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Job sequencing with a Gantt chart

Paste the bottleneck machine’s jobs and see in seconds which order is least late, which spends least on setups and when each job is done. Print the shift order with a check column.

Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.

Pre-sizingRevised 11/02/2026
Scheduling problem
Jobs (single machine)
See what was read

Family can be a color, mold, tool or material. Due time in working hours from the start (e.g. 12) or date and time (e.g. 11/03 3:00 PM as 11/03 15:00).

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—End of the last job (makespan)
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Rule comparison

Click a row to see the Gantt chart and dispatch list for that rule. ✓ marks the best value in each column.

Priority rules and Johnson’s rule give a good sequence that is easy to explain on the shop floor, but not necessarily the optimum for every criterion at once (Johnson’s rule is optimal only for the two-stage makespan).

Gantt chart of the sequence

Metrics by rule

Makespan, total tardiness and total setup for each rule, in the same hours.

Tap the chart to see the values.

Dispatch list

Next step

Take this page’s results to another calculator with the fields already filled in.

The calculation report gathers this page's inputs, results, equations, assumptions and references, with fields for project, engineer and revision. The full report also includes the charts and interpretations, in color. In the print dialog, choose Save as PDF.

Method, assumptions and references

Equations used

Job j completion: C_j = C_(j−1) + setup_j + p_j; setup_j = short setup if family_j = family_(j−1), otherwise full setup; the first job uses the full setup
Makespan = C_n; mean flow time = Σ C_j ÷ n; tardiness T_j = max(0, C_j − due_j); utilization = Σ p_j ÷ makespan
SPT: increasing p; EDD: increasing due date; CR = due ÷ (p + full setup), increasing; family: groups by the group’s earliest due date, within by due date (or by p)
Johnson (2 stages): set 1 = {a_j < b_j} by increasing a; set 2 = {a_j ≥ b_j} by decreasing b; sequence = set 1 + set 2
Stage 2: start_j = max(stage 1 end_j, stage 2 end_(j−1)); stage 2 idle = Σ (start_j − stage 2 end_(j−1)), including the initial wait
Clock time: day = ⌊x ÷ h_day⌋; time = start + (x − day · h_day)

Assumptions and limits

  • All jobs are released at the start (material and tooling available), no breakdowns and no job splitting; one machine at a time, or two stages in series with the same order (permutation flow shop).
  • Setup depends only on the previous family (full or short); the critical ratio is computed once, at the start (static version). Ties keep the order entered.
  • The rules give a good sequence, not necessarily the optimum; Johnson’s rule is optimal for the two-stage makespan. The calendar repeats the same hours per day from the start time, without weekends or holidays.

Standards and technical documents

  • Johnson, S. M. Optimal two- and three-stage production schedules with setup times included. Naval Research Logistics Quarterly, 1(1), 61–68, 1954
  • Pinedo, M. L. Scheduling: Theory, Algorithms, and Systems, 6th ed., Springer, 2022
  • Baker, K. R.; Trietsch, D. Principles of Sequencing and Scheduling, 2nd ed., Wiley, 2019
  • Jacobs, F. R.; Chase, R. B. Operations and Supply Chain Management, 16th ed., McGraw-Hill, 2020 (priority rules and critical ratio)
  • Tubino, D. F. Planejamento e Controle da Produção: teoria e prática, 3ª ed., Atlas, 2017

U.S. regulations

  • Fair Labor Standards Act: overtime premium when the schedule requires extra hours
  • OSHA 29 CFR 1910.147: lockout/tagout applies to setups and changeovers

Frequently asked questions

What is production scheduling (job sequencing)?

It is choosing the order in which jobs go through a machine or a line. The order changes time spent on setups, when each job is finished and how many are late. This calculator tests six simple rules at once and shows the Gantt chart and dispatch list for the one picked.

Where do I get processing and setup times?

Processing time = job quantity × standard time per part (from a time study or routing) ÷ actual efficiency. Full setup is the measured changeover from one family to another; the short setup is the adjustment between jobs of the same family (only changing color or length, for example). Use measured times, not the machine manual’s.

How do I read the example result?

With the five example jobs and a 0.25-hour short setup within a family, the order entered (FIFO) finishes at 32.50 h with 26.00 h of tardiness in three jobs. EDD (earliest due date first) finishes at 31.25 h with 6.00 h of tardiness in two jobs; grouping families finishes at 29.50 h with 3 h less setup, but delays the urgent jobs more.

Which rule should I use?

If customers press on dates, use the least total tardiness or EDD, which usually gives the smallest maximum delay. If the machine is the bottleneck and setups are long, the family rule gains production hours. SPT cuts average queue time and work in process. The criterion on the form picks automatically; click the table to see another rule.

What is Johnson’s rule?

For two stages in series with the same order at both (e.g. machining then heat treating), Johnson (1954) proved this order gives the minimum makespan: first the jobs faster at stage 1, in increasing order; then the jobs faster at stage 2, in decreasing order of stage 2. In the example the makespan drops from 34 h to 30 h.

Is the sequence the best possible?

Not necessarily. Priority rules give a good sequence that is quick to compute and easy to explain, but with sequence-dependent setups the problem is hard and the exact optimum needs mathematical programming. For dozens of jobs at a bottleneck, the best rule on this page is usually close to the optimum; always check with the people who know the machine.

What are the calculator’s limits?

It assumes all jobs are released at the start, one machine (or two in series), no breakdowns, no material shortages and no splitting a job. The calendar is hours per day from the start time, without weekends or holidays. For several parallel machines or different routings, use a scheduling (APS) system or split the load first with the capacity calculator.