Question

There are five jobs, each of which is to be processed through three machines A, B and C in the order CBA. Processing times in hours are:$$\begin{array}{cccc}Job& A& B& C\\ 1& 7& 4& 3\\ 2& 9& 5& 8\\ 3& 5& 1& 7\\ 4& 6& 2& 5\\ 5& 10& 3& 4\end{array}$$What is the optimum sequence for minimizing the elapsed time?

• A. 4-1-5-2-3
• B. 3-4-1-5-2
• C. 3-2-5-1-4
• D. 3-2-4-1-5

Answer 1

The correct option is C 3-2-5-1-4

$\text{Minimum of}{A}_i\text{= 5,}$

$\text{Maximum of}{B}_i\text{= 5,}$

$\text{Maximum of}{C}_i\text{= 3,}$

$\therefore \text{Maximum of}{B}_i\text{= Minimum of}{A}_i$

Hence, we can replace three machines by equivalent two machines and we can use johnson's algorithm.

$\text{Machine}{G}_i=A_i+B_i$

$\text{Machine}{H}_i=B_i+C_i$

$\begin{array}{ccc}\text{Job}& \text{Machine G}& \text{Machine H}\\ 1& 11& 7\\ 2& 14& 13\\ 3& 6& 8\\ 4& 8& 7\\ 5& 13& 7\end{array}$

Now, by Johnson's rule, sequence for minimizing the elapsed time is,
$3-2-5-1-4.$