Industrial Engineering and Operations Research
This domain tests your ability to model a production or service system, solve or bound the model, and translate the answer into a management decision. Method study, work measurement, queueing, linear programming and simulation are the recurring themes.
Work measurement and line balancing
- Standard time = observed time × rating factor × (1 + allowance fraction). Allowances cover personal needs, fatigue and unavoidable delay.
- Predetermined motion time systems (MTM, MOST) build times from basic motions and are used before a job exists, for example at design stage.
- Minimum stations N = ceil(Σ task times ÷ cycle time). Line efficiency = Σt /(N × cycle time); balance delay = 1 − efficiency. The rank-positional-weight heuristic assigns the highest-weight eligible task first.
Queueing
- For M/M/1 with arrival rate λ and service rate μ: ρ = λ/μ, Lq = ρ²/(1 − ρ), Wq = ρ/(μ − λ), W = 1/(μ − λ), and Little's law L = λW links all four.
- M/M/c uses the Erlang C formula. Where arrivals or service are not exponential, discrete-event simulation replaces the formula, with output reported as a confidence interval over replications.
Linear programming and sensitivity
- Formulate decision variables, objective and constraints explicitly, then check the solution against reality.
- The dual value (shadow price) is the marginal change in the objective per extra unit of a binding resource, valid only within the reported allowable increase or decrease.
- Integer and binary formulations handle assignment (one task to one machine), knapsack and fixed-charge decisions; LP relaxation gives a bound, not the answer.
Worked example
A service centre receives λ = 20 jobs/day and one technician completes μ = 25/day. ρ = 0.8, so Wq = 0.8/(25 − 20) = 0.16 days = about 1.28 hours, and Lq = λWq = 3.2 jobs waiting. Adding a second technician (M/M/2) would cut waiting sharply, but the decision needs the cost of idle capacity against the cost of 3.2 jobs in the queue per day - that comparison, not the queue length alone, is what earns the marks.
Traps that cost marks
- Mixing units (per hour versus per shift) or using W when Wq is asked.
- Quoting a shadow price beyond its allowable range, where the basis changes.
- Applying Little's law to an unstable system where ρ ≥ 1.
- Reporting a single simulation run as if it were a result.