27. × expected overstock at retailer
´ expected overstock at retailer
CSL* = probability (demand ≤O*) =
Cu
Cu +Co
=
(1– f )p – c
(1– f )p – sR
CSL*=probability (demand £O*)=
C
u
C
u
+C
o
=
(1–f)p–c
(1–f)p–s
R
Expected manufacturers profits = (c – v)O *
Expected manufacturers profits=(c–v)O*
+ fp(O * – expected overstock at retailer)
+fp(O*– expected overstock at retailer)
28. Expected retailer profit
Expected retailer profit
+sR × expected overstock at retailer – cO *
+s
R
´ expected overstock at retailer–cO*
= (1– f )p(O * – expected overstock at retailer)
=(1–f)p(O*– expected overstock at retailer)
Expected quantity purchased by retailer, QR
Expected quantity purchased by retailer, Q
R
= qF(q)+Q 1– F(Q)⎡ ⎣ ⎤ ⎦
=qF(q)+Q1–F(Q)
é
ë
ù
û
+µ Fs
Q – µ
34. –sf
s
q–m
s
æ
è
ç
ö
ø
÷
Expected quantity overstock
at manufacturer
Expected quantity overstock
at manufacturer
Expected retailer profit = DR × p+ QR – DR( )sR – QR ×c
Expected retailer profit=D
R
´p+Q
R
–D
R
( )
s
R
–Q
R
´c
Expected manufacturer profit = QR ×c+ Q – QR( )sM – Q×v
60. T+L
=F
–1
(CSL)´T+L´s
H
=F
–1
(0.997)´4+1´5=30.7 units
Total HighVal inventory =Q
H
/2+ss
H
=(8/2)+30.7=34.7 units
Average lot size, QL = expected demand during T weeks
=TµH = 4 × 20 = 80 units
Safety inventory, ssL = F
–1(CSL) ×σT+L = F
–1(CSL) × T + L ×σL
= F–1(0.997) × 4 +1× 5 = 30.7 units
Total LowVal inventory = QL / 2 + ssL = (80 / 2) + 30.7 = 70.7
units
Average lot size, Q
L
= expected demand during T weeks
=Tm
H
=4´20=80 units
Safety inventory, ss
L
=F