/algo-sc-eoq

name: "\"algo-sc-eoq\""
description: "\"Calculate Economic Order Quantity to minimize total inventory cost (ordering + holding). Use this skill when the user needs to determine optimal order size, balance ordering frequency against storage costs, or set reorder points — even if they say 'how much to order', 'optimal batch size', or 'inventory cost minimization'.\"."
allowed-tools: Bash, Read, Write, Edit, Glob, Grep

Economic Order Quantity (EOQ)

Overview

EOQ determines the order quantity that minimizes total inventory cost = ordering cost + holding cost. Formula: EOQ = √(2DS/H) where D=annual demand, S=ordering cost per order, H=holding cost per unit per year. Assumes constant demand and instantaneous replenishment.

When to Use

**Trigger conditions:**

• Setting standard order quantities for inventory replenishment
• Balancing ordering frequency against warehousing costs
• Baseline calculation before applying safety stock adjustments

**When NOT to use:**

• When demand is highly uncertain (use newsvendor model)
• When products are perishable with short shelf life
• When quantity discounts change the cost structure significantly

Algorithm

IRON LAW: EOQ Assumes CONSTANT, KNOWN Demand
If demand is variable or uncertain, EOQ gives the wrong answer.
Real-world application: use EOQ as a starting point, then add
safety stock for demand variability and lead time uncertainty.
Total cost curve is flat near EOQ — ±20% from optimal Q changes
total cost by only ~2%.

Phase 1: Input Validation

Determine: D (annual demand in units), S (fixed cost per order), H (holding cost per unit per year = unit cost × holding rate, typically 20-30% of unit value). **Gate:** All costs positive, demand estimate reasonable.

Phase 2: Core Algorithm

1. EOQ = √(2 × D × S / H) 2. Number of orders per year = D / EOQ 3. Reorder point = d × L (daily demand × lead time in days) 4. Total annual cost = (D/Q × S) + (Q/2 × H) at Q = EOQ

Phase 3: Verification

Check: ordering cost component ≈ holding cost component (they're equal at EOQ). Total cost is at minimum. **Gate:** Ordering cost ≈ holding cost (±5%).

Phase 4: Output

Return EOQ with cost breakdown and reorder point.

Output Format

{
  "eoq": 500,
  "orders_per_year": 20,
  "reorder_point": 150,
  "annual_cost": {"ordering": 2000, "holding": 2000, "total": 4000},
  "metadata": {"demand": 10000, "order_cost": 100, "holding_cost": 4.0}
}

Examples

Sample I/O

**Input:** D=10,000 units/year, S=$100/order, H=$4/unit/year **Expected:** EOQ = √(2×10000×100/4) = √500000 = 707 units

Edge Cases

| Input | Expected | Why | |-------|----------|-----| | Very high S, low H | Large EOQ, few orders | Minimize expensive ordering | | Very low S, high H | Small EOQ, frequent orders | Minimize expensive holding | | D = 0 | EOQ = 0, no ordering | No demand, no orders needed |

Gotchas

• **Holding cost underestimation**: H should include: capital cost, storage, insurance, obsolescence, handling. Companies often only count warehouse rent, understating true H.
• **Flat cost curve**: Total cost is insensitive near EOQ. Rounding EOQ to a convenient number (full pallet, container) costs very little.
• **Quantity discounts**: Price breaks at certain quantities may make it cheaper to order MORE than EOQ. Compare total cost at EOQ vs discount breakpoints.
• **Lead time variability**: EOQ doesn't address when to order, only how much. Add safety stock: SS = z × σ_demand × √(lead time).
• **Multi-item coordination**: When multiple items share ordering costs (same supplier), use joint replenishment models, not individual EOQs.

Scripts

| Script | Description | Usage | |--------|-------------|-------| | `scripts/eoq.py` | Compute Economic Order Quantity and cost breakdown | `python scripts/eoq.py --help` |

Run `python scripts/eoq.py --verify` to execute built-in sanity tests.

References

• For EOQ with quantity discounts, see `references/eoq-discounts.md`
• For safety stock calculation, see algo-sc-safety-stock