inventory control
TRANSCRIPT
UNIT- 3
INVENTORY CONTROLINVENTORY CONTROL
Delivered By: Sarita Saxena
Copyright 2006 John Wiley & Sons, Inc. 12-2
• Stock of items kept to meet future demand
• Purpose of inventory control
What & how much of various items to be kept in stock.
Time & quantity of various items to be produced.
What Is Inventory ?
Copyright 2006 John Wiley & Sons, Inc. 12-3
Raw materials
Purchased parts and supplies
Work-in-process (partially completed)
products (WIP)
Items being transported
Tools and equipment
Types of Inventory
Reducing amounts of raw materials and purchased
parts and subassemblies by having suppliers deliver
them directly.
Reducing the amount of works-in process by using
just-in-time production.
Reducing the amount of finished goods by shipping
to markets as soon as possible.
Zero Inventory ?
RawMaterials
WorksinProcess Finished
Goods Finished Goodsin Field
Inventory Positions in the Supply Chain
Improve customer service. Economies of purchasing. Economies of production. Transportation savings. Protection of material from spoilage & deterioration . Unplanned shocks (labor strikes, natural disasters,
surges in demand, etc.). To maintain independence of supply chain.
Benefits of Inventory Control
• Lead Time-It is the time that lapses b/w raising of indent by the stores & receipt of materials.
Administrative Lead TimeDelivery Lead Time
• Safety Stock- Difference b/w amount stocked & average expected demand.
Terms used in inventory
Copyright 2006 John Wiley & Sons, Inc. 12-8
Types of Demand
DependentDependent
Demand for items used to produce final products Demand for items used to produce final products
Ex. : Tires stored at a Goodyear plant..
IndependentIndependent
Demand for items used by external customersDemand for items used by external customers
Ex. : Cars, appliances, computers, and houses.
Copyright 2006 John Wiley & Sons, Inc. 12-9
Carrying costCarrying cost Cost of holding an item in inventory e.g cost related to storage.Cost of holding an item in inventory e.g cost related to storage.
Ordering costOrdering cost Cost of replenishing inventory , e.g travelling expenses.Cost of replenishing inventory , e.g travelling expenses.
Shortage costShortage cost Temporary or permanent loss of sales when demand cannot be met.Temporary or permanent loss of sales when demand cannot be met.
Inventory Costs
Copyright 2006 John Wiley & Sons, Inc. 12-10
• EOQ Optimal order quantity that will minimize total
inventory (Ordering + Carrying costs)
EOQ = (2nco / ch)0.5
Economic Order Quantity
Copyright 2006 John Wiley & Sons, Inc. 12-12
Demand is known with certainty and is constant over time.Demand is known with certainty and is constant over time.
No shortages are allowed.No shortages are allowed.
Lead time for the receipt of orders is constant.Lead time for the receipt of orders is constant.
Order quantity is received all at once.Order quantity is received all at once.
Assumptions of Basic EOQ Model
Copyright 2006 John Wiley & Sons, Inc. 12-17
• Class A5 – 15 % of units70 – 80 % of value
• Class B30 % of units15 % of value
• Class C50 – 60 % of units 5 – 10 % of value
ABC Analysis
Copyright 2006 John Wiley & Sons, Inc. 12-18
11 $ 60$ 60 909022 350350 404033 3030 13013044 8080 606055 3030 10010066 2020 18018077 1010 17017088 320320 505099 510510 6060
1010 2020 120120
PARTPART UNIT COSTUNIT COST ANNUAL USAGEANNUAL USAGE
ABC Classification: Example
Copyright 2006 John Wiley & Sons, Inc. 12-19
Demand Demand raterate
TimeTimeLead Lead timetime
Lead Lead timetime
Order Order placedplaced
Order Order placedplaced
Order Order receiptreceipt
Order Order receiptreceipt
Inve
nto
ry L
evel
Inve
nto
ry L
evel
Reorder point, Reorder point, RR
Order quantity, Order quantity, QQ
00
Inventory Order Cycle
Copyright 2006 John Wiley & Sons, Inc. 12-20
CCoo - cost of placing order - cost of placing order DD - annual demand - annual demand
CCcc - annual per-unit carrying cost - annual per-unit carrying cost QQ - order quantity - order quantity
Annual ordering cost =Annual ordering cost =CCooDD
Annual carrying cost =Annual carrying cost =CCccQQ
22
Total cost = +Total cost = +CCooDD
CCccQQ
22
EOQ Cost Model
Copyright 2006 John Wiley & Sons, Inc. 12-21
EOQ Cost Model
TC = +CoD
Q
CcQ
2
= +CoD
Q2
Cc
2
TC
Q
0 = +C0D
Q2
Cc
2
Qopt =2CoD
Cc
Deriving Qopt Proving equality of costs at optimal point
=CoD
Q
CcQ
2
Q2 =2CoD
Cc
Qopt =2CoD
Cc
Copyright 2006 John Wiley & Sons, Inc. 12-22
EOQ Cost Model (cont.)
