ppt 06 inventory management rop
DESCRIPTION
omTRANSCRIPT
Inventory ManagementInventory Management
Review Period Review Period Sanjay Choudhari
Indian Institute of Management Indore
Inventory Control SystemsInventory Control Systems
Two important questions: How much? When?
Review PeriodReview Period
Continuous Review / Q Continuous Review / Q SystemSystem
Periodic Review / P systemPeriodic Review / P system
1. T : Time interval
2. OUL = TI : Target inventory level
1. Q*= EOQ : Economic Order Quantity
2. R : Reorder point
Q is fixed T is fixed
Continuous Review PeriodContinuous Review PeriodDemand is either Deterministic or Stochastic
Lead Time is either Deterministic or Stochastic
Constant demand rate, constant lead time
Variable demand rate, constant lead time
Constant demand rate, variable lead time
Variable demand rate, variable lead time
Continuous Review SystemsContinuous Review Systems
Time
On
-han
d in
ven
tory
TBO1 TBO2 TBO3
LT LT2 LT
R
Orderreceived
Q
Orderplaced
Orderplaced
Orderreceived
IP IP
Q
Orderplaced
Q
Orderreceived
Orderreceived
0
IP
Q System When Demand Is Uncertain
σt = 2
+5
Demand for day 1
σt = 3.46
15Demand for 3-days lead time
+5
Demand for day 2
σt = 2
=5
Demand for day 3
σt = 2
Demand During Lead TimeDemand During Lead Time
Demand During Lead TimeDemand During Lead Time
Average demand
during lead time
Cycle-service level = 85%
Probability of stockout(1.0 – 0.85 = 0.15)
zσdLT
R
Reorder point (R) = Expected demand + Safety stock
d LT
dLT
Z *+=
d = Mean demand
LT = Lead time
2 22LT d LTd
dLT
=
Continuous Review PeriodContinuous Review Period
Where
dLT = Standard deviation of demand during lead time
d = Std. deviation of the demand
LT = Std. deviation of the lead time
Z = Standard normal deviate associated with the cycle service level
during lead time
SAPSAP
Continuous Review Period Continuous Review Period
Cycle Service Level :
Probability that a stockout will not occur during the lead time of inventory cycle…
Service Levels, Safety Stock and Service Levels, Safety Stock and ShortagesShortages
Robert G. BrownRobert G. Brown shows relationship……..
the number of standard deviations of safety stock, the service level and the expected number of units short correspondence
Service level Cycle Service Level: Prob (No stock-out during lead time)
Fill rate: Fraction of annual demand satisfied immediately from stocks Expected number of unit short in each order cycle
Service Levels, Safety Stock and Service Levels, Safety Stock and ShortagesShortages
EN = (1- Fill Rate) * D
D = Annual demand
Q = EOQ
E (Z) = Expected number of units short from a normalized table where mean = 0 and = 1
dLT = Standard deviation of demand during lead time
/ ( ) *D
No of stockout year EN E nQ
Where, E(n) = Expected no. of units short per Cycle
= E(z)* dLT
Periodic Review Periodic Review
OUL
LT
SS
Time
Inventory
TOrder Placed
Order Received
Order Placed
Imax
Imin
Q1
Q1
Q2
Q2
LT
Order Received
Q3
LTOrder Received
Q3
Order Placed
T
Variable Demand (d),
Constant Lead Time (LT)
Order upto level (OUL) = Expected demand + Safety stock
Z *+= dLT
Periodic Review Periodic Review
during protection interval
( )d T LT
dLT
= Mean demand
LT = Lead time
=
Where
dLT = Standard deviation of demand during lead time
d= Std. deviation of the demand
LT= Std. deviation of the lead time
Z = Standard normal deviate associated with the cycle service level
2 22( )T LT d LTd
dT = Review period
Total Annual Inventory Cost Total Annual Inventory Cost
𝑇𝐴𝐶 = 𝐷𝑑𝑇ሺ𝐶𝑂ሻ+ 𝑑𝑇2 ሺ𝐶𝐻ሻ+ 𝑆𝑆∗ሺ𝐶𝐻ሻ+ 𝐷∗𝐶𝑖
𝑇𝐴𝐶 = 𝐷𝑄ሺ𝐶𝑂ሻ+ 𝑄2ሺ𝐶𝐻ሻ+ 𝑆𝑆∗(𝐶𝐻) + 𝐷∗𝐶𝑖
Continuous Review : Q System Continuous Review : Q System
Periodic Review : P System Periodic Review : P System
No of orders is fixed due to constant Review Period T
Comparative AdvantagesComparative Advantages
Continuous Review : Q System Continuous Review : Q System Lower safety stocks Fixed lot sizes can result in quantity discounts Review frequency may be individualized
Periodic Review : P System Periodic Review : P System Convenient, Less time consuming Allow for combining orders to the same
supplier Inventory recordkeeping cost can be reduced
: need to know IP when review is made