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William J. Stevenson Operations Management 8 th edition
11-1 Inventory Management
William J. Stevenson
Operations Management
8th edition
11-2 Inventory Management
Chapter ContentsChapter Contents
1) Introduction2) Functions3) Objectives4) Requirements of effective inventory
management5) EOQ models: EOQ quantity model6) Quantity discounts7) When to reorder with EOQ ordering.
11-3 Inventory Management
Independent Demand
A
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand
Independent demand is uncertain. Dependent demand is certain.
Inventory: a stock or store of goods
11-4 Inventory Management
Types of InventoriesTypes of Inventories
Raw materials & purchased parts Partially completed goods called
work in progress Finished-goods inventories
(manufacturing firms) or merchandise (retail stores)
11-5 Inventory Management
Types of Inventories (ContTypes of Inventories (Cont’’d)d)
Replacement parts, tools, & supplies
Goods-in-transit to warehouses or customers
11-6 Inventory Management
Q. Functions of InventoryQ. Functions of Inventory
To meet anticipated demand
To smooth production requirements
To decouple operations
To protect against stock-outs
11-7 Inventory Management
Functions of Inventory (ContFunctions of Inventory (Cont’’d)d)
To take advantage of order cycles
To help hedge against price increases
To permit operations
To take advantage of quantity discounts
11-8 Inventory Management
Q. Objectives of Inventory ControlQ. Objectives 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
11-9 Inventory Management
A system to keep track of inventory A reliable forecast of demand Knowledge of lead times (time interval
between ordering and receiving the order) Reasonable estimates of
Holding costs Ordering costs Shortage costs
A classification system
Q. Effective Inventory ManagementQ. Effective Inventory Management
11-10 Inventory Management
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
Shortage costs: costs when demand exceeds supply
Key Inventory TermsKey Inventory Terms
11-11 Inventory Management
Economic order quantity model
Economic production model
Quantity discount model
Q. Economic Order Quantity ModelsQ. Economic Order Quantity Models
11-12 Inventory Management
a) Only one product is involved
b) Annual demand requirements known
c) Demand is even throughout the year
d) Lead time does not vary
e) Each order is received in a single delivery
f) There are no quantity discounts
Assumptions of EOQ ModelAssumptions of EOQ Model
11-13 Inventory Management
The Inventory CycleThe Inventory CycleFigure 11.2
Profile of Inventory Level Over Time
Quantityon hand
Q
Receive order
Placeorder
Receiveorder
Placeorder
Receiveorder
Lead time
Reorderpoint
Usage rate
Time
11-14 Inventory Management
Total CostTotal Cost
Annualcarryingcost
Annualorderingcost
Total cost = +
Q2 H D
QSTC = +
11-15 Inventory Management
Cost Minimization GoalCost Minimization Goal
Order Quantity (Q)
The Total-Cost Curve is U-Shaped
Ordering Costs
QO
Ann
ual C
ost
(optimal order quantity)
SQD
HQ
TC ��
Figure 11.4C
11-16 Inventory Management
Deriving the EOQDeriving 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.
Q = 2DSH
= 2(Annual Demand )(Order or Setup Cost )Annual Holding CostOPT
11-17 Inventory Management
Minimum Total CostMinimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal.
Q = 2DSH
= 2(Annual Demand )(Order or Setup Cost )Annual Holding CostOPT
11-18 Inventory Management
Production done in batches or lots Capacity to produce a part exceeds the part’s
usage or demand rate Assumptions of EPQ are similar to EOQ
except orders are received incrementally during production
Economic Production Quantity (EPQ)Economic Production Quantity (EPQ)
11-19 Inventory Management
Problem 01Problem 01 A local distributor for a national tire company expects to
sell approximately 9600 steel- belted radial tires of a certain size and tread design next year. Annual carrying cost is &16 per tire and ordering cost is $75. The distributor operates 288 days a year.
1)What is EOQ?2)How many times per year does the store reorder?3)What is the length of an order cycle? 4)What is the total annual cost if the EOQ quantity is
ordered?
11-20 Inventory Management
SolutionSolution--01 01 D= 9600 tires per year H = $ 16 per unit per year S= $ 75
1)
2) Number of order per year= D/Qo=9600/300=32 3) Length of order cycle= Qo/D =300 tires/9600tires, yr 4) Total cost ,TC = Carrying cost + Ordering cos
=(Qo/2)H+(D/Qo)S=(300/2)16+(9600/300)75=$2400+$2400=$4800
tires 300 =16
)2(9600)(75 =
CostHolding AnnualCost) Setupor derDemand)(Or 2(Annual
= H
2DS = Q OPT
11-21 Inventory Management
Problem 02Problem 02
Piddling Manufacturing assembles security monitors. It purchases 3600 black and white cathode ray tubes a year at $65 each. Ordering costs are $ 31, and annual carrying costs are 20 percent of the purchase price .
Compute the optimal quantity and the total annual cost of ordering and carrying the inventory.
11-22 Inventory Management
SolutionSolution--0202 D= 3600 cathode ray tubes per year S =$31 H =.20($65)=$13
Total cost ,TC = Carrying cost + Ordering cost=(Qo/2)H+(D/Qo)S=(131/2)13+(3600/131)31=$852+$852=$1704
tuberay cathode131 =13
)2(3600)(31 =
CostHolding AnnualCost) Setupor derDemand)(Or 2(Annual
= H
2DS = Q OPT
11-23 Inventory Management
ProblemProblem--33 A museum of natural history opened a gift shop two years ago. One
of the top selling items at the museum’s gift shop is a bird feeder. Sales are 18 units per week and supplier charges $60 per unit. The cost of placing an order with the supplier is $45. Annual holding cost is 25% of a feeder’s value and the museum operates 52 weeks per year. Management chooses a 390 unit lot size so that new orders could be placed less frequently.
a. What is the annual cost of the current policy of using a 390 unit lot size?
b. Would a lot size of 468 be better? c. What is the EOQ?
