PRODUCTIONS/OPERATIONS MANAGEMENT

1
CHAPTER
12
Inventory Management
Homework problems 1,3,4,8,9,10,14,15,17,24,26,36
,37 on pp. 593-600.
2
Inventory

• Inventory
• A stock or store of goods
• Independent demand items
• Items that are ready to be sold or used

3
Independent vs. Dependent Demand

• Independent Demand
• When items demand is influenced by market
  conditions and is not related to (i.e., is
  independent of) production decision for any
  other item.
• Wholesale and retail merchandise (finished
  goods), service industry inventory, end-item and
  replacement-part inventories, spare-parts, MRO
  (maintenance, repair, and operating) supplies.
• Demand must be forecasted
• Dependent Demand
• When items demand derives from (i.e., depend
  on) the production decisions for its parents.
• All intermediate and purchased items in
  manufacturing.
• Demand must be derived.

4
Inventory a stock or store of goods
5
Types of Inventories

• Raw materials and purchased parts
• Work-in-process
• Finished goods inventories or merchandise
• Maintenance and repairs (MRO) inventory, tools
  and supplies
• Goods-in-transit to warehouses or customers
  (pipeline inventory)

6
Functions of Inventory

• Inventories serve a number of functions such as
• To meet anticipated customer demand
• To smooth production requirements
• To decouple operations
• To protect against stockouts
• To take advantage of order cycles
• To hedge against price increases
• To permit operations
• To take advantage of quantity discounts

7
Inventory Management

• Management has two basic functions concerning
  inventory
• Establish a system for tracking items in
  inventory
• Make decisions about
• When to order
• How much to order

8
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

9
Inventory Counting Systems

• Periodic System
• Physical count of items in inventory made at
  periodic intervals
• Perpetual Inventory System
• System that keeps track of removals from
  inventory continuously, thus monitoring current
  levels of each item
• Two-bin system
• Two containers of inventory reorder
• when the first is empty

10
Demand Forecast and Lead Time

• Forecasts
• Inventories are necessary to satisfy customer
  demands, so it is important to have a reliable
  estimates of the amount and timing of demand
• Lead time
• Time interval between ordering and receiving the
  order
• Point-of-sale (POS) systems
• A system that electronically records actual sales
• Such demand information is very useful for
  enhancing forecasting and inventory management

11
ABC Classification System

• A-B-C approach
• Classifying inventory according to some measure
  of importance, and allocating control efforts
  accordingly
• A items (very important)
• 10 to 20 percent of the number of items in
  inventory and about 60 to 70 percent of the
  annual dollar value
• B items (moderately important)
• C items (least important)
• 50 to 60 percent of the number
• of items in inventory but only
• about 10 to 15 percent of the
• annual dollar value

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Cycle Counting

• Cycle counting
• A physical count of items in inventory
• Cycle counting management
• How much accuracy is needed?
• A items 0.2 percent
• B items 1 percent
• C items 5 percent
• When should cycle counting be performed?
• Who should do it?

13
How Much to Order EOQ Models

• Economic order quantity model
• Economic production model
• Quantity discount model

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Basic EOQ Model

• The basic EOQ model is used to find a fixed order
  quantity that will minimize total annual
  inventory costs
• Assumptions
• Only one product is involved
• Annual demand requirements are known
• Demand is even throughout the year
• Lead time does not vary
• Each order is received in a single delivery
• There are no quantity discounts

15
The Inventory Cycle
Figure 12.2
16
Total Cost
17
Cost Minimization Goal
Figure 12.4C
The Total-Cost Curve is U-Shaped
Annual Cost
Ordering Costs
Order Quantity (Q)
QO
(optimal order quantity)
18
Deriving the EOQ

• Using calculus, we take the derivative of the
  total cost function and set the derivative
  (slope) equal to zero and solve for Q.

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Minimum Total Cost

• The total cost curve reaches its minimum where
  the carrying and ordering costs are equal.

20
EOQ Sensitivity

• What happens to optimal order quantity (and cycle
  inventory) if the demand rate increase?
• What happens to lot sizes if setup/ordering
  costs decrease?
• What happens if interest rates drop?
• How critical are errors in estimating D, H, and
  S?
• EOQ is robust insenstitive to parameter
  estimation errors!

