Sequencing problem in Operations Research is about deciding the best order to process jobs on one or more machines so that a goal like minimum total time, minimum idle time, or minimum cost is achieved. In simple terms, it asks: “Which job should be done first, second, third, and so on?”

Quick Scoop

A sequencing problem usually appears in production, scheduling, and service systems where many jobs must pass through machines in a specific order. The main purpose is to find the optimal sequence instead of checking every possible order, because the number of possible sequences grows very fast as jobs increase.

Core idea

  • Jobs are the tasks to be done.
  • Machines are the resources that process those jobs.
  • Sequence is the order in which jobs are processed.
  • The objective is often to minimize total elapsed time , machine idle time , or waiting time.

Why it matters

If a factory, shop floor, or office chooses the wrong order, machines may stay idle, jobs may wait too long, and overall output becomes slower. Sequencing helps managers use time and equipment more efficiently.

Common assumptions

Typical sequencing problems assume that processing times are known in advance and do not change with the order of jobs. They also often assume jobs are processed one at a time on each machine and that the route through machines is fixed.

Common types

  • n jobs on 2 machines.
  • n jobs on 3 machines.
  • n jobs on k machines.
  • 2 jobs on k machines.

Example

If five books must be typed, printed, bound, and cut, the question is the same sequencing question: in what order should the books move through the stages so the whole process finishes fastest? That is a classic Operations Research sequencing setup.

Bottom line

So, the sequencing problem in Operations Research is a job-order optimization problem : choose the best processing order for jobs across machines to make the system run efficiently.