11-24 Inventory Management
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
Economic Production Quantity AssumptionsEconomic Production Quantity Assumptions
11-25 Inventory Management
ProblemProblem--0404 A toy manufacturer uses 48000 rubber wheels per year for
its poplar dump truck series the firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is $1 per wheel a year. Setup cost for a production run of wheels is $45. the firm operates 240 days per year . Determine the
a)Optimal run size or Economic Run sizeb)Minimum total annual cost for carrying and setupc)Cycle time for the optimal run size d)Run time
11-26 Inventory Management
SolutionSolution--0404 D( annual demand)=48000 wheels per year S( holding cost)= $45 H( carrying cost) =$1 per wheel per year P( Production rate) = 800 wheels per day u( usage rate) = 48000 wheels per 240 days or 200 wheels
per day Imax= Maximum inventory.
a) \
2400200800
800*
1)45)(48000(2
20
��
�
��
upp
HDS
Q
11-27 Inventory Management
SolutionSolution--0404…………
b) TC min=Carrying cost + setup cost={Imax /2}H+(D/Qo)S
Imax ={Qo/p}(p-u)=(2400/800)(800-200)=1800 wheels
TC min={Imax /2}H+(D/Qo)S=(1800/2)$1+(48000/2400)($45)=1800
11-28 Inventory Management
SolutionSolution--0404……....
c) Cycle time = Qo/u= 2400 wheels /200 wheels per day=12 days (a run of wheels will be
made every 12 days)
d) Run time = Qo/p= 2400 wheels / 800 wheels per day=3 days ( each run will require three
days to complete)
11-29 Inventory Management
Total Costs with Purchasing CostTotal Costs with Purchasing Cost
Annualcarryingcost
PurchasingcostTC = +
Q2 H D
QS(O)TC = +
+Annualorderingcost
PD+
11-30 Inventory Management
Total Costs with PDTotal Costs with PDC
ost
EOQ
TC with PD
TC without PD
PD
0 Quantity
Adding Purchasing costdoesn’t change EOQ
Figure 11.7
11-31 Inventory Management
Total Cost with Constant Carrying Costs Total Cost with Constant Carrying Costs
OC
EOQ Quantity
Tota
l Cos
t
TCa
TCc
TCbDecreasingPrice
CC a,b,c
Figure 11.9
11-32 Inventory Management
ProblemProblem--o5o5 A small manufacturing firm uses roughly 3400 pounds of
chemical dye a year. Currently the firm purchases 300 pounds per order and pays $3 per pound. The supplier has just an announced that orders of 1000 pounds or more will be filled at a price of $ 2 per pound. The manufacturing firm incurs a cost of $100 cash time it submits an order and assigns an annual holding cost of 17 percent of the purchase price per pound.
A) determine the order size that will minimize the total cost.
B) if the supplier offered the discount at 1500 pounds instead of 1000 pounds what order size would minimize total cost?
11-33 Inventory Management
SolusionSolusion--0505 D= 3400 pounds per year S = $100 H= .17pA) compute the EOQ for $2 per pound
the quality range are Range unit price 1to 999 $31000+ $2
Because this quantity is feasible at $2 per pound it is the optimum
pounds 1414 =.17(2)
0)2(3400)(10 =
CostHolding AnnualCost) Setupor derDemand)(Or 2(Annual
= H
2DS pounds ·Q$2 �
11-34 Inventory Management
SolusionSolusion--0505……....
B) When the discount is offered at 1500 pounds the EOQ for the $2 per pound range is no longer feasible . Consequently it becomes necessary to compute the EOQ for $3 per pound and compare the total cost for that order size with the total cost using the price break quantity (i.e1500)
pounds 1155 =.17(3)
0)2(3400)(10 =
CostHolding AnnualCost) Setupor derDemand)(Or 2(Annual
= H
2DS pounds ·Q$3 �
11-35 Inventory Management
SolusionSolusion--0505……....Annualcarryingcost
PurchasingcostTC = +
Q2 H D
QSTC1155 = +
+Annualorderingcost
PD+
=1155(.17)(3)/2+3400(100)/1155+3(3400) =$10789
Q2 H D
QS(O)TC1500 = + PD+
=1500(.17)(2)/2+3400(100)/1500+2(3400) =$7282( It is lowest total cost ) 1500 is the optimal order size
11-36 Inventory Management
Q. When to Reorder with EOQ OrderingQ. 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.
11-37 Inventory Management
Determinants of the Reorder PointDeterminants of the Reorder Point
The rate of demand The lead time Demand and/or lead time variability Stockout risk (safety stock)
11-38 Inventory Management
Safety StockSafety Stock
LT Time
Expected demandduring lead time
Maximum probable demandduring lead time
ROP
Qua
ntity
Safety stock
Figure 11.12
Safety stock reduces risk ofstockout during lead time
11-39 Inventory Management
Reorder PointReorder Point
ROP
Risk ofa stockout
Service level
Probability ofno stockout
Expecteddemand Safety
stock0 z
Quantity
z-scale
Figure 11.13
The ROP based on a normalDistribution of lead time demand
11-40 Inventory Management
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