This preview shows page 1. Sign up to view the full content.
Unformatted text preview: se exactly one of our sales. From this it follows that
in the long run we make a proﬁt of
13.2 (.036)12 = 12.7636 dollars per day Our inventory holding cost under the new system is
2· 30
40
21
60 + 160 + 126
+4·
+6·
=
= 3.1454
110
110
110
110 so now our proﬁts are 12.7636 3.1454 = 9.6128. Suppose we use a 0,3 inventory policy. In this case the transition probability is
0
1
2
3 0
.1
.7
.3
.1 1
.2
.3
.4
.2 2
.4
0
.3
.4 3
.3
0
0
.3 From the equations for the stationary distribution we get
⇡ (0) = 343/1070 ⇡ (1) = 300/1070 ⇡ (2) = 280/1070 ⇡ (3) = 147/1070 29 1.6. SPECIAL EXAMPLES To compute our proﬁt we note, as in the previous calculation if we always had
enough stock then we would make 13.2 dollars per day. Considering the various
lost sales scenarios shows that in the long run we make sales of
✓
◆
280
300
13.2 12 ·
0.1 +
(0.1 · 2 + 0.2 · 1) = 11.54 dollars per day
1070
1070
Our inventory holding cost until the new scheme is 300
280
147
600 + 1120 + 882
4720
+4·
+6·
=
=
= 2.43
1070
1070
1070
1070
1472
so the long run pro...
View
Full
Document
 Spring '10
 DURRETT
 The Land

Click to edit the document details