(a) (i) How does the balancing line reduce the cost of idleness? Describe the steps involved in solving a line balancing problem…

(a)(i) Line balancing and the cost of idleness

Line balancing assigns tasks to workstations so that each station's work content is close to the cycle time, which cuts waiting time and so the cost of idle labour and machines. Steps: (1) list tasks, times and precedence; (2) compute cycle time = available time ÷ required output; (3) find the minimum stations = total task time ÷ cycle time, rounded up; (4) assign tasks using a rule such as longest task time or ranked positional weight, within precedence and cycle time; (5) compute efficiency = total task time ÷ (stations × cycle time), and idle time; (6) rebalance until efficiency is satisfactory.

(a)(ii) Deming's 85 per cent and World Class Manufacturing

Deming held that most defects arise from the system (design, equipment, materials, methods, training and targets), which only management can change, not from workers' carelessness. World Class Manufacturing (JIT, TQM, TPM, lean) accepts this: managers must build quality into process and product design, develop suppliers, invest in training and maintenance, and remove fear. The 85% figure is a rule of thumb, not a measured constant, and workers still own the remaining special causes. The statement is broadly valid.

(a)(iii) Six Sigma belts in a software firm

Six Sigma aims at about 3.4 defects per million opportunities through DMAIC. Green Belts, part-time, work on defined projects such as reducing defects in code reviews and testing, and collect data. Black Belts lead projects full-time, apply advanced statistics, and coach Green Belts. Master Black Belts train and mentor the Black Belts, choose projects aligned with strategy, and guide the quality programme at firm level.

(a)(iv)(A) Network diagram

Arrows (nodes): A 1→2 (11); B 2→3 (10); C 2→4 (8); D 2→5 (5); E 3→6 (6); F 4→6 (9); G 5→7 (2); H 6→7 (7); I 7→8 (12); J 7→9 (5). Earliest event times: node 1 = 0; node 2 = 11; node 3 = 21; node 4 = 19; node 5 = 16; node 6 = max(27, 28) = 28; node 7 = max(35, 18) = 35; node 8 = 47; node 9 = 40.

(a)(iv)(B) Critical path

The longest path is 1 → 2 → 4 → 6 → 7 → 8, that is A–C–F–H–I: 11 + 8 + 9 + 7 + 12 = 47. The project takes 47 time units. B and E have a float of 1, D and G 17, and J 7.

(b)(i) Rank correlation

d = efficiency rank − service rank: A −1, B 1, C −2, D 2, E −4, F −2, G 0, H 2, I 5, J −1, K 1, L 1. Σd² = 1 + 1 + 4 + 4 + 16 + 4 + 0 + 4 + 25 + 1 + 1 + 1 = 62.

Ties need a correction of m(m² − 1)/12: for three tied efficiency ranks (5), 2; for the service ranks 7, 7 and 11, 11, 0.5 each. Total correction = 3, so Σd² + correction = 65.

ρ = 1 − 6 × 65 ÷ (12 × 143) = 1 − 0.227 ≈ 0.77 (0.78 without the correction). Efficiency and length of service are positively and fairly strongly associated.

(b)(ii) Central limit theorem and standard error

Tenets of the CLT: for random samples of size n from a population with mean μ and variance σ², the sampling distribution of the sample mean tends to a normal distribution as n grows (usually n ≥ 30), whatever the population shape; its mean is μ and its standard deviation is σ/√n.

Standard error is the standard deviation of the sampling distribution of a statistic, for the mean σ/√n (estimated by s/√n). It shows how much a sample statistic varies from sample to sample and falls as the sample grows.

Utility in testing: the test statistic is Z or t = (x̄ − μ₀)/SE, which turns a sample difference into units of chance variation; it fixes critical regions and p-values, builds confidence intervals, and helps plan sample size for the desired precision.

(c)(i) Importance of ERP

ERP puts finance, production, purchasing, sales, HR and logistics on a single integrated database, giving real-time, consistent information. It removes duplicate entry, cuts inventory and lead times, speeds closing of accounts, improves customer service and compliance, standardises processes across units, and gives better data for decisions and scaling.

(c)(ii) Economic aspects and hidden costs

Visible costs: software licences or subscriptions, hardware or cloud, consultants, and training. Benefits: lower inventory and working capital, shorter cycle times, productivity and better decisions; judged by total cost of ownership, payback and ROI over the life cycle.

Hidden costs: customisation and integration with legacy systems, data cleaning and migration, extensive testing, staff time and backfill during training, business process re-engineering, key-staff turnover, productivity dip after go-live, ongoing support and upgrades, and consultant overruns.

(c)(iii) Three ERP implementation strategies

Big-bang: all modules and sites go live on one date. It is quick and avoids dual systems but carries high risk and disruption.

Phased: modules or locations are introduced stage by stage. It spreads risk and learning but takes longer and needs temporary interfaces.

Parallel run: old and new systems run together for a period and results are compared. It is the safest but costly and a burden on staff.

The choice depends on size, risk appetite, the number of units and readiness; some firms pilot a unit first.