Single Period Inventory Models

A single period inventory model is used to identify the amount of inventory to purchase given a perishable good or single opportunity to purchase.

The amount of the single order is based on balancing the cost of over- and under-estimating demand. This is a very common problem in areas such as:
  • Overbooking of airline seats or hotel rooms
  • Ordering of fashion items
  • Any type of one-time order (t-shirts for a sporting event)
When you know:
  • Co = the cost per unit of overestimating demand
  • Cu = the cost per unit of overestimating demand
  • µ = the average number of units sold over the planning horizon
  • σ = the standard deviation of units sold over the planning horizon
You can calculate the safety stock needed to balance the costs of over- and under-estimating demand, by (assuming sales are normally distributed):

1. Calculate the probability of a unit will not be sold:

P <= Cu / (Co + Cu)

2. Find the point on our demand distribution that corresponds to the cumulative probability of a unit not being sold by finding the Z-score (using a table or by using the NORMSINV function in Excel).

Z-score = NORMSINV(P)

3. Calculate the amount of safety stock as:

Safety stock = ROUND(Z-score * σ)

    4. Total order = µ + Safety stock