Intermediate Industrial interview questions

150 questions with answers (IND-151 to IND-300). Try each one aloud before reading the answer.

Work Study & Ergonomics

IND-151 · How is standard time calculated? Give an example.

NT = observed time × rating, and ST = NT × (1 + allowance). Example: observed time 2.0 min, rating 110% and allowance 15% give NT = 2.2 min and ST = 2.2 × 1.15 = 2.53 min.

IND-152 · How do you decide the number of cycles to time in a stopwatch study?

n = (z·s / (a·x̄))², where s is the sample standard deviation, x̄ the mean element time, a the desired relative accuracy and z the confidence factor. For 95% confidence and ±5% accuracy, z = 1.96 and a = 0.05.

IND-153 · How is the sample size for work sampling calculated?

n = z²·p(1 − p)/e², where p is the estimated proportion and e the absolute accuracy. For p = 0.20, e = 0.03 and 95% confidence (z = 1.96): n = 3.8416 × 0.16 / 0.0009 ≈ 683 observations.

IND-154 · What are predetermined motion time systems (PMTS)?

PMTS build a task's normal time by adding tabulated times for basic motions such as reach, grasp and move. Examples are MTM, MOST and Work-Factor. In MTM, 1 TMU = 0.00001 h = 0.036 s.

IND-155 · What are the principles of motion economy?

They fall under three headings: use of the human body, workplace arrangement and tool design. Examples: both hands start and finish together and move symmetrically; tools have fixed locations within the normal work area; gravity-feed bins are used; holding is done by fixtures.

IND-156 · What is a left-hand/right-hand (two-handed) process chart?

A chart that records the activities of each hand side by side with process symbols. It exposes idle or holding hands so work can be balanced between them.

IND-157 · What is a SIMO chart?

A simultaneous motion cycle chart, built from micromotion (film or video) analysis. It records the therbligs of each hand on a common time scale and is used for very short, repetitive cycles.

IND-158 · What is a string diagram?

A scale plan on which a thread traces the paths of a worker or material between work points. The thread length gives the distance travelled, so layouts can be compared to reduce movement.

IND-159 · What is a man–machine (multiple activity) chart used for?

It plots the simultaneous activities of worker and machine on a common time scale over one cycle. It shows idle time for each and helps decide how many machines one operator can tend.

IND-160 · What are RULA and REBA?

Rapid Upper Limb Assessment and Rapid Entire Body Assessment are observational tools. They score posture, force and repetition to rank musculoskeletal-disorder risk and decide how urgently a task needs change.

IND-161 · What is the revised NIOSH lifting equation?

RWL = LC × HM × VM × DM × AM × FM × CM, with load constant LC = 23 kg. The multipliers reduce it for horizontal distance, vertical height, travel distance, asymmetry, frequency and coupling. Lifting Index = load ÷ RWL. LI > 1 indicates increased risk.

IND-162 · How are percentiles used in workplace design?

Clearances, such as door height and leg room, are designed for a large user, typically the 95th percentile. Reaches and controls are designed for a small user, typically the 5th percentile. Adjustable ranges cover 5th–95th.

IND-163 · What are common performance-rating systems?

Speed (pace) rating, the Westinghouse system (skill, effort, conditions, consistency), synthetic rating against PMTS values, and objective rating (pace plus a job-difficulty adjustment).

Production Planning & Control

IND-164 · What are the main aggregate planning strategies?

A chase strategy varies output, through hiring, layoffs or overtime, to match demand. A level strategy keeps output constant and uses inventory or backorders to absorb fluctuations. A mixed strategy combines both at minimum total cost.

IND-165 · How does MRP calculate net requirements and planned orders?

Net requirement = gross requirement − projected on-hand − scheduled receipts (+ safety stock). Net requirements are lot-sized into planned order receipts, then offset by the lead time to give planned order releases.

IND-166 · What lot-sizing rules are used in MRP?

Lot-for-lot (order exactly the net requirement), fixed order quantity or EOQ, period order quantity (POQ), and dynamic methods such as Silver–Meal, least unit cost, part-period balancing and the optimal Wagner–Whitin algorithm.

IND-167 · How does MRP II differ from MRP?

MRP II (manufacturing resource planning) extends MRP into a closed-loop system. It adds business and sales planning, capacity requirements planning, shop floor control and financial integration.

