1. Types of Inventories (manufacturing firms) (retail stores)
Raw materials & purchased parts
Partially completed goods called work in progress
Finished-goods inventories or merchandise
(manufacturing firms) (retail stores)

2. Types of Inventories (Cont’d)
Replacement parts, tools, & supplies
Goods-in-transit to warehouses or customers

3. Functions of Inventory
To meet anticipated demand
To smooth production requirements
To decouple operations
To protect against stock-outs
To take advantage of quantity discounts
To help hedge against price increases
To permit operations

4. 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

5. Key Inventory Terms
Lead time: time interval between ordering and receiving the order
Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year
Ordering costs: costs of ordering and receiving inventory

6. Economic Order Quantity Models

7. Costs Associated with Inventory Control
Three categories of costs associated with inventory:
Purchasing costs
Ordering costs
Carrying costs

8. Purchasing Costs
Purchasing costs are the costs of goods acquired from suppliers including incoming freight or transportation costs.
These costs usually make up the largest single cost category of inventory.
Discounts for different purchase-order sizes and supplier credit terms affect purchasing costs.

9. Ordering Costs
Ordering costs are the costs of preparing, issuing, and paying purchase orders, plus receiving and inspecting the items included in the orders.
Purchase approval and special processing costs are related to the number of purchase orders processed.
MGT 504 by Dr. Bin Jiang

10. Purchasing Process Needs Identification Purchasing requisition
Reorder point system
Statement of work/scope of work
2. Description by:
Market grade/industry standard
Brand
Specification
Performance characteristics
3. Supplier Selection/Contracting
Competitive bidding
Selecting
Negotiating
Contracting
4. Ordering
Purchase orders
EDI
5. Follow-up and Expediting
6. Receipt and Inspection
7. Settlement and Payment
8. Records Maintenance
Order Cycle
MGT 504 by Dr. Bin Jiang

11. Carrying Costs
Carrying costs arise when an organization holds an inventory of goods for sale.
These costs include the opportunity cost of the investment tied up in inventory and the costs associated with storage such as space rental, insurance, obsolescence, and spoilage.
MGT 504 by Dr. Bin Jiang

12. Economic-Order-Quantity Decision Model
The economic-order-quantity (EOQ) is a decision model that calculates the optimal quantity of inventory to order under a restrictive set of assumptions.
The simplest version of this model incorporates only ordering costs and carrying costs into the calculations.
MGT 504 by Dr. Bin Jiang

13. Simplest EOQ Model
The simplest EOQ model minimizes the relevant ordering costs and carrying costs.
Relevant total costs = Relevant ordering costs + Relevant carrying costs
MGT 504 by Dr. Bin Jiang

14. The Simplest EOQ Assumptions
Demand is known
Lead time is known & constant
No quantity discounts are available
Ordering (or setup) costs are constant
All demand is satisfied (no shortages)
The order quantity arrives in a single shipment
MGT 504 by Dr. Bin Jiang

15. Profile of Inventory Level Over Time
The Inventory Cycle
Profile of Inventory Level Over Time
Quantity
on hand Q
Receive
order
Place
Lead time
Reorder
point
Usage
rate
Time
MGT 504 by Dr. Bin Jiang

16. Costs Holding Cost: Setup Costs: A per lot Cost Function:
MGT 504 by Dr. Bin Jiang

17. EOQ Model How Much to Order?
Annual Cost
Total Cost Curve
Holding Cost Curve
Order (Setup) Cost Curve
Order Quantity
Optimal Order Quantity (Q*)
MGT 504 by Dr. Bin Jiang

18. Economic Order Quantity
EOQ Square Root Formula
MGT 504 by Dr. Bin Jiang

19. Minimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal.
MGT 504 by Dr. Bin Jiang

20. The Key Insight of EOQ
There is a tradeoff between lot size and inventory costs.
Large lot size = high inventory and infrequent orders.
Small lot size = frequent orders lower average inventory
MGT 504 by Dr. Bin Jiang

21. Total Inventory Cost (TC)
Example: A computer company has annual demand of 10,000. They want to determine EOQ for circuit boards which have an annual holding cost (H) of $6 per unit, and an ordering cost (S) of $75. They want to calculate TC and the reorder point (R) if the purchasing lead time is 5 days.
EOQ (Q)
Reorder Point (R)
Total Inventory Cost (TC)
MGT 504 by Dr. Bin Jiang

