Short Answers — every unit

The three stages of the model

• Inputs — the resources consumed: material, machines, labour, management, capital and information.
• Transformation — the value-adding conversion itself, which may be physical (manufacturing), locational (transport), exchange (retail), physiological (healthcare), psychological (entertainment) or informational (communication).
• Outputs — the goods and services delivered, plus the feedback used to measure performance and correct the process.

Why the process must add value

• Value added = value of output − value of inputs; if it is not positive the firm is destroying value.
• Value added is what pays wages, profit and reinvestment, so it is the operations manager's scoreboard.
• Feedback closes the loop — measure the output, compare it with the standard, adjust the inputs or the process.

Why it matters to the business

• Operations holds most of the firm's people, assets and costs, so it is the single largest lever on profitability.
• It is one of the three core functions with marketing and finance — the other two cannot deliver without it.
• It is where strategy stops being a statement and becomes something the customer actually receives.

Example

• Manufacturing: a car plant converts steel, robots, labour and designs into finished cars — a physical transformation.
• Service: a hospital converts doctors, equipment and patients into treated, discharged patients — a physiological transformation.

Closing line: every organisation, factory or service, is a transformation process — which is exactly why operations management applies universally and not only to manufacturing.

The four internal linkages

• Marketing tells operations what the customer wants, in what volume and by when; operations tells marketing what it can realistically promise.
• Finance supplies the capital for capacity, equipment and inventory, and holds operations to a cost and return target.
• Human resources supplies the skills, training and staffing levels the chosen process needs.
• Suppliers feed the process; late or defective supply stops operations regardless of how well the plant is run.

The two kinds of decision operations makes

• Design issues — long-term, hard to reverse, capital-heavy: product and process design, capacity, location, layout, technology, quality system, job design.
• Operational control issues — short-term and repeated: forecasting, scheduling, loading and sequencing, inventory levels, maintenance, quality control.

Why the linkage matters

• An operations decision taken alone will usually be wrong — a promise made by marketing that operations cannot meet destroys the customer relationship faster than a slow promise would have.
• Conflicts are structural, not personal: marketing wants variety, finance wants low inventory, operations wants stable runs. Resolving that trade-off is the point of operations strategy.

Example

• A smartphone launch date set by marketing fixes the capacity ramp for operations, the working-capital release by finance and the hiring plan by HR — one decision, four functions.

Closing line: operations is the technical core, but the core only performs when the functions around it agree on the same set of priorities.

Draw this table — the key answers this question with a table every time

The goods–service continuum

• Every offering is a bundle of a physical good and a service, and it sits somewhere on a line between the two extremes.
• Pure good end — steel, salt, sugar: almost no service content.
• Good with accompanying service — a car with warranty, installation and financing.
• Service with accompanying good — a restaurant meal: the food is a good, but the ordering, cooking, ambience and serving are the service.
• Pure service — teaching, consulting, counselling: no physical good changes hands.

Why the position on the continuum matters to operations

• The further towards services you sit, the less you can buffer with inventory — so capacity must be flexed to demand instead.
• High contact means the customer is inside the process, so process design becomes experience design and quality has to be measured by perception, not by gauge.

Closing line: a firm should manage the good part and the service part of its bundle with different operating rules — inventory and standardisation for the good, capacity and staff training for the service.

The stages, in order

• Craft production — skilled artisans making one unique item at a time; high customisation, very high cost per unit.
• Industrial Revolution (1770s onward) — the steam engine and the factory system replace hand tools; division of labour raises output.
• Scientific management (Taylor, Gilbreth, Gantt) — time and motion study, the one best method, standard times, the Gantt chart.
• Mass production (Ford, 1913) — the moving assembly line and interchangeable parts; huge volumes of a standard product at low unit cost.
• Operations research (1940s) — wartime mathematical methods: linear programming, queuing, simulation, inventory models.
• Quality revolution (1970s–80s) — Deming, Juran and Japanese manufacturers make quality a competitive weapon rather than an inspection cost.
• Lean / JIT (Toyota Production System) — eliminate waste, pull production, small lots, continuous improvement.
• Globalisation and digitisation (1990s onward) — global supply chains, ERP, e-commerce, analytics and automation.

The two challenges facing operations managers today

• Rising customer expectations — customers now want variety, speed, low price and high quality simultaneously, so the old trade-offs are no longer accepted.
• Environmental and sustainability pressure — resource depletion, waste and emissions, urbanisation and regulation force operations to design for reuse, energy efficiency and reverse logistics.

Example

• Ford's Model T is the mass-production milestone; Toyota's TPS is the lean milestone; Amazon's fulfilment network is the digitised-globalisation milestone.

Closing line: the direction of travel is constant — each stage bought more variety and responsiveness without giving up the cost advantage of the stage before it.

The three levels of measure

• Single-factor (partial) productivity — output divided by one input, usually labour. Easy to compute and to communicate, but it can be improved simply by substituting capital for labour, which is not a real gain.
• Multifactor productivity — output divided by a group of inputs. It stops the substitution illusion and shows whether the firm is genuinely more efficient.
• Total-factor productivity — output over all inputs. The truest measure, and the hardest to compile because everything must be converted into common money terms.

Why the indices matter — the significance the key asks for

• They measure efficiency of converting labour, material and capital into output, so waste becomes visible as a number.
• They locate the problem: comparing partial indices tells the manager which resource is being used badly.
• They allow benchmarking — against last year, against another plant, against a competitor or an industry norm.
• Rising productivity means lower unit cost, which funds either a price cut or a higher margin — this is the link to competitiveness.
• They support capacity, staffing and wage decisions, because they convert operational effort into a comparable ratio.
• At national level, productivity growth is what raises the standard of living.

How to read a value — this is what the application question will ask

• An index above 1.0 or rising means output is growing faster than the resources consumed: the process is improving.
• Labour productivity up but multifactor flat means the firm has bought machines, not efficiency.
• A falling index with steady output means input creep — overtime, scrap, rework or idle capacity.

Example

• A plant producing 10,000 units with 500 labour hours has a labour productivity of 20 units/hour. If output rises to 12,000 units on the same hours, productivity is 24 units/hour — a 20 % gain, achieved with no extra resource.

Closing line: productivity is the one number that connects what happens on the shop floor to the firm's cost position in the market, which is why it is measured continuously rather than annually.

How operations strategy contributes to competitiveness

• It aligns operations with the market. The firm competes on whatever the customer actually buys on — price, speed, quality or variety — and operations is configured for that, not for everything at once.
• It converts capability into advantage. A capability that is hard for rivals to copy (Toyota's changeover times, Amazon's fulfilment network) becomes a core competency and a durable edge.
• It makes the trade-offs deliberate. No process is simultaneously the cheapest, fastest, most flexible and highest quality; strategy chooses which to lead on and which to merely qualify on.
• It gives consistency across decisions. Capacity, location, layout, technology, sourcing, inventory and workforce decisions all point the same way instead of cancelling each other out.
• It lowers cost through efficiency, not through cuts. Better layout, fewer defects and shorter lead times reduce cost while improving service.
• It makes the firm responsive. Shorter lead times and flexible capacity let it react to demand shifts faster than rivals can.

