Average demand, d = 90 bags per week

Std dev of weekly demand, = 15 bags

Order cost, K = $54 per order

Unit cost, C = $11.7 per bag

Unit carrying cost, h = 27% of C = $3.159 per annum

Lead time, L = 3 weeks

CSL = 80% i.e. z = NORMSINV(0.8) = 0.8416

1. Annual demand, D = d * 52 weeks = 90*52 = 4680 bags

EOQ = (2.D.K / h)1/2 = (2*4680*54/3.159)^0.5 = 400 units

Time between orders = EOQ / d = 400 / 90 = 4.44 weeks

2. Reorder point, R = d.L + z..L = 90*3 + 0.8416*15*3 = 291.9 or,

292 bags

3. The on-hand inventory is given as 320 units

A withdrawal of 10 bags will lead to the on-hand inventory falling to

320 - 10 = 310 bags which is still more than the R=292.

So, it is not the time to reorder.

4. Q = 500

Annual holding cost = (Q/2)*h = (500/2)*3.159 = $789.75

Annual ordering cost = (D/Q)*K = (4680/500)*54 = $505.44

Note that at EOQ, the above two % figures should match. But here,

the holding cost is more than the ordering cost meaning we are

carrying more inventory in each cycle and ordering less frequently.

This means that we are ordering more units than the EOQ-based

policy.

5. Total annual cost for the above policy = 789.75 + 505.44 = $1,295.19

Total cost the EOQ-based policy = (EOQ/2)*h + (D/EOQ)*K =

(400/2)*3.159 + (4680/400)*54 = $1,263.6

So, the annual savings will be = 1295.19 - 1263.6 = $31.59

question :

Consider again the kitty litter ordering policy for Pet Empire, suppose that weekly demand forecast of 90 bags is incorrect and actual demand averages only 60 bags per week. How much higher will total costs be, owing to distorted EOQ caused by this forecast error? Suppose again that actual demand is 60 bags but that ordering costs are cut to only $6 by using the internet to automate order placing. However, the buyer does not tell anyone, and the EOQ is not adjusted to reflect this reduction in ordering costs. How much higher will total costs be, compared to what they could be if the EOQ were adjusted?

Suppose that Pet Empire uses a P system instead of a Q system. The average daily demand is d = 90/6 = 15 bags and the standard deviation of daily demand is (15/6) = 6.124 bags and at zero amount of inventory on hand. Calculate average time between orders, new safety stock quantity and also order quantity with variable demands should be used to approximate the cost trade-offs of the EOQ. How much more safety stock is need than with a Q system?