Petty House operates 52 weeks per year, 6 days per week, and uses a continuous review inventory
Petty House 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 $ 10 per bag. The following information is available about these bags. Demand = 102 bags/ week Order cost = $ 49/ order Annual holding cost = 25 percent of cogs Desired cycle service level = 80 percent Lead time = 3 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 600 bags (i. e., Q = 600). What is the annual holding cost of this current policy? Annual ordering cost? Without considering 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 600- bag lot size to the EOQ?
Homework Answers
Given data,
Days of operations = 6 days per week / 52 Weeks = 312 Days
Demand per week =d = 102 ==> demand per year = 102*52 = 5304 days = D
Order Cost = C = $ 49/order
Price kitty liter = P = $10/bag
Annual Holding Cost = H = 25% of COGS = 0.25* P = 0.25 * 10 = 2.5 $
a) EOQ = SQRT (2* D*C/ H) = SQRT (2*5304*49/2.5) = 455.97= 456 bags
Average Time between orders = EOQ/D = 456/5304 = 0.0859 Year = 4.47 weeks
b) Given Standard Deviation = s = 15 = Sigmat
Lead time = 3 weeks
Service level desired = 80%
Reorder point = R = Demand Serviced in order to not lose sales during lead time + Safety stock
Demand Serviced in order to not lose sales during lead time = 102 * 3 = 306
safety stock = z SigmaL = > SigmaL = Sigmat* sqrt(lead time) = 15*sqrt(3) = 25.98
for 80% service level , Z = 0.85 ==> safety stock = 306+ (25.8*0.85) = 328
c) Inventory withdrawal = 10 bag
==> 328 - 10 = 318 bags
Since inventory post withdrawal is less than reorder point, reorder is required
d) Annual holding cost with lot size = 600 bags = Q ==> = QH/2 = 600*2.5/2 = $750
Annual ordering cost = Cannual = DC/Q = 5304* 49/600 = $433.16
Here annual ordering cost is lesser than holding cost which means current lot size is very large
e) Current annual cost with EOQ = (QH/2) + (DC/Q) = 456*2.5/2 + (5304* 49/456) = $ 1139.94
Total savings = 1183.16 – 1139.94 = $43.22
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