21
EOQ Sensitivity (Fig. 12-5)
22
Economic Production Quantity (EPQ)

• Production done in batches or lots
• Capacity to produce a part exceeds the parts
  usage or demand rate
• Assumptions of EPQ are similar to EOQ except
  orders are received incrementally during
  production

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Economic Production Quantity Assumptions

• Only one item is involved
• Annual demand is known
• Usage rate is constant
• Usage occurs continually
• Production rate is constant
• Lead time does not vary
• No quantity discounts

24
Economic Run Size
25
Economic Production Quantity (EPQ) or Run Size
e.g., p15 units/day, u5 units/day, and Q45
units
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Total Costs with Purchasing Cost
27
Total Costs with PD
Figure 12.7
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Total Costs with Variable PD
Figure 12.8
29
Constant and variable carrying costs
Figure 12.9
30
EOQ with Quantity Discounts

• Two-Step Procedure
• Step 1. Beginning with lowest price, calculate
  the EOQ for each price level until a feasible
  EOQ is found. It is feasible if it lies in the
  range corresponding to its price.
• Step 2. If the first feasible EOQ found is for
  the lowest price level, this quantity is best.
  Otherwise, calculate the total cost for the
  first feasible EOQ and for the price break
  quantity at each lower price level. The quantity
  with the lowest total cost is optimal.

31
Quantity Discounts Example

• The following quantity discount schedule is
  provided by a supplier
• Order size Discount Unit cost
• 049 0 30.00
• 5099 5 28.50
• 100 or more 10 27.00
• If annual demand is 120 units, ordering cost is
  20 per order, and annual unit inventory holding
  cost is 25, what order quantity would minimize
  total inventory costs?

32
When to Reorder with EOQ Ordering

• Reorder Point - When the quantity on hand of an
  item drops to this amount, the item is reordered
• Safety Stock - Stock that is held in excess of
  expected demand due to variable demand rate
  and/or lead time.
• Service Level - Probability that demand will not
  exceed supply during lead time.

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Determinants of the Reorder Point

• The rate of demand
• The lead time
• Demand and/or lead time variability
• Stockout risk (safety stock)

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Safety Stock
Figure 12.12
35
Reorder Point
Figure 12.13
The ROP based on a Normal distribution of lead
time demand
36
Reorder Point
Figure 12.14
37
Reorder Point Model

• Variable demand and constant lead time
• R d x LT ZvLT sd
• Constant demand and variable lead time
• R d x LT ZdsLT
• Variable demand and variable lead time
• R d x LT ZvLT sd2 d 2 s2LT

Where d average daily or weekly demand, sd
standard deviation of demand per day or
week, sLT standard deviation of lead time per
day or week
38
Reorder Point Example
The injection molding department of a company
uses 40 ponds of a powder a day. Inventory is
reordered when the amount on hand is 240 pounds.
Lead time averages five days. It is normally
distributed and has a standard deviation of two
days. a). What is the probability of a stockout
during lead time? b). What reorder point would
provide a 5 stockout?
39
Fixed-order-interval Model (Figure 12-15)
40
Fixed-Interval Benefits

• Tight control of inventory items
• Items from same supplier may yield savings in
• Ordering
• Packing
• Shipping costs
• May be practical when inventories cannot be
  closely monitored

41
Fixed-Interval Disadvantages

• Requires a larger safety stock
• Increases carrying cost
• Costs of periodic reviews

42
Fixed-order-interval order quantity
Amount to order

• d x (OILT) Z sd vOILT - A

Where OI order (review) interval A amount
on hand at reorder time
43
Fixed-order-interval order quantity
a. Given D520 units, EOQ62 units, 99 service
level, ?d 8 units/wk, LT3 wk b. Reorder
Interval p(EOQ/D)(52)(62/520)(52)6.2 or 6
wk c. Safety stock d. Amount to order

44
Single Period Model

• Single period model model for ordering of
  perishables and other items with limited useful
  lives
• Shortage cost generally the unrealized profits
  per unit
• Excess cost difference between purchase cost and
  salvage value of items left over at the end of a
  period

45
Single Period Model

• Continuous stocking levels
• Identifies optimal stocking levels
• Optimal stocking level balances unit shortage and
  excess cost
• Discrete stocking levels
• Service levels are discrete rather than
  continuous
• Desired service level is equaled or exceeded

46
Single Period Model Example

• Great Farmers Market buys organic mixed salad
  for 2.00 per pound and sells it for 4.20 per
  pound. At the end of each week, any remaining
  mixed salad is sold to a producer of canned soup
  for 0.6 per pound. Weekly demand can be
  approximately by a normal distribution with a
  mean of 100 pounds and a standard deviation of 10
  pounds. What is the optimal stocking level?

47
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