## Batch Costing and Economic Batch Quantity (EBQ)
### Batch Costing — Definition
Batch Costing is a specific order costing method where articles are produced in predetermined lots called batches. The cost object is the batch, not the individual unit.
$$\text{Cost per Unit} = \frac{\text{Total Batch Cost}}{\text{Number of Units in the Batch}}$$
### Why Batch Manufacturing?
Producing one unit at a time is often economically unviable.
- Example: Producing 1 pen of a specific design per run is too expensive. Producing 10,000 pens per batch dramatically lowers per-unit cost.
### Batch-Level Costs (Incurred Each Time a Batch is Run)
Regardless of how many units are in the batch, each batch run incurs:
- Worker engagement and supervision costs
- Machine setup costs
- Other batch-level preparatory costs
### Batch Costing vs. Job Costing
| Feature | Job Costing | Batch Costing |
|---|---|---|
| Product type | Non-standard, non-repetitive; per customer specification | Homogeneous products in continuous lots |
| Cost object | Each individual job | The entire batch |
| Unit individuality | Each job is unique | Units within a batch are identical |
| Cost determination | Per job directly | Aggregate for batch → divided by units |
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### Economic Batch Quantity (EBQ)
Also called Optimum Batch Quantity (OBQ) — the batch size that minimises total production cost.
#### The Two Competing Costs
| Cost Type | Behaviour with Batch Size |
|---|---|
| Setup costs (machine setup per batch) | Decrease as batch size increases — fewer batches needed per year |
| Holding / Carrying costs (inventory carrying) | Increase as batch size increases — more units held in inventory longer |
EBQ is the point where total setup cost = total holding cost — the minimum of the combined cost curve.
#### EBQ Formula
$$EBQ = \sqrt{\frac{2DS}{C}}$$
Where:
- D = Annual demand for the product (units per year)
- S = Setup cost per batch (₹ per batch)
- C = Carrying/holding cost per unit per annum (₹ per unit per year)
#### Intuition of the Formula
- Larger batch → fewer setups (↓ setup cost) but more inventory (↑ holding cost)
- Smaller batch → more setups (↑ setup cost) but less inventory (↓ holding cost)
- EBQ is the batch size that perfectly balances these two opposing forces
#### Benefits of EBQ
- Minimises total production cost
- Improves production planning and scheduling
- Optimises inventory levels and reduces wastage