Operations Research in the context of Identical-machines scheduling


Operations Research in the context of Identical-machines scheduling

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⭐ Core Definition: Operations Research

Operations research (British English: operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and decision-making. The term management science is occasionally used as a synonym.

Employing techniques from other mathematical sciences, such as modeling, statistics, and optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlapped with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries.

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👉 Operations Research in the context of Identical-machines scheduling

Identical-machines scheduling is an optimization problem in computer science and operations research. We are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m identical machines, such that a certain objective function is optimized, for example, the makespan is minimized.

Identical machine scheduling is a special case of uniform machine scheduling, which is itself a special case of optimal job scheduling. In the general case, the processing time of each job may be different on different machines; in the case of identical machine scheduling, the processing time of each job is the same on each machine. Therefore, identical machine scheduling is equivalent to multiway number partitioning. A special case of identical machine scheduling is single-machine scheduling.

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Operations Research in the context of Single-machine scheduling

Single-machine scheduling or single-resource scheduling is an optimization problem in computer science and operations research. We are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on a single machine, in a way that optimizes a certain objective, such as the throughput.

Single-machine scheduling is a special case of identical-machines scheduling, which is itself a special case of optimal job scheduling. Many problems, which are NP-hard in general, can be solved in polynomial time in the single-machine case.

View the full Wikipedia page for Single-machine scheduling
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