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2
Inventory Control
Inventory System Defined
Inventory Costs
Independent vs. Dependent Demand
Basic Fixed-Order Quantity Models
Quantity Discounts-also known as price break models.
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Inventory SystemDefined
Inventory raw materials, finished products, component parts, supplies, and work-in-process.
An inventory system is the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be.
4
Purposes of Inventory1. To maintain independence of operations.
2. To meet variation in product demand.
3. To allow flexibility in production scheduling.
4. To provide a safeguard for variation in raw material delivery time.
5. To take advantage of economic purchase-order size.
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Inventory CostsHolding (or carrying) costs.
Costs for storage, handling, insurance, etc.
Setup (or production change) costs.Costs for arranging specific equipment setups, etc.
Ordering costs.Costs of someone placing an order, etc.
Shortage costs.Costs of canceling an order, etc.
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Independent vs. Dependent Demand
Independent Demand (Demand not related to other items or the final end-product)
Dependent Demand
(Derived demand items for
component parts,
subassemblies, raw materials,
etc.)
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Classifying Inventory ModelsFixed-Order Quantity Models Event triggered (Example: running out of
stock)
The sale of an item reduces the inventory position to the re order point.
Fixed-Time Period Models Time triggered (Example: Monthly sales call by sales representative)
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Fixed-Order Quantity Models:Model Assumptions (Part 1)
Demand for the product is constant and uniform throughout the period.
Lead time (time from ordering to receipt) is constant.
Price per unit of product is constant.
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Fixed-Order Quantity Models:Model Assumptions (Part 2)
Inventory holding cost is based on average inventory.
Ordering or setup costs are constant.
All demands for the product will be satisfied. (No back orders are allowed.)
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Basic Fixed-Order Quantity Model and Reorder Point Behavior
R = Reorder pointQ = Economic order quantityL = Lead time
L L
Q QQ
R
Time
Numberof unitson hand
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Cost Minimization Goal
Ordering Costs
HoldingCosts
QOPT
Order Quantity (Q)
COST
Annual Cost ofItems (DC)
Total Cost
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Basic Fixed-Order Quantity (EOQ) Model Formula
H 2
Q + S
Q
D + DC = TC
Total Annual Cost =Annual
PurchaseCost
AnnualOrdering
Cost
AnnualHolding
Cost+ +
TC = Total annual costD = DemandC = Cost per unitQ = Order quantityS = Cost of placing an order or setup costR = Reorder pointL = Lead timeH = Annual holding and storage cost per unit of inventory
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Deriving the EOQ
Cost Holding Annual
Cost) Setupor der Demand)(Or 2(Annual =
H
2DS = QOPT
Reorder point, R = d L_
d = average daily demand (constant)
L = Lead time (constant)
_
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EOQ Example Problem Data
Annual Demand = 1,000 unitsDays per year considered in average daily demand = 365Cost to place an order = Rs10Holding cost per unit per year = Rs2.50Lead time = 7 daysCost per unit = Rs15
Given the information below, what are the EOQ and reorder point?
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EOQ Example Solution
Q = 2DS
H =
2(1,000 )(10)
2.50 = 89.443 units or OPT 90 units
d = 1,000 units / year
365 days / year = 2.74 units / day
Reorder point, R = d L = 2.74units / day (7days) = 19.18 or _
20 units
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Safety Stock
LT Time
Expected demandduring lead time
Maximum probable demandduring lead time
ROP
Qu
an
tity
Safety stockSafety stock reduces risk ofstockout during lead time
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Reorder Point
ROP
Risk ofa stockout
Service level
Probability ofno stockout
Expecteddemand Safety
stock0 z
Quantity
z-scale
The ROP based on a normalDistribution of lead time demand
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Special Purpose Model: Price-Break Model Formula
Cost Holding Annual
Cost) Setupor der Demand)(Or 2(Annual =
iC
2DS = QOPT
Based on the same assumptions as the EOQ model, the price-break model has a similar Qopt formula:
i = annual percentage of unit cost attributed to carrying inventoryC = cost per unit
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Price-Break Example Problem Data (Part 1)
Order Quantity(units) Price/unit(Rs.)0 to 2,499 1.202,500 to 3,999 1.004,000 or more .98
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Price-Break Example Solution (Part 2)
units 1,826 = 0.02(1.20)
4)2(10,000)( =
iC
2DS = QOPT
Annual Demand (D)= 10,000 unitsCost to place an order (S)= Rs.4
First, start with the lowest price per unit.
units 2,000 = 0.02(1.00)
4)2(10,000)( =
iC
2DS = QOPT
units 2,020 = 0.02(0.98)
4)2(10,000)( =
iC
2DS = QOPT
Carrying cost % of total cost (i)= 2%Cost per unit (C) = Rs1.20, Rs.1.00, Rs.0.98
Interval from 0 to 2499, the Qopt value is feasible.
Interval from 2500-3999, the Qopt value is not feasible.
Interval from 4000 & more, the Qopt value is not feasible.
Next, determine if the computed Qopt values are feasible or not.
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Price-Break Example Solution (Part 3)
iC 2
Q + S
Q
D + DC = TC
TC(1826)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20) = Rs12,043.82
TC(2500) = Rs10,041
TC(4000) = Rs9,949.20
Next, Compare total cost for the feasible root Q and price break Q values.
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Price-Break Example
Since the feasible solution occurred in the first price-break, it means that all the other true Qopt values occur at the beginnings of each price-break interval. Why?
0 1826 2500 4000 Order Quantity
Total annual costs
Because the total annual cost function is a “u” shaped function.
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ABC Classification System
Items kept in inventory are not of equal importance in terms of:
Amount invested
profit potential
sales or usage volume
stock-out penalties
0
30
60
30
60
AB
C
% of $ Value
% of Use
So, identify inventory items based on percentage of total value , where “A” items are roughly top 15 %, “B” items as next 35 %, and the lower 65% are the “C” items.