The two strategies to explain (pick these — the key names them)

• Quality-based strategy. Superior product or service quality is the primary competitive edge. It works through design quality (features the customer values) and conformance quality (consistently meeting the specification). Fewer defects mean less rework, less warranty cost and a stronger brand — quality pays for itself. Example: Toyota and Lexus.
• Time-based strategy. The firm competes on speed — rapid order fulfilment, short lead times, fast product development and quick response to market change. It is delivered through process simplification, concurrent (parallel) activities, supplier integration and eliminating waiting. Example: Zara moving a design to store in weeks, or Amazon same-day delivery.

The nine decision areas operations strategy must make consistent

• Products and services · processes and technology · capacity · facilities (location) · layout · human resources and job design · quality system · sourcing and supply chain · operating systems (planning and inventory).

Closing line: operations strategy is what stops a good corporate plan from failing at the point of delivery — it is the translation of intent into capability.

The four terms, defined

Core competency

• What the firm does better than any competitor, built from a combination of skills, processes and technology rather than a single asset.
• To count as a core competency it must give access to many markets, contribute clearly to customer benefit, and be hard to imitate.
• It is the thing you build the operations strategy around and outsource everything else away from.

Order qualifiers vs order winners

• Order qualifiers are the minimum characteristics that get the firm onto the customer's shortlist — safety in a car, hygiene in a restaurant, a working app in a bank. They must be met, but exceeding them wins nothing.
• Order winners are the criteria on which the customer finally chooses — price, delivery speed, styling, customisation. This is where operations should invest.
• They change over time: yesterday's winner becomes today's qualifier once rivals match it. Reliability in cars was once a winner; it is now a qualifier.

Worked example — a startup, written the way the question asks

• Vision — "To make fresh, home-style meals the default lunch choice of every office worker in the city."
• Mission — "We prepare hygienic, nutritionally balanced meals in cloud kitchens and deliver them within 30 minutes of the lunch window, at a price working professionals can pay daily."
• Strategy — locate small cloud kitchens inside a 3 km delivery radius (facility decision), keep a fixed rotating menu to allow batch cooking (process decision), and cook to a forecast released two hours before the window (planning decision).
• How it guides action: the 30-minute promise is the order winner, so the location and layout decisions are made to protect delivery time even at higher rent; hygiene and taste are qualifiers, so they are controlled by standard recipes and audits but not advertised as the differentiator.

Closing line: vision sets the destination, mission defines the daily job, and the order winner tells operations which of its many possible improvements is the one worth paying for.

The four positions

• Competing on cost. Eliminate waste, invest in high-volume standardised processes, drive high capacity utilisation and tight cost control. Requires scale and stable demand. Example: Big Bazaar, IndiGo, Xiaomi.
• Competing on speed (time-based competition). Compress order-to-delivery time and product-development time by running activities in parallel, simplifying processes and integrating suppliers. Example: Zara, Amazon, Domino's 30-minute promise.
• Competing on quality. Deliver either superior design quality (features and performance the customer values) or superior conformance quality (no defects, every time). Example: Apple on design, Toyota on conformance.
• Competing on flexibility. Produce a wide variety, or change volume quickly, without a cost penalty — achieved by fast changeovers, cellular layouts, cross-trained staff and modular design; at its extreme this becomes mass customisation. Example: Dell's configure-to-order PCs, Nike By You.

How the choice changes the operation

• Cost leadership pushes towards product layout, mass production, high utilisation and low variety.
• Flexibility pushes towards process or cellular layout, general-purpose machines and skilled labour.
• Speed pushes towards buffer capacity, decentralised facilities near the customer and shorter supply chains.
• Quality pushes towards process control, supplier development, training and prevention spending.

The trade-off, and how modern firms soften it

• Classically you cannot lead on all four at once — high utilisation kills flexibility, wide variety raises cost.
• Modern practice softens the trade-off through lean methods, flexible automation, modular design and postponement (adding variety as late as possible in the process).

Closing line: positioning is not about being good at one thing and bad at the rest — it is about deciding which one you will be measured on, and qualifying comfortably on the others.

Policy deployment (hoshin kanri)

• Converts a small number of strategic objectives into specific action plans with owners, measures and deadlines at each level.
• Works by catchball — goals are passed down and commitments passed back up, so each level agrees what it can deliver instead of being told.
• Deliberately limits the number of priorities, so the organisation works on a few things that matter rather than everything at once.
• Reviewed on a fixed cycle, so the plan is corrected during the year rather than judged at the end of it.

The balanced scorecard (Kaplan & Norton) — four perspectives

• Financial — how do we look to shareholders? Revenue, margin, return on assets.
• Customer — how do customers see us? On-time delivery, satisfaction, retention, complaints.
• Internal business process — what must we excel at? Cycle time, defect rate, utilisation, productivity.
• Learning and growth — can we continue to improve? Training hours, employee skills, new-product introductions.

Why both are needed

• Financial measures are lagging indicators — they tell you what already happened. The other three perspectives are leading indicators that tell you what is about to happen.
• Policy deployment answers "who does what"; the scorecard answers "how do we know it is working". Deployment without measurement drifts; measurement without deployment is a report nobody acts on.

Example

• A firm whose strategy is time-based competition deploys it as: customer perspective — cut order-to-delivery from 6 days to 3; internal process — cut changeover time by 50 %; learning — cross-train every operator on two machines; financial — hold unit cost flat while doing it.

Closing line: deployment is where most strategies actually fail — not in the choice, but in the failure to convert the choice into a measure somebody owns.

The five standard symbols

• Operation (circle) — work is done on the item; the only symbol that always adds value.
• Inspection (square) — the item is checked. Necessary, but it adds cost, not value.
• Transport (arrow) — the item moves. Pure waste in lean terms.
• Delay (D shape) — the item waits. Where most of the total flow time usually sits.
• Storage (triangle) — the item is held in inventory under control.

What flowcharting reveals

• The ratio of value-adding to total time, which is usually shockingly low — often under 10 %.
• Rework loops, duplicated inspections and unnecessary handoffs between departments.
• The bottleneck, once activity times are written on the chart.
• A swimlane (cross-functional) flowchart additionally shows who does each step, which exposes handoff delays between functions.

Types of processes

• Single-stage — one activity; multi-stage — several stages in sequence, which is where buffering, blocking and starving arise.
• Make-to-stock vs make-to-order — decided by whether production starts before or after the customer order (Topic 11).
• By volume and variety — project, job shop, batch, mass and continuous (Topic 28).

Example

• Flowcharting a hospital outpatient visit typically shows 15 minutes of operation (consultation, tests) inside a 3-hour flow time — the other 2 h 45 min is delay and transport, and that is where the improvement is.

Closing line: you cannot improve a process you have not drawn — the flowchart converts a vague complaint about slowness into a specific list of steps to remove.

The hybrid — assemble-to-order

• Common components are made to stock; final assembly waits for the order. This is postponement, and it gets MTS speed with MTO variety.
• The point in the process where the order takes over is the customer order decoupling point; everything upstream of it runs on forecast, everything downstream on the order.
• Example: Dell builds PCs to order from stocked modules; a car plant paints and trims to order from a stocked body shell.