IND-168 · What is capacity requirements planning (CRP)?

CRP converts MRP planned and released orders into hours of load on each work centre by period, using routings and standard times. It compares the load with available capacity to reveal overloads.

IND-169 · What is Johnson's rule?

It minimizes makespan for n jobs on two machines in the same order. Pick the smallest remaining time. If it is on machine 1, schedule that job as early as possible; if on machine 2, as late as possible. Remove the job and repeat.

IND-170 · What are common priority dispatching rules?

FCFS (first come, first served), SPT (shortest processing time), EDD (earliest due date), LPT (longest processing time), CR (critical ratio) and minimum slack.

IND-171 · What does the SPT rule optimize on a single machine?

SPT minimizes mean flow time, mean waiting time, average number of jobs in the system and mean lateness. However, long jobs may be delayed badly.

IND-172 · What does the EDD rule optimize on a single machine?

EDD minimizes maximum lateness and maximum tardiness. It does not necessarily minimize the number of tardy jobs or the mean flow time.

IND-173 · What is the critical ratio rule?

CR = (due date − current date) ÷ remaining processing time. Jobs with the smallest CR go first. CR < 1 means the job is behind schedule.

IND-174 · What is rough-cut capacity planning (RCCP)?

RCCP checks whether the MPS is feasible against key or bottleneck resources, using bills of resources or load profiles, before detailed MRP and CRP are run.

IND-175 · What is the difference between utilization and efficiency in capacity terms?

Utilization = actual output ÷ design capacity. Efficiency = actual output ÷ effective capacity. Efficiency is always ≥ utilization because effective capacity ≤ design capacity.

IND-176 · What is Drum–Buffer–Rope scheduling?

A Theory of Constraints method. The drum is the bottleneck schedule that sets the pace. The buffer is a time buffer that protects the bottleneck from starving. The rope ties material release to the drum, which limits WIP.

Inventory Management

IND-177 · What is the EOQ formula?

EOQ = √(2DS/H), where D is annual demand (units/yr), S the cost per order and H the holding cost per unit per year. It minimizes the sum of annual ordering and holding costs.

IND-178 · What is the total annual cost in the basic EOQ model?

TC = (D/Q)·S + (Q/2)·H + D·C, where C is the unit price. At Q = EOQ, the annual ordering cost equals the annual holding cost.

IND-179 · Calculate EOQ for D = 1,000 units/yr, S = $50 per order and H = $4/unit/yr.

EOQ = √(2 × 1000 × 50 / 4) = √25,000 ≈ 158 units. Orders per year ≈ 1000/158 ≈ 6.3.

IND-180 · What is the economic production quantity (EPQ)?

For gradual replenishment at production rate p > demand rate d: EPQ = √(2DS / (H(1 − d/p))). Maximum inventory = Q(1 − d/p), so EPQ exceeds EOQ.

IND-181 · What are the assumptions of the basic EOQ model?

Demand is known and constant, lead time is constant, replenishment is instantaneous, there are no stockouts, there are no quantity discounts, ordering and holding costs are constant, and there is a single item.

IND-182 · How is safety stock calculated when demand is variable?

With constant lead time L and daily demand standard deviation σ_d: SS = z·σ_d·√L, where z sets the service level (z = 1.645 for 95%). ROP = d̄·L + SS.

IND-183 · What is service level in inventory control?

Cycle service level is the probability of no stockout during a replenishment cycle. Fill rate is the fraction of demand met directly from stock. For the same safety stock, fill rate is usually higher than cycle service level.

IND-184 · How do you solve an EOQ problem with quantity discounts?

For each price break, compute the EOQ. If it falls below the break quantity, raise it to the minimum quantity for that price. Compute total cost including purchase cost for each candidate and pick the lowest.

IND-185 · What is the newsvendor model?

A single-period model for perishable or seasonal items. The optimal order Q* satisfies P(D ≤ Q*) = Cu/(Cu + Co), where Cu is the underage cost (lost margin) and Co the overage cost (unit cost − salvage).

IND-186 · How is the order-up-to level set in a periodic review system?

S = d̄(R + L) + z·σ_d·√(R + L), where R is the review interval and L the lead time. At each review, order S − inventory position. Protection must cover R + L, not just L.

