Time that ipt gets to the ql level we place a

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Unformatted text preview: denotes
 the
 “pipeline”
 inventory
 at
 time
 t
 (i.e.,
 material
 ordered
 but
 not
 received
 yet);
 • BO(t)
 denotes
 the
 backorders
 at
 time
 t.
 
 Also,
 let
 Ql
 =
 lD
 denote
 the
 demand
 experienced
 over
 a
 replenishment
 lead
 time
 interval
 l.
 In
 our
 case,
 this
 quantity
 is
 Ql
 =
 (3/12)x20000
 =
 5000.
 
 Since
 we
 want
 to
 have
 no
 shortages,
 
 
 
 
 
 
 
 
 BO(t)
 =
 0
 for
 all
 t
 
 
 
 
 
 
 
 (2)
 
 Consider
 also
 the
 OHI(t)
 at
 any
 time
 t,
 and
 notice
 that
 at
 time
 t+l,
 
 
 
 
 OHI(t+l)
 –
 BO(t+l)
 =
 OHI(t)
 +
 O(t)
 –
 Ql
 
 
 
 
 
 
 (3)
 Furthermore,
 in
 the
 light
 of
 (1),
 Equation
 (3)
 becomes
 
 OHI(t+l)
 –
 BO(t+l)
 =
 IP(t)
 –
 Ql
 
 
 
 
 
 
 
 (4)
 
 Since
 t
 was
 chosen
 arbitrarily,
 Equation
 (4)
 implies
 that
 we
 shall
 have
 BO(t)
 =
 0
 for
 all
 t,
 as
 long
 as
 IP(t)
 ≥
 Ql
 at
 all
 t
 
 
 
 
 
 
 (5)
 
 The
 condition
 of
 Equation
 (5)
 can
 be
 satisfied
 in
 a
 way
 that
 minimizes
 the
 incurred
 holding
 cost,
 by
 setting
 the
 reorder
 point
 with
 respect
 to
 the
 IP(t)
 signal
 equal
 to
 Ql
 (since,
 in
 this
 case,
 every
 time
 that...
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This note was uploaded on 07/20/2013 for the course ISYE 6201 taught by Professor Staff during the Fall '08 term at Georgia Tech.

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