Sequencing problems involve determining the optimal order of tasks given constraints to minimize time, cost or other criteria. They are common in manufacturing, logistics, projects and healthcare. The goal is to optimize performance by determining the best task sequence. Types include job, flow shop, assembly line and project sequencing. Elapsed time refers to the total time from starting the first to completing the last task, and is a key measure to minimize in sequencing problems.

1. What is Sequencing?
 Sequencing problems are a class of problems in operations research that
involve determining the optimal order in which a set of tasks or activities
should be performed, given a set of constraints or objectives.
 The sequencing problem typically involves determining the optimal sequence
or schedule of tasks that minimizes the total time, cost, or other performance
criteria, subject to constraints such as resource availability, task dependencies,
and deadlines.
 Sequencing problems are common in many operational settings, such as
manufacturing, logistics, project management, and healthcare, among others.
 The goal of sequencing problems is to optimize the performance of the
system by determining the optimal order in which tasks should be performed,
given the constraints and objectives of the system.

2. Types of Sequencing Problem
 Job sequencing: This involves determining the optimal order in which a set
of jobs or tasks should be processed on a single machine or production line.
 Flow shop sequencing: This involves determining the optimal order in which
a set of jobs or tasks should be processed on a series of machines or
workstations, subject to constraints such as machine availability and task
dependencies.
 Assembly line sequencing: This involves determining the optimal order in
which a set of tasks should be performed on an assembly line, subject to
constraints such as workstation availability, task dependencies, and cycle
time.
 Project scheduling: This involves determining the optimal schedule for a set
of activities in a project, subject to constraints such as resource availability,
task dependencies, and deadlines.

3. Elapsed Time
 In sequencing problems, elapsed time refers to the amount of time that has passed between
the start and completion of a particular task or sequence of tasks. i.e Time that lapses
between the starting of first job and the completion of the last job.
 For example, in job sequencing problems, the elapsed time is the total time required to
complete all jobs in a given sequence.
 In flowshop sequencing problems, the elapsed time is the time taken to process all jobs on
all machines in the given sequence. Similarly, in assembly line sequencing problems, the
elapsed time is the time taken to complete all tasks in the given sequence on the assembly
line.
 Elapsed time is an important performance measure in sequencing problems, as it directly
affects the overall efficiency and productivity of the system.
 The goal of sequencing problems is to find a sequence of tasks that minimizes the elapsed
time while satisfying the given constraints and objectives of the problem.
 In some cases, it may be necessary to prioritize other objectives, such as minimizing setup
time or maximizing machine utilization, which can also impact the elapsed time of the
overall system.

4. Glossary
 Processing time: The amount of time required to complete a task
on a particular machine.
 Setup time: The time required to prepare a machine for processing
a particular task.
 Release time: The time at which a task becomes available for
processing.
 Due date: The deadline by which a task must be completed.
 Completion time: The time at which a task is completed.
 Flow time: The total time taken to complete a task, including
waiting time and processing time.
 Idle Time ; The time for which the machines or facilities are not
utilized during the total elapsed time.