IND-187 · What is the difference between inventory position and on-hand inventory?

Inventory position = on-hand + on-order (scheduled receipts) − backorders. Reorder decisions must use inventory position, otherwise duplicate orders are placed.

IND-188 · How sensitive is total cost to errors in EOQ?

Very little. If Q = k × EOQ, then relevant cost ÷ minimum = (k + 1/k)/2. Ordering twice the EOQ raises ordering plus holding cost by only 25%.

IND-189 · How are inventory turns and days of inventory related?

Days of inventory on hand = 365 ÷ annual inventory turns. For example, 8 turns per year ≈ 46 days of supply.

Operations Research

IND-190 · What are the steps of the simplex method?

Convert to standard form with slack variables and form the initial basic feasible solution. Select the entering variable (most negative Cj − Zj for maximization, or most positive reduced cost) and the leaving variable by the minimum ratio test. Pivot, and repeat until no improving variable remains.

IND-191 · What is the minimum ratio test in simplex?

Divide each RHS value by the corresponding positive coefficient in the entering column. The row with the smallest ratio leaves the basis, so all variables stay non-negative.

IND-192 · What is the Big-M method?

For ≥ or = constraints, artificial variables are added with a very large penalty M in the objective (−M for maximization). This drives them out of the basis. If an artificial remains positive at the optimum, the LP is infeasible.

IND-193 · What is the two-phase method?

Phase 1 minimizes the sum of artificial variables to find a basic feasible solution; a positive minimum means the LP is infeasible. Phase 2 drops the artificials and optimizes the original objective from that basis.

IND-194 · What is a shadow price?

The change in the optimal objective value per unit increase in a constraint's RHS, valid within the RHS's range of feasibility. It equals the optimal dual variable. A non-binding constraint has a shadow price of zero.

IND-195 · What is degeneracy in LP?

A basic feasible solution in which one or more basic variables equal zero. It arises from ties in the ratio test and can cause stalling or, rarely, cycling. Bland's rule prevents cycling.

IND-196 · How do you recognize unbounded and infeasible LPs?

Unbounded: an entering variable has no positive coefficient in its column, so there is no ratio test and the objective improves indefinitely. Infeasible: an artificial variable stays positive at the optimum of Phase 1 or Big-M.

IND-197 · How does Vogel's Approximation Method work?

For each row and column, the penalty is the difference between its two lowest costs. Allocate as much as possible to the lowest-cost cell of the row or column with the highest penalty, cross out the satisfied line and repeat.

IND-198 · What is the MODI (u–v) method?

An optimality test for transportation solutions. For basic cells, set uᵢ + vⱼ = cᵢⱼ with one u = 0. For non-basic cells, compute Δᵢⱼ = cᵢⱼ − (uᵢ + vⱼ). If all Δᵢⱼ ≥ 0 the solution is optimal (minimization); otherwise improve along a closed loop.

IND-199 · What is degeneracy in a transportation problem?

When the number of occupied cells is less than m + n − 1. A tiny allocation ε is placed in an independent empty cell so that the u–v values can be computed.

IND-200 · How do you handle an unbalanced assignment problem?

Add dummy rows or columns with zero cost to make the matrix square, then apply the Hungarian method. Jobs or workers assigned to dummies are left unassigned.

IND-201 · How do you solve a maximization assignment problem?

Convert it to minimization by subtracting every element from the largest element (or multiplying by −1). Then apply the Hungarian method.

IND-202 · Solve graphically: maximize Z = 3x + 2y subject to x + y ≤ 4, x + 3y ≤ 6, x, y ≥ 0.

The corners are (0,0), (4,0), (3,1) and (0,2), with Z = 0, 12, 11 and 4. The optimum is x = 4, y = 0, Z = 12.

Queueing Theory & Simulation

IND-203 · State Little's Law.

L = λW: the average number in the system equals the arrival rate times the average time in the system. Likewise, Lq = λWq for the queue alone. It holds for any stable system in steady state.

IND-204 · Why must ρ < 1 for a single-server queue to be stable?

If λ ≥ μ, customers arrive at least as fast as they can be served, so the queue grows without bound and there is no steady state.

IND-205 · What are P₀ and Pₙ for an M/M/1 queue?

