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Inventory & store management 
Mohit mendiratta
What is inventory? 
Inventory is the raw materials, component 
parts, work-in-process, or finished products 
that are held at a location in the supply chain.
Costs of Inventory 
• Physical holding costs: 
– out of pocket expenses for storing inventory 
(insurance, security, warehouse rental, cooling) 
– All costs that may be entailed before you sell it 
(obsolescence, spoilage, rework...) 
• Opportunity cost of inventory: foregone return on 
the funds invested. 
• Operational costs: 
– Delay in detection of quality problems. 
– Delay the introduction of new products. 
– Increase throughput times.
Benefits of Inventory 
• Hedge against uncertain demand 
• Hedge against uncertain supply 
• Economize on ordering costs 
• Smoothing 
To summarize, we build and keep inventory in 
order to match supply and demand in the 
most cost effective way.
12-5 
Types of Inventories 
• Raw materials & purchased parts 
• Partially completed goods called 
work in progress 
• Finished-goods inventories 
– (manufacturing firms) 
or merchandise 
(retail stores)
12-6 
Types of Inventories (Cont’d) 
• Replacement parts, tools, & supplies 
• Goods-in-transit to warehouses or customers
12-7 
Functions of Inventory 
• To meet anticipated demand 
• To smooth production requirements 
• To decouple operations 
• To protect against stock-outs
12-8 
Functions of Inventory (Cont’d) 
• To take advantage of order cycles 
• To help hedge against price increases 
• To permit operations 
• To take advantage of quantity discounts
12-9 
Objective of Inventory Control 
• To achieve satisfactory levels of customer 
service while keeping inventory costs 
within reasonable bounds 
– Level of customer service 
– Costs of ordering and carrying inventory 
Inventory turnover is the ratio of 
average cost of goods sold to 
average inventory investment.
12-10 
Effective Inventory Management 
• A system to keep track of inventory 
• A reliable forecast of demand 
• Knowledge of lead times 
• Reasonable estimates of 
– Holding costs 
– Ordering costs 
– Shortage costs 
• A classification system
12-11 
Operations Strategy 
• Too much inventory 
– Tends to hide problems 
– Easier to live with problems than to eliminate 
them 
– Costly to maintain 
• Wise strategy 
– Reduce lot sizes 
– Reduce safety stock
Inventory Control Systems 
Continuous system (fixed-order-quantity) 
constant amount ordered when 
inventory declines to 
predetermined level 
Periodic system (fixed-time-period) 
order placed for variable amount 
after fixed passage of time
Economic Order Quantity (EOQ) 
Models 
• EOQ 
– optimal order quantity that will 
minimize total inventory costs 
• Basic EOQ model 
• Production quantity model
Assumptions of Basic EOQ 
Model 
Demand is known with certainty and is constant over time 
No shortages are allowed 
Lead time for the receipt of orders is constant 
Order quantity is received all at once
Inventory Order Cycle 
Demand 
rate 
Lead Lead 
Time 
time 
time 
Order 
placed 
Order 
placed 
Order 
receipt 
Order 
receipt 
Order quantity, Q 
Inventory Level 
Reorder point, R 
0
EOQ Cost Model 
Co - cost of placing order D - annual demand 
Cc - annual per-unit carrying cost Q - order quantity 
Annual ordering cost = 
CoD 
Q 
Annual carrying cost = 
CcQ 
2 
CoD 
Q 
Total cost = + 
CcQ 
2
EOQ Cost Model (cont.) 
Annual 
cost ($) Total Cost 
Carrying Cost = 
CcQ 
2 
Order Quantity, Q 
Slope = 0 
Minimum 
total cost 
Optimal order 
Qopt 
Ordering Cost = 
CoD 
Q
Production Order Quantity Model 
 Used when inventory builds up over 
a period of time after an order is 
placed 
 Used when units are produced and 
sold simultaneously 
© 2011 Pearson Education, Inc. 
publishing as Prentice Hall
Production Order Quantity Model 
Inventory level 
Part of inventory cycle during 
which production (and usage) is 
taking place 
© 2011 Pearson Education, Inc. 
