Inventory control and MRP

In short

Inventory control decides how much to order or make and when, so that material is available without locking up excess working capital. It splits into two worlds: independent demand items (finished goods, spares, consumables) handled by statistical models such as EOQ, reorder point and safety stock; and dependent demand items (components, sub-assemblies, raw material) handled by Material Requirements Planning (MRP), which explodes a bill of materials against a master production schedule. The topic carries heavy marks in GATE (Industrial Engineering section), university Industrial Engineering papers and in placement tests for Maruti Suzuki, Tata Motors, Bosch, Ashok Leyland, L&T, BHEL, Hindustan Unilever, Flipkart/Amazon supply-chain roles and every ERP implementation job. Inventory is also typically the largest current asset on an Indian manufacturer's balance sheet, so planners are judged on turnover ratio and stock-out rate together.

Explained

Why inventory exists, and its costs

• Functions: decouple successive stages, absorb demand and lead-time variability, allow economic lot sizes, buffer against supply disruption, exploit price discounts, and hold seasonal/pipeline stock.
• Types by function: cycle (lot-size) stock, safety (buffer) stock, pipeline/in-transit stock, anticipation stock, decoupling stock, dead stock.
• Types by stage: raw material, bought-out components, work-in-process (WIP), finished goods, spares, consumables and tooling.
• Four cost heads:
  1. Purchase/production cost (C per unit) - relevant only if price varies with quantity.
  2. Ordering/setup cost (Co per order or setup) - requisition, follow-up, inspection, paperwork; for in-house items it is the set-up cost.
  3. Carrying/holding cost (Ch per unit per year) = interest on capital + storage + insurance + obsolescence + handling; usually taken as Ch = i × C, with i about 15-25% per year in Indian industry.
  4. Shortage/stock-out cost (Cs) - lost contribution, expediting, line stoppage, penalty; hardest to measure, so it is often replaced by a service level target.
• Cycle stock cost rises with lot size, ordering cost falls with lot size - EOQ is the balance point.

Selective inventory control (classification)

No firm can control 20,000 items equally tightly; classification decides where effort goes.

• Policy: A items - tight control, frequent small orders, perpetual records, low safety stock, continuous review; C items - bulk orders, two-bin or periodic review, loose control.
• Combinations are what Indian stores actually use: an A-V item (costly and vital, e.g. a turbine rotor spare) is never stocked out; a C-D item is ordered once a year. Non-moving (N) and dead stock are reviewed for disposal.
• ABC is drawn as a Pareto / distribution-by-value curve: items sorted by descending annual value, cumulative value plotted against cumulative item count.

Deterministic inventory models

• Assumptions of basic EOQ (Wilson/Harris model): constant and known demand, constant lead time, instantaneous replenishment of the whole lot, no shortages, fixed price, infinite horizon, single item. Stock profile is a sawtooth.
• Derivation outline: TC(Q) = DC + (D/Q)Co + (Q/2)Ch. Set dTC/dQ = 0 → −DCo/Q² + Ch/2 = 0 → Q\* = √(2DCo/Ch). At the optimum, annual ordering cost = annual carrying cost, and TC is flat near the optimum (a ±20% error in Q raises variable cost by only about 2% - 1.7% at +20%, 2.5% at −20%) - the model's most useful practical property.
• EBQ / finite replenishment rate (manufacturing model): production p > demand d, stock builds at (p − d) during the run. Lot size is inflated by 1/√(1 − d/p).
• EOQ with planned shortages (back-ordering): optimal lot and maximum shortage follow from the ratio Cs/(Ch + Cs); allowing shortages raises the lot size.
• Quantity discounts: all-units discount is solved by computing EOQ at each price, replacing infeasible EOQs by the nearest feasible price-break quantity, then comparing total cost including material cost for each candidate. Never compare only the variable costs.
• Limitations: real demand is lumpy and uncertain, lead times vary, Co and Ch are estimates, multi-item budget and space constraints are ignored (handled by Lagrange multipliers), and for dependent demand the whole premise of smooth independent demand fails - which is why MRP exists.