The probability the system is empty is P₀ = 1 − ρ. The probability of n customers in the system is Pₙ = (1 − ρ)ρⁿ, a geometric distribution. The probability of more than n is P(N > n) = ρⁿ⁺¹.

IND-206 · How are Poisson arrivals related to exponential interarrival times?

If arrivals follow a Poisson process with rate λ, the times between arrivals are independent and exponentially distributed with mean 1/λ, and vice versa.

IND-207 · What is the memoryless property?

P(T > s + t | T > s) = P(T > t): the remaining time does not depend on the time already elapsed. The exponential is the only continuous distribution with this property.

IND-208 · What is the Erlang C formula used for?

It gives the probability that an arriving customer must wait in an M/M/c queue with unlimited waiting room. It is widely used to staff call centres.

IND-209 · How does M/D/1 compare with M/M/1?

With constant service times, Lq = ρ²/(2(1 − ρ)), exactly half the M/M/1 value. Removing service-time variability halves the queue.

IND-210 · What is the Pollaczek–Khinchine formula?

For an M/G/1 queue: Lq = (λ²σ² + ρ²) / (2(1 − ρ)), where σ² is the service-time variance. It shows that queue length rises with service variability.

IND-211 · Is one common queue better than separate queues for each server?

Yes. A single pooled queue feeding c servers (M/M/c) gives lower average waiting time than c separate M/M/1 queues with the same total load, because no server sits idle while customers wait elsewhere. It is also fairer.

IND-212 · What are the main steps of a simulation study?

Formulate the problem and objectives, build the conceptual model, collect input data and fit distributions, code the model, verify, validate, design experiments, make runs and replications, analyse output, then document and implement.

IND-213 · What is the difference between verification and validation of a simulation model?

Verification checks that the computer model is coded correctly and runs as intended. Validation checks that the model accurately represents the real system for the intended purpose.

IND-214 · What is the inverse transform method?

Generate U ~ Uniform(0,1) and set X = F⁻¹(U). For an exponential with rate λ: X = −ln(1 − U)/λ, or equivalently −ln(U)/λ.

IND-215 · What is a warm-up period in simulation?

The initial transient period, when the model starts empty and idle, is discarded before collecting statistics. This removes initialization bias from steady-state estimates.

Statistical Quality Control

IND-216 · When do you use an X̄–R chart and when a p-chart?

X̄–R charts are for variables data: X̄ monitors the process mean and R monitors the spread within subgroups. A p-chart is for attributes data and monitors the proportion defective.

IND-217 · What are the control limits for X̄ and R charts?

X̄ chart: X̿ ± A₂R̄. R chart: UCL = D₄R̄ and LCL = D₃R̄. For subgroup size n = 5, A₂ = 0.577, D₃ = 0 and D₄ = 2.114.

IND-218 · What are the control limits for a p-chart?

p̄ ± 3√(p̄(1 − p̄)/n), where p̄ is the average fraction defective and n the sample size. A negative LCL is set to zero.

IND-219 · What are the control limits for a c-chart?

c̄ ± 3√c̄, where c̄ is the average number of defects per unit. This follows from the Poisson property that variance equals the mean.

IND-220 · What is the difference between an np-chart and a p-chart?

An np-chart plots the number of defectives and needs a constant sample size: limits np̄ ± 3√(np̄(1 − p̄)). A p-chart plots the proportion defective and can handle variable sample sizes.

IND-221 · What is a u-chart?

A chart for defects per unit when the sample size or inspection area varies. Its limits are ū ± 3√(ū/nᵢ), so they change with each sample size nᵢ.

IND-222 · What are Cp and Cpk?

Cp = (USL − LSL)/6σ measures potential capability, ignoring centring. Cpk = min(USL − μ, μ − LSL)/3σ accounts for the location of the mean. Cpk = Cp only when the process is centred.

IND-223 · What are the Western Electric rules?

Out-of-control signals: one point beyond 3σ; two of three consecutive points beyond 2σ on the same side; four of five beyond 1σ on the same side; eight consecutive points on one side of the centre line.

IND-224 · Why are control limits usually placed at ±3σ?

For a normal statistic, ±3σ gives a false-alarm probability of about 0.27% per point (ARL₀ ≈ 370). This balances unnecessary investigations against detection of real shifts.

