????????? ?2? ???????? ????

1
??????????2???????????????????????pp.
49-52, 3.2.1?????????????

• ??????
• ?? ??

2
?????(Economic Ordering Quantity EOQ)???

• d (?/?) 1???????????
• Q (?) ???(??) ????????????
• K (?) ??1????????? ???????????
• h ( ?/(??) ) ??1????1???????????
• ?????????????(????????????????)????(??,????????
  ??)????.
• ??????????.
• ??????????(?????0?)????. ????? 0 ???.

3
??????????

• K????????????????????????????????.????????????????
  ??????,1????????????,1???? 10??,??????????????????
  1????300????.??,??????????????1??10???????????????
  ?.???(???????????)????????.

4
?????
d??-???????
Q
h??
?????? (T ?)
??
T ?????? ???? ??????
f(Q) 1???????
5
EOQ???

• ??? f(Q)
• ?f(Q)/?Q
• ?2f(Q)/?Q2
• f(Q) ? ??.
• Q
• f(Q )

6
???? 2-1 (?)

• Find the optimal ordering quantities when d 10
  items/dayK 300 yenh10 yen/dayitem.
• Check the dimension of the EOQ formula.

7
???? 2-2 (?)

• Consider EOQ model in a factory. When the
  inventory is zero, production of Q items starts
  at a rate of p (items/day) (p ?d).The set-up
  cost is K (yen) and every time production starts
  at a level p, we incur a cost of ap (agt0).
• What is the optimal production rate?

8
???? 2-3(?)

• Consider EOQ model at a warehouse. When an order
  of size Q is placed, the items are delivered by
  trucks of capacity q thus the number of trucks
  used to deliver Q is . The set-up
  cost is a linear function of the number of trucks
  used (yen) .
• What is the optimal ordering quantities?

9
????(????????????????p.52 ?3-1)

• ??????????????????.????????,????????????????-gt????
  
• ????????

Table3-1.xls
10
??????
????20?????????,???(???)1.6 ??????! -gt
EOQ????????(robust)???!
11
2??????(Power-of-two Policy)

• ???????1.732??1.4142???????
• ????,????????,?????1??,2??,1??(4??)??????????.
• 2??????????????? B (Basic????)???,k???(-2,-1,0
  ,1,2,)?????,???????B 2k ??????????.

12
2??????(???)

• ??????K,??????h,???d
• gh d/2 ???(?????????)
• (???Q???)?????? T??????!2????????? f(T) K/T
  g T ?? T B 2k
  k?-2,-1,0,1,2, T ? 0

13
2???????????????(????6??)(????????,???????????pp
.34-35??)

• 2?????????????(????)???????????????EOQ????
• 2??????????????????????
• ??????

14
?????( 2??)???
3 ????
2 ?
1 ???
?? d
h1
h2
h3 0
?2??(?)
?1??(???)
2
2
T2
T1
??????????!
15
???????
?2??????????
2
1
?? d
?2??(???????)
h1
h2
??????????(???) ????????????
?1??
2
2
T2
T1
16
?????????
3 ????
2 ?
1 ???
?? d
h1
h2
h3 0
?2??(?)? ?????????? h2 h2-h3 h2
?1??(???) ?????????? h1 h1-h2

• ??(???)????????????????
• (????????????)
• ??(????)??????0 ???.
• ????????? ??????????????????????????

17
????????????????????
?????????(4??)
?1??(???)4 h1

?2??(?)24 h2

??????(4??)
?1??(???)4 h1
?2??(?)4 h2
2
1
T2
T1
18
????2-4

• ???????????????,?????????????????????????????????
  ?.
• 3???????????
• 1?????????

???1 ??????1,??1
?? ??????4,??3
???2 ??????2,??2
19
?????(nested policy)

• ??????????????????,??????????????????.
• ?????????????,???????????????.
• 2??????????, ??????????????????????????.

20
??????????
?2??(?)
???????
2??(?)????? ????????
?1??(???)
2
2
0??????????
21
2???????????2?????????

• ???d,? i?????????????Ki,???????????hi,??????(??)T
  i
• gihi d/2 ???(?????????)
• 2???????????? Si Ki/Ti gi Ti ??
  Ti B 2k k?-2,-1,0,1,2,, i1,2
  Ti ? Ti-1 i2
• Ti ? 0 i1,2

2??????
????? (2????????)
22
2???????????Lagrange??(1)

• ??? 10
• ? 1?????????????K1300
• ???????????h15(10-5), g1h1 d/225
• ? 2?????????????K2100(?????????????????)
• ???????????h25(5-0), g2h2 d/225
• 2???????????? Si Ki/Ti gi Ti (-Ti
  Ti-1)??? Ti B 2k
  k?-2,-1,0,1,2,, i1,2 Ti ?
  Ti-1 i2
• Ti ? 0 i1,2

???????0??
0???Lagrange??
23
2???????????Lagrange??(2)

• 2????????????(???)?
• 0??????????????????? -gt??(???????)?????!???
  Si Ki/Ti gi Ti (-Ti Ti-1)??? Ti ? 0
  i1,2
• -gt2??EOQ?????? ?1????? K1/T1 (g1 ?) T1
  ?2????? K2/T2 (g2 -?) T2

24
2???????????Lagrange??(3) Excel???????
SQRT(300/(50B1))
B1
SQRT(500/(100-B1))
Section2-3.xls
25
1????????????????????
???1 ????1 ??2 ?????????1
?? ???? 1 ??2e?????????1
???2 ???? K(????) ??e(????) ?????????1
???????1,???????,???2??
??1???-gt1???? ???????
?????1???2?? ??1????????????
??1????1??????????????,
??? ?????2???2,??????????2????? ? K ???