Probabilistic models: reorder point and safety stock

• Reorder level (ROL/ROP): stock level at which a replenishment is triggered = expected demand during lead time + safety stock.
• Safety stock covers only the variability during the lead time, not the whole cycle. Higher service level → higher z → higher SS, with sharply diminishing returns above 95%.
• Service level definitions: *cycle service level* = probability of no stock-out in a cycle (used with z); *fill rate* = fraction of demand met from stock. They are not equal.
• Review systems:
  • Q-system (continuous review, fixed order quantity): order a fixed Q whenever stock falls to ROL. Needs perpetual records; lower safety stock; suits A items.
  • P-system (periodic review, fixed interval): review every T; order up to a target level. Order quantity varies; safety stock must cover T + L, hence larger; convenient for grouped ordering from one supplier.
  • Two-bin system: the second bin is the ROL - when it is opened, you order. Cheap, visual, used for C items, fasteners and consumables.
  • s-S (min-max) and base-stock (S, one-for-one) systems for spares.
• Inventory valuation (Indian practice): Ind AS 2 / AS 2 require inventories at the lower of cost and net realisable value; cost by FIFO or weighted average - LIFO is not permitted. Physical verification and discrepancies are reported under CARO. Government stores follow the General Financial Rules (GFR) 2017 and GeM procurement; Indian Railways uses its own Stores Code with ABC/VED-type classification. (Thresholds and rules here are revised from time to time - verify the current version before quoting.)

MRP: inputs, logic and outputs

• Core idea: demand for components is dependent - it is *calculated* from the schedule of parent items, not forecast. MRP answers what to order, how much, and when to release it.
• Three inputs:
  1. Master Production Schedule (MPS) - what end items are to be completed, in what quantity, in which period (time bucket, usually a week).
  2. Bill of Materials (BOM) - the product structure tree with quantity-per and levels; low-level coding assigns each part the lowest level at which it appears, so all its requirements are netted at once.
  3. Inventory records file - on-hand stock, scheduled receipts (open orders), lead time, lot-size rule, safety stock, scrap allowance.
• MRP computation per item, per period:
  1. Gross requirement = demand from all parents (plus any independent/service demand).
  2. Projected available = on hand at start + scheduled receipts − gross requirement.
  3. Net requirement = gross requirement − on hand − scheduled receipts + safety stock (zero if negative).
  4. Planned order receipt = net requirement adjusted to the lot-size rule.
  5. Planned order release = receipt offset backwards by the lead time (time phasing).
  6. Explode the planned releases into the children, level by level, top-down.
• Lot-sizing rules: lot-for-lot (exact net requirement - minimum inventory, maximum set-ups, used for costly/JIT items), EOQ, Periodic Order Quantity / POQ (cover a fixed number of periods), fixed order quantity / multiples, least unit cost, least total cost / part-period balancing, Silver-Meal heuristic, and Wagner-Whitin (dynamic programming, optimal but rarely used in practice).
• Outputs: planned order releases (the primary output), purchase and shop order schedules, rescheduling/exception notices, pegging reports (which parent caused a requirement), inventory projections and performance reports.
• Key refinements: regenerative (full recomputation, typically weekly) vs net-change MRP (only affected items); firm planned orders and planning time fences to stop system nervousness (small MPS changes causing large lower-level churn); safety lead time instead of safety stock for purchased items; phantom assemblies and planning BOMs for options.
• Extensions: Closed-loop MRP adds capacity feedback; CRP (Capacity Requirements Planning) converts planned orders into load on work centres; MRP II adds the financial and business plan, making one integrated plan in units and rupees; ERP (SAP, Oracle, Infor, Zoho/Tally at smaller scale) extends it across the whole enterprise; DRP applies the same logic to distribution warehouses.
• Advantages: valid priorities and realistic delivery promises, lower WIP, visibility of future needs, systematic rescheduling, supports engineering changes.
• Limitations: needs very accurate BOM and stock records (above ~98-99%; cycle counting is essential), assumes fixed lead times and infinite capacity in basic MRP, computationally heavy, nervous to MPS changes, and gives a "push" plan - whereas a pull/kanban system reacts to actual consumption. Most Indian plants use MRP for purchased and long-lead items and kanban for repetitive high-volume feeding.