IND-225 · What is the difference between single and double sampling plans?

Single sampling takes one sample of size n and accepts if defectives d ≤ c. Double sampling takes a smaller first sample and decides, or takes a second sample if results are borderline. It gives a lower average sample number for very good or very bad lots.

IND-226 · What are AOQ and AOQL?

Average outgoing quality (AOQ) is the expected fraction defective after rectifying inspection, where rejected lots are 100% screened. AOQ ≈ Pa·p. AOQL is the maximum AOQ over all incoming quality levels, which is the worst-case average outgoing quality.

IND-227 · When is an X̄–s chart preferred over an X̄–R chart?

When subgroup sizes are large (commonly n > 10) or variable. The standard deviation uses all data points and estimates σ more efficiently than the range, which uses only two.

IND-228 · What is rational subgrouping?

Forming subgroups, such as consecutive parts made close together in time, so that within-subgroup variation reflects only common causes. Assignable causes then show up as variation between subgroups.

Six Sigma

IND-229 · What is Six Sigma and what is DMAIC?

Six Sigma is a data-driven method for reducing variation and defects, targeting 3.4 defects per million opportunities. Its improvement cycle is DMAIC: Define, Measure, Analyze, Improve, Control.

IND-230 · Why does Six Sigma equal 3.4 DPMO rather than about 0.002 ppm?

A centred ±6σ process gives about 0.002 ppm. Six Sigma assumes the mean drifts 1.5σ over the long term, leaving 4.5σ to the nearest limit. The one-tail area beyond 4.5σ is 3.4 ppm.

IND-231 · What DPMO corresponds to 3σ, 4σ and 5σ (with the 1.5σ shift)?

Approximately 66,807 DPMO at 3σ, 6,210 at 4σ, 233 at 5σ and 3.4 at 6σ.

IND-232 · What is rolled throughput yield (RTY)?

RTY is the probability that a unit passes through all process steps defect-free the first time. It is the product of the first-pass yields of the steps. For steps of 95%, 90% and 98%, RTY = 0.95 × 0.90 × 0.98 ≈ 83.8%.

IND-233 · What is a Gage R&R study?

A measurement system analysis that splits measurement variation into repeatability (equipment variation, one appraiser) and reproducibility (variation between appraisers). Common guidance: %GRR < 10% acceptable, 10–30% conditionally acceptable, > 30% unacceptable.

IND-234 · What is FMEA and how is RPN calculated?

Failure Mode and Effects Analysis systematically lists potential failure modes, their effects and causes. Risk Priority Number = Severity × Occurrence × Detection, each rated 1–10, so RPN ranges from 1 to 1000.

IND-235 · How is hypothesis testing used in the Analyze phase?

It tests whether an observed difference or relationship is statistically significant. If the p-value < α (commonly 0.05), H₀ is rejected. Common tests: t-tests for means, ANOVA for several means, chi-square for proportions, F-test for variances.

IND-236 · What is design of experiments (DOE)?

DOE changes several input factors together in a planned way and measures their main effects and interactions with few runs. A 2ᵏ full factorial tests k factors at two levels in 2ᵏ runs, and fractional factorials reduce the runs further.

IND-237 · What is Lean Six Sigma?

An integrated approach that combines lean's focus on speed, flow and waste elimination with Six Sigma's statistical reduction of variation and defects, usually within the DMAIC framework.

IND-238 · What is a control plan?

A Control-phase document that lists, for each critical characteristic, the specification, measurement method, sample size, frequency, control method and reaction plan. It keeps the gains of a project.

IND-239 · What is the 5 Whys technique?

Asking "why?" repeatedly, typically about five times, to move from a symptom to the underlying root cause. It is simple, but it works best when backed by data.

IND-240 · A process has 50 defects in 500 units with 4 opportunities each. What is the DPMO?

DPMO = 50 / (500 × 4) × 10⁶ = 25,000. The yield is 97.5% (z ≈ 1.96), which is a sigma level of about 3.5 including the 1.5σ shift.

Lean Manufacturing & TPM

IND-241 · Calculate OEE for availability 90%, performance 95% and quality 98%.

OEE = 0.90 × 0.95 × 0.98 ≈ 0.838, or 83.8%.

IND-242 · What are the six big losses in TPM?

