Industrial Engineering: Quantitative Decision Models
Industrial Engineering in GATE PI tests the quantitative side of production systems: work measurement, inventory, forecasting, project scheduling, quality control and operations research models.
Work study and time standards
Standard time = observed time × performance rating × (1 + allowance). Allowances cover personal needs, fatigue and unavoidable delay and are applied after rating, never before. Method study uses therbligs and questioning techniques to eliminate motion before timing begins.
Inventory and forecasting
- Economic order quantity: EOQ = √(2DS/h), where h is holding cost per unit per year, not a percentage alone.
- Total annual cost at EOQ = √(2DSh); number of orders = D/EOQ.
- Reorder level = demand during lead time + safety stock.
- Exponential smoothing: F_{t+1} = αD_t + (1 − α)F_t; higher α tracks changes faster.
Project scheduling and quality
PERT expected time t_e = (a + 4m + b)/6 with variance ((b − a)/6)². Only critical-path variances combine for project variance. Process capability: C_p = (USL − LSL)/6σ and C_pk = min[(USL − μ)/3σ, (μ − LSL)/3σ].
Worked example
Annual demand D = 10,000 units, ordering cost S = Rs 200 per order, holding cost h = Rs 40 per unit-year. EOQ = √(2 × 10,000 × 200/40) = √100,000 ≈ 316 units. Orders per year = 10,000/316 ≈ 31.6. Minimum total cost = √(2 × 10,000 × 200 × 40) = √(1.6 × 10⁸) ≈ Rs 12,649.
Traps that cost marks
- Using a percentage holding cost without multiplying by unit price.
- Adding variances of non-critical activities to PERT project variance.
- Treating C_p as adequate when C_pk is low because the process is off-centre.
- Forgetting dummy activities when converting activity-on-arrow networks.