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PRODUCTION MANAGEMENTfarrah detuya
Page 2
INVENTORY MANAGEMENT’S OBJECTIVE
TO STRIKE A BALANCE BETWEEN
INVENTORY INVESTMENT
AND
CUSTOMER SERVICE
Page 3
1.Improve customer service
2.Economies of purchasing
3.Economies of production
4.Transportation savings
5.Hedge against future
6.Unplanned shocks (labor strikes, natural disasters, surges in demand, etc.)
7.To maintain independence of supply chain
REASONS FOR INVENTORIES
Page 4
TYPES OF INVENTORIES
Raw Materials Inventory
Work-In-Process Inventory
MRO (maintenance/repair/operating)
Finished Goods Inventory
Page 5
INVENTORY CLASSIFICATION
ABC analysis
A method which divides inventory into 3 groups (A, B, and C) in descending order of importance and level of monitoring on the basis of the investment in each.
Page 6
ABC analysis (con’t)…
Class A
– 5 – 15 % of units
– 70 – 80 % of value
Class B
– 30 % of units
– 15 % of value
Class C
– 50 – 60 % of units
– 5 – 10 % of value
Page 7
ABC analysis example
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
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 USAGETOTAL % OF TOTAL % OF TOTALPART VALUE VALUE QUANTITY % CUMMULATIVE
9 $30,600 35.9 6.0 6.08 16,000 18.7 5.0 11.02 14,000 16.4 4.0 15.01 5,400 6.3 9.0 24.04 4,800 5.6 6.0 30.03 3,900 4.6 10.0 40.06 3,600 4.2 18.0 58.05 3,000 3.5 13.0 71.0
10 2,400 2.8 12.0 83.07 1,700 2.0 17.0 100.0
$85,400
AA
BB
CC
% OF TOTAL % OF TOTALCLASS ITEMS VALUE QUANTITY
A 9, 8, 2 71.0 15.0B 1, 4, 3 16.5 25.0C 6, 5, 10, 7 12.5 60.0
Page 8
Item Class Qty Cycle Counting PolicyNumber of items counted per day
A 500 Each month (20 working days) 500/20 = 25/dayB 1,750 Each quarter (60 working days) 1750/60 = 29/dayC 2,750 Every 6 months (120 working days) 2750/120 = 23/day
77/day
MAINTAINING ACCURATE RECORDS
Cycle Counting
A continuing reconciliation of inventory with inventory records
Advantages:
1. Eliminates the shutdown and interruption of production for annual physical counts
2. Eliminates annual inventory adjustments
3. Trained personnel audit the accuracy of inventory
4. Cause of errors are identified and remedial actions are taken
5. Maintains accurate inventory records
Page 9
CONTROL OF SERVICE INVENTORIES
SHRINKAGE AND PILFERAGES
Items unaccounted between receipt and time of sale
Inventory theft
Applicable techniques:
1. Good personnel selection, training, and discipline
2. Tight control of incoming shipments
3. Effective control of all goods leaving the facility
Page 10
INVENTORY MODELS
COSTS:
1. Holding cost
2. Ordering cost
3. Setup cost/set up time
Assume that demand for an item is either Independent of or Dependent on the demand for the other item.
Page 11
ECONOMIC ORDER QUANTITY (EOQ)
Optimal order quantity that will minimize total inventory costs
Demand is known with certainty Demand is known with certainty and is constant over timeand is constant over time
No shortages are allowedNo shortages are allowedLead time for the receipt of Lead time for the receipt of
orders is constantorders is constantOrder quantity is received all at Order quantity is received all at
onceonce
Assumptions of EOQ:
Page 12
INVENTORY ORDER CYCLE
Demand Demand raterate
TimeTimeLead Lead timetime
Lead Lead timetime
Order Order placedplaced
Order Order placedplaced
Order Order receiptreceipt
Order Order receiptreceipt
Inve
ntor
y Le
vel
Inve
ntor
y Le
vel
Reorder point, Reorder point, RR
Order quantity, Order quantity, QQ
00
Page 13
EOQ COST MODEL
Co - cost of placing order D - annual demandCc - annual per-unit carrying cost Q - order quantity
Annual ordering cost =CoD
Q
Annual carrying cost =CcQ
2
Total cost = +CoD
Q
CcQ
2
Page 14
EOQ (con’t)…
Order Quantity, Q
Annual cost ($) Total Cost
Carrying Cost =CcQ
2
Slope = 0
Minimum total cost
Optimal order Qopt
Ordering Cost =CoD
Q
Page 15
EOQ example
Cc = $0.75 per yard Co = $150 D = 10,000 yards
Qopt =2CoD
Cc
Qopt =2(150)(10,000)
(0.75)
Qopt = 2,000 yards