Availability losses: breakdowns, setups and adjustments. Performance losses: minor stops and idling, reduced speed. Quality losses: startup rejects and production rejects or rework.

IND-243 · What is SMED?

Single-Minute Exchange of Dies (Shingo) reduces changeover time to under 10 minutes. Separate internal (machine stopped) from external (machine running) setup, convert internal to external, then streamline both.

IND-244 · What is heijunka?

Production levelling: smoothing both the volume and the mix of products over time, for example A-B-A-C-A-B instead of large batches. It gives steady demand on upstream processes.

IND-245 · What is jidoka?

"Automation with a human touch": machines or operators stop the process automatically when an abnormality occurs and signal it, for example with an andon light. This prevents defects from passing downstream.

IND-246 · How is the number of kanbans calculated?

N = D × L × (1 + α) / C, where D is the demand rate, L the replenishment lead time (including waiting), α the safety factor and C the container quantity. Round up.

IND-247 · What are the pillars of TPM?

Autonomous maintenance, planned maintenance, focused improvement (kobetsu kaizen), quality maintenance, early equipment management, training and education, safety–health–environment, and office (administrative) TPM, all built on a 5S foundation.

IND-248 · How is inherent availability related to MTBF and MTTR?

Availability = MTBF / (MTBF + MTTR). For example, MTBF = 190 h and MTTR = 10 h give A = 95%.

IND-249 · Calculate takt time for 450 minutes available per shift and demand of 900 units per shift.

Takt time = 450 / 900 = 0.5 min = 30 seconds per unit.

IND-250 · How do takt time, cycle time and lead time differ?

Takt time is the required pace set by customer demand. Cycle time is the actual time between successive units leaving a process (it must be ≤ takt). Lead time is the total time one unit takes to pass through the whole value stream.

IND-251 · What is gemba?

Gemba is "the real place" where value is created, such as the shop floor. A gemba walk means managers go and see the actual process and talk to the people doing the work, rather than relying on reports.

IND-252 · What is one-piece flow?

Moving parts one at a time from step to step without batching. It minimizes WIP and lead time and reveals defects immediately. It requires short setups and balanced operations.

Supply Chain & Logistics

IND-253 · What is the SCOR model?

The Supply Chain Operations Reference model describes supply chains through core processes: Plan, Source, Make, Deliver, Return and Enable. It provides standard metrics and best practices for benchmarking.

IND-254 · What is the push–pull boundary (decoupling point)?

The point in the supply chain where operations switch from forecast-driven (push) to order-driven (pull). It is usually where strategic inventory is held, for example in assemble-to-order.

IND-255 · What is the difference between an efficient and a responsive supply chain?

Fisher's framework: functional products with stable demand need efficient, low-cost chains with high utilization and low inventory. Innovative products with uncertain demand need responsive chains with buffer capacity, speed and flexibility.

IND-256 · What is risk pooling?

Aggregating demand across locations or products reduces relative variability. For n independent, identical demands, pooled σ = √n·σ instead of n·σ, so centralization needs less total safety stock.

IND-257 · What is the square-root law for inventory?

Total safety stock is roughly proportional to the square root of the number of stocking locations. Consolidating from n to m warehouses changes inventory by a factor of about √(m/n).

IND-258 · What is CPFR?

Collaborative Planning, Forecasting and Replenishment: trading partners jointly develop plans and forecasts and share replenishment decisions. This reduces forecast error, inventory and stockouts.

IND-259 · What is a milk run?

A pick-up or delivery route on which one vehicle visits several suppliers or customers in a fixed sequence on a fixed schedule. Small, frequent loads are consolidated into one efficient trip.

IND-260 · How is a weighted scoring model used for supplier selection?

Assign weights to criteria such as quality, cost, delivery and service, rate each supplier on each criterion, multiply rating by weight and sum. The highest total score is preferred.

IND-261 · What is landed cost?

The total cost of getting a product to the buyer's location: purchase price + freight + insurance + duties and taxes + handling and brokerage. It is the right basis for comparing domestic and overseas suppliers.

IND-262 · What is the cash-to-cash cycle time?

Cash-to-cash = days inventory outstanding + days sales outstanding − days payables outstanding. It measures how long cash is tied up in operations. Shorter is better.

IND-263 · What is the centre-of-gravity method?