publishing as Prentice Hall 
Time 
Demand part of cycle 
with no production 
t 
Maximum 
inventory 
Figure 12.6
Production Order Quantity Model 
Q = Number of pieces per order p = Daily production rate 
H = Holding cost per unit per year d = Daily demand/usage rate 
t = Length of the production run in days 
© 2011 Pearson Education, Inc. 
publishing as Prentice Hall 
= (Average inventory level) x 
Annual inventory 
holding cost 
Holding cost 
per unit per year 
= (Maximum inventory level)/2 
Annual inventory 
level 
= – 
Maximum 
inventory level 
Total produced during the 
production run 
Total used during the 
production run 
= pt – dt
Production Order Quantity Model 
Q = Number of pieces per order p = Daily production rate 
H = Holding cost per unit per year d = Daily demand/usage rate 
t = Length of the production run in days 
© 2011 Pearson Education, Inc. 
publishing as Prentice Hall 
= – 
Maximum 
inventory level 
Total produced during the 
production run 
Total used during the 
production run 
= pt – dt 
However, Q = total produced = pt ; thus t = Q/p 
Q 
p 
Q 
p 
Maximum 
inventory level = p – d = Q 1 – 
d 
p 
Holding cost = (H) = 1 – H 
d 
p 
Q 
2 
Maximum inventory level 
2
Production Order Quantity Example 
D = 1,000 units p = 8 units per day 
S = $10 d = 4 units per day 
H = $0.50 per unit per year 
© 2011 Pearson Education, Inc. 
publishing as Prentice Hall 
Q* = 
2DS 
H[1 - (d/p)] 
2(1,000)(10) 
0.50[1 - (4/8)] 
Q* = = 80,000 
= 282.8 or 283 hubcaps
Probabilistic Models and Safety 
© 2011 Pearson Education, Inc. 
publishing as Prentice Hall 
Stock 
 Used when demand is not constant or 
certain 
 Use safety stock to achieve a desired 
service level and avoid stockouts 
ROP = d x L + ss 
Annual stockout costs = the sum of the units short x the probability x the 
stockout cost/unit 
x the number of orders per year
Safety Stock Example 
ROP = 50 units Stockout cost = $40 per frame 
Orders per year = 6 Carrying cost = $5 per frame per year 
Number of Units Probability 
© 2011 Pearson Education, Inc. 
publishing as Prentice Hall 
30 .2 
40 .2 
ROP  50 .3 
60 .2 
70 .1 
1.0
Safety Stock Example 
ROP = 50 units Stockout cost = $40 per frame 
Orders per year = 6 Carrying cost = $5 per frame per year 
Safety 
Stock 
Additional 
Holding Cost Stockout Cost 
© 2011 Pearson Education, Inc. 
publishing as Prentice Hall 
Total 
Cost 
20 (20)($5) = $100 $0 $100 
10 (10)($5) = $ 50 (10)(.1)($40)(6) = $240 $290 
0 A safet$y s t0ock( 1o0f )2(0.2 f)r(a$m4e0s) (g6i)v e+s (t2h0e) l(o.1w)e($st4 t0o)t(a6l) c=ost$960 $960 
ROP = 50 + 20 = 70 frames
Probabilistic Demand 
© 2011 Pearson Education, Inc. 
publishing as Prentice Hall 
ROP = 350 + safety stock of 16.5 = 366.5 
Safety stock 16.5 units 
ROP  
Place 
order 
Inventory level 
Time 
0 
Minimum demand during lead time 
Maximum demand during lead time 
Mean demand during lead time 
Normal distribution probability of 
demand during lead time 
Expected demand during lead time (350 kits) 
Receive 
order 
Lead 
time 
Figure 12.8
Probabilistic Demand 
Use prescribed service levels to set safety stock 
when the cost of stockouts cannot be determined 
ROP = demand during lead time + ZsdLT 
where Z = number of standard deviations 
© 2011 Pearson Education, Inc. 
publishing as Prentice Hall 
sdLT = standard deviation of demand during lead time
Probabilistic Demand 
© 2011 Pearson Education, Inc. 
