Date post: | 28-Nov-2014 |
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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