Key points

• Independent demand - forecast (finished goods, spares); dependent demand - calculated from parents by MRP.
• EOQ - the lot size where annual ordering cost equals annual carrying cost; cost curve is flat near it.
• Carrying cost - usually i × unit cost, i ≈ 15-25%/yr in India, covering interest, storage, insurance and obsolescence.
• EBQ - EOQ for in-house production, inflated by 1/√(1 − d/p) because stock builds gradually.
• Reorder level - demand during lead time plus safety stock; it triggers the order, it does not fix its size.
• Safety stock - covers lead-time variability only; SS = z × σ over lead time.
• σ over lead time = σd√L when only demand varies; use √(Lσd² + d²σL²) when lead time also varies.
• Q-system - fixed quantity, continuous review, less safety stock; P-system - fixed interval, variable quantity, more safety stock.
• Two-bin system - visual ROL control for cheap C items.
• ABC - by annual consumption value; VED - by criticality; FSN - by movement; use them in combination.
• Quantity discounts - compare total cost *including* material cost at each feasible candidate quantity.
• MRP inputs - MPS, BOM, inventory records file; output - time-phased planned order releases.
• Net requirement = gross − on hand − scheduled receipts + safety stock, floored at zero.
• Time phasing / lead-time offsetting - a receipt required in week t is released in week t − L.
• Low-level coding - net a part only at the lowest level it appears, so all parents are counted once.
• MRP II - closed-loop MRP plus capacity and finance; ERP extends it enterprise-wide.
• Inventory turnover = annual cost of goods sold / average inventory; higher is leaner, but check the stock-out rate with it.
• Ind AS 2 - inventory at lower of cost and NRV; FIFO or weighted average; LIFO not allowed.

Formulas and examples

Example 1 - EOQ and total cost. A pump maker buys a casting: D = 10,000/yr, Co = ₹400/order, C = ₹50/unit, i = 20%/yr.

• Ch = 0.20 × 50 = ₹10 per unit per year.
• Q\* = √(2 × 10,000 × 400 / 10) = √800,000 = 894 units.
• Orders per year = 10,000/894.4 = 11.18; cycle = 365/11.18 ≈ 32.6 days.
• Ordering cost = 11.18 × 400 = ₹4,472; carrying = (894.4/2) × 10 = ₹4,472 (equal, as expected).
• Minimum variable cost = √(2 × 10,000 × 400 × 10) = ₹8,944/yr; with material, TC = 5,00,000 + 8,944 = ₹5,08,944/yr.
• If the buyer insists on ordering 1,200: TC(var) = (10,000/1,200)×400 + 600×10 = 3,333 + 6,000 = ₹9,333 - only 4.3% worse, showing the flatness of the curve.

Example 2 - Economic batch quantity. A gear is machined in-house: D = 24,000/yr over 240 working days (d = 100/day), p = 200/day, set-up cost ₹1,500, Ch = ₹20/unit/yr.

• 1 − d/p = 1 − 100/200 = 0.5.
• Q\* = √(2 × 24,000 × 1,500 / (20 × 0.5)) = √(72,000,000/10) = √7,200,000 = 2,683 units.
• Run time = 2,683/200 = 13.4 days; cycle = 2,683/100 = 26.8 days; set-ups = 24,000/2,683 = 8.94/yr.
• Max inventory = 2,683 × 0.5 = 1,342; average = 671 → carrying = ₹13,416; set-up = 8.94 × 1,500 = ₹13,416; total ₹26,833/yr.
• Plain EOQ would give √(2×24,000×1,500/20) = 1,897 units - using it here understates the lot by 29%.

Example 3 - Reorder level and safety stock. Average demand 500 units/week, σ of weekly demand 80, lead time 3 weeks (constant), Ch = ₹50/unit/yr.

• σL = 80 × √3 = 138.6 units.
• At 95% service level: SS = 1.645 × 138.6 = 228 units; ROL = 500 × 3 + 228 = 1,728 units.
• At 99%: SS = 2.33 × 138.6 = 323 units; ROL = 1,823 units. The last 4 percentage points of service cost (323 − 228) × 50 = ₹4,750/yr extra carrying.

Example 4 - Quantity discount (all-units). D = 5,000/yr, Co = ₹500/order, i = 25%/yr. Price: ₹100 for Q < 1,000; ₹98 for 1,000 ≤ Q < 2,500; ₹95 for Q ≥ 2,500.

• Order 1,000 units at ₹98 - the deepest discount is *not* optimal: moving from 1,000 to 2,500 adds ₹17,438 of carrying cost while saving only ₹15,000 on material and ₹1,500 on ordering, a net ₹938 worse.

Example 5 - MRP explosion. Product A = 2 B + 1 C; each B = 3 D. Lead times: A 1 week, B 2 weeks, D 1 week. On hand: A 20, B 50, D 100. No scheduled receipts, no safety stock. Lot rules: A and D lot-for-lot; B in multiples of 200. MPS for A: 100 in week 6, 150 in week 8.

• Week-5 B stock = 50 + 200 − 160 = 90; week-7 = 90 + 400 − 300 = 190. Carrying 190 spare B is the price of the 200-multiple rule.

