Competitive Strategies for On-line Production Order Disposal Problem

Abstract

In this paper we study the on-line production order disposal problem considering preemption and abortion penalty. We discuss the cases when orders have uniform and nonuniform lengths. For the case of uniform order length, the GR strategy is proved to be $2\rho + 2\sqrt{(1+\rho)^2 + \rho + 3}$ -competitive, where ρ ≥ 0 is the coefficient of the punishment. For the case of nonuniform order lengths, GR is $2(\lambda + \lambda\rho) + 2\sqrt{(\lambda+\lambda\rho)^2 + \lambda\rho + 1}$ -competitive where λ is the ratio of length between the longest and shortest orders. When abortion penalty is not counted, the ER strategy is proposed and proved to be eλ + e + 1 -competitive, where e ≈ 2.718. The result is much better than that of GR. We show that ER is not competitive when abortion penalty is counted.

This research is supported by NSF of China under Grants 10371094 and 70471035.