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In: Operations Management

Problem 13: Sam's Cat Hotel operates 52 weeks per year, 6 days per week, and uses...

Problem 13: 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 $11.70 per bag. The following information is available about these bags.

Demand = 90 bags/week

Order Cost= $54/0rder

Annual Holding cost = 27% of cost

Desired cycle-service level = 80%

Lead time = 3 weeks (18 working days)

Standard deviation of weekly demand = 15 bags

Current on-hand inventory is 320 bags, with no open orders or backorders.

Suppose that Sam's Cat Hotel in Problem 13 uses a P system instead of a Q system. The average weekly demand is d = 90 bags and the standard deviation of the weekly demand is σ= 15 bags.

a. What P (in weeks) and T should be used to approximate the cost trade-offs of the EOQ?

b. How much more safety stock is needed than with a Q system?

c. It is time for the periodic review. How much kitty litter should be ordered?"

Solutions

Expert Solution


[ Note for students : no rounding is done as no such instruction is mentioned in the question]

a) EOQ = sqrt((2*annual demand*ordering cost)/holding cost per unit per year) = sqrt((2*90*52*54)/(27%*11.7)) = 400

P = time between 2 orders in weeks = Total number of weeks available/(Annual demand/EOQ) = 52/((90*52)/400) = 4.444444444

T = target inventory = Weekly Demand*(lead time in weeks+P) + z*standard deviation of weekly demand*sqrt(lead time in weeks+P)  

=90*(3+4.444444444)+normsinv(0.8)*15*sqrt(3+4.444444444) = 704.4448334 [ Answer is 704 if rounding is required]

b)

Safety stock with Q system => z*standard deviation of weekly demand*sqrt(lead time in weeks) = normsinv(0.8)*15*sqrt(3) = 21.86596106

Safety stock with P system => z*standard deviation of weekly demand*sqrt(lead time in weeks+P) = normsinv(0.8)*15*sqrt(3+4.444444444) = 34.44483348

P system has 34.44483348-21.86596106 = 12.57887242 safety stock more than Q system [ Answer is 13 if rounding is required]

c)

Amount of litter Kitty should order = target inventory-on hand inventory = 704.4448334-320 = 384.4448334 [Answer is 384 if rounding is required]

keosha answered 1 week ago
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