Where it is used

• Automotive and auto components: Maruti Suzuki, Tata Motors, Bajaj, Bosch and their tier-1 suppliers run MRP/ERP for purchased parts with kanban and milk-run supply for high-volume feeding; vendor-managed and consignment stock at the plant gate.
• Capital goods, power and process plants: BHEL, L&T, NTPC and refineries use ABC-VED spares policies - vital insurance spares are stocked regardless of slow movement, while C-class hardware goes on two-bin or rate contracts.
• Public procurement and railways: Indian Railways stores depots, defence and hospital drug stores classify by ABC, VED and FSN; purchases follow GFR 2017 and the GeM portal.
• Retail, FMCG and e-commerce: HUL, ITC, DMart, Flipkart and Amazon India use periodic review and DRP across distribution centres, with service-level-driven safety stock per SKU-location.
• Job roles: materials/stores manager, production planner, PPC engineer, supply-chain analyst, SAP MM/PP consultant, demand planner; interview focus is EOQ arithmetic, ABC policy and MRP explosion.
• Performance measures used on the job: inventory turnover, days of inventory, fill rate, stock-out frequency, non-moving and obsolete stock value, inventory accuracy from cycle counting.

Interview questions

• Q: At EOQ, what is the relation between ordering and carrying cost? A: They are equal, and the total variable cost equals √(2DCoCh); the total-cost curve is flat near the optimum, so modest deviations cost little.
• Q: If the ordering cost halves, what happens to EOQ? A: EOQ falls by a factor of √2, that is to about 70.7% of its earlier value, since Q\* varies as √Co.
• Q: Why is the EBQ larger than the EOQ for the same data? A: Because production and consumption overlap, average stock is only (1 − d/p)Q/2, so carrying cost per unit lot is lower and the economic lot grows by 1/√(1 − d/p).
• Q: Does safety stock depend on the order quantity? A: No - it depends on demand and lead-time variability and the chosen service level; the order quantity sets the cycle stock, not the buffer.
• Q: Difference between reorder level and order quantity? A: ROL is the stock level that triggers replenishment (lead-time demand plus safety stock); the order quantity is how much is then bought, typically the EOQ.
• Q: ABC versus VED - can an item be C and V at the same time? A: Yes; a cheap O-ring can stop a compressor. Low value, high criticality - stock it generously but with simple control.
• Q: Why can't you forecast demand for a gearbox shaft in an MRP system? A: Its demand is dependent - it is derived exactly from the parent gearbox schedule through BOM explosion; forecasting it would double-count uncertainty.
• Q: What are the three inputs to MRP and which error hurts most? A: MPS, BOM and the inventory records file; inaccurate BOM or stock records destroy the whole plan, because MRP trusts them absolutely.
• Q: What is MRP system nervousness and how is it controlled? A: Small changes in the MPS cascade into large rescheduling at lower levels; controlled by planning time fences, firm planned orders, frozen near-term schedule and net-change processing.
• Q: MRP II versus ERP? A: MRP II is closed-loop MRP plus capacity planning and a financial plan for manufacturing; ERP extends the same integrated database to finance, sales, HR and the whole enterprise.
• Q: In a quantity-discount problem, why must purchase cost be included? A: Because the price itself changes between candidates; comparing only ordering and carrying costs would always favour the smallest lot and miss the material saving.
• Q: Would you use MRP or kanban for a high-volume fastener from a local supplier? A: Kanban or a two-bin pull system - demand is steady and lead time short, so consumption-triggered replenishment is simpler than time-phased planning.

Common mistakes

• Using inconsistent time units - monthly demand with annual carrying cost, or daily demand with weekly lead time - in EOQ and ROL.
• Taking carrying cost as the interest rate instead of i × C, or forgetting that Ch changes with the price in discount problems.
• Comparing only variable costs across price breaks, and so wrongly choosing the largest discount quantity.
• Applying plain EOQ to an in-house manufactured batch instead of EBQ with the (1 − d/p) factor.
• Computing safety stock from σ of demand over a *year* or a *cycle* rather than over the lead time (missing the √L).
• In MRP, forgetting to subtract scheduled receipts, forgetting to offset the release by lead time, or netting a common part at two different levels instead of its low-level code.
• Treating the MRP planned *receipt* date as the *release* date, which makes every lower-level order late by one lead time.

Related topics

Production planning and control · Operations research basics · Lean manufacturing and Six Sigma · Engineering economics and costing · Supply chain and logistics management · Forecasting techniques