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© 1995 Corel Corp.© 1984-1994 T/Maker Co. © 1984-1994 T/Maker Co.
© 1995 Corel Corp.
What is Inventory?
The Functions of Inventory
To ”decouple” or separate various parts of the production processTo provide a stock of goods that will provide a “selection” for customersTo take advantage of quantity discountsTo hedge against inflation and upward price changes
Inventory
Process stage
Demand Type
Number & Value Other
Raw Material WIP & Finished
Goods
Independent Dependent
A Items B Items C Items
Maintenance Dependent Operating
Inventory Classifications
Sources of Waste JIT “fights” seven types of waste
Waste of motion --excessive or unnecessary human activity Waste of waiting --jobs waiting to be processed Waste of inventory --building up unnecessary inventory
stocks Waste of conveyance --jobs being unnecessary moved Waste of processing --excessive or unnecessary operations Waste of overproduction --producing more than demanded Waste of correction (defective products) --waste due to
scrap, rework, repair, etc.
Higher costs Ordering (or setup) cost
Costs of processing, clerks’ wages etc. Holding (or carrying) cost
Building lease, insurance, opportunity, taxes etc.
Difficult to controlHides production problems
Disadvantages of Inventory
Holding Costs Breakdown(Approximate Ranges)
Category
Housing costs
Material handling costs
Labor and administration cost
Investment costs
Pilferage, scrap, and obsolescence
Cost as a % of Inventory Value
6%(3 - 10%
3%(1 - 3.5%0
3%(3 - 5%)
11%(6 - 24%)
3%(2 - 5%)
Order QuantityOrder Quantity
CostCost
Holding Cost Curve
Holding Cost CurveTotal Cost Curve
Total Cost Curve
Ordering & Setup Costs CurveOrdering & Setup Costs Curve
Optimal Optimal Order Quantity (Q*)Order Quantity (Q*)
EOQ Model:Minimize the overall Costs
Inventory Holding Costs
ObsolescenceInsuranceExtra staffingInterestPilferageDamageWarehousingEtc.
Ordering Costs & Setup Costs
Order processingClerical supportClean-up costsRe-tooling costsRelocation or adjustment costs
Underline Decisions Supported by EOQ Models
Objective: Minimizing the total inventory costsHow much to order (Economic Order Quantity)When to order? (Reorder Point)How often should we place orders (Ordering Period)Others How to Take advantage of quantity discount What if the lead time and demand are not constant? Heuristics: Fixed Period Systems
Basic EOQ Model (Constant Demand and Lead Time)
Reorder Reorder Point Point (ROP)(ROP)
TimeTime
Inventory LevelInventory Level
AverageAverageInventory Inventory
(Q*/2)(Q*/2)
Lead TimeLead Time
Optimal Optimal Order Order QuantityQuantity(Q*)(Q*)
Derive the EOQ: Finding Q* that Minimizes the Total Costs
HQ
SQ
DTC
2
Total inventory cost = Order (Setup) cost + Holding cost
To minimize TC, we set the derivative of TC with respect to Q* equal to 0
02
)()(
2
H
Q
DS
dQ
TCd
Thus,
H
DSQ
2*
Optimal Order Quantity
Expected Number of Orders
Expected Time Between Orders Working Days / Year
= =× ×
= =
= =
Q*D SH
ND
Q*
TN
2
DD = Demand per year = Demand per year
SS = Setup (order) cost per order = Setup (order) cost per order
HH = Holding (carrying) cost = Holding (carrying) cost
EOQ Model Equations: How much to Order
Reorder Point: When to Order?
When there is lead time between order and delivery, we need to identify the reorder point to avoid out of stock.This provides answer for the second inventory “When to order?”ROP = (Demand per day)(Lead time for a new order in days) = d L Working Days / Year
=dD
EOQ ExampleElectronic Assembler, Inc. has to order 2920 TX5 circuit boards per year. The
ordering cost is $80 per order; and the holding cost per unit per year is $50. The purchase price is $28. The items can be delivered in 5 days. The company would like to reduce its inventory costs by determining the optimal number of circuit boards to obtain per order. The conditions of ordering and inventory handling satisfy the assumptions of the EOQ model.