publishing as Prentice Hall 
Probability of 
no stockout 
95% of the time 
Safety 
stock 
Mean 
demand 
350 
ROP = ? kits Quantity 
Number of 
standard deviations 
0 z 
Risk of a stockout 
(5% of area of 
normal curve)
Probabilistic Example 
Average demand = m = 350 kits 
Standard deviation of demand during lead time = sdLT = 10 kits 
5% stockout policy (service level = 95%) 
Using Appendix I, for an area under the curve of 95%, the Z = 1.65 
Safety stock = ZsdLT = 1.65(10) = 16.5 kits 
Reorder point = expected demand during lead time + safety stock 
© 2011 Pearson Education, Inc. 
publishing as Prentice Hall 
= 350 kits + 16.5 kits of safety stock 
= 366.5 or 367 kits
Inventory & store management m

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Inventory & store management m

  • 1. Inventory & store management Mohit mendiratta
  • 2. What is inventory? Inventory is the raw materials, component parts, work-in-process, or finished products that are held at a location in the supply chain.
  • 3. Costs of Inventory • Physical holding costs: – out of pocket expenses for storing inventory (insurance, security, warehouse rental, cooling) – All costs that may be entailed before you sell it (obsolescence, spoilage, rework...) • Opportunity cost of inventory: foregone return on the funds invested. • Operational costs: – Delay in detection of quality problems. – Delay the introduction of new products. – Increase throughput times.
  • 4. Benefits of Inventory • Hedge against uncertain demand • Hedge against uncertain supply • Economize on ordering costs • Smoothing To summarize, we build and keep inventory in order to match supply and demand in the most cost effective way.
  • 5. 12-5 Types of Inventories • Raw materials & purchased parts • Partially completed goods called work in progress • Finished-goods inventories – (manufacturing firms) or merchandise (retail stores)
  • 6. 12-6 Types of Inventories (Cont’d) • Replacement parts, tools, & supplies • Goods-in-transit to warehouses or customers
  • 7. 12-7 Functions of Inventory • To meet anticipated demand • To smooth production requirements • To decouple operations • To protect against stock-outs
  • 8. 12-8 Functions of Inventory (Cont’d) • To take advantage of order cycles • To help hedge against price increases • To permit operations • To take advantage of quantity discounts
  • 9. 12-9 Objective of Inventory Control • To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds – Level of customer service – Costs of ordering and carrying inventory Inventory turnover is the ratio of average cost of goods sold to average inventory investment.
  • 10. 12-10 Effective Inventory Management • A system to keep track of inventory • A reliable forecast of demand • Knowledge of lead times • Reasonable estimates of – Holding costs – Ordering costs – Shortage costs • A classification system
  • 11. 12-11 Operations Strategy • Too much inventory – Tends to hide problems – Easier to live with problems than to eliminate them – Costly to maintain • Wise strategy – Reduce lot sizes – Reduce safety stock
  • 12. Inventory Control Systems Continuous system (fixed-order-quantity) constant amount ordered when inventory declines to predetermined level Periodic system (fixed-time-period) order placed for variable amount after fixed passage of time
  • 13. Economic Order Quantity (EOQ) Models • EOQ – optimal order quantity that will minimize total inventory costs • Basic EOQ model • Production quantity model
  • 14. Assumptions of Basic EOQ Model Demand is known with certainty and is constant over time No shortages are allowed Lead time for the receipt of orders is constant Order quantity is received all at once
  • 15. Inventory Order Cycle Demand rate Lead Lead Time time time Order placed Order placed Order receipt Order receipt Order quantity, Q Inventory Level Reorder point, R 0
  • 16. EOQ Cost Model Co - cost of placing order D - annual demand Cc - annual per-unit carrying cost Q - order quantity Annual ordering cost = CoD Q Annual carrying cost = CcQ 2 CoD Q Total cost = + CcQ 2
  • 17. EOQ Cost Model (cont.) Annual cost ($) Total Cost Carrying Cost = CcQ 2 Order Quantity, Q Slope = 0 Minimum total cost Optimal order Qopt Ordering Cost = CoD Q
