Scheduling, Work Study and Quality Control

This lesson covers short-term scheduling, work study (how long a job should take), break-even analysis, and statistical quality control.

Sequencing jobs on one machine

Johnson's rule (n jobs, 2 machines)

Every job goes through machine 1 then machine 2. To minimise the makespan:

1. Find the smallest time among all jobs on both machines.
2. If it is on machine 1, put that job as early as possible; if on machine 2, as late as possible.
3. Remove the job and repeat.

Work study

• Method study finds a better way to do the job (process charts, therbligs).
• Time study: observed time × rating factor = normal time. Standard time = normal time × (1 + allowance fraction).
• Work sampling: many random observations estimate the fraction of time spent on each activity.

Break-even analysis

With fixed cost F, selling price p and variable cost v per unit:

• Break-even quantity = F/(p − v). (p − v) is the contribution per unit.
• Profit at quantity Q = Q(p − v) − F.

Statistical quality control

• Control charts for variables: X̄ chart (mean) and R chart (range). Control limits for X̄: X̿ ± A₂R̄.
• Control charts for attributes: p chart (fraction defective): p̄ ± 3√(p̄(1 − p̄)/n); c chart (defects per unit): c̄ ± 3√c̄.
• A point outside the limits means an assignable cause to investigate.
• Acceptance sampling: inspect a sample of n and accept the lot if defects ≤ c. The OC curve shows the probability of accepting lots of each quality. Producer's risk α (rejecting a good lot), consumer's risk β (accepting a bad lot).

Worked example

Observed time 2.0 min, rating 110%, allowances 10%.

• Normal time = 2.0 × 1.10 = 2.2 min. Standard time = 2.2 × 1.10 = 2.42 min.

Practice