Allison has a profitable online business, TryceraStopper, selling high-velocity

Question

Allison has a profitable online business, TryceraStopper, selling high-velocity dinosaur stun guns for $45/gun. Demand is fairly steady throughout the year (the website is available 365 days/year), and is approximately normally distributed with mean 30 guns/day and a standard deviation of 10 guns/day. Her supplier in Montana charges $15 per gun and a flat rate of $100 