Order Quantity, Order Quantity, QQ
Annual Annual cost ($)cost ($) Total CostTotal Cost
Carrying Cost =Carrying Cost =CCccQQ
22
Slope = 0Slope = 0
Minimum Minimum total costtotal cost
Optimal orderOptimal order QQoptopt
Ordering Cost =Ordering Cost =CCooDD
Copyright 2006 John Wiley & Sons, Inc. 12-23
EOQ Example
CCcc = $0.75 per yard = $0.75 per yard CCoo = $150 = $150 DD = 10,000 yards = 10,000 yards
QQoptopt = =22CCooDD
CCcc
QQoptopt = =2(150)(10,000)2(150)(10,000)
(0.75)(0.75)
QQoptopt = 2,000 yards = 2,000 yards
TCTCminmin = + = +CCooDD
CCccQQ
22
TCTCminmin = + = +(150)(10,000)(150)(10,000)
2,0002,000(0.75)(2,000)(0.75)(2,000)
22
TCTCminmin = $750 + $750 = $1,500 = $750 + $750 = $1,500
Orders per year =Orders per year = DD//QQoptopt
== 10,000/2,00010,000/2,000
== 5 orders/year5 orders/year
Order cycle time =Order cycle time = 311 days/(311 days/(DD//QQoptopt))
== 311/5311/5
== 62.2 store days62.2 store days
Copyright 2006 John Wiley & Sons, Inc. 12-24
Production QuantityModel
• An inventory system in which an order is received gradually, as inventory is simultaneously being depleted
• AKA non-instantaneous receipt model– assumption that Q is received all at once is relaxed
• p - daily rate at which an order is received over time, a.k.a. production rate
• d - daily rate at which inventory is demanded
Copyright 2006 John Wiley & Sons, Inc. 12-25
Production Quantity Model (cont.)
QQ(1-(1-d/pd/p))
InventoryInventorylevellevel
(1-(1-d/pd/p))QQ22
TimeTime00
OrderOrderreceipt periodreceipt period
BeginBeginorderorder
receiptreceipt
EndEndorderorder
receiptreceipt
MaximumMaximuminventory inventory levellevel
AverageAverageinventory inventory levellevel
Copyright 2006 John Wiley & Sons, Inc. 12-26
Production Quantity Model (cont.)
pp = production rate = production rate dd = demand rate = demand rate
Maximum inventory level =Maximum inventory level = QQ - - dd
== QQ 1 - 1 -
QQpp
ddpp
Average inventory level = Average inventory level = 1 - 1 -QQ22
ddpp
TCTC = + 1 - = + 1 -ddpp
CCooDD
CCccQQ
22
QQoptopt = =22CCooDD
CCcc 1 - 1 - ddpp
Copyright 2006 John Wiley & Sons, Inc. 12-27
Production Quantity Model: Example
CCcc = $0.75 per yard = $0.75 per yard CCoo = $150 = $150 DD = 10,000 yards = 10,000 yards
dd = 10,000/311 = 32.2 yards per day = 10,000/311 = 32.2 yards per day pp = 150 yards per day = 150 yards per day
QQoptopt = = = 2,256.8 yards = = = 2,256.8 yards
22CCooDD
CCcc 1 - 1 - ddpp
2(150)(10,000)2(150)(10,000)
0.75 1 - 0.75 1 - 32.232.2150150
TCTC = + 1 - = $1,329 = + 1 - = $1,329ddpp
CCooDD
CCccQQ
22
Production run = = = 15.05 days per orderProduction run = = = 15.05 days per orderQQpp
2,256.82,256.8150150
Copyright 2006 John Wiley & Sons, Inc. 12-28
Production Quantity Model: Example (cont.)
Number of production runs = = = 4.43 runs/yearDQ
10,0002,256.8
Maximum inventory level = Q 1 - = 2,256.8 1 -
= 1,772 yards
dp
32.2150
Copyright 2006 John Wiley & Sons, Inc. 12-29
Quantity Discounts
Price per unit decreases as order Price per unit decreases as order quantity increasesquantity increases
TCTC = + + = + + PDPDCCooDD
CCccQQ
22
wherewhere
PP = per unit price of the item = per unit price of the itemDD = annual demand = annual demand
Copyright 2006 John Wiley & Sons, Inc. 12-30
Quantity Discount Model (cont.)
