6. Sam\'s Cat Hotel operates 52 weeks per year, 6 days per week, and uses a cont
ID: 362597 • Letter: 6
Question
6. Sam's Cat Hotel operates 52 weeks per year, 6 days per week, and uses a continuous review inventory system (i.e.Q system. It purchases kitty litter for $ 11.50 per bag. The following information is available about these bags. Demand = 90 bags/ week Order cost $50/ order Annual holding cost 27 percent of cogs Desired cycle service level-80 percent Lead time = 4 weeks Standard deviation of weekly demand 15 bags Current on- hand inventory is 320 bags, with no open orders or backorders. a. What is the EOQ? What would be the average time between orders (in weeks)? b. What should R (i.e. reorder point) be? c.An inventory withdrawal of 10 bags was just made. Is it time to reorder? d. The store currently uses a lot size of 550 bags (i.e., Q = 550), what is the annual holding cost of this current policy? Annual ordering cost? Without calculating the EoQ, how can you conclude from these two calculations that the current lot size is too large? e. What would be the annual cost saved by shifting from the 500- bag lot size to the EOQ?Explanation / Answer
a) EOQ = sqrt(2*Annual Demand*Order cost/Holding cost)
Annual demand = 90*52 = 4680
Holding cost = 27%*11.5 = 3.11
EOQ = sqrt(2*4680*50/3.11) = 388 units
Number of orders = 4680/388 = 12
Time between orders = 52*6/12 = 26 days
b) Reorder point = Demand*Lead time + z*Standard deviation*sqrt(Lead time)
z value for 80% service level is 0.842
Reorder point = 90*4 + 0.842*15*sqrt(4) = 385
c) Current on hand is 320. The withdrawal of 10 units will trigger reorder point
d) Q = 550
Annual Holding cost = Q/2*Holding cost = 550/2*3.11 = 855.25
Annual ordering cost = Annual demand/Q*Order cost = 4680/550*50 = 425.45
Current lot size is too large as at optimum point both Holding and Ordering cost should match or be very close to each other. In this case, difference is very high
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