inventory control model kusdhianto setiawan gadjah mada university
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Inventory Control Model
Kusdhianto Setiawan
Gadjah Mada University
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Inventory Planning & Control
Planning on whatInventory to stock And how to acquire
it
Planning on whatInventory to stock And how to acquire
it
ForecastingParts/Product
Demand
ForecastingParts/Product
Demand
ControllingInventory
Levels
ControllingInventory
Levels
Feedback MeasurementsTo revise plans and forecasts
Feedback MeasurementsTo revise plans and forecasts
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Importance of Inventory Control
• The Decoupling Function….. Inventory as a buffer
• Storing Resources…. Where JIT is not possible
• Irregular Supply and Demand
• Quantity Discount
• Avoiding stockouts and shortages
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Inventory Decision
• How much to order• When to order
With respect to (constraint) inventory cost:• Cost of the items• Cost of ordering• Cost of carrying/holding• Cost of safey stock• Cost of stockouts
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Inventory Cost FactorsOrdering Cost Factors Carrying Cost Factor
Developing & Sending Purchase Order (PO)
Cost of Capital
Processing & inspecting incoming iventory
Taxes
Bill Paying Insurance
Inventory Inquiries Spoilage
Utilities, phone bills, etc for the purchasing dept.
Theft
Salaries & wages for purchasing dept. employees
Obselescence
Supplies e.g: paper, toner printer, billing form, etc. for the purchasing dept.
Salaries & wages for warehouse employees
Utilities & building cost for the warehouse
Supplies such as forms & papers for the warehouse.
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Economic Order Quantity (EOQ)
• Objective: Determining how much to order• Assumptions:
– Demand is known and constant– Lead time, the time between the placement of the
order and the receipt of the order, is known and constant
– The receipt of inventory is instantaneous– Quantity discount are not possible– Variable costs: ordering cost and holding/carrying
cost– If orders are placed at the right time,
stockouts/shortages can be avoided completely
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EOQ Continued….
Order Quantity = Q = Maximum inventory level
Inve
ntor
y Le
vel
0
Minimum Inventory Level
Time
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EOQ Continued….Cost
Minimum Total Cost
Carrying Cost C
urve
Ordering Cost Curve
Optimal Order Quantity
Order Quantity
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Computing Average Inventory
DayInventory Level
Beginning Ending Average
1 (order received) 10 8 9
2 8 6 7
3 6 4 5
4 4 2 3
5 2 0 1
Demand: Constant, 2 units/day
Ending Inventory is assumed to be always zero
Maximum level = 10 units
Total of Daily average = 9 + 7 + 5 + 3 + 1 = 25
Number of days = 5
Average inventory level = 25/5 = 5 …… Q/2
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Finding the EOQ
• Expression:Q = number of pieces per order
Q* = optimal number of pieces per order
D = annual demand in units for the inventory items
C0 = ordering cost for each order
Ch = holding cost per unit per year
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Finding the EOQ1. Annual Ordering Cost
= no. of order placed per year x order cost per order
2. Annual Holding or Carrying Cost= Average inventory level x carrying cost per unit per year= (Q/2) Ch
3. Optimal Order Quantityordering cost = carrying cost(D/Q)Co = (Q/2)Ch
4.
)()(Q
D
order)per cost (ordereach in units of no.