How to choose

• Choose MTS when demand is predictable, variety is low and the customer will not wait.
• Choose MTO when the product is expensive, customised or perishable in specification, so holding it finished is too risky.

Closing line: the real decision is not MTS or MTO but where to place the decoupling point — as late as the customer's patience allows.

The three terms and what causes each

• Buffering — deliberate inventory placed between stages to absorb differences in speed and short stoppages, so one stage's problem does not immediately stop the next.
• Blocking — the downstream stage is slower or has stopped, and the buffer in front of it is full, so the upstream stage must halt even though it can still work.
• Starving — the upstream stage is slower or has stopped, so the downstream stage runs out of work and sits idle.
• Both blocking and starving are symptoms of the same underlying condition: unbalanced stage capacities and variability in processing times.

The trade-off buffers create

• Buffers raise utilisation and protect throughput by decoupling stages.
• But they cost money (working capital, space, handling) and they lengthen flow time — by Little's Law, more inventory at the same throughput rate means a longer wait.
• They also hide problems: with a big buffer, a machine that breaks down twice a shift is never noticed. This is why lean deliberately shrinks buffers to expose the defects underneath ("lowering the water to reveal the rocks").

How a manager fixes it

• Balance the line so stage capacities are closer together, rather than adding more buffer.
• Reduce variability — preventive maintenance, faster changeovers, standard work.
• Add capacity at the bottleneck only; adding it anywhere else just moves the blocking.

Example

• On a bottling line, if the labeller is slower than the filler, bottles pile up on the conveyor until it is full and the filler is blocked; the packer downstream then has nothing arriving in bursts and is starved.

Closing line: blocking and starving are not machine faults — they are design faults, and the cure is balance and lower variability, not a bigger buffer.

The rules that follow from the definition

• The process can never run faster than its bottleneck, however fast every other stage is.
• An hour lost at the bottleneck is an hour lost for the entire process; an hour lost at a non-bottleneck costs nothing.
• Improving a non-bottleneck stage does not increase output — it only builds inventory in front of the bottleneck.
• When the bottleneck is relieved, the constraint moves to another stage; bottleneck management is therefore continuous, not a one-off fix.

How to manage the bottleneck

• Never let it starve — keep a small buffer immediately in front of it.
• Do not process defects through it — inspect before the bottleneck, so its scarce time is never spent on a unit that will be scrapped.
• Take work off it — offload tasks to non-bottleneck stages, run it through breaks and shift changes, add a parallel machine, or outsource part of its load.
• Schedule the whole process to its drumbeat — release work at the bottleneck's rate, not at the first stage's rate.

Reading a utilisation figure

• Low utilisation at a non-bottleneck is normal and healthy, not a problem to be fixed.
• Utilisation pushed near 100 % everywhere produces long queues and long flow times, because there is no slack to absorb variability.

Example

• A burger line where grilling takes 30 s, assembly 20 s and packing 15 s has grilling as the bottleneck: process capacity is 2 burgers/minute, so buying a faster packer changes nothing.

Closing line: capacity decisions, staffing and improvement money should all be aimed at one place — the bottleneck — because that is the only stage where they change the output of the business.

The measures, in order of scope

• Setup time — preparing the machine for a new job; incurred once per batch, so it is the reason large batches exist.
• Run time — time actually processing the units in the batch.
• Operation time — setup plus run, i.e. the full time the machine is committed to the batch.
• Flow time / throughput time — the elapsed time from entering the process to leaving it, including every delay. This is what the customer experiences.
• Value-added time — only the portion of flow time in which the product is actually being changed.
• Cycle time — the interval between successive completions; it is set by the bottleneck.

Reading process velocity — the interpretation the exam wants

• Process velocity is always greater than 1, and the closer it is to 1 the leaner the process.
• A velocity of 20 means the unit spends nineteen-twentieths of its life waiting — the improvement target is the waiting, not the machine.
• Cutting setup time cuts the economic batch size, which cuts inventory, which cuts flow time — one lever, three effects.

Example

• A component with 4 hours of value-added work that takes 5 days (120 hours) to get through the shop has a process velocity of 30. Nothing about the machining needs to improve; the queues do.

Closing line: measuring only run time flatters the process — flow time is the honest measure, because it is the one the customer is waiting through.

What the law tells a manager

• The three quantities are locked together — you cannot change one without changing another. Any two of them determine the third.
• If throughput is fixed by demand, then the only way to cut waiting time is to cut work-in-process. This is the entire logic of lean and of small batch sizes.
• Conversely, if WIP is allowed to grow while throughput is unchanged, flow time must rise — which is why a busier-looking shop floor often serves customers more slowly.
• It gives a free measurement: count the units in the system and divide by the completion rate, and you have the average waiting time without timing anyone.

The three application patterns

• Given WIP and throughput, find flow time — "40 customers in the branch, 20 served per hour → each waits 2 hours."
• Given flow time target and throughput, find allowable WIP — "to hold the wait to 15 minutes at 20 per hour, no more than 5 people may be in the system."
• Given WIP and flow time, find throughput — used to check whether a process can meet a promised rate.

Example

• A bank processes 60 loan files a day and has 300 files in progress at any time. T = 300 / 60 = 5 days. To promise 2-day turnaround without hiring, work-in-process must be capped at 120 files — so the fix is to stop releasing new files, not to work faster.

Closing line: Little's Law is why controlling the amount of work released into a process is a more reliable way to shorten lead time than asking people to hurry.

Retail and service facilities — the key's own list

• Proximity to customers — as near as possible; footfall is the revenue driver. "Location is everything."
• Construction costs — less important, because the building is small relative to the revenue it generates.
• Land costs — usually high, and accepted as the price of the location.
• Labour costs — less important; staff numbers are small.
• Transportation — must be well connected: parking, public transport, last-mile access.
• Add: visibility, catchment population and income, competitor proximity, and complementary neighbours (a coffee shop next to a bookshop).

Heavy industry — the key's own list

• Construction costs — should be minimum; the plant is enormous.
• Land costs — should be minimum; large acreage is needed, so cheap peripheral land wins.
• Raw material and finished goods shipment modes — rail, port or pipeline access decides feasibility.
• Mode of transport — must be easily available and well connected.
• Proximity to raw materials — decisive when the material is bulky or loses weight in processing.
• Utilities — assured power, water and fuel in industrial quantities.
• Means of waste disposal — effluent treatment and environmental clearance.
• Labour availability at minimum wages — a large semi-skilled workforce at low cost.

The three levels the decision is taken at

• Regional / national — market access, labour climate, taxes and incentives, political stability, exchange rates.
• Community — labour pool and unionisation, local taxes, infrastructure, quality of life, supporting industry.
• Site — size, cost, access roads, utilities, zoning, room to expand.

Example

• Retail: a coffee chain pays premium mall rent because footfall is the business. Heavy: a steel plant sits at Jamshedpur near ore and coal, far from any customer, because moving raw material costs more than moving steel.

Closing line: the rule is simple — locate near the customer when the output is expensive to move or the customer must come to you; locate near the input when the raw material is expensive to move.

The five steps

• List the factors that genuinely affect this decision — labour, market access, utilities, taxes, quality of life.
• Assign each a weight reflecting its importance to the firm's strategy; the weights must sum to 1.00.
• Score every candidate site on every factor on a common scale (say 1–10 or 1–100).
• Multiply weight × score for each factor and sum down each site's column.
• Choose the highest total — but review the runner-up before committing.