22. Example
A large bakery buys flour in 25-pound bags. The bakery uses an average of 4,860 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $10 per order. Annual carrying costs are $75 per bag.
Determine the economic order quantity.
What is the average number of bags on hand?
How many orders per year will there be?
Compute the total cost of ordering and carrying flour.
If ordering costs were to increase by 10% per order, how much would that affect the minimum total annual cost?
If holding costs were to increase by 10%, how much would that affect the minimum total annual cost?
If holding costs were to increase by 10%, but ordering cost were to decrease 10%, how much would that affect the minimum total annual cost?
MGT 504 by Dr. Bin Jiang

23. Production Order Quantity Model
Assumptions:
Demand is known
Lead time is known & constant
No quantity discounts are available
Ordering (or setup) costs are constant
All demand is satisfied (no shortages)
The order quantity arrives in a single shipment
MGT 504 by Dr. Bin Jiang

24. Production Order Quantity Model
Used when units are produced and sold simultaneously
Inventory level
Time
Part of inventory cycle during which production (and usage) is taking place
Demand part of cycle with no production
Maximum inventory t
MGT 504 by Dr. Bin Jiang

25. 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
= (Average inventory level) x
Annual inventory holding cost
Holding cost per unit per year
= (Maximum inventory level)/2
Average inventory level
= –
Maximum inventory level
Total produced during the production run
Total used during the production run
= pt – dt
MGT 504 by Dr. Bin Jiang

26. 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
= –
Maximum inventory level
Total produced during the production run
Total used during the production run
= pt – dt
Q = total produced = pt ; thus t = Q/p
Maximum inventory level
= p – d = Q 1 – Q p d
Holding cost = (H) = – H d p Q 2
Maximum inventory level
MGT 504 by Dr. Bin Jiang

27. 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
D = Annual demand
Setup cost = (D/Q)S
Holding cost = (1/2)HQ[1 - (d/p)]
(D/Q)S = (1/2)HQ[1 - (d/p)]
Q2 =
2DS
H[1 - (d/p)]
Q* =
2DS
H[1 - (d/p)] p
MGT 504 by Dr. Bin Jiang

28. Quantity Discount Model
Assumptions:
Demand is known
Lead time is known & constant
No quantity discounts are available
Ordering (or setup) costs are constant
All demand is satisfied (no shortages)
The order quantity arrives in a single shipment
MGT 504 by Dr. Bin Jiang

29. Quantity Discount Model
Reduced prices are often available when larger quantities are purchased
Trade-off is between reduced product cost and increased holding cost
Total cost = Setup cost + Holding cost + Product cost
MGT 504 by Dr. Bin Jiang

30. Quantity Discount Model
A typical quantity discount schedule
Discount Number
Discount Quantity
Discount (%)
Discount Price (P) 1
0 to 999
no discount
$5.00 2
1,000 to 1,999 4
$4.80 3
2,000 and over 5
$4.75
Total Annual Demand is 5000
MGT 504 by Dr. Bin Jiang

31. Quantity Discount Model
Steps in analyzing a quantity discount
For each discount, calculate Q*
If Q* for a discount doesn’t qualify, choose the smallest possible order size to get the discount
Compute the total cost for each Q* or adjusted value from Step 2
Select the Q* that gives the lowest total cost
MGT 504 by Dr. Bin Jiang

32. Quantity Discount Model
Total cost $
Order quantity
1,000
2,000
Total cost curve for discount 2
Total cost curve for discount 1
Total cost curve for discount 3
Q* for discount 2 is below the allowable range at point a and must be adjusted upward to 1,000 units at point b a b
1st price break
2nd price break
MGT 504 by Dr. Bin Jiang

33. Quantity Discount Example
2DS IP
Calculate Q* for every discount
Q1* = = 700 units/order
2(5,000)(49)
(.2)(5.00)
Q2* = = 714 units/order
2(5,000)(49)
(.2)(4.80)
Q3* = = 718 units/order
2(5,000)(49)
(.2)(4.75)
MGT 504 by Dr. Bin Jiang

34. Quantity Discount Example
2DS IP
Calculate Q* for every discount
Q1* = = 700 units/order
2(5,000)(49)
(.2)(5.00)
Q2* = = 714 units/order
2(5,000)(49)
(.2)(4.80)
1,000 — adjusted
Q3* = = 718 units/order
2(5,000)(49)
(.2)(4.75)
2,000 — adjusted
MGT 504 by Dr. Bin Jiang

35. Quantity Discount Example
Discount Number
Unit Price
Order Quantity
Annual Purchase Cost
Annual Ordering Cost
Annual Holding Cost
Total 1
$5.00
700
$25,000
$350
$25,700 2
$4.80
1,000
$24,000
$245
$480
$24,725 3
$4.75
2,000
$23,750
$122.50
$950
$24,822.50
Choose the price and quantity that gives the lowest total cost
Buy 1,000 units at $4.80 per unit
MGT 504 by Dr. Bin Jiang

