Online scheduling of two job types on a set of multipurpose machines with unit processing times

Authors:
Dvir Shabtay;Shlomo Karhi
Affiliations:
Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel;Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Venue:
Computers and Operations Research
Year:
2012

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Abstract

We study a problem of scheduling a set of n jobs with unit processing times on a set of m multipurpose machines in which the objective is to minimize the makespan. It is assumed that there are two different job types, where each job type can be processed on a unique subset of machines. We provide an optimal offline algorithm to solve the problem in constant time and an online algorithm with a competitive ratio that equals the lower bound. We show that the worst competitive ratio is obtained for an inclusive job-machine structure in which the first job type can be processed on any of the m machines while the second job type can be processed only on a subset of m/2 machines. Moreover, we show that our online algorithm is 1-competitive if the machines are not flexible, i.e., each machine can process only a single job type.