Why the method is used — the "why this method" answer

• It is the only common technique that can handle intangible factors (quality of life, community attitude, political risk) alongside costs.
• It forces the decision-makers to state their priorities as numbers, which surfaces disagreement before the money is spent rather than after.
• It produces an auditable record of why a site was chosen — valuable for board approval.

Its limitations — say these to earn the analysis mark

• The weights and scores are subjective; different managers produce different winners from the same data.
• A close result is meaningless — if two sites are within a few points, the method has not decided anything and you should run a sensitivity check by varying the weights.
• It ignores the scale of differences: a site that is disastrous on one factor can still win on total score unless you set minimum thresholds.

Example

• If labour cost carries weight 0.30 and Site A scores 80 against Site B's 60, A gains 6 points on that factor alone — enough to decide the whole comparison if the other factors are close. The manager's real job is defending the 0.30.

Closing line: the number the method produces is only as good as the weights, so its real value is in making the priorities explicit, not in the arithmetic.

Centre-of-gravity — what it does and when to use it

• Places existing customers or suppliers on a coordinate grid, weights each by the volume shipped, and returns the weighted average position — the point that minimises total weighted distance.
• Use it when the sites are not yet chosen and transport cost per unit-distance is roughly the same in all directions — typically siting a distribution centre or warehouse among known demand points.
• It is a starting point, not an answer: the computed coordinates often land in a river or a residential zone, so the manager searches for real property near them.

Load–distance — what it does and when to use it

• Takes a shortlist of real candidate sites and, for each, sums load × distance over all the destinations it must serve.
• Use it when the shortlist already exists, or when the geography is irregular so straight-line coordinates would mislead.
• The LD value is a relative score, not a cost — it ranks sites, it does not price them.

Choosing between them — the comparison the exam wants

Example

• An e-commerce firm uses centre-of-gravity on its city-wise order volumes to find that its ideal national warehouse sits near Nagpur, then applies load–distance to three actual industrial plots around Nagpur to pick one.

Closing line: use centre-of-gravity to decide where to look, and load–distance to decide which of what you found to take.

The method

• Identify the fixed cost (land, building, rates, permanent staff) and the variable cost per unit (labour, material, utilities, transport) at each location.
• Write a total-cost line for each location and plot them all on the same axes — volume on the x-axis, total cost on the y-axis.
• The lower envelope of the lines shows which location is cheapest at each volume; the crossover points are the boundaries.
• Read off the expected volume and choose the location whose line is lowest there.

How to read the result

• Low fixed, high variable locations win at low volumes — leased premises, subcontracting, a low-automation site.
• High fixed, low variable locations win at high volumes — an owned, automated plant.
• If the expected volume sits close to a crossover, the two locations are effectively equal on cost and the decision should be made on qualitative factors instead.
• Some locations are never cheapest at any volume — they are dominated and can be dropped immediately.

Assumptions and limits

• Fixed costs are constant and variable cost per unit does not change with volume — both break down at very high volumes.
• Revenue is assumed to be the same at every location, which is false for retail, where location changes sales.
• It captures only cost, so it must be combined with factor rating for the intangibles.

Example

• Site A: FC ₹10,000, VC ₹5/unit. Site B: FC ₹40,000, VC ₹2/unit. They are equal at v = 30,000 / 3 = 10,000 units — below that choose A, above it choose B.

Closing line: the technique does not choose a location, it tells you which volume forecast you are betting on — so the real question becomes how confident you are in that forecast.

Why layout design matters in operations

• It ensures the optimal arrangement of resources so work flows smoothly, movement is reduced and delays are minimised.
• Material handling is pure cost — it adds no value at all — and layout is the single biggest lever on how much of it there is.
• It sets the flow time and the amount of work-in-process: longer travel means longer queues between stages.
• It determines effective capacity, because a badly placed bottleneck or a congested aisle caps throughput regardless of machine speed.
• It affects safety, ergonomics and employee morale — lighting, noise, walking distance and congestion are all layout outcomes.
• It governs space utilisation, and space is a fixed cost that is paid whether it is used well or not.
• It is expensive to change once machines are foundationed and services are laid, so the decision is effectively long-term.
• In services it is also a marketing decision: the layout is part of what the customer experiences and buys.

The objectives, stated as a list

• Minimise material handling and travel distance · eliminate bottlenecks · maximise use of space, labour and equipment · provide flexibility for future change · ensure worker safety and comfort · facilitate communication and supervision · maintain quality by keeping incompatible activities apart.

Closing line: layout is where operations strategy becomes concrete — the same machines arranged differently give a completely different cost, speed and flexibility profile.

Fixed-position layout

• The product is too large, too heavy or too fragile to move, so it stays put and everything else comes to it.
• Characteristics: very low volume, long duration, high skill, heavy coordination and scheduling of trades and space.
• Examples: building construction, shipbuilding, aircraft assembly, a bridge, a film shoot.

Choosing between them

• The choice is driven by volume and variety: high variety and low volume → process; low variety and high volume → product; single large project → fixed-position.
• The cellular layout is the hybrid that gets much of the product layout's efficiency at the process layout's variety (Topic 23).

Closing line: a bakery making six kinds of bread in small daily batches should stay with a process layout; if one bread grows to a continuous high-volume line, that product alone should be moved onto a dedicated product layout.

Block diagramming — the quantitative route

• Build a from–to chart (load summary chart) recording the number of unit loads moved between every pair of departments.
• Add the two directions to get composite movements for each pair, and rank the pairs from heaviest to lightest.
• Place departments on a grid so that the heaviest-moving pairs are adjacent, working down the ranked list.
• Score the result by counting non-adjacent loads; iterate by swapping departments until the count stops falling.
• Finally convert the abstract blocks into a real layout that respects actual department areas, aisles, doors and services.

Relationship diagramming and Muther's grid — the qualitative route

• Used when movement cannot be counted — in offices, hospitals and retail, where the reason for closeness is noise, supervision, hygiene or convenience rather than tonnage.
• Managers rate every pair of departments on the closeness scale A–E–I–O–U–X: A absolutely necessary, E especially important, I important, O ordinary, U unimportant, X undesirable.
• The ratings are recorded in a triangular Muther's grid, then drawn as a relationship diagram in which the line weight represents the closeness rating.
• Departments are shuffled until the A and E pairs are adjacent and the X pairs are separated.

Which to use

• Use block diagramming when material movement is measurable and dominant — a factory or warehouse.
• Use Muther's grid when closeness is driven by judgement, or when a pair must be kept apart — an X rating has no equivalent in movement data.
• In practice both are used together, and computer routines (CRAFT, CORELAP, ALDEP) automate the iteration.

Example

• In a hospital, radiology and the emergency department earn an A; the mortuary and the cafeteria earn an X. No from–to chart would ever have produced that second constraint.

Closing line: both methods are searches, not formulas — they produce a good layout quickly, not a mathematically optimal one, which is why the designer's judgement still decides the final plan.