36. Safety Stock Model Demand is known Lead time is known & constant
Assumptions:
Demand is known
Lead time is known & constant
No quantity discounts are available
Ordering (or setup) costs are constant
All demand is satisfied (no shortages)
The order quantity arrives in a single shipment
MGT 504 by Dr. Bin Jiang

37. Safety Stock Model
In the simplest EOQ model, ROP = dL In the safety stock model, ROP = (safety stock)
Q+SS SS
MGT 504 by Dr. Bin Jiang

38. Safety Stock Model SS is decided by the following five factors:
The variability of demand;
The variability of lead time;
The average demand;
The average lead time;
The desired service level.
MGT 504 by Dr. Bin Jiang

39. Safety Stock: Two Uncertainties
MGT 504 by Dr. Bin Jiang

40. Safety Stock Model z-Value Associated Service Level 0.84 80% 1.28 90%
1.65
95%
2.33
99%
MGT 504 by Dr. Bin Jiang

41. Safety Stock Model Example
A retailer sells, on average, 16 Panasonic microwave ovens a day ( ), with a standard deviation in daily demand of 3 ( ). If a retailer reorders suppliers directly from its supplier, they will take, on average, nine days to arrive ( ), with a standard deviation in lead time of 2 ( ). The retailer has decided to maintain a 95% service level. How many safety stock should the retailer hold? What is the retailer’s reorder point?
MGT 504 by Dr. Bin Jiang

42. Safety Stock Model Example
MGT 504 by Dr. Bin Jiang

43. Warehouse Effect in Supply Chain Risk Pooling and Inventory Impact
Consider a distribution supply chain consisting of a set of n downstream retailers linked to a common source warehouse. Suppose the supplier lead time is L and every retailer faced a demand with a mean of µ and a variance of σ2
Supplier
Lead time: L
Warehouse
Retailer 1
Retailer 2
………….
………….
………….
Retailer n
Customer
µ, σ2
Customer
µ, σ2
Customer
µ, σ2
MGT 504 by Dr. Bin Jiang

44. Warehouse Effect in Supply Chain Risk Pooling and Inventory Impact
MGT 504 by Dr. Bin Jiang

45. Net Requirements Plan
MGT 504 by Dr. Bin Jiang

46. Lot-Sizing Techniques
Lot-for-lot techniques order just what is required for production based on net requirements
May not always be feasible
If setup costs are high, costs may be high as well
Economic order quantity (EOQ)
EOQ expects a known constant demand and MRP systems often deal with unknown and variable demand
MGT 504 by Dr. Bin Jiang

47. Lot-for-Lot Example 1 2 3 4 5 6 7 8 9 10 Gross requirements 35 30 4055
Scheduled receipts
Projected on hand
Net requirements
Planned order receipts
Planned order releases
MGT 504 by Dr. Bin Jiang

48. Lot-for-Lot Example No on-hand inventory is carried through the system
Total holding cost = $0
There are seven setups for this item in this plan
Total setup cost = 7 x $100 = $700 1 2 3 4 5 6 7 8 9 10
Gross requirements 35 30 40 55
Scheduled receipts
Projected on hand
Net requirements
Planned order receipts
Planned order releases
MGT 504 by Dr. Bin Jiang

49. EOQ Lot Size Example Holding cost = $1/week; Setup cost = $100;2 3 4 5 6 7 8 9 10
Gross requirements 35 30 40 55
Scheduled receipts
Projected on hand
Net requirements 16
Planned order receipts 73
Planned order releases
Holding cost = $1/week; Setup cost = $100;
Average weekly gross requirements = 27; EOQ = 73 units
MGT 504 by Dr. Bin Jiang

50. EOQ Lot Size Example Annual demand = 1,404
Total cost = setup cost + holding cost
Total cost = (1,404/73) x $100 + (73/2) x ($1 x 52 weeks)
Total cost = $3,798
Cost for 10 weeks = $3,798 x (10 weeks/52 weeks) = $730 1 2 3 4 5 6 7 8 9 10
Gross requirements 35 30 40 55
Scheduled receipts
Projected on hand
Net requirements 16
Planned order receipts 73
Planned order releases
Holding cost = $1/week; Setup cost = $100;
Average weekly gross requirements = 27; EOQ = 73 units
MGT 504 by Dr. Bin Jiang