Question

Tucson General Hospital sometimes has to treat people bitten by rattlesnakes. In the past havson scernedat he wpnizl sometimes has to treat people bitten by rattesnakes. In the past 15 years they following numbers of rattlesnake-bite cases years, they Year Number of Cases 2001 2002 2003 2004 2005 2006 2007 2008 | 2009 2010 2011 2012 2013 2014 2015 4 4 12 4 0.0 10 At the beginning of each year, the hospital has the opportunity to pre-order anti-venom kits at cost of $350 each. Treating each snake-bite case requires one anti-venom kit. The kits expire after one year after which any unused kits must be disposed of at a cost of S10 each. If the hospital runs out of pre- ordered anti-venom kits before the end of the year, it may immediately obtain a functionally equivalent packet of medications from a local pharmacy, but the cost is $500 per case treated. Assuming the past data presented above are representative of the number of snake-bite cases that may be expected in the future, how many anti-venom kits should the hospital pre-order each year. Page 2 of 2

Answer 1

Average annual demand based on past 15 years data = (4+8+9+2+3+4+12+8+4+3+5+10+11+6+7)/15 = 6.4

Standard deviation of annual demand = SQRT(((4-6.4)² + (8-6.4)² + (9-6.4)² + (2-6.4)² + (3-6.4)² + (4-6.4)² + (12-6.4)² + (8-6.4)² + (4-6.4)² + (3-6.4)² + (5-6.4)² + (10-6.4)² + (11-6.4)² + (6-6.4)² + (7-6.4)² )/(15-1)) = 3.158

Assuming that annual demand is normally distributed

Underage cost, Cu = 500 - 350 = 150

Overage cost, Co = 350 + 10 = 360

Critical ratio = Cu/(Cu+Co) = 150/(150+360) = 0.2941

z = NORMSINV(0.2941) = -0.5414

Number of anti-venom kits hospital should pre-order each year = Average demand + z * Std deviation of demand

= 6.4 + (-0.5414)*3.158

= 5