Cellular layout (group technology)

• Parts are first sorted into families that share similar shapes, sizes or processing sequences — this classification step is called group technology.
• A cell containing all the different machines that family needs is then laid out in sequence, often in a U-shape so one operator can tend several machines.
• Benefits: shorter travel and handling, much less WIP, shorter flow time, faster changeovers, simpler scheduling, and a small team that owns the quality of a whole part.
• Costs: duplicated machines across cells, lower utilisation of any one machine, and the whole cell must be rebalanced when the part mix changes.

Flexible manufacturing system (FMS)

• An automated cell of CNC machines linked by automated material handling and run under central computer control.
• It can switch between products with almost no changeover time, so it gives variety at near-line efficiency.
• Very high capital cost and high technical complexity, so it is justified only for a stable family with sustained volume.

Mixed-model assembly line

• A single product line that builds several models in sequence — for example three car variants down one line — instead of dedicating a line to each.
• Requires very short changeovers, flexible workers and a levelled schedule so the work content per station stays roughly constant across models.
• This is the layout that makes mass customisation physically possible.

Example

• A pump manufacturer that ran a process layout with 6-week lead times moved to four cells by part family and cut lead time to 4 days with the same machines — the gain came from the arrangement, not new equipment.

Closing line: hybrid layouts exist because the volume–variety trade-off is not a law of nature — it can be softened by grouping the variety into families and giving each family its own small flow line.

The four layouts and what each achieves

• Free-flow layout — fixtures and aisles arranged informally with no fixed path. It encourages browsing, increases impulse purchasing, is flexible and visually appealing. Costs: poor space utilisation, higher fixture cost, easier shoplifting, and customers can miss sections. Best for boutiques, apparel and department stores where discovery is the point.
• Grid layout — long parallel aisles of standard shelving. It encourages customer familiarity, is low cost, easy to clean and secure, and good for repeat customers who want to get in and out quickly. Costs: monotonous, low impulse buying, restricted browsing. Best for supermarkets, pharmacies and hardware stores.
• Loop (racetrack) layout — a single main aisle that circles the store past all departments and returns to the entrance. It increases customer sightlines and exposure to products and encourages customers to circulate through the entire store. Best for large-format stores; IKEA is the standard example.
• Spine layout — one central aisle running the length of the store with departments branching off it. Like the loop it raises sightlines and exposure, while keeping navigation simple and allowing departments to be resized easily. Best for medium-sized speciality stores.

The evaluation — efficiency vs satisfaction

• Grid wins on operational efficiency: highest selling area per square metre, cheapest fixtures, simplest replenishment and stock control.
• Free-flow wins on customer experience and basket value, but at the cost of space and security.
• Loop and spine are the compromise: they raise exposure like free-flow while keeping a controlled path like the grid.
• The right choice follows the customer's mission: a task-oriented shopper wants a grid, a browsing shopper wants free-flow, a large mixed store wants a loop.

Beyond retail — service layout principles generally

• Separate the front office (high customer contact) from the back office (no contact), and design each for its own objective — experience in front, efficiency behind.
• Manage the waiting line deliberately: position it out of sight of the entrance, and give waiting customers something to look at.
• Servicescape factors — lighting, signage, music, cleanliness, temperature — are part of the layout because they shape the perception of quality.

Closing line: in services the layout is part of the product, so it must be judged on revenue per square metre and customer satisfaction together, not on handling cost alone.

How it is done

• List every task with its time and its precedence requirements (which tasks must finish first) and draw the precedence diagram.
• Compute the required cycle time from the desired output rate — this is the maximum time any one station may take.
• Assign tasks to stations in precedence order, filling each station until adding the next task would exceed the cycle time.
• Compute efficiency and balance delay, then rebalance by splitting long tasks, resequencing, or adding a parallel station.

What the numbers mean — the interpretation the exam wants

• The cycle time is set by the customer (the required output rate), not by the machines. It is the drumbeat the line must hold.
• The slowest station becomes the bottleneck and determines the actual output, so the goal is to level station times, not to speed up one station.
• High balance delay means paid idle time at the faster stations — labour cost with no output.
• A perfect balance is usually impossible because tasks cannot be split indefinitely and precedence constrains the order.

Constraints that make balancing hard

• Precedence relationships, indivisible tasks, equipment tied to a particular station, and variability in human task times.

Example

• A line with 12 minutes of total work and a required cycle time of 3 minutes needs at least 4 stations. If the balance actually achieved uses 5 stations, efficiency is 12 / (5 × 3) = 80 %, so 20 % of paid line time is idle.

Closing line: line balancing is where a product layout's theoretical efficiency is either realised or thrown away — the machines are the same either way, the balance is not.

The measures of capacity

• Design capacity — the theoretical maximum under ideal conditions.
• Effective capacity — design capacity less allowances for maintenance, changeovers, breaks and product mix; this is what is realistically achievable.
• Actual output — what was really produced. Utilisation = actual ÷ design; efficiency = actual ÷ effective.
• Best operating level — the volume at which average unit cost is lowest; the plant is designed for it.

The three expansion strategies

• Capacity lead (expansionist). Add capacity ahead of demand. Never turns a customer away, deters entrants and captures market share; risks expensive idle capacity if demand does not arrive. Suits growing markets and firms competing on service and speed.
• Capacity lag (wait-and-see). Add capacity after demand is proven. Maximises utilisation and return, low risk; but stockouts, lost sales and possibly lost customers in the meantime. Suits cost-led firms and mature markets.
• Average / smoothing capacity. Add in increments that track average expected demand, meeting some peaks and missing others, often topped up with overtime, subcontracting or temporary staff. The common middle path.

Economies and diseconomies of scale

• Economies of scale — as volume rises towards the best operating level, average unit cost falls, because fixed costs spread over more units, bulk purchasing lowers input prices, specialised equipment and division of labour raise efficiency, and setup is amortised over larger runs.
• Diseconomies of scale — beyond the best operating level, average cost rises again: congestion and queues, layers of coordination and bureaucracy, communication delays, higher distribution distances, lower morale in a very large plant, and loss of flexibility.
• The result is the familiar U-shaped average cost curve, and the modern response is the focused factory — several smaller plants each doing one thing, rather than one plant doing everything.

Example

• A cement producer commissions a full new line ahead of a highway programme (lead strategy) because the plant takes three years to build; a restaurant chain adds outlets only after existing ones run at capacity (lag strategy) because an outlet takes ten weeks.

Closing line: the right strategy follows the lead time to add capacity and the cost of a lost sale — the longer the build and the more valuable the customer, the more you should lead.

The six criteria in a make-or-buy decision

• Cost — is it cheaper to make, counting the fixed investment, or to buy at the supplier's price?
• Capacity — is there spare capacity in-house, and is the demand steady enough to justify dedicating it?
• Quality — can we hold the specification better than the supplier, and how critical is that item to the product's performance?
• Speed — which route delivers faster and more predictably?
• Reliability — can the supplier be depended on for delivery and continuity of supply?
• Expertise — is this a core competency we must protect, or a commodity somebody else does better?

The sourcing continuum

• Sourcing is not a binary choice. It runs along a continuum of increasing control and commitment: arm's-length purchase → single contract → long-term contract → strategic alliance → joint venture → full vertical integration.
• The further right you move, the more control and the less flexibility — and the more capital is locked in.

