling, vehicle routing, telecommunication network design, etc., where a set of jobs have to be assigned to a set of capacitated agents in an online manner such that multi-dimensional capacity constraints can be respected. In this paper, we initiate the study of online MDGAP with predictions — the decision parameters such as coefficients of service (switching) costs and resource consumption can be accurately predicted or error-bounded, with the objective of minimizing the sum of service costs and switching costs in the long run. Furthermore, we design a two-stage online algorithm with performance guarantees. Rigorous theoretical analysis in terms of competitive ratio and regret demonstrates that our algorithm can produce an integer solution in polynomial time with bounded dimension constraints violation, robust to the coefficient variations and resource consumption uncertainty. Finally, trace-driven simulations show that our algorithm can achieve near optimal, high utilization, low constraint violation, and strong robustness.