QQoptopt
Carrying cost Carrying cost
Ordering cost Ordering cost
Inve
ntor
y co
st (
$)In
vent
ory
cost
($)
QQ((dd1 1 ) = 100) = 100 QQ((dd2 2 ) = 200) = 200
TC TC ((dd2 2 = $6 ) = $6 )
TCTC ( (dd1 1 = $8 )= $8 )
TC TC = ($10 )= ($10 ) ORDER SIZE PRICE0 - 99 $10100 – 199 8 (d1)200+ 6 (d2)
Copyright 2006 John Wiley & Sons, Inc. 12-31
Quantity Discount: ExampleQUANTITYQUANTITY PRICEPRICE
1 - 491 - 49 $1,400$1,400
50 - 8950 - 89 1,1001,100
90+90+ 900900
CCoo = = $2,500 $2,500
CCcc = = $190 per computer $190 per computer
DD = = 200200
QQoptopt = = = 72.5 PCs = = = 72.5 PCs22CCooDD
CCcc
2(2500)(200)2(2500)(200)190190
TCTC = + + = + + PD PD = $233,784 = $233,784 CCooDD
QQoptopt
CCccQQoptopt
22
For For QQ = 72.5 = 72.5
TCTC = + + = + + PD PD = $194,105= $194,105CCooDD
CCccQQ
22
For For QQ = 90 = 90
Copyright 2006 John Wiley & Sons, Inc. 12-32
Reorder Point
Level of inventory at which a new order is placed Level of inventory at which a new order is placed
RR = = dLdL
wherewhere
dd = demand rate per period = demand rate per periodLL = lead time = lead time
Copyright 2006 John Wiley & Sons, Inc. 12-33
Reorder Point: Example
Demand = 10,000 yards/yearDemand = 10,000 yards/yearStore open 311 days/yearStore open 311 days/yearDaily demand = 10,000 / 311 = 32.154 Daily demand = 10,000 / 311 = 32.154 yards/dayyards/dayLead time = L = 10 daysLead time = L = 10 days
R = dL = (32.154)(10) = 321.54 yardsR = dL = (32.154)(10) = 321.54 yards
Copyright 2006 John Wiley & Sons, Inc. 12-34
Safety Stocks
Safety stockSafety stockbuffer added to on hand inventory during lead buffer added to on hand inventory during lead
timetime
Stockout Stockout an inventory shortagean inventory shortage
Service level Service level probability that the inventory available during lead probability that the inventory available during lead
time will meet demandtime will meet demand
Copyright 2006 John Wiley & Sons, Inc. 12-35
Variable Demand with a Reorder Point
ReorderReorderpoint, point, RR
LTLT
TimeTimeLTLT
Inve
nto
ry le
vel
Inve
nto
ry le
vel
00
Copyright 2006 John Wiley & Sons, Inc. 12-36
Reorder Point with a Safety Stock
ReorderReorderpoint, point, RR
LTLT
TimeTimeLTLT
Inve
nto
ry le
vel
Inve
nto
ry le
vel
00
Safety Stock
Copyright 2006 John Wiley & Sons, Inc. 12-37
Reorder Point With Variable Demand
RR = = dLdL + + zzdd L L
wherewhere
dd == average daily demandaverage daily demandLL == lead timelead time
dd == the standard deviation of daily demand the standard deviation of daily demand
zz == number of standard deviationsnumber of standard deviationscorresponding to the service levelcorresponding to the service levelprobabilityprobability
zzdd L L == safety stocksafety stock
Copyright 2006 John Wiley & Sons, Inc. 12-38
Reorder Point for a Service Level
Probability of Probability of meeting demand during meeting demand during lead time = service levellead time = service level
Probability of Probability of a stockouta stockout
RR
Safety stock
ddLLDemandDemand
zd L
Copyright 2006 John Wiley & Sons, Inc. 12-39
Reorder Point for Variable Demand
The carpet store wants a reorder point with a 95% The carpet store wants a reorder point with a 95% service level and a 5% stockout probabilityservice level and a 5% stockout probability
dd = 30 yards per day= 30 yards per dayLL = 10 days= 10 days
dd = 5 yards per day= 5 yards per day
For a 95% service level, For a 95% service level, zz = 1.65 = 1.65
RR = = dLdL + + zz dd L L
= 30(10) + (1.65)(5)( 10)= 30(10) + (1.65)(5)( 10)
= 326.1 yards= 326.1 yards
Safety stockSafety stock = = zz dd L L
= (1.65)(5)( 10)= (1.65)(5)( 10)
= 26.1 yards= 26.1 yards
Copyright 2006 John Wiley & Sons, Inc. 12-40
Order Quantity for a Periodic Inventory System
QQ = = dd((ttbb + + LL) + ) + zzdd ttbb + + LL - - II
wherewhere
dd = average demand rate= average demand ratettbb = the fixed time between orders= the fixed time between orders
LL = lead time= lead timedd = standard deviation of demand= standard deviation of demand
zzdd ttbb + + LL = safety stock= safety stock
II = inventory level= inventory level
Copyright 2006 John Wiley & Sons, Inc. 12-41
Fixed-Period Model with Variable Demand
dd = 6 bottles per day= 6 bottles per daydd = 1.2 bottles= 1.2 bottles
ttbb = 60 days= 60 days
LL = 5 days= 5 daysII = 8 bottles= 8 bottleszz = 1.65 (for a 95% service level)= 1.65 (for a 95% service level)
QQ = = dd((ttbb + + LL) + ) + zzdd ttbb + + LL - - I I
= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8
= 397.96 bottles= 397.96 bottles