EOQ – P MODEL

Submitted by

Saurav Kumar

Economic Order Quantity Model

• The economic order-quantity model considers the tradeoff between ordering cost and storage cost in choosing the quantity to use in replenishing item inventories.

P model

• In p model, inventory situations(records)is reviewed at fixed intervals of time when the required replenishment orders are placed.

• We have a predetermined time (P) between orders (sales rep comes by every 10 days) or the average time between orders from EOQ = Q/r year

• Used for bulk materials and services like refineries, petrol pumps ,etc.

• Also called as fixed time Model because the review of purchase is done after some fixed time say 5 or 10 days

Cntd…

• Stocks at petrol pump is say 120 kl and consumption per week is 100 kl, thus safety stock is 20kl

• Demand is always variable and in 95% cases it may not exceed 120 kl, thus it is called 95% service level stocks

Symbols and explanations

• There is some lead time (L) to get the supply and thus the variation in demand during lead time is “σL”

• Due to this variation, the stocks level will also vary and the stock level variation is denoted by “z”

Therefore:

Safety Stocks = z x σL

Cntd…

• If the review time in days is “T”, then variation in “T+L” days will be

σT+L=d ^2)Where d is daily demand variation• The quantity to be ordered in

q= (r x (T+L)) + (z x σT+L) – I

Where I is inventory

Example 1

Daily demand at a petrol pump os 10 KL and variation in daily demand is 3 KL. Review period is 30 days and lead time is 14 days. Opening Inventory is 150 KL and variation in stock level is 0.21 . Find q?

Example-2

• In a chemical company , average demand for product is 10 KL per day and standard variation is 2 Kl per day. The inventory levels was 20 kl. The review time is 60 days and lead time is 15 days. Find q so as to maintain 95% service level stock ( z at 95% is 1.645)

Solution

Given data :

T=60,L=15,

σT+L= 2

d=10 and I = 20

we have

q= (r x (T+L)) + (z x σT+L) – I

q= 10x(60+15)+(1.645x2)-20 = 733 KL

Example 3

• Consider an item for which

Annual demand= 1000 units

Standard deviation of demand per week = 10 units

Cost per unit = Rs 5

Ordering cost per order = Rs 150

Inventory carrying cost= 30 percent

Average lead time = 4 weeks

Maximum delay in lead time = 3 weeks

Probability of delay = 0.30

Service level= 95%

solution

Example 4

• Hema garment Manufacturing Company uses basic cloth, ‘two by two’ , in most of its products. It buys its annual requirement of 16000 metres of cloth in economic lots of 4000 metres each. The lead time for procurement is generally taken as 6 weeks . Hema maintains a safety sticks of 1000 metres. If Hema were to change over to a fixed order cycle system, maintaining the safety stocks

solution