Qwestrum Engineering360 · Mechanical Engineering · Industrial Engineering
Inventory Management
Inventory models minimise total cost by balancing ordering and carrying costs: EOQ = √(2DS/C_c). Reorder point ROP = demand during lead time + safety stock guards against stockouts, per industrial-engineering texts.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.
Key formulas & points
Skim these first — then read the full notes below.
- JIT minimises inventory; requires reliable suppliers
- Perpetual vs periodic inventory systems
- Stockout cost vs holding cost trade-off
Topic details
Introduction
Inventory management decides how much to order and when, minimising the combined cost of ordering, holding, and shortage. It is a heavily examined IE topic with reliable numericals.
Scope in B.Tech and GATE syllabus
The EOQ model assumes constant demand and gives the order size that minimises ordering plus carrying cost. Extensions add quantity discounts, finite replenishment (EBQ), and probabilistic demand with safety stock.
Why this topic matters in practice
The reorder point triggers a new order when stock falls to the expected lead-time demand plus a safety buffer sized to a target service level. ABC analysis prioritises control effort by value. Computing EOQ, ROP, and total cost is the standard exam demand.
Key relations & formulas
(D = annual demand, S = order cost, C_c = holding)
(d = daily demand, L = lead time)
(z from service level)
(Pareto)
Notation and sign conventions
Relation 1 —
(D = annual demand, S = order cost, C_c = holding)
Write this relation with symbols exactly as in Industrial Engineering & Management — O.P. Khanna before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
(d = daily demand, L = lead time)
Write this relation with symbols exactly as in Industrial Engineering & Management — O.P. Khanna before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
(z from service level)
Write this relation with symbols exactly as in Industrial Engineering & Management — O.P. Khanna before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 4 —
(Pareto)
Write this relation with symbols exactly as in Industrial Engineering & Management — O.P. Khanna before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Fundamentals and definitions
Total inventory cost = ordering cost (D/Q × S) + carrying cost (Q/2 × C_c). Minimising it gives EOQ = √(2DS/C_c); at the EOQ, ordering and carrying costs are equal — a useful check.
Governing relations in practice
The order cycle repeats: stock depletes at the demand rate, and a new order of size EOQ arrives when stock hits the reorder point. ROP = d × L (demand rate × lead time) for deterministic demand.
Design and analysis considerations
Under uncertain demand, safety stock = z × σ_L (z from the desired service level, σ_L the lead-time demand standard deviation) is added: ROP = d̄L + safety stock. More safety stock raises service level but also carrying cost.
Advanced theory and extensions
ABC classification focuses tight control on high-value A items and looser control on C items. Quantity-discount models compare total cost (including purchase price) at price-break quantities. These tools together minimise inventory cost at a chosen service level.
Assumptions and validity limits
State assumptions explicitly before using any relation for inventory management — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Industrial Engineering viva and GATE descriptive questions, listing valid assumptions often earns separate marks.
Step-by-step problem approach
1. Read the question and list given data with SI units (common in Industrial Engineering papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to inventory management.
4. Use equation 1:
5. Use equation 2:
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to inventory management.
4. Use equation 1:
.
5. Use equation 2:
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.
Applications & exam relevance
Inventory Management appears in factories, logistics, and service systems. In Indian mechanical curricula this topic is tested because it connects theory to productivity, layout, and operations.
GATE and semester exams often combine inventory management with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use inventory management?" — answer with a lab, mini-project, or plant visit example if possible.
Common mistakes in exams
• Forgetting safety stock in the reorder point under variable demand
• Using annual demand where lead-time demand is needed for ROP
• Ignoring purchase price in quantity-discount comparisons
• Inconsistent carrying-cost units (per unit vs percentage of price)
• Using annual demand where lead-time demand is needed for ROP
• Ignoring purchase price in quantity-discount comparisons
• Inconsistent carrying-cost units (per unit vs percentage of price)
Quick revision checklist
Before attempting inventory management problems, confirm you can:
1. JIT minimises inventory; requires reliable suppliers
2. Perpetual vs periodic inventory systems
3. Stockout cost vs holding cost trade-off
2. Perpetual vs periodic inventory systems
3. Stockout cost vs holding cost trade-off
Revise the solved examples in Industrial Engineering & Management — O.P. Khanna and one previous-year GATE or university paper for this unit.
Worked examples
Try the problem first — open the solution when you are ready to check.
Reorder point
Problem
Daily demand is 50 units, lead time is 6 days, and safety stock is 100 units. Find the reorder point.
Solution
ROP = (demand rate × lead time) + safety stock = (50 × 6) + 100 = 300 + 100 = 400 units.
Conceptual check — Inventory Management
Problem
In a Industrial Engineering semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of inventory management." What should a complete answer include?
Practice questions
Most-asked interview and GATE questions for this topic — expand any item for a model answer.
- 1What is Inventory Management, and why does it appear in B.Tech / GATE syllabi?
Model answer
Inventory models minimise total cost by balancing ordering and carrying costs: EOQ = √(2DS/C_c). Reorder point ROP = demand during lead time + safety stock guards against stockouts, per industrial-engineering texts. - 2State the relation EOQ = √ and name each symbol.
Model answer
The governing relation is . Write every symbol with SI units before substituting numbers. - 3State the relation Reorder point R = d·L + safety stock and name each symbol.
Model answer
The governing relation is . Write every symbol with SI units before substituting numbers. - 4State the relation Safety stock = z·σ_d·√L and name each symbol.
Model answer
The governing relation is . Write every symbol with SI units before substituting numbers. - 5State the relation ABC analysis: A = 20% items, 80% value and name each symbol.
Model answer
The governing relation is . Write every symbol with SI units before substituting numbers. - 6Explain: JIT minimises inventory; requires reliable suppliers
Model answer
JIT minimises inventory; requires reliable suppliers — state the assumption range and one exam trap linked to this point. - 7Explain: Perpetual vs periodic inventory systems
Model answer
Perpetual vs periodic inventory systems — state the assumption range and one exam trap linked to this point. - 8Explain: Stockout cost vs holding cost trade-off
Model answer
Stockout cost vs holding cost trade-off — state the assumption range and one exam trap linked to this point. - 9How would you correct this error in a viva: Forgetting safety stock in the reorder point under variable demand?
Model answer
Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check. - 10How would you correct this error in a viva: Using annual demand where lead-time demand is needed for ROP?
Model answer
Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check. - 11How would you correct this error in a viva: Ignoring purchase price in quantity-discount comparisons?
Model answer
Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check. - 12How would you correct this error in a viva: Inconsistent carrying-cost units (per unit vs percentage of price)?
Model answer
Identify the wrong assumption or unit mix-up, rewrite the correct relation, and recompute with a one-line sanity check.
Exams & GATE
- 1O.P. Khanna Ch. 9 — EOQ assumes constant demand and instant replenishment.
- 2Avoid: Forgetting safety stock in the reorder point under variable demand
- 3Avoid: Using annual demand where lead-time demand is needed for ROP
- 4Avoid: Ignoring purchase price in quantity-discount comparisons
📖 Standard books (India)
Industrial Engineering & Management — O.P. Khanna
Read: Syllabus unit
Work study, PPC, and OR basics
Explore related topics
See real mechanical engineering careers
After exams and interviews, see how engineers actually built careers — milestones and decisions from people in the field.