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Question 26 of 32
Q.

Find the sequence that minimizes the total elapsed time to complete the following jobs in the order AB. Find the total elapsed time and idle times for both the machines.

JobIIIIIIIVVVIVII
Machine A716191014155
Machine B121414101657
Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2025Subjective· 4mImportance★★★★★
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Johnson's rule gives the sequence VII–I–IV–V–II–III–VI. Total elapsed time =91= 91; machine A idle =5= 5; machine B idle =13= 13.

Step 1 — Johnson's rule (order A then B). Repeatedly find the smallest time in the table: if it is under machine A, place that job as early as possible; if under machine B, place it as late as possible.

  • Smallest =5= 5: at A(VII) ⇒\Rightarrow VII first; at B(VI) ⇒\Rightarrow VI last.
  • Next =7= 7 at A(I) ⇒\Rightarrow I next.
  • Next =10= 10 at IV (both A and B) ⇒\Rightarrow IV next.
  • Next =14= 14 at A(V) ⇒\Rightarrow V next; then B ties place II, III before VI.

Sequence: VII→I→IV→V→II→III→VI\text{VII} \to \text{I} \to \text{IV} \to \text{V} \to \text{II} \to \text{III} \to \text{VI}.

Step 2 — Elapsed and idle time table. Times (A, B): VII(5,7)(5,7), I(7,12)(7,12), IV(10,10)(10,10), V(14,16)(14,16), II(16,14)(16,14), III(19,14)(19,14), VI(15,5)(15,5).

JobA-inA-outB-inB-out
VII05512
I5121224
IV12222434
V22363652
II36525266
III52717185
VI71868691
…

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