The rule of thumb

• Keep in-house what is a core competency, quality-critical, or strategically sensitive.
• Outsource what is standard, non-core, available competitively, and where a supplier has genuine scale advantage.
• Watch the hidden costs of outsourcing: loss of learning and skills, longer supply chains, coordination overhead, IP leakage and supplier dependence.

Example

• Apple designs its chips in-house (core competency) and outsources assembly to Foxconn (scale and cost). The choice is different for each component, not one policy for the whole product.

Closing line: outsource the activity, never the competency — once the skill leaves the firm it is very expensive to bring back.

Project

• A production system in which a single product is made to customer specification.
• Unique output, highest cost per unit, low automation, highly flexible, needs experts and heavy coordination; fixed-position layout.
• Examples: building construction, shipbuilding, event management, a large IT implementation.

Job shop

• Small-scale production of customised products where each order differs in specification and process sequence.
• Functional (process) layout with machines grouped by function; high variety, low volume; skilled labour needed for flexibility; irregular workflow and long lead times; high cost per unit but high differentiation.
• Examples: tailor-made furniture, a machine tool room, a print shop, a diagnostic laboratory.

Batch

• Production of a group (batch) of identical products before switching to another batch; each batch moves through the stages together.
• Moderate volume and variety; functional layout but better scheduling than a job shop; economies of scale within each batch; changeover time is needed between batches, which is what limits batch size.
• Examples: bakery, pharmaceuticals, paint manufacture, book printing, garment manufacture.

Mass

• Production of large quantities of a standardised product using assembly-line techniques, each operation performed continuously at a dedicated workstation.
• Product layout (machines in operation sequence); high volume, low variety; specialised semi-skilled labour; low unit cost from economies of scale; very low flexibility, and a breakdown stops the line.
• Examples: automobile assembly lines, packaged food, consumer electronics.

Continuous

• Uninterrupted 24 × 7 production of a highly standardised commodity, usually measured in volume or weight rather than units.
• Extremely capital intensive, almost fully automated, lowest unit cost, essentially zero flexibility; shutting down is very expensive.
• Examples: oil refining, cement, steel, sugar, electricity generation, chemicals.

Closing line: as you move from project to continuous, unit cost falls and control tightens, but flexibility disappears — so the choice of system is really a choice about how much variety the market will demand.

The two axes

• Rows (process structure) — project / job shop → batch → assembly line → continuous flow, i.e. increasing standardisation and capital intensity.
• Columns (product structure) — one-of-a-kind, low volume → low volume, many products → higher volume, few major products → high volume, standard commodity.

The diagonal rule

• Firms that sit on the diagonal have matched their process to their product and are competitive.
• Above the diagonal (too flexible a process for a high-volume standard product) means unnecessarily high unit cost — using a job shop to make a commodity.
• Below the diagonal (too rigid a process for a varied, low-volume product) means lost orders and an inability to serve variety — running an assembly line for custom work.
• Movement along the diagonal is the normal product life cycle path: a new product starts as a job shop item and migrates to batch and then to line production as volume grows and the design settles.

What the matrix is used for

• To diagnose a mismatch — if the process no longer suits the volume, the matrix says which way to move.
• To plan process change ahead of demand, because moving down the diagonal takes capital and time.
• To make deliberate off-diagonal choices visible: a firm may accept a position above the diagonal to keep flexibility as a competitive weapon, but it should know it is paying for it.

Example

• Early Tesla built cars in a semi-batch process (above the diagonal, high cost per car). As the Model 3 volume grew, it had to move down to a true assembly line — the matrix predicted the transition and the difficulty of it.

Closing line: the matrix's real message is that process choice is not permanent — as the product matures, the process must move with it or the firm slides off the diagonal.

The method

• Write the total-cost equation for each process.
• Equate them pair by pair and solve for the indifference volume of each pair.
• Plot all the cost lines on one graph and read off the lower envelope.
• State the answer as a set of volume ranges, not a single number — that is what the question is really asking for.

Interpreting the pattern

• Low fixed, high variable processes (manual, general-purpose, subcontracted) are cheapest at low volume.
• High fixed, low variable processes (automated, dedicated) are cheapest at high volume.
• Some crossovers are irrelevant: if a third process is cheaper than both at the volume where two lines cross, that crossover never governs a decision. Always check the crossover against the full envelope before quoting it.
• A process that is never lowest at any volume is dominated and should be dropped.

Worked example — Final Q1(a)

• A: FC 10,000, VC 5 · B: FC 40,000, VC 2 · C: FC 70,000, VC 1.
• A vs B: v = 30,000 / 3 = 10,000 units. B vs C: v = 30,000 / 1 = 30,000 units. A vs C: v = 60,000 / 4 = 15,000 units.
• Decision: below 10,000 units use A; between 10,000 and 30,000 use B; above 30,000 use C. The A-vs-C crossover at 15,000 never applies, because B is cheaper than both there.

Closing line: the analysis does not choose a process — it converts the process decision into a demand-forecast decision, and tells the manager exactly how wrong the forecast can be before the answer changes.

The four types of inventory

• Raw material — purchased inputs not yet processed.
• Work-in-process (WIP) — partly finished units inside the process.
• Finished goods — completed units awaiting sale or dispatch.
• MRO supplies — maintenance, repair and operating items that support production without entering the product.

Why firms hold it — the six reasons

• To meet expected demand and serve customers immediately from stock (cycle stock).
• To absorb uncertainty in demand or in supplier lead time (safety stock).
• To decouple stages so a stoppage in one does not immediately stop the next (buffer stock).
• To smooth seasonal or uneven demand by producing steadily and stocking ahead (anticipation stock).
• To capture price and quantity advantages — bulk discounts, or buying ahead of a price rise (hedge stock).
• To cover goods in transit between locations (pipeline stock).

Why planning, ordering, storage and control matter — the FMCG structure

• Inventory planning — ensures sufficient stock for high and fluctuating consumer demand, avoids stockouts that cost sales and goodwill, and optimises working capital by balancing investment against turnover.
• Ordering — decides when and how much to order to keep production and distribution smooth, reduces ordering cost, prevents overstocking and supports just-in-time replenishment.
• Storage — provides safe, organised storage that protects product quality, allows fast retrieval for distribution to retail outlets, and minimises spoilage and obsolescence, which matters most for perishable FMCG lines.
• Inventory control — tracks stock levels through ERP or inventory systems, separates fast-moving from slow-moving items for better decisions, and reduces carrying cost while improving overall operational efficiency.

The tension

• Inventory is simultaneously an asset on the balance sheet and a liability in operations: it ties up working capital, occupies space, risks obsolescence and hides process problems.
• So the objective is never "no inventory" — it is the least inventory that still delivers the target service level.

Closing line: in an FMCG business inventory decisions are made daily and at scale, so a one-percent improvement in inventory efficiency is worth more than most cost-cutting programmes.

Why the distinction decides the system used

• Because dependent demand is lumpy, applying EOQ to it produces stock that sits idle between builds — the average-demand assumption behind EOQ simply does not hold.
• Because independent demand is uncertain but smooth, the EOQ and reorder-point family is exactly right for it.
• Using the wrong system is a classic and expensive error: forecasting components that could have been calculated wastes both stock and effort.

