Use Johnson's rule to determine the optimal sequencing for the five jobs to be processed on two machines in a fixed order (Machine 1 before Machine 2). The processing times in days are given in the table below.
a. What is the optimal sequence?
b. What is the total makespan for this sequence?
c. What is the total idle time for Machine 2?.
$$\begin{array}{lrr}& \text{ Machine 1 }& \text{ Machine 2 }\\ \text{ A }& 3& 2\\ \text{ B }& 4& 8\\ \text{ C }& 8& 3\\ \mathrm{D}& 1& 7\\ \mathrm{E}& 9& 4\\ \mathrm{F}& 5& 5\end{array}$$

Idle Time

Periods when resources, such as machinery or labor, are available but not in use due to lack of work, setup, or maintenance.

Johnson's Rule

A sequencing rule for minimizing the total processing time and setup time on two machines or processes.

Optimal Sequence

The best or most efficient order in which to perform a series of tasks or operations, usually determined based on criteria like minimizing time or maximizing output.