Model of Inventory Management

Here, we discuss a model in which the inventory level is reviewed periodically, and orders are placed at regular intervals to order up to a certain base stock.

last updated Wednesday, November 19, 2025
#Inventory Management #supply chain

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by John Burson

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Firms use various methods of inventory management to minimize supply-and-demand imbalances in the supply chain. Uncertain demand complicates the problem, as it can cause stockouts in which inventory is depleted and orders cannot be filled.

Here, we discuss a model in which the inventory level is reviewed periodically and orders are placed at regular intervals to maintain a certain base stock. This policy is known as a Policy of Periodic Review, Order-Up-To Base Stock.

Under this policy, one orders a variable quantity  Q  every fixed period of time  p to maintain an inventory position ( Qty on hand  +  Qty on order ) at a predefined base stock level  S,  also known as the "order-up-to level." The base stock level S is determined by calculating the quantity needed between the time the order is placed and the time the next period's order is received, and adding a quantity of safety stock to allow for demand variation.

The time between the placing of the order and the receiving of the next period's order is the sum of the review period p  and the replenishment lead time l  (lowercase L). The demand per unit of time, μ, is multiplied by the time between the order placement and the next period's order arrival (p + l) to determine the expected quantity to be sold. The safety stock depends on demand variability and the desired order fill rate.

To calculate the safety stock, first compute the standard loss function, L(z). This function is dependent on the values of the desired fill rate  f,  the demand  μ  and its standard deviation  σ,  the time between orders  p,  and the replenishment lead time l :

L(z)  =  ( 1 - f ) µ p / σ  ( p + l )^1/2

Once L(z) is known, z can be found in a look-up table, and the safety stock can be calculated by:

Safety Stock  =  z σ ( p + l )^1/2

If the review period p is reduced, the safety stock does not necessarily decrease because p appears in both the numerator and denominator of the standard loss function, which determines the value of z.

The average level of on-hand inventory is the sum of the cycle stock ( equal to  µp/2 ) and the safety stock. The on-hand inventory does not include those units in the delivery pipeline.

This model can be complicated by the following real-world issues: variable lead times, non-stationary demand, multiple inventory sites, multiple customer classes, and multi-item order fill rate.

When several components are needed to build a system, each component having the same fill rate, the overall system order fill rate (multi-item fill rate) will be lower than the component fill rate, since an order cannot be completed even if only a single component is missing. The multi-item fill rate is the product of the individual item fill rates. For n items having the same component fill rate:

Order fill rate  =  (component fill rate)ⁿ

When shipping times are long, delaying the final assembly stages until the product reaches the distribution center (DC) may become attractive. At the DC, units can be localized and customized based on the demand patterns observed at that time. The result is that the total safety stock required at the DC is reduced by a factor of n^ (1/2), where n is the number of SKUs for which customization is postponed.

To maximize the benefits of postponement, the product should be designed to be localized at the distribution center. The product's variable features can be isolated into one or two modules to be installed at the distribution center.

 
 
 

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