Example

• A bicycle manufacturer forecasts demand for finished bicycles (independent). Once it schedules 500 bicycles, it calculates that it needs exactly 1,000 tyres and 500 saddles (dependent) — no forecast required.
• Note the same tyre sold as a spare part is independent demand and must be forecast, so one item can be both.

Closing line: forecast only what you cannot calculate — every item whose requirement can be derived should be planned, not predicted.

Carrying (holding) cost

• The cost of having stock: capital tied up (usually the largest component), warehousing and space, handling, insurance, taxes, spoilage, pilferage and obsolescence.
• Expressed either as a rupee amount per unit per year, or as a percentage of unit value per year (typically 20–40 %).
• It rises directly with order quantity, because a larger order means a larger average inventory.

Ordering (or setup) cost

• The cost of getting stock: raising the requisition and purchase order, supplier follow-up, transport, receiving, inspection and invoice processing. In a plant the equivalent is the machine setup / changeover cost.
• It is incurred per order, regardless of order size, so total annual ordering cost falls as the order quantity rises.
• This opposition between carrying and ordering cost is exactly what the EOQ model balances.

Shortage (stockout) cost — the Final Q1(c) answer

• A stockout occurs when customer demand cannot be met because of insufficient inventory.
• If the shortage results in a permanent loss of sale, the shortage cost includes the lost profit on that sale.
• Shortages also cause customer dissatisfaction and loss of goodwill, which can lead to a permanent loss of the customer and all their future sales — this is the reputational damage the question asks about.
• When the demand is internal, a shortage causes work stoppages, delays, downtime costs and the cost of lost production.
• It is the hardest cost to measure, which is why firms set a service level instead and let it imply the safety stock.

Hidden costs of inventory — the Re-Exam Q4(a) answer

• Component devaluation cost — component prices usually fall by the time the product is released, so the manufacturer is forced to devalue the stock it already holds. Example: memory chips held for a phone launched six months later.
• Price protection cost — the retailer is refunded the difference if the item's price drops after purchase, within a stated window. It forces shorter manufacturing turnaround, more frequent replenishment and incentives to distributors to keep inventory low. Example: consumer electronics channel agreements.
• Product return cost — unsold goods resulting from excess inventory are returned by distributors to the manufacturer, sometimes for a full refund. Example: publishers taking back unsold books.
• Obsolescence cost — a short product life cycle leads to obsolete stock, so new models must be launched only after existing stock clears the shelves. Example: last year's smartphone model.

Closing line: the visible costs decide the order quantity, but the hidden costs decide whether holding the inventory was worth it at all — and in short-life-cycle industries they are the larger number.

Why the P system needs more safety stock

• In a Q system you are exposed to demand uncertainty only during the lead time, because stock is watched continuously and an order can be placed the moment it is needed.
• In a P system, if stock falls just after a review you cannot order until the next review, so you are exposed for the whole review period plus lead time — a longer exposure requires more safety stock for the same service level.

Choosing between them

• Use the Q system for expensive or critical items where the extra monitoring cost is justified by the lower stock.
• Use the P system when ordering many items from one supplier (you consolidate into one delivery), when a supplier's representative calls on a fixed schedule, or when continuous monitoring is impractical.
• Many firms use both — Q for A items, P for B and C items — which links directly to ABC classification.

Closing line: the P system buys administrative simplicity with extra safety stock; the Q system buys lower stock with extra monitoring. The right choice depends on which of the two is cheaper for that item.

The steps

• Compute annual usage value for every item (annual demand × unit cost).
• Sort items in descending order of that value.
• Compute the cumulative percentage of total value and of item count.
• Cut the list into A, B and C at the natural breakpoints and assign each class its control policy.

Why it matters

• Management time is scarce; ABC ensures it is spent on the 20 % of items carrying 80 % of the value.
• It allocates safety stock rationally — heavy stock on cheap C items costs almost nothing and prevents stockouts; heavy stock on A items is expensive and must be avoided.
• It sets cycle-counting frequency: A items counted monthly, B quarterly, C annually.

The critical caveat

• A cheap C-class item can still stop the line. A ₹5 gasket that halts an assembly line is not a C item in practice, whatever its usage value says.
• So ABC by value is often overlaid with a criticality classification (VED — vital, essential, desirable), and the two are used together.

Example

• In a car plant, engines and gearboxes are A items counted and tracked daily; nuts, bolts and washers are C items kept in bins and reordered in bulk twice a year.

Closing line: ABC is not a stock-reduction technique — it is an attention-allocation technique, and its payoff comes from spending scarce control effort where a percentage point is worth the most.

The logic

• Order in large quantities → few orders → low ordering cost, but a large average inventory of Q/2 → high carrying cost.
• Order in small quantities → the reverse.
• The minimum of the total-cost curve is exactly where the two cost curves cross — which is why annual ordering cost equals annual carrying cost at the EOQ. Use that as your check: if the two halves of TC are not equal, you have made an arithmetic error.

The assumptions — say these, they are marked

• Demand is known, constant and continuous; lead time is known and constant.
• The whole order is received in one delivery (instantaneous receipt).
• No shortages are permitted, and no quantity discounts are available.
• Ordering cost and carrying cost per unit are constant and independent of order size.

Why it still matters despite the assumptions

• The total-cost curve is flat near the minimum, so an order quantity 20 % away from EOQ costs only about 2 % more. The model is robust to imprecise inputs.
• It shows the right direction of response: if ordering cost falls (electronic ordering), EOQ falls and small frequent orders become optimal — which is the economic argument for just-in-time.

Worked example — Final Q4(b)

• D = 10,000, C₀ = ₹200, C_c = ₹5, 250 working days.
• Q_opt = √(2 × 200 × 10,000 / 5) = √800,000 = 894 units.
• Orders/year = 10,000 / 894.4 = 11.18 ≈ 12 orders. Cycle = 250 / 11.18 = ≈ 22 days.
• TC = 2,236 + 2,236 = ₹4,472 — note the two halves are equal, confirming the answer.

Closing line: the EOQ is not a target to be defended to the unit — it is a statement of where the cost trade-off balances, and the flatness of the curve is what makes it usable in practice.

How it differs from basic EOQ

• In EOQ the whole order arrives at once, so inventory jumps to Q. In EBQ the batch is built up gradually at rate p while being consumed at rate d, so stock rises only at the net rate (p − d).
• Peak stock is therefore Q(1 − d/p), always less than Q, and average stock is half of that.
• Lower carrying cost per unit of batch size means the optimal batch is larger than the equivalent EOQ.
• C₀ here is the setup (changeover) cost of the production run rather than a purchase-order cost.

The condition and its meaning

• p must exceed d. If the production rate is not faster than the demand rate, stock never accumulates and no batch size works — the plant simply cannot keep up.
• As p becomes very large relative to d, (1 − d/p) approaches 1 and the EBQ collapses back to the ordinary EOQ. EOQ is the special case of instantaneous production.

The managerial reading

• Because setup cost drives the batch size, reducing setup time directly reduces the economic batch — which reduces inventory and flow time. This is the quantitative justification for SMED and quick changeover in lean manufacturing.