demand annual
oo CQ
DCx
orderx
IP
DC
C
DCQ o
h
o 22*
IP
DC
C
DCQ o
h
o 22*
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Finding Reorder Point (ROP)
• ROP = (demand/day) x (lead time for a
new order in days)
• ROP = d x L
Inve
ntor
y Le
vel (
Uni
ts)Q* Slope = units/day = d
Lead Time = L
Time(days)
ROP(units)
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EOQ Without The Instantaneous Receipt Assumption
Inventory Level
Maximum Inventory
Part of inventory cycle during whichProduction is taking placeThere is no productionDuring this part of the inventory cycle
t
Production Run Model
time
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Annual Carrying Cost• New terms:
t = length of the production run (days)p = daily production rate
1. Annual inventory holding/carrying cost= average inventory level x carrying cost/unit/year= average inventory level x Ch
2. Average inventory level = ½ Maximum inventory level3. Maximum inventory level
= (total produced during the production run)- (total used during the production run)Q = pt t = Q/pMax Inv. Level = p(Q/p) – d(Q/p) = Q – (d/p)Q = Q(1-d/p)
4. Annual Inventory carrying cost= ½ (max. inv. Level) x Ch
= ½ Q(1-d/p)Ch
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Annual Setup/Ordering Cost
1. Annual setup cost= (no. of setup/year) x (setup cost/setup)
= (D/Qp)Cs
where: D = annual demand in units
Qp = Quantity produced in one batch
Cs = setup cost per setup2. Annual Ordering Cost
= (D/Q)Co
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Optimal Order Quantityfor Production Run Model
• Ordering Cost = Carrying Cost• (D/Q)Co = ½ ChQ(1-d/p)• Optimal Order Quantity
pd
C
DCQ
pd
C
DCQ
h
o
h
o
1
2*
1
22
Optimal Production Quantity, Q*p
pd
C
DCQ
h
s
1
2*
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Quantity Discount Model
Discount Number
Discount Quantity
Discount (%)Discount Cost ($)
1 0-999 05.00 (normal
cost)
2 1,000 – 1,999 4 4.80
3 2,000 – over 5 4.75
Quantity Discount Schedule
Total Cost = material cost + ordering cost + carrying cost = DC + (D/Q)Co + ½ QCh
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Total Cost CurveTC for Disc. 1
TC for Disc. 2
TC for Disc. 3
Q* for Disc. 2
1,000 2,0000
Total Cost
Order Quantity
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Use of Safety Stock
• Safety stock: additional stock that is kept on hand
• It is used only when demand is uncertain• Main purpose: to avoid stockouts when the
demand is higher than expected• ROP = d x L (normal condition)• ROP = d x L + SS (demand is uncertain)• Because it is dealing with decision under risk,
knowing the probability of demand is necessary.
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Safety Stock with Known Stockout Costs
Case of ABCO• ROP = 50 units (= d x L)• Ch = $5 (per unit per year)• Cso = $40/unit (stockout cost)• Optimal number of orders per year is 6• Objective: to find the reorder point, including
safety stock, that will minimize total expected cost
• Total expected cost is the sum of expected stockout cost plus expected additional carrying cost
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Probability of Demand for ABCO
Number of Units Probability
30 0.2
40 0.2
50 (ROP) 0.3
60 0.2
70 0.1
Total 1.0
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Annual Expected Stockout Cost
• When the ROP < demand over lead time
Total Cost = Stockout Cost
= no. of units short x stockout cost/unit x
no. of orders per year
• When the ROP > demand over lead time
Total Cost = total additional carrying cost
= no. of surplus units x carrying cost
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ABCO’s Stockout CostsProbability 0.20 0.20 0.30 0.20 0.10
State of Nature
Alternative
30 40 50 60 70 EMV
30 0 2,400 4,800 7,200 9,600 4,320
40 50 0 2,400 4,800 7,200 2,410
50 100 50 0 2,400 4,800 990
60 150 100 50 0 2,400 305
70 200 150 100 50 0 110
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Safety Stock with Unknown Stockout Cost
• There are many situation when stockout cost are unknown or extremely difficult to determine, i.e: major stockout cost is the loss of goodwill, how to measure it?
• Alternative approach: using service level
• Service level = 1 – probability of a stockout or
• Probability of a stockout = 1 – service level
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Hinsdale Company Example
• Average demand = 350 units
• Standard Deviation = 10
• Hinsdale wants to follow a policy that result in stockout occuring only 5% of the time.
• How much safety stock should be maintained?
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Safety Stock & Normal Distribution
X=?
SS
μ=350
σ=10X = mean + safety stockSS = safety stock = X – μZ = (X – μ) / σ = SS/ σ
Z value for an area under the normal curve of 0.95 (=1-0.05) is 1,65 (see appendix A)
SS = 1.65 (10) = 16.5 units or 17 units
SS = Z σ