Minimum Makespan on Unrelated Machines

Keywords and Synonyms

Schedule of minimum length on different machines      

Problem Definition

Consider the following scheduling problem. There are m parallel machines and n independent jobs. Each job is to be assigned to one of the machines. The processing of job j on machine i requires $p_{ij}$ units of time. The objective is to find a schedule that minimizes the makespan, defined to be the time by which all jobs are completed. This problem is denoted $R||C_{\mathrm{max}}$ using standard scheduling notation terminology [6].

There are few important special cases of the problem: the restricted assignment problem with $p_{ij}\in \{1,\infty\}$, the identical parallel machines with $p_{ij}=p_j$ and the uniform parallel machines $p_{ij}=p_j/s_i$ where $s_i \mathchar"313E 0$ is a speed of machine i. These problems are denoted $R|p_{ij}\in\{1,\infty\}|C_{\mathrm{max}}$, $P||C_{\mathrm{max}}$ and $Q||C_{\mathrm{max}}$, respectively. Two later problems admit...