Question

Daily demand is normally distributed with mean 22 units and SD=6. Ordering cost is $21/order, carrying cost is $2.5 per unit per year. The item is used 365 days a year. Order lead time is 4 days. The order point should have a 99% target service level.

Find:

-avg inventory level

-avg number of orders/yr

-avg number of stockouts/yr

-avg time (years) between stockouts

Policy I is the (Q,R) policy determined above.

Policy II: Increase the order quantity by 10 units, and re-evaluate the policy using the original order point from policy I

Policy III: Increase the order point by 5 units, and re-evaluate the policy using the original order quantity from Policy I.

Both policies II and III should have the same total average inventory (cycle stock and safety stock). However, the mix of cycle stock vs. safety stock varies between the two.

Answer 1

Mean	M	22
Standard Deviation	SD	4
No. of Days	N	365
Annual Demand	D=MxN	8030
Ordering Cost	Co	$21	/order
Inventory Holding Cost	Ch	$2.5	/unit/year
Order Lead time	Lt	4	days
Standard Deviation of Lead Time	SDlt	0
Target Service Levels	SLt	99%
Risk	a=1-SLt	1%
Normal distribution contactn Z	Za	2.58

Above is Given data.

Answers as per policy I, II & III are as follows:

Policy I
Economic Order Quantity	Q=Square Root (2xDxC0/Ch)	367.2927987	368
Reorder point	ROP=M*Lt+Za x Square Root(Lt x SD x SD+ M x M x SDlt x SDlt)	108.64	109
Orders/year	ECQ=D/EOQ	21.86266659	22
Order Cycle	1/ECQ years	0.045740075	year
Order Cycle	365/ECQ days	16.69512722	days
Average Inventoy level	IL=(Q+0)/2	184
Average stockouts per year	SO=N*a	3.65
Average time between Stockouts	Tso=1/So	0.27	years

Policy II
Economic Order Quantity	Q	378
Reorder point	ROP=M*Lt+Za x Square Root(Lt x SD x SD+ M x M x SDlt x SDlt)	108.64	109
Orders/year	ECQ=D/EOQ	21.24338624	22
Order Cycle	1/ECQ years	0.047073474	years
Order Cycle	1/ECQ years	17.18181818	days
Average Inventoy level	IL=(Q+0)/2	189
Average stockouts per year	SO=N*a	3.65
Average time between Stockouts	Tso=1/So	0.27	years

Policy III
Economic Order Quantity	Q=Square Root (2xDxC0/Ch)	367.2927987	368
Reorder point	ROP	114
Orders/year	ECQ=D/EOQ	21.86266659	22
Order Cycle	1/ECQ years	0.045740075	years
Order Cycle	1/ECQ years	16.69512722	days
Average Inventoy level	IL=(Q+0)/2	184
Average stockouts per year	SO=N*a	3.65
Average time between Stockouts	Tso=1/So	0.27	years