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# Supply Chain Costs

Cost optimization based on inventory policies starts with understanding how order quantity impacts annual cost. In IBP, the point is not to minimize one cost bucket in isolation, but to balance service level, working capital, and operating cost.

We start with a simplified single-item replenishment model:

  • Goods are provided by a single supplier,
  • to a single stocking location,
  • For a single product,
  • At a fixed order quantity Q,
  • with constant annual demand D,
  • and stable replenishment behavior.

In this model, average cycle stock is Q/2.

Cycle stock:
Average stock through the order cycle to fulfill demand.

Order cycle:
The time that elapses between two consecutive orders.

# Holding Costs

Holding costs:
Costs related to storing products.

Holding costs typically come in two flavors:

  • Fixed holding costs: employee salaries, rent, equipment, etc.
  • Variable holding costs: product cost (labor, burden, material), scrap, obsolescence, shrink, and capital cost.

Typically, fixed holding costs are excluded or added at the end to simplify estimation.

Annual holding cost can be expressed as:

\text{Holding Cost} = (h \cdot c)\frac{Q}{2}

Where:

  • h = annual holding rate as a percentage of unit cost
  • c = unit cost
  • Q/2 = average cycle stock

# Transaction (Ordering) Costs

Transaction costs:
Costs incurred each time an order is placed (planner time, admin effort, freight setup, receiving effort).

If S is the cost per order event, annual ordering cost is:

\text{Ordering Cost} = \frac{D}{Q}S

Where:

  • D/Q = number of orders per year
  • S = cost per order

Larger order quantities reduce order frequency and ordering cost, but they increase holding cost.

# Total Annual Cost View

For the baseline model:

\text{Total Annual Cost}(Q) = (h \cdot c)\frac{Q}{2} + \frac{D}{Q}S

This creates the classic trade-off curve:

  • very small Q: high ordering cost, low holding cost
  • very large Q: low ordering cost, high holding cost
  • optimal Q: minimum combined cost

# EOQ Reference Point

The economic order quantity (EOQ) for this baseline case is:

Q^* = \sqrt{\frac{2DS}{h \cdot c}}

EOQ is a starting point, not a mandate. In real supply chains, minimum order quantities, pallet constraints, lead-time variability, and service-level requirements will shift the practical target.

# Worked Example

Assume:

  • Annual demand D = 24,000 units
  • Unit cost c = $20
  • Holding rate h = 20% per year
  • Cost per order S = $120

EOQ:

Q^* = \sqrt{\frac{2(24,000)(120)}{0.2 \cdot 20}} = \sqrt{1,440,000} = 1,200

At Q = 1,200:

  • Holding cost = (0.2 * 20) * (1,200/2) = 4 * 600 = $2,400
  • Ordering cost = (24,000/1,200) * 120 = 20 * 120 = $2,400
  • Total relevant annual cost = $4,800

Decision implication for IBP:

  • If finance pressure is on working capital, test slightly lower Q and evaluate service risk.
  • If service risk is high and suppliers are unstable, accept higher holding cost to protect fill rate.

# Practical Limits in IBP

Before locking policy parameters, validate:

  • Supplier minimum order quantity and pack constraints
  • Warehouse capacity and inbound handling windows
  • Service level targets by SKU segment
  • Demand volatility and obsolescence risk
  • Cross-functional agreement between supply, procurement, and finance

Cost math should inform the discussion, but policy settings must align with business priorities and risk tolerance.

# Related Concepts