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JIMO

In this paper, we firstly propose a technique
named

**Duplicating**, which duplicates machines in batch scheduling environment. Then we discuss several applications of**Duplicating**in solving batch scheduling problems. For the batch scheduling problem on unrelated parallel machines to minimize makespan, we give a $(4 - \frac{2}{B})$- approximation algorithm and a $(2 - \frac{1}{B} + \epsilon)$ algorithm when $m$ is fixed. We also present a $4(2 - \frac{1}{B} + \epsilon)$-competitive algorithm for the on-line scheduling problem on identical machines to minimize total weighted completion time by another technique-$\rho-dual$, which is proposed originally by Hall et al.(1997).
JIMO

This special issue is dedicated to Professor Changyu Wang on the
occasion of his 70th birthday in recognition of his contributions to
Operations Research and its applications and his lasting impact as
an educator.

keywords:

JIMO

We claim a conclusion on Multi-Dimensional
Knapsack Problem (MKP), which extends an important proposition by
Dantzig firstly, then address to a special case of this problem,
and constitute a polynomial algorithm, extending Zukerman et al's
work.

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