Annual demand D = 2,920 unitsDaily demand d = 2,920/365=8 unitsHolding cost H = $50 per unit per yearOrdering cost S = $80 per orderPurchase price P = $28 per unit Lead time LT = 5 days
Answer the following questions with detailed calculations and explanation:
1. Optimal quantity per order (EOQ):2. Annual total relevant costs (optimal):3. Annual total costs (optimal):4. Number of orders per year: 5. Inventory cycle time (Nd=365 working days per year): 6. Reorder Point (ROP):
Allows partial receipt of material Other EOQ assumptions apply
Suited for production environment Material produced, used immediately Provides production lot size
Lower holding cost than EOQ model
Production Order Quantity Model
POQ Model
Reorder Reorder Point Point (ROP)(ROP)
TimeTime
Inventory LevelInventory Level
AverageAverageInventoryInventory
Lead TimeLead Time
Optimal Optimal Order Order QuantityQuantity(Q*)(Q*)
POQ Model Inventory Levels
TimeTime
Inventory LevelInventory Level
Production Production Portion of CyclePortion of Cycle
Max. Inventory Max. Inventory Q·(1- d/p)Q·(1- d/p)
Q*Q*
Supply Supply BeginsBegins
Supply Supply EndsEnds
Inventory level with no demandInventory level with no demand
Demand portion of cycle Demand portion of cycle with no supplywith no supply
D = Demand per year
S = Setup cost
H = Holding cost
d = Demand per day
p = Production per day
POQ Model EquationsOptimal Order Quantity
Setup Cost
Holding Cost
= =
-
= *
= *
=
Q
H* dp
Q
D
QS
p*
1
(
0.5 * H * Q -d
p1
)-d
p1
( )
2*D*S
( )Maximum inventory level
Answers how much to order & when to orderAllows quantity discounts Reduced price when item is
purchased in larger quantities Other EOQ assumptions apply
Trade-off is between lower price & increased holding cost
Quantity Discount Model
Quantity Discount ModelHow Much to Order?
Lowest cost not in Lowest cost not in discount rangediscount range
Order Order QuantityQuantity
Total Total CostCost
Quantity which would Quantity which would be orderedbe ordered
TC for Discount 2
TC for Discount 2
Quantity to Quantity to earn earn
Discount 2Discount 2
Discount 2 Discount 2 PricePrice
Quantity to Quantity to earn earn
Discount 1Discount 1
TC for Discount 1
TC for Discount 1
Discount 1 Discount 1 PricePrice
TC forTC for
No Discount
No Discount
Initial PriceInitial Price
Allow demand and lead time to vary Follows normal distribution Other EOQ assumptions apply
Consider service level & safety stock Service level = 1 - Probability of stockout Higher service level means more safety
stock More safety stock means higher ROP
Probabilistic Models
Probabilistic ModelsWhen to Order?
Reorder Reorder Point Point (ROP)(ROP)
OptimalOptimal Order Order
QuantityQuantity XX
Safety Stock (SS)Safety Stock (SS)
TimeTime
Inventory LevelInventory Level
Lead TimeLead Time
SSSSROPROP
Service Service LevelLevel P(Stockout)P(Stockout)
Place Place orderorder
Receive Receive orderorder
FrequencyFrequency
0
20
40
60
80
100
0 50 100% of Inventory Items% of Inventory Items
% Annual $ Usage% Annual $ Usage
AABB CC
Class % $ Vol % ItemsA 80 15B 15 30C 5 55
ABC Classification: Pareto Principle (Critical few and trivial many)
Orders placed at fixed intervals Inventory brought up to target amount Amount ordered varies
No continuous inventory count Possibility of stockout between intervals
Useful when vendors visit routinely Example: P&G representative visits every
2 weeks
Heuristics: Fixed Period Model
TimeTime
Inventory LevelInventory Level Target maximumTarget maximum
PeriodPeriod PeriodPeriodPeriodPeriod
Heuristics: Fixed Period Model
Traditional: inventory exists in case problems ariseJIT objective: Eliminate redundant inventoryJIT requires Small lot sizes Low setup time Containers for fixed number of parts
JIT inventory: Minimum inventory to keep system running (lean but agile)
Implementing JIT via Agile Inventory Management
Scrap
Work in process inventory level(hides problems)
Unreliable Vendors
Capacity Imbalances
Lowering Inventory Reduces Waste
Scrap
Reducing inventory revealsproblems so they can be solved.
Unreliable Vendors
Capacity Imbalances
WIP
Lowering Inventory Reduces Waste
To Lower Inventory, Reduce Lot Sizes
Time
Inventory Level
Lot Size 200
Lot Size 80
Average inventory = 100
Average inventory = 40
Average inventory = (Lot size)/2
…Which Increases Inventory Costs
Lot Size
Cost
Holding CostTotal Cost
Setup Cost
Optimal Lot Size
SmallerLot Size
Unless Setup Costs are Reduced
Lot Size
Cost
Holding CostTotal Cost
Setup Cost
Original optimal lot size
New optimal lot size
Steps to Reduce Setup Time (Honda Assembly Line)
Initial Setup Time
Separate setup into preparation, and actual setup, doing as much as possible while the
machine/process is running (save 30 minutes)
Move material closer and improve material handling (save 20
minutes)Standardize and improve tooling
(save 15 minutes)
90 min
60 min
45 min
25 min
15 min
Use one-touch system to eliminate adjustments (save 10
minutes)Training operators and
standardizing work procedures (save 2 minutes)
Step 1
Step 2
Step 3
Step 5 13 minStep 4
Reducing Lot Sizes Increases the Number of Lots
Small lots increase flexibility to meet customer demands
Strategies for eliminating wasteand for eliminating waiting
A A B B B C
JIT Small Lots
Time
A A B B B C
Freeze Part of the Schedule
Flexibility between Nissan plant and Dealers
Five day before delivery: 100% flexibility
Four day before: Freeze number of each model
Three day before: Freeze change color
Two day: Freeze major options
One day before: Freeze minor options