IGNOU MSTE 2 2026 - Using the graphical method to minimise the time required to process Jo

Question

Using the graphical method to minimise the time required to process Job 1 and Job 2 on five machines A, B, C, D and E, find the minimum elapsed times an idle times to complete both jobs.

	Sequence	A	B	C	D	E
Job 1	Time (in hours)	1	2	3	5	4
Job 2	Sequence	C	A	D	E	B
	Time (in hours)	3	4	2	1	5

19 Jan 2026

Answer :

Word Count : 761

We are asked to minimize the elapsed time and idle times for two jobs processed on five machines using the graphical (Gantt chart) method. Let’s solve it step by step manually. --- Step 1: Represent the jobs on the machines We have: | Machine | Job 1 Time | Job 2 Time | | ------- | ---------- | ---------- | | A | 1 | 3 | | B | 2 | 4 | | C | 3 | 2 | | D | 5 | 1 | | E | 4 | 5 | Job 2 sequence is given as C → A → D → E → B, which means Job 2 will visit C first, then A, then D, then E, then B. Job 1 sequence is A → B → C → D → E. --- Step 2: Draw the Gantt chart step by step We track the start and finish times for both jobs on each machine. Let’s denote: * `Sij` = start time of Job i on Machine j * `Fij` = finish time = start + processing time Machine A: * Job 1 starts at 0 → finishes at 1 (0 + 1) * Job 2 arrives after its previous machine (C), we’ll calculate later Machine B: * Job 1 starts after Job 1 on A → 1, finishes at 3 (1 + 2) * Job 2 on B is last in its sequence, so it waits until Job 1 on B finishes? We'll calculate with precedence Machine C: * Job 1 arrives after B → starts at 3, finishes at 6 (3 + 3) * Job 2 starts on C at 0 → finishes

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