A location heuristic: Cx = ΣxᵢVᵢ/ΣVᵢ and Cy = ΣyᵢVᵢ/ΣVᵢ, where Vᵢ is the volume shipped to or from point (xᵢ, yᵢ). It gives a good starting site for a distribution centre.

IND-264 · What is the Kraljic matrix?

A purchasing portfolio tool that classifies items by profit impact and supply risk into four groups: strategic (partner), leverage (exploit buying power), bottleneck (secure supply) and non-critical (simplify).

Facility Layout & Material Handling

IND-265 · How are line efficiency and balance delay calculated?

Line efficiency = Σtᵢ / (n × C) × 100%, where Σtᵢ is the total work content, n the number of stations and C the cycle time. Balance delay = 100% − efficiency.

IND-266 · What is the theoretical minimum number of workstations?

N_min = ⌈Σtᵢ / C⌉: total task time divided by cycle time, rounded up. Precedence and zoning constraints may require more stations.

IND-267 · What is CRAFT?

Computerized Relative Allocation of Facilities Technique is an improvement heuristic. Starting from an initial layout, it tests pairwise (or three-way) department exchanges and keeps the one that most reduces Σ flow × distance × cost, until no exchange helps.

IND-268 · What is systematic layout planning (SLP)?

Muther's procedure. It uses flow analysis and an activity relationship (REL) chart with closeness ratings A (absolutely necessary), E, I, O, U (unimportant) and X (undesirable) to develop and evaluate alternative block layouts.

IND-269 · What is a from-to chart?

A matrix showing the material flow (trips or loads) between every pair of departments or machines. It is used to place high-flow pairs close together and to evaluate layouts.

IND-270 · What is the load–distance method?

Layouts or locations are compared by the total load–distance score Σ(load × distance) over all department pairs. The alternative with the lowest score minimizes material movement.

IND-271 · What is rank order clustering?

King's algorithm for cell formation. Rows and columns of a binary machine–part incidence matrix are repeatedly sorted by their binary weights until block-diagonal clusters appear. These are the machine cells and part families.

IND-272 · What is the unit load principle?

Material should be moved in the largest practical unit load, such as a pallet, tote or container, rather than as individual items. This reduces the number of handling moves and the damage.

IND-273 · Name some key principles of material handling.

Planning, standardization, work (minimize moves), ergonomics, unit load, space utilization, system integration, automation, environmental impact and life-cycle cost.

IND-274 · How is the factor-rating method used for facility location?

List relevant factors, assign weights summing to 1, score each site on each factor, compute the weighted sum for each site and select the highest. It mixes qualitative and quantitative factors.

IND-275 · What is locational break-even analysis?

Total cost (fixed + variable × volume) is plotted against volume for each candidate site. The site with the lowest cost at the expected volume is chosen, and crossover points show which volume range favours each site.

IND-276 · How should fast-moving items be placed in a warehouse?

Use ABC slotting: put the highest pick-frequency items in the most accessible locations, near the shipping dock and at waist height. This minimizes travel and picking time.

Project Management

IND-277 · What is the difference between CPM and PERT?

CPM uses deterministic activity durations and supports cost–time trade-offs (crashing). PERT uses probabilistic three-point estimates to compute expected durations and the probability of meeting a deadline.

IND-278 · How are expected time and variance calculated in PERT?

tₑ = (a + 4m + b)/6 and σ = (b − a)/6, so σ² = ((b − a)/6)², where a is optimistic, m most likely and b pessimistic. These assume a beta distribution.

IND-279 · What are the forward and backward passes?

The forward pass computes earliest start and finish: ES = max EF of predecessors, EF = ES + t. The backward pass computes latest finish and start: LF = min LS of successors, LS = LF − t.

IND-280 · What is the difference between total float and free float?

Total float = LS − ES = LF − EF: the delay possible without delaying the project. Free float = min ES of successors − EF: the delay possible without delaying any successor's early start.

IND-281 · How is the probability of completing a project by a deadline calculated in PERT?

Z = (T − Tₑ)/σ_cp, where Tₑ is the sum of tₑ on the critical path and σ_cp = √(Σσ² of critical activities). The probability is read from the standard normal table.

IND-282 · What is the cost slope in crashing?

