# Types Of Sequencing Problems

**Introduction:**

Sequencing model is the another part of operation research which is not include in linear programming, used to minimise the production time and maximise the profit.

**Solution for sequencing problem: N’ Jobs and Two Machines:**

**(a) **If the problem given has two machines and two or three jobs, then it can be solved by using the Gantt chart.

**(b) **But if the numbers of jobs are more, then this method becomes less practical.

**(c) **Gantt chart consists of X -axis on which the time is noted and Y-axis on which jobs or machines are shown.

**(d) **For each machine a horizontal bar is drawn. On these bars the processing of jobs in given sequence is marked

**Example 1. ****There are two jobs job 1 and job 2. They are to be processed on two machines, machine A and Machine B in the order AB. Job 1 takes 2 hours on machine A and 3 hours on machine B. Job 2 takes 3 hours on machine A and 4 hours on machine B. Find the optimal sequence which minimizes the total elapsed time by using Gantt chart.**

**Solution:**

Total elapsed time for sequence 1,2 *i.e. *first job 1 is processed on machine *A *and then on second machine and so on.

**Procedure: **Draw *X *- axis and Y- axis, represent the time on *X *- axis and two machines by two bars on *Y*axis.

Mark the times on the bars to show processing of each job on that machine.

Sequence 1,2 Total = elapsed time = 9 Hrs. (optimal sequence)

Both the sequences shows the elapsed time = 9 hours.

**The drawback of this method is for all the sequences, we have to write the Gantt chart and find the total elapsed times and then identify the optimal solution. **