Online tradeoff scheduling on a single machine to minimize makespan and maximum lateness

Abstract

In this paper, we consider the following single machine online tradeoff scheduling problem. A set of n independent jobs arrive online over time. Each job $J_{j}$ has a release date $r_{j}$, a processing time $p_{j}$ and a delivery time $q_{j}$. The characteristics of a job are unknown until it arrives. The goal is to find a schedule that minimizes the makespan $C_{\max } = \max _{1 \le j \le n} C_{j}$ and the maximum lateness $L_{\max } = \max _{1 \le j \le n} L_{j}$, where $L_{j} = C_{j} + q_{j}$. For the problem, we present a nondominated $( \rho , 1 + \displaystyle \frac{1}{\rho } )$-competitive online algorithm for each $\rho$ with $1 \le \rho \le \displaystyle \frac{\sqrt{5} + 1}{2}$.