EOQ Model:
Total cost= DC +(D/Q)S +(Q/2)H =annual purchase cost + annual ordering cost+ annual
holding cost
total holding cost= average inventory * annual holding cost= q/2 *H
Total set up cost= annual ordering cost= Demand/quantity * set up cost each time
Total purchasing cost= quantity per batch * number of orders/year * price/unit
Economic order quantity= the batch that incurs the least costs
Number of orders= annual demand/ order quantity
Frequency of orders= 12months/ number of orders
Quantity that minimizes the cost=
sqrt(2DS/h)
Optimal batch size= EOQ= sqrt(2DS/H)=sqrt(2*Annual demand* annual set up cost/ annual holding
cost/unit)
Inventory related cost= D/q*S + Q/2*H
Newsvendor Model
: S:
Setup cost (per order) / h:
Holding cost (per unit per period) / c:
Purchasing
cost (per unit) / v:
Salvage value (per unit)–The value of salvage, at the end of the horizon, for excess
inventory /
p:
Revenue per unit / g: Goodwill cost
When probabilities given, calculate the orders with proba given to find the best order quantity
Shortage cost= pc
Overage cost= cv
Marginal value analysis:
The expected Marginal Value = 
Expected overage cost : (c  v) * Pr
{Demand<=Q} + Expected additional profit: (p  c) * Pr {Demand>Q}
To find the optimal purchase quantity, set the marginal value to zero (or choose the first purchase
quantity for which the marginal value becomes negative for a discrete demand distribution

So, increase the order size until P(D
Q)
C
≤
≥
U
/ (C
O
+Cu) where Co is overage cost and Cu underage
cost
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 Spring '07
 Vaitsos
 Management, Normal Distribution, 75%, 60%, 12months

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