TCmin = +CoD
Q
CcQ
2
TCmin = +(150)(10,000)
2,000(0.75)(2,000)
2
TCmin = $750 + $750 = $1,500
Orders per year = D/Qopt
= 10,000/2,000= 5 orders/year
Order cycle time = 311 days/(D/Qopt)
= 311/5= 62.2 store days
Page 16
PRODUCTION QTY MODEL
An EOQ technique applied to production orders
An inventory system in which an order is received gradually, as inventory is simultaneously being depleted
p - daily rate at which an order is received over time, a.k.a. production rate
d - daily rate at which inventory is demanded
Page 17
PRODUCTION QTY MODEL ( con’t)…
Q(1-d/p)
Inventorylevel
(1-d/p)Q2
Time0
Orderreceipt period
Beginorder
receipt
Endorder
receipt
Maximuminventory level
Averageinventory level
Page 18
PRODUCTION QTY MODEL (con’t)…
p = production rate d = demand rate
Maximum inventory level = Q - d
= Q 1 -
Qp
dp
Average inventory level = 1 -Q2
dp
TC = + 1 -dp
CoDQ
CcQ2
Qopt =2CoD
Cc 1 - dp
Page 19
PRODUCTION QTY MODEL (con’t)…
Cc = $0.75 per yard Co = $150 D = 10,000 yards
d = 10,000/311 = 32.2 yards per day p = 150 yards per day
Qopt = = = 2,256.8 yards
2CoD
Cc 1 - dp
2(150)(10,000)
0.75 1 - 32.2150
TC = + 1 - = $1,329dp
CoD
Q
CcQ
2
Production run = = = 15.05 days per orderQp
2,256.8150
Page 20
PRODUCTION QTY MODEL (con’t)…
Number of production runs = = = 4.43 runs/yearDQ
10,0002,256.8
Maximum inventory level = Q 1 - = 2,256.8 1 -
= 1,772 yards
dp
32.2150
Page 21
QUANTITY DISCOUNTS
Price per unit decreases as order quantity increases
TC = + + PDCoD
Q
CcQ
2
where
P = per unit price of the itemD = annual demand
Page 22
QUANTITY DISCOUNTS (con’t)…
Qopt
Carrying cost
Ordering cost
Inve
ntor
y co
st ($
)
Q(d1 ) = 100 Q(d2 ) = 200
TC (d2 = $6 )
TC (d1 = $8 )
TC = ($10 ) ORDER SIZE PRICE0 - 99 $10100 – 199 8 (d1)
200+ 6 (d2)
Page 23
QUANTITY DISCOUNTS (con’t)…
QUANTITY PRICE
1 - 49 $1,40050 - 89 1,100
90+ 900
Co = $2,500
Cc = $190 per computer
D = 200
Qopt = = = 72.5 PCs2CoD
Cc
2(2500)(200)190
TC = + + PD = $233,784 CoD
Qopt
CcQopt
2
For Q = 72.5
TC = + + PD = $194,105CoD
Q
CcQ
2
For Q = 90
Page 24
PROBABILISTIC MODELS
Reorder Point = Level of inventory at which a new order is placed
R = dLR = dLwherewhere
dd = demand rate per period = demand rate per periodLL = lead time = lead time
Demand = 10,000 yards/yearStore open 311 days/yearDaily demand = 10,000 / 311 = 32.154 yards/dayLead time = L = 10 days
R = dL = (32.154)(10) = 321.54 yards
Applicable when product demand or any other variable is not known but can be specified by means of a probability distribution
Page 25
Safety Stock Safety stock - buffer added to on hand inventory during lead time
Reorderpoint, R
LTLTTimeTime
LTLT
Inve
ntor
y le
vel
00Safety Stock
Reorder Point with a Safety Stock
Page 26
Reorder point with variable demand
R = dL + zd L
where
d = average daily demandL = lead time
d = the standard deviation of daily demand z = number of standard deviations
corresponding to the service levelprobability
zd L = safety stock
Page 27
Reorder Point with variable demand (con’t)…
Probability of meeting demand during lead time = service level
Probability of a stockout
R
Safety stock
dLDemand
zd L
Page 28
Reorder Point with variable demand example
The carpet store wants a reorder point with a 95% service level and a 5% stockout probability
d = 30 yards per dayL = 10 days
d = 5 yards per day
For a 95% service level, z = 1.65
R = dL + z d L
= 30(10) + (1.65)(5)( 10)
= 326.1 yards
Safety stock = z d L
= (1.65)(5)( 10)
= 26.1 yards
Page 29
Order Quantity for a Periodic Inventory System
Q = d(tb + L) + zd tb + L - I
where
d = average demand ratetb = the fixed time between ordersL = lead time
sd = standard deviation of demand
zd tb + L = safety stockI = inventory level
Page 30
Fixed-Period Model with Variable Demand
d = 6 bottles per daysd = 1.2 bottlestb = 60 daysL = 5 daysI = 8 bottlesz = 1.65 (no. of sd for a 95% service level)
Q = d(tb + L) + zd tb + L - I
= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8
= 397.96 bottles