Cost slope = (crash cost − normal cost) / (normal time − crash time): the extra cost per unit of time saved. Crash the critical activity with the lowest cost slope first.

IND-283 · What is the difference between resource levelling and resource smoothing?

Resource levelling adjusts start dates to resolve over-allocation and may extend the project end date. Resource smoothing evens out resource use only within available float, without changing the project end date.

IND-284 · What are the basic earned value metrics?

PV (planned value), EV (earned value: budgeted cost of work performed) and AC (actual cost). CV = EV − AC, SV = EV − PV, CPI = EV/AC and SPI = EV/PV. CPI or SPI < 1 means over budget or behind schedule.

IND-285 · An activity has a = 2, m = 5 and b = 14 days. Find tₑ and σ.

tₑ = (2 + 4×5 + 14)/6 = 36/6 = 6 days. σ = (14 − 2)/6 = 2 days, so the variance is 4 days².

IND-286 · What are the four types of precedence relationships?

Finish-to-Start (most common), Start-to-Start, Finish-to-Finish and Start-to-Finish (rare). Leads and lags can be added to any of them.

IND-287 · What is critical chain project management?

Goldratt's TOC-based method. It schedules around both task and resource dependencies, removes safety time from individual tasks and pools it into a project buffer at the end and feeding buffers where non-critical chains join.

IND-288 · What is the difference between fast tracking and crashing?

Fast tracking shortens the schedule by doing sequential activities in parallel, which raises rework risk. Crashing shortens activities by adding resources, which raises cost.

Engineering Economics & Forecasting

IND-289 · What is the future value of $1,000 at 10% compound interest after 3 years?

F = P(1 + i)ⁿ = 1000 × 1.1³ = $1,331. With simple interest it would be $1,300.

IND-290 · What is the uniform-series present worth factor?

(P/A, i, n) = [(1 + i)ⁿ − 1] / [i(1 + i)ⁿ]. It converts an equal annual amount A over n years into its present worth P = A × (P/A).

IND-291 · How is straight-line depreciation calculated?

Annual depreciation D = (P − S)/n, where P is the first cost, S the salvage value and n the useful life. Book value falls linearly.

IND-292 · How is declining balance depreciation calculated?

Each year's depreciation Dₜ = d × book value at the start of year t. For double-declining balance, d = 2/n. Depreciation is front-loaded and book value never reaches zero on its own.

IND-293 · How is sum-of-years'-digits depreciation calculated?

Dₜ = [(n − t + 1) / (n(n + 1)/2)] × (P − S). For n = 5 the digits sum to 15, so year 1 gets 5/15 and year 5 gets 1/15 of the depreciable amount.

IND-294 · What is the effective annual interest rate for 12% compounded monthly?

i_eff = (1 + r/m)ᵐ − 1 = (1 + 0.12/12)¹² − 1 ≈ 12.68%.

IND-295 · Find the break-even volume for fixed cost $50,000, price $25/unit and variable cost $15/unit.

BEP = F/(p − v) = 50,000/(25 − 15) = 5,000 units, or $125,000 of revenue.

IND-296 · What is simple exponential smoothing?

Fₜ₊₁ = αAₜ + (1 − α)Fₜ, with smoothing constant 0 < α < 1. It weights past data with exponentially decreasing weights. A higher α responds faster but follows noise more.

IND-297 · What are MAD, MSE and MAPE?

MAD = Σ|error|/n. MSE = Σerror²/n, which penalizes large errors. MAPE = (Σ|error|/actual)/n × 100%, which is scale-free. All measure forecast accuracy, and lower is better.

IND-298 · What is a tracking signal?

Tracking signal = running sum of forecast errors (RSFE) ÷ MAD. It detects bias: values persistently outside limits such as ±4 indicate that the forecast consistently over- or under-predicts.

IND-299 · What is a weighted moving average?

A moving average with different weights for each past period, usually heavier for recent data, with weights summing to 1. For example, F = 0.5A₁ + 0.3A₂ + 0.2A₃, where A₁ is the most recent period.

IND-300 · How is linear regression used for forecasting?

Fit y = a + bx by least squares, where b = (nΣxy − ΣxΣy)/(nΣx² − (Σx)²) and a = ȳ − b·x̄. x may be time (trend projection) or a causal variable such as advertising spend.

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