Example

• A paint plant producing 150 gallons/day against demand of 32.2 gallons/day, with C₀ = 150 and C_c = 0.75 on D = 10,000, gets Q_opt ≈ 2,257 gallons — larger than the 2,000-gallon basic EOQ, exactly as the gradual build-up predicts.

Closing line: EBQ says that when you make it yourself, you can afford a bigger batch — but the better move is to attack the setup cost and make a smaller batch economic.

Why the EOQ is not enough

• The basic EOQ ignores purchase price because price is constant and therefore does not affect the choice. With discounts, price changes with Q, so it must be included.
• Annual purchase cost (P × D) is usually far larger than ordering and carrying cost combined, so even a small percentage discount can dominate the whole comparison.

The two shapes of the answer

• If the EOQ at the lowest price is feasible, that is the answer immediately — nothing else can beat it.
• If it is not, the optimum is always either an EOQ that is feasible at its own price level, or a price-break quantity — the minimum quantity that unlocks a lower price. Those are the only candidates you need to test.

What the manager must also weigh

• Higher risk of obsolescence and spoilage on a large lot.
• Warehouse space and working capital tied up, which the model prices only through C_c and may understate.
• Whether the discount is being used by the supplier to shift its own inventory onto your balance sheet.

Example

• If a supplier drops the price from ₹100 to ₹98 for orders of 2,000 or more, on D = 10,000 the annual saving is ₹20,000 — which will usually swamp the extra carrying cost of the larger lot, so the price break wins.

Closing line: with discounts you are no longer minimising inventory cost, you are minimising total spend — and the answer is often a bigger order than the EOQ would suggest.

ROP vs EOQ — the distinction the Re-Exam asks for

How safety stock behaves

• Safety stock rises with √L, not with L — so halving lead time cuts safety stock by about 30 %, not 50 %.
• It rises with demand variability σ_d: a more erratic item needs more buffer for the same service level.
• It rises steeply and non-linearly with the service level. Going from 95 % to 99 % raises z from 1.65 to 2.33 — about 40 % more safety stock for four percentage points of protection. This is the trade-off the manager must actually decide.

Worked example — Re-Exam Q5(a)

• D = 15,000 over 300 days → d̄ = 50 gallons/day; L = 12 days; σ_d = 8; z = 1.65.
• Safety stock = 1.65 × 8 × √12 = 45.73 gallons.
• ROP = (50 × 12) + 45.73 = 600 + 45.73 = 645.73 gallons.

Closing line: EOQ and ROP are complements, not alternatives — the EOQ sets the order size, the reorder point sets its timing, and safety stock prices the service level in between.

Reading the formula, term by term

• d̄(t_b + L) — expected demand over the whole exposure window: from now until the next order actually arrives.
• z·σ_d·√(t_b + L) — safety stock sized for that same window.
• − I — subtract what is already on the shelf, since only the shortfall needs ordering.

Why the exposure window is longer than in a Q system

• In a continuous system the risk window is just the lead time, because an order can be triggered the instant stock hits the reorder point.
• In a periodic system, if stock drops sharply just after a review you must wait until the next review and then the lead time on top — so the window is t_b + L and safety stock must be correspondingly larger.
• This is the price paid for the administrative convenience of a fixed review schedule.

Worked example — Final Q5(a)

• d̄ = 6 packages/day, σ_d = 1.2, t_b = 60 days, L = 5 days, I = 8, z = 1.65.
• Q = 6(60 + 5) + 1.65 × 1.2 × √65 − 8
• Q = 390 + 15.96 − 8 = 397.96 → ≈ 398 packages (or 400 if shipped in boxes of 100).

Closing line: the order quantity in a P system is never fixed — it is whatever is needed to refill the pipeline for the next review-plus-lead-time window, which is why it changes at every review.

Loading

• Assigning jobs to machines, work centres or people so that capacity is not exceeded and the load is balanced.
• Infinite loading assigns work without regard to capacity and then shows the overload; finite loading assigns only up to available capacity and pushes the rest out in time.
• The assignment method (a special case of linear programming) allocates n jobs to n machines to minimise total cost or time — useful when each job can go to any machine but at different efficiencies.

Sequencing

• Deciding the priority order once jobs are queued at a work centre. Different rules optimise different objectives (Topic 42).
• For two machines in series, Johnson's Rule gives the sequence with the shortest makespan (Topic 43).

Monitoring and control

• Gantt chart — a bar chart of jobs against time, showing planned versus actual progress, machine loading and idle time. Simple, visual and still the standard shop-floor control tool.
• Input/output control — compares the work released into a work centre with the work completed by it. If input persistently exceeds output the queue grows without limit, and the correct fix is to throttle the input, not to push the operators.
• Both feed back into loading: a work centre falling behind gets less new work, not more.

Example

• A machine shop uses a Gantt chart on the wall to show which job is on which machine today, and an input/output report weekly to detect that grinding has been receiving 20 % more work than it can complete for a month — the cause of the growing queue.

Closing line: scheduling problems usually look like capacity problems, but input/output control shows that most of them are release problems — too much work let into the shop too early.

The main rules

The measures used to compare rules

• Flow time for a job = its completion time measured from the start of the schedule. Average flow time is the usual efficiency measure.
• Lateness = completion time − due date (can be negative); tardiness counts only positive lateness.
• Makespan = total elapsed time to finish all jobs — unaffected by the sequence on a single machine.

The key insight

• On a single machine the makespan is the same whatever the sequence — the total work does not change. What the sequence changes is who waits.
• SPT is provably optimal for average flow time, which is why it dominates when throughput is the objective; EDD is optimal for maximum lateness, which is why it dominates when due-date performance is the objective.

Example

• A print shop uses SPT on internal jobs to clear the queue fastest, but switches to EDD in the week before a large customer deadline, and to FCFS at the walk-in counter where the customer can see the order.

Closing line: there is no best rule — state the objective first, and the rule follows from it.

Why the rule works

• Putting short first-machine jobs early gets the second machine started as soon as possible, cutting its initial idle time.
• Putting short second-machine jobs last means the tail of the schedule — where machine 1 is already finished — is as short as possible.
• Both moves attack the same thing: idle time on Machine 2, which is the only thing that makes the makespan longer than the total work on Machine 2.

Worked example — Re-Exam Q5(b)

• Jobs A(4,9) B(7,3) C(8,10) D(6,5) E(9,8). Smallest is 3 → B on M2 → B last. Next 4 → A on M1 → A first. Next 5 → D on M2 → D fourth. Of C and E, C's 8 is on M1 → C second, E third.
• Sequence: A – C – E – D – B.
• M1: 0–4, 4–12, 12–21, 21–27, 27–34. M2: 4–13, 13–23, 23–31, 31–36, 36–39.
• Makespan = 39 hours. Idle time M1 = 39 − 34 = 5 hours; idle M2 = 39 − 35 = 4 hours.

Assumptions and limits

• Exactly two machines, every job goes through both in the same order, processing times are known and independent of sequence, and no job may be interrupted.
• It optimises makespan only — it says nothing about due dates or average flow time.
• It extends to three machines only under a restrictive condition, and beyond that heuristics are needed.

Closing line: Johnson's Rule is one of the few scheduling results that is provably optimal, which is why it is worth applying exactly — the sequence it gives cannot be beaten on makespan.