Inventory Model With Uncertain Demand


Sometime in inventory come across a situation where demand cannot be deterministic or in other words demands cannot be predetermined or fluctuate in different ways In the process of management the yield of the firm can be increased by some methods like, By maximizing the margin of profit; or By maximizing the production with a given amount of capital.


Inventory problem with uncertain demands (MODELS WITH BUFFER STOCK):

 In many situations, both demand and lead-time are fluctuating due to uncontrollable reasons. They are highly uncertain in nature. To face these uncertainties in consumption rate and lead time, an extra stock is maintained to meet out the demands, if any. This extra stock is generally known as Safety stock’ or ‘Buffer stock’.

To Determine the Buffer Stock and Re-order Level (ROL)

·         We must know the maximum lead-time and normal lead-time and the demand during these periods to estimate the buffer stock or safety stock required.

·         The buffer stock is calculated by multiplying the consumption rate during the lead – time by the difference between maximum lead-time and normal lead-time. Let

B= Buffer stock,

L = Lead time,

LD= Difference between maximum lead-time and minimum lead- time.

r = Demand rate.

·         Total inventory consumption during lead-time, if buffer stock is not maintained = L × r = Lr.

·         Thus as soon as stock level reaches ‘Lr’, quantity ‘q’ should be ordered.

·         This point where we order is known as reorder level or ROL.

·         However due to uncertainty in supply, this policy of ordering when stock level reaches ‘Lr’ will create shortages and leads to back orders or lost sales. In order to avoid the shortages, a buffer stock is maintained. Hence,

ROL = Lr Buffer stock = Lr B. = Lr Ld r = (L Ld) × r

Now maximum inventory= q B,

Minimum inventory= S

Average inventory= [(q B) B] / 2 = (q / 2) B.

Optimum Buffer stock:

·         When buffer stock maintained is very low, the inventory holding cost would be low but the shortages will occur very frequently and the cost of shortages would be very high.

·         As against this if the buffer stock maintained is rather large, storages would be rather rare, resulting into low shortage costs but inventory holding costs would be high. Hence it becomes necessary to strike balance between the cost of shortages and cost of inventory holding to arrive at an Optimum Buffer Stock.

Example: The average monthly consumption for an item is 300 units and the normal lead-time is one month. If the maximum consumption has been up to 370 units per month and maximum lead-time is 1 ½ months, what should be the buffer stock for the item.


Maximum lead – time demand = Maximum lead-time × maximum demand rate = (3/2) × 370 = 555 units.

Normal lead-time demand = 1 × 300 = 300 units.

Buffer stock = Maximum lead-time demand – Normal lead- time demand = 555 – 300 = 255 units.