Sam\'s Cat Hotel operates 52 weeks per year, 6 days per week, and uses a continu

Question

Sam's Cat Hotel operates 52 weeks per year, 6 days per week, and uses a continuous review inventory system. It purchases kitty litter for $13.00 per bag. The following information is available about these bags: followsDemandequals=95 bags/week followsOrder costequals=$58.00/order followsAnnual holding costequals=35 percent of cost followsDesired cycle-service levelequals=80 percent followsLead timeequals=2 weeks (12 working days) followsStandard deviation of weekly demandequals=15 bags followsCurrent on-hand inventory is 320 bags, with no open orders or backorders. a. Suppose that the weekly demand forecast of 95 bags is incorrect and actual demand averages only 75 bags per week. How much higher will total costs be, owing to the distorted EOQ caused by this forecast error? The costs will be $ nothing higher owing to the error in EOQ. (Enter your response rounded to two decimal places.) b. Suppose that actual demand is 75 bags but that ordering costs are cut to only $9.00 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 S. How much higher will total costs be, compared to what they could be if the EOQ were adjusted? The costs will be $ nothing higher owing to the error in EOQ.

Explanation / Answer

Sam’s Cat Hotel

Economic Order Quanity

Demand Annual = 95 Bag / Week

Annual Demand (D) = 95*52 = 4940 Bags

Cost / bag = 13 $

Annual Holding cost per bag (H) = 35% (13$)= 4.55 $

ordering cost (S) = 58

EoQ = sqrt (2* D*S/H) = sqrt( 2*4940*58/4.55) = 354.884 or 355 bags ( round off)

Order frequency = (Q/D) = 355/ 4940 = 0.071862 year or 3.736 weeks

Calculating cost :

C1= Q*H/2+D*S/Q

C1= 1614.724$

When demand is 75 bags / week ,

New demand = 75 * 52 = 3900 bags

New EOQ = 315.323 bags or 316 bags (rounded ff)

Calculating cost now :

C2= Q*H/2+D*S/Q

C2= 1434.723 $

So, We can see that cost when forecase is 75 bags is much less than the wrong forecast of 95 bags.

current inventory on hand = 320 bags

for service level of 80% , Z= .84

demand during protection interval = 15 * sqrt (2) = 21.21 or rounded off to 21 bags

15 = sd , 2 = lead time

Safety stock = .84*21= 17.81

Demand during lead time = 95*2 = 190

including safety stock = 190 +17.81 = 208 which is less than current inventory in hand of 320 bags

measuring impact of reduced ordering cost from 58 $ to 9 $

Now correct demand is = 75 bags/order

correct ordering cost is 9 $ and incorrect ordering cost is 58$

eoq incorrect = 315.23

eoq correct= 124.118

Calculating total cost in both the cases using C= Q*H/2+D*S/Q

for eoq 316 , order cost 58$ , Total cost = 1434.723 $

for eoq 124 , order cost 9$ , Total cost = 2103.687 $

Difference in cost = 668.9644 or 668.96$ is the extra cost.

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