# 2 dollars per day considering the various lost sales

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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...
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