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Inventory Management
Why keep inventory?
•
Fluctuations in demand: Seasonal, economic,variability
•
Lead times and uncertainty in lead times.
•
Supply chain disruptions
•
Economies of scale
•
Opportunity cost of losing sales
Inventory comes in three forms:
•
Finished product
•
Unfinished product (work in progress)
•
Raw materials (Just in time)
Characteristics of the supply chain:
Customer demand, lead time, capacity, throughput, product portfolio, holding costs,
service level requirements, depreciation, transportation costs, costs.
Single Echelon Inventory Theory
Single Period Models (Newsvendor problem)
•
Assumes there is only one period
•
Overage (C
o
) for ordering too much
•
Underage (C
u
) for ordering too little.
•
Probability density function of demand is known.
•
F(Q)= C
u
/C
o
+C
u
This is the
Critical Ratio
•
D
min
+ (D
max
 D
min
) * Critical Ratio =
optimal inventory level
•
Overly simplistic because only one ordering period
Fixed Cost
•
We are given several demand scenarios with probability of occurring.
1.
Pick an order quantity, Q
2.
For each order quantity, calculate expected profit (loss) based on demand
scenarios
3.
Pick order quantity that results in the highest expected profit
•
If overage>underage, order less than mean demand
•
If overage<underage, order more than mean demand
Multi Period Models
Economic Lot Size Model (EOQ model)
Assumptions:
•
Supplier has infinite capacity.
•
Demand is constant at a
rate
of
D
items per unit of time
•
Quantities are
fixed at Q
items per order.
•
Cost:
Ordering cost –
K
, units
Inventory holding –
h
•
Lead time is zero
•
Initial inventory is zero
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Planning horizon is infinite
•
Average inventory: (Q/2)
•
Average holding cost: h(Q/2)
•
Ordering cost: D/Q*K (D=total demand)
•
During a
cycle
of T, average cost is: K+
h
Q/2
•
Order quantity that minimizes the average cost is: Q*=sqrt(2KD/
h
)
•
TC=(Dk/Q)+(
h
Q/2)
•
If we derivate from Q*, and order
b
Q*, cost will derivate by how much we
derivate Q* by.
(
b
1)
2
/2
b
If we order 10% too much, then change in cost is .
45%
EOQ in the presence of quantity discounts
•
Think of
h
as a function of production cost:
h
=
i
C.
•
So, total cost is (DK/Q)+(
i
C
j
Q/2)+DC
j
where DC
j
is the purchasing cost.
•
Holding cost is
i
C
j
Q/2
•
Assume pricing schedule has specified break points (q0, q1…qr) so that order
placed Q is greater than q
j
, but less than q
j1
, the cost is C
j
.
•
Biggest drawback of EOQ:
Demand is deterministic
Continuous Review Policy
Assumptions:
•
Demand is normally distributed. (Mean:AVG, Standard Deviation:STD)
•
Fixed(K) and proportional ordering cost
•
Inventory holding cost per item unit of time (
h
)
•
Replenishments from supplier take L periods
•
Demand is
lost
when not immediately satisfied
•
Require a probability of
α
for not stocking out during a lead time.
•
If inventory drops to R, we order Q.
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 Fall '11
 EIXMANN
 Sales

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