REVIEW EXERCISE 3

I HAVE TYPED THE TABLE OUT AT THE BOTTOM OF THE QUESTION FOR YOUR CONVENIENCE. THANKS IN ADVANCE

Parameter	Notation	Value	Measurement			Answers
Mean annual demand	D	89530	units per year		Q.1	G(Q*,R*)
Standard deviation of annual demand	sD	9840	units per year
Mean lead time	L	0.08	years
Standard deviation of lead time	sL	0.02	years		Q.2	# of cycles w/ stockout
Inventory holding cost factor (annual)	k	0.24	per year per dollar of average inventory
Unit purchase cost	C	32	per unit
Holding cost per unit per year	H		per unit per year		Q.3	G(Q,R) @ 99% type 1 SL
Backordering cost per unit	P	3.1	per unit backordered			% cost increase
Ordering cost per order	S	1050	per order
Order Quantity	Q		units
Mean demand during the lead time	DL		units per lead time
Standard deviation of demand during the lead time	sDL		units per lead time	=SQRT(L*sD^2+D^2*sL^2)
Type 1 Service Level	alpha
Standard normal variate	z
Safety Stock	SS		units
Expected units out of stock during the lead time	nR		units per cycle	=sDL*NORMDIST(z,0,1,0)-SS*(1-NORMDIST(z,0,1,1))
Type 2 Service Level	beta
Reorder point	R		units
Annual Cycle Stock Holding Cost	CSH		per year
Annual Safety Stock Holding Cost	SSH		per year
Annual Ordering Cost	OC		per year
Annual Backordering Cost	BC		per year
Annual Total Relevant Cost	G(Q,R)		per year

Please consider the data for SKU RQ3C in the attached template. Inventories for this SKU are managed via an optimal reorder point policy. 1 What is the total cost (per year) in the optimum? 2 In how many cycles per year will we stock out (on average) in the optimum? 3 The VP of Sales argues that the company should strive for higher levels of customer service. Specifically, she suggests a 99% in-stock rate would be more appropriate. All else equal, by how much would total costs increase (in % terms) relative to the optimal solution (see Q.1) in this case? B C D E F G Answers 0.1 GIQ*R*) Q.2 # of cycles w/ stockout 9.3 GIQR) 99% type 1 SL % cost increase A Page Break Preview 2 Mean annual demand 3 Standard deviation of annual demand 4 Mean lead time 5 Standard deviation of lead time Inventory holding cost factor (annual) Unit purchase cost & Holding cost per unit per year 9 Backordering cost per unit 10 Ordering cost per order 11 Order Quantity 12 Mean demand during the lead time 13 Standard deviation of demand during the lead time 14 Type 1 Service Level 15 Standard normal variate 16 Safety Stock 17 Expected units out of stock during the lead time 18 Type 2 Service Level 19 Reorder point 20 Annual Cycle Stock Holding Cost 21 Annual Safety Stock Holding Cost 22 Annual Ordering Cost 23 Annual Backordering Cost 24 Annual Total Relevant Cost 25 26 27 28 29 30 31 32 33 Questions Template + Notation Value Measurement D 89530 units per year SD 9940 units per year L 0.08 years SL 0.02 years k 0.24 per year per dollar of average inventory c 32 per unit H per unit per year P 3.1 per unit backordered 5 1050 per order units DL units per lead time SDL units per lead time alpha Z SS units nR units per cycle beta R units CSH per year SSH per year OC per year BC per year GQ,R) per year =SORTILDA2D42 SL2) -SDL NORMDIST(2,0,1,0-SS (1-NORMDIST(2,0,1,1))