IEOR150F10_hw07_sol

IEOR150F10_hw07_sol - IEOR 150, Fall 2010 Homework 6 1....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: IEOR 150, Fall 2010 Homework 6 1. Because D ∼ U (0 , 1), we have its pdf f ( x ) = 1 and cdf F ( x ) = x for all x ∈ [0 , 1]. We also have the inverse cdf F- 1 ( y ) = y for all y ∈ [0 , 1]. (a) i. The unit overage cost is c = 1 and the unit underage cost is r- c = 1. Therefore, we have q D = F- 1 ( 1 1 + 1 ) = 1 2 . ii. The expected sales quantity under an inventory level q ∈ [0 , 1] is E min { D,q } = Z q xf ( x ) dx + Z 1 q qf ( x ) dx = Z q xdx + q Z 1 q dx = 1 2 q 2 + q (1- q ) = q- 1 2 q 2 . Therefore, we have M D = r h q D- 1 2 ( q D ) 2 i- cq D = 1 4 . (b) i. The unit overage cost is w and the unit underage cost is r- w = 1. Therefore, we have q I ( w ) = F- 1 ( r- w r- w + w ) = r- w r . ii. We have M I = max w ( w- c ) ‡ r- w r · = max w- w 2 + ( r + c ) w- cr r . Take first order derivative and set it to 0, we get- 2 w * + ( r + c ) = 0 ⇔ w * = r + c 2 = 3 2 . Note that w c > c = 1....
View Full Document

This document was uploaded on 01/13/2011.

Page1 / 2

IEOR150F10_hw07_sol - IEOR 150, Fall 2010 Homework 6 1....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online