Notation:
Q
Size of order for Model (I) (size of production for Model (II)) in units
S
Size of backorders in units
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Total annual cost function of Q and S for Model (I) in $ per year
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Total annual cost function of Q and S for Model (II) in $ per year
D
Demand rate in units per unit of time
P
Production rate in units per unit of time for Model (II)
K
Ordering cost per order/setup
h
Holding cost per unit, per unit of time
p
Backorder cost per unit, per unit of time (linear backorder cost)
π
Backorder cost per unit (fixed backorder cost)
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The optimal solution of View the MathML source for i=1,2.