Two Machine Flow Shop Scheduler
Find a Johnson-rule job order minimizing makespan for a two-machine sequential flow shop.
YOUR CALCULATION
Result
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Calculation steps
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How to calculate
Apply Johnson’s partition-and-sort rule, then build both machines’ start and finish times.
First group a≤b: ascending a; remaining group: descending b; M2start=max(M1finish,previous M2finish)
Worked example
Jobs A=(3,5),B=(6,2),C=(4,4) produce order A,C,B with makespan 15. The listed A,B,C order finishes at 17.
Assumptions and input details
Use 1–50 uniquely named jobs with nonnegative durations at most 1e9 in the chosen common unit. Every job is ready at time zero and visits machine 1 then machine 2; no preemption, setup time, transport, due date, blocking or limited intermediate buffer. One job at a time per machine, same order on both machines. Johnson’s makespan result applies to this model, not general multi-machine scheduling. Ties retain input order.
References: UC Berkeley: Johnson algorithm assumptions
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