Introduction

Unlike deterministic models, probabilistic inventory models account for uncertainty in demand and variability in lead time. These models aim to minimize the risk of stock-outs while controlling incremental costs associated with safety stock.

Safety or buffer stock is introduced to absorb fluctuations, but it requires additional investment. Probabilistic models help balance service levels with cost efficiency.

Single-Period Model

Applied in scenarios with uncertain demand and a single selling period (e.g., seasonal goods, perishables).

Key trade-off:

• Overstocking cost: Loss due to unsold inventory
• Understocking cost: Missed profit from unmet demand

The optimal order quantity balances these opposing risks using probabilistic demand distributions.

Q-ROP Model (Order Quantity – Reorder Point)

Suitable for continuous demand scenarios with variable lead time. The model defines:

• Order Quantity (Q): Fixed lot size
• Reorder Point (ROP): Inventory level at which a new order is triggered

ROP is calculated as: $$ \text{ROP} = \text{Expected demand during lead time} + \text{Safety stock} $$

Safety stock is determined based on desired service level and standard deviation of demand during lead time.

Least Unit Cost (LUC) Technique

This method selects a lot size that covers demand for \( k \) future periods, where \( k \geq 1 \).

For each \( k \), compute: $$ \text{Average cost per unit} = \frac{\text{Ordering cost} + \text{Holding cost for } k \text{ periods}}{\text{Total units ordered}} $$

Increment \( k \) until the average cost per unit starts increasing. The optimal \( k \) is the last value before cost rises.