What critical ratio and minimum slack are
The critical ratio (CR) is a priority rule that divides the time left until the due date by the work left to do. Minimum slack (MST, minimum slack time) subtracts the two instead of dividing. In both, the job with the smallest value is processed first: it is the one closest to running late.
Unlike FIFO, SPT, and EDD, which use only arrival, processing time, or due date, these rules look at due date and remaining work together and update at every decision.
Visual map: time remaining versus work remaining
The map shows the three formulas, the five jobs in the example, and the sequence each rule produces.
The formulas
CR = (due date − today) ÷ remaining processing time
Slack = (due date − today) − remaining processing time
S/RO = slack ÷ number of remaining operations
- CR < 1: the job is already behind its due date.
- CR = 1: right on the edge; any wait makes it late.
- CR > 1: there is slack; the larger, the more room.
Slack is in time units (days, hours) and CR is dimensionless. S/RO (slack per remaining operation) spreads the slack over the steps still to come: a job with 2 days of slack and 1 operation left is less urgent than one with the same 2 days and 4 operations, because the second still faces 4 queues.
Example: five jobs on day 10
Illustrative example. Today is day 10 (running working days) and five jobs are waiting at the same work center:
| Job | Due (day) | Work remaining (days) | Operations remaining |
|---|---|---|---|
| A | 18 | 6 | 1 |
| B | 15 | 5 | 2 |
| C | 20 | 8 | 4 |
| D | 13 | 4 | 1 |
| E | 25 | 10 | 5 |
| Job | Time to due date | CR | Slack | S/RO |
|---|---|---|---|---|
| A | 18 − 10 = 8 | 8 ÷ 6 = 1.33 | 8 − 6 = 2 | 2 ÷ 1 = 2.0 |
| B | 15 − 10 = 5 | 5 ÷ 5 = 1.00 | 5 − 5 = 0 | 0 ÷ 2 = 0 |
| C | 20 − 10 = 10 | 10 ÷ 8 = 1.25 | 10 − 8 = 2 | 2 ÷ 4 = 0.5 |
| D | 13 − 10 = 3 | 3 ÷ 4 = 0.75 | 3 − 4 = −1 | −1 ÷ 1 = −1.0 |
| E | 25 − 10 = 15 | 15 ÷ 10 = 1.50 | 15 − 10 = 5 | 5 ÷ 5 = 1.0 |
Resulting sequences:
- Critical ratio: D (0.75), B (1.00), C (1.25), A (1.33), E (1.50).
- Minimum slack: D (−1), B (0), then A and C tied at 2, and E (5).
- S/RO: D (−1.0), B (0), C (0.5), E (1.0), A (2.0).
All three agree on the first two positions: D is already late (CR 0.75 and negative slack) and B has no margin at all. The differences come after that. Slack ties A and C; CR breaks the tie in favor of C, which has more work to do; S/RO sends A to the end, because A has a single operation and can recover time faster.
Check: for D, the remaining work (4 days) is longer than the time available (3 days). Even starting now, the job finishes on day 14, 1 day after its due date. The rule does not create time; it shows that D needs action (overtime, lot splitting, renegotiation) ahead of the others.
Recompute at every decision
These rules are dynamic. After 1 day, "today" moves and the values change. On day 11, if B has not been processed, its time to due date falls to 4 while remaining work stays 5: CR = 4 ÷ 5 = 0.80, slack = −1. A job that was on the margin becomes late just because it waited. That is why the list must be recomputed whenever the resource frees up, in the system or in a spreadsheet, and not printed once a week.
Remaining work should include queue and move times where they matter, or the result will be optimistic. It is the same logic as lead time: processing time is only a fraction of total time in the plant.
When to use each rule
| Rule | Strengths | Watch out |
|---|---|---|
| Critical ratio | Compares jobs of different sizes; flags lateness with a value below 1 | Loses meaning if the due date has passed or remaining work is zero |
| Minimum slack | Simple; shows the margin in time | Ignores how many operations remain; ties easily |
| S/RO | Accounts for the number of remaining steps | Needs an up-to-date routing for every job |
| EDD | Minimizes maximum lateness on one machine | Does not see remaining work |
Use CR or slack in make-to-order job shops with many jobs, different routings, and their own due dates. In repetitive flow lines, takt time and fixed sequencing fit better. For two resources in series, see Johnson's rule. With a constraint resource, schedule first with drum-buffer-rope. And when load already exceeds capacity, no priority rule fixes it: see finite scheduling and APS.
Common mistakes and limits
- Computing once and not updating: the values change every day.
- Using processing time without queue and move time, and calling a job CR 1.2 when in practice it is late.
- Reading CR without checking the sign of the slack: an expired due date gives zero or negative CR and the job should be treated as top priority.
- Ignoring setup: jobs sharing a tool could be grouped, and the pure rule separates them.
- Always pushing the most late jobs and never finishing the rest; combine the rule with a WIP limit.
- Due dates that are sales guesses: the rule is only as good as the date.
Frequently asked questions
What is the critical ratio?
The time remaining until the due date divided by the work remaining. Below 1 the job is late; above 1 there is slack.
What is the difference between critical ratio and minimum slack?
Critical ratio divides (time to due date ÷ remaining work) and slack subtracts (time to due date − remaining work). CR is dimensionless; slack is in days or hours.
What does a CR of 1 mean?
The job is exactly at the edge of its due date: available time equals remaining work, with no margin for waiting.
What is S/RO?
Slack divided by the number of remaining operations. It gives priority to jobs with little slack per step still to go.
Which is better, CR or EDD?
It depends on the goal. EDD minimizes maximum lateness on one machine; CR and slack react better when many jobs have different remaining work.
In the example, which job goes first?
Job D, under every rule: CR of 0.75, slack of −1 day, and S/RO of −1.0. It can no longer meet the day 13 due date.
Sources
- BAKER, K. R. Introduction to Sequencing and Scheduling. Wiley.
- VOLLMANN, T. E. et al. Manufacturing Planning and Control for Supply Chain Management. McGraw-Hill.
- PINEDO, M. L. Scheduling: Theory, Algorithms, and Systems. Springer.
- SLACK, N. et al. Operations Management. Pearson.
Keep studying: trusted sources and links
- ASCM: Association for Supply Chain Management
- ABEPRO: Associação Brasileira de Engenharia de Produção (in Portuguese)
- Wikipedia: Scheduling (production processes)
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About the author
Lean Manufacturing & Behavioral Management Specialist
Over 20 years in the automotive and metalworking industries (GM and Dana), Lean Manufacturing practitioner since 2006. SENAI instructor and mentor in Brazil’s Brasil Mais Produtivo program, delivering consulting, training and audits for 50+ companies, combining quality, productivity and people development.