  • 18. Production Order Quantity Model  Used when inventory builds up over a period of time after an order is placed  Used when units are produced and sold simultaneously © 2011 Pearson Education, Inc. publishing as Prentice Hall
  • 19. Production Order Quantity Model Inventory level Part of inventory cycle during which production (and usage) is taking place © 2011 Pearson Education, Inc. publishing as Prentice Hall Time Demand part of cycle with no production t Maximum inventory Figure 12.6
  • 20. Production Order Quantity Model Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate t = Length of the production run in days © 2011 Pearson Education, Inc. publishing as Prentice Hall = (Average inventory level) x Annual inventory holding cost Holding cost per unit per year = (Maximum inventory level)/2 Annual inventory level = – Maximum inventory level Total produced during the production run Total used during the production run = pt – dt
  • 21. Production Order Quantity Model Q = Number of pieces per order p = Daily production rate H = Holding cost per unit per year d = Daily demand/usage rate t = Length of the production run in days © 2011 Pearson Education, Inc. publishing as Prentice Hall = – Maximum inventory level Total produced during the production run Total used during the production run = pt – dt However, Q = total produced = pt ; thus t = Q/p Q p Q p Maximum inventory level = p – d = Q 1 – d p Holding cost = (H) = 1 – H d p Q 2 Maximum inventory level 2
  • 22. Production Order Quantity Example D = 1,000 units p = 8 units per day S = $10 d = 4 units per day H = $0.50 per unit per year © 2011 Pearson Education, Inc. publishing as Prentice Hall Q* = 2DS H[1 - (d/p)] 2(1,000)(10) 0.50[1 - (4/8)] Q* = = 80,000 = 282.8 or 283 hubcaps
  • 23. Probabilistic Models and Safety © 2011 Pearson Education, Inc. publishing as Prentice Hall Stock  Used when demand is not constant or certain  Use safety stock to achieve a desired service level and avoid stockouts ROP = d x L + ss Annual stockout costs = the sum of the units short x the probability x the stockout cost/unit x the number of orders per year
  • 24. Safety Stock Example ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Number of Units Probability © 2011 Pearson Education, Inc. publishing as Prentice Hall 30 .2 40 .2 ROP  50 .3 60 .2 70 .1 1.0
  • 25. Safety Stock Example ROP = 50 units Stockout cost = $40 per frame Orders per year = 6 Carrying cost = $5 per frame per year Safety Stock Additional Holding Cost Stockout Cost © 2011 Pearson Education, Inc. publishing as Prentice Hall Total Cost 20 (20)($5) = $100 $0 $100 10 (10)($5) = $ 50 (10)(.1)($40)(6) = $240 $290 0 A safet$y s t0ock( 1o0f )2(0.2 f)r(a$m4e0s) (g6i)v e+s (t2h0e) l(o.1w)e($st4 t0o)t(a6l) c=ost$960 $960 ROP = 50 + 20 = 70 frames
  • 26. Probabilistic Demand © 2011 Pearson Education, Inc. publishing as Prentice Hall ROP = 350 + safety stock of 16.5 = 366.5 Safety stock 16.5 units ROP  Place order Inventory level Time 0 Minimum demand during lead time Maximum demand during lead time Mean demand during lead time Normal distribution probability of demand during lead time Expected demand during lead time (350 kits) Receive order Lead time Figure 12.8
  • 27. Probabilistic Demand Use prescribed service levels to set safety stock when the cost of stockouts cannot be determined ROP = demand during lead time + ZsdLT where Z = number of standard deviations © 2011 Pearson Education, Inc. publishing as Prentice Hall sdLT = standard deviation of demand during lead time
  • 28. Probabilistic Demand © 2011 Pearson Education, Inc. publishing as Prentice Hall Probability of no stockout 95% of the time Safety stock Mean demand 350 ROP = ? kits Quantity Number of standard deviations 0 z Risk of a stockout (5% of area of normal curve)
  • 29. Probabilistic Example Average demand = m = 350 kits Standard deviation of demand during lead time = sdLT = 10 kits 5% stockout policy (service level = 95%) Using Appendix I, for an area under the curve of 95%, the Z = 1.65 Safety stock = ZsdLT = 1.65(10) = 16.5 kits Reorder point = expected demand during lead time + safety stock © 2011 Pearson Education, Inc. publishing as Prentice Hall = 350 kits + 16.5 kits of safety stock = 366.5 or 367 kits