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Qwestrum Engineering360 · Industrial & Production · Operations Research

Inventory Models

Inventory models choose order size and reorder timing to balance ordering and holding costs.
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.

  • D annual demand; S order cost; H holding cost/unit/year
  • Production model EPQ variant
  • Safety stock for demand/lead time variability

Topic details

Introduction

Inventory control is a core bridge between OR and production planning. Chase and Buffa both frame EOQ as a foundational but assumption-sensitive model.

Key relations & formulas

Formulas (Indian textbook notation)

  • EOQQ∗=2DSHEOQ Q* = \sqrt{\frac{2DS}{H}}

Formulas (Indian textbook notation)

  • totalcostTC=DSQ+HQ2total cost TC = \frac{DS}{Q} + \frac{HQ}{2}
reorderpointR=d×Lreorder point R = d\times L
(demand × lead time)

Notation and sign conventions

Relation 1 —
EOQQ∗=√EOQ Q* = √

Formulas (Indian textbook notation)

  • EOQQ∗=2DSHEOQ Q* = \sqrt{\frac{2DS}{H}}
Write this relation with symbols exactly as in Operations Research — Hamdy Taha before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
totalcostTC=DSQ+HQ2total cost TC = \frac{DS}{Q} + \frac{HQ}{2}

Formulas (Indian textbook notation)

  • totalcostTC=DSQ+HQ2total cost TC = \frac{DS}{Q} + \frac{HQ}{2}
Write this relation with symbols exactly as in Operations Research — Hamdy Taha before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
reorderpointR=d×Lreorder point R = d\times L
reorderpointR=d×Lreorder point R = d\times L
(demand × lead time)
Write this relation with symbols exactly as in Operations Research — Hamdy Taha before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

EOQ assumes steady demand, fixed ordering cost, and no stockout in the basic form. Reorder point handles replenishment lead time exposure, and safety stock protects service level under variability. Groover production text links these calculations to material flow reliability on shop floors.

Assumptions and validity limits

State assumptions explicitly before using any relation for inventory models — 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 Operations Research 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 Operations Research 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 models.
4. Use equation 1:
EOQQ∗=√EOQ Q* = √
.
5. Use equation 2:
totalcostTC=DSQ+HQ2total cost TC = \frac{DS}{Q} + \frac{HQ}{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 Models appears in logistics and planning. In Indian industrial curricula this topic is tested because it connects theory to mathematical decision models.
GATE and semester exams often combine inventory models with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use inventory models?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

A standard mistake is using monthly demand in D while keeping H annual, causing unit mismatch. Another mistake is treating ROP and EOQ as interchangeable values.

Quick revision checklist

Before attempting inventory models problems, confirm you can:
1. D annual demand; S order cost; H holding cost/unit/year
2. Production model EPQ variant
3. Safety stock for demand/lead time variability
Revise the solved examples in Operations Research — Hamdy Taha 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.

EOQ and reorder point

Problem

D = 10000 units/year, S = Rs 250/order, H = Rs 5/unit/year, daily demand = 40 units, lead time = 6 days. Find EOQ and ROP.

Solution

EOQ = sqrt(2 x 10000 x 250 / 5) = sqrt(1000000) = 1000 units. ROP = d x L = 40 x 6 = 240 units.

Conceptual check — Inventory Models

Problem

In a Operations Research semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of inventory models." What should a complete answer include?

Exams & GATE

EOQ and ROP numericals are GATE IE staples.

📖 Standard books (India)

  • Operations Research — Hamdy Taha

    Read: Syllabus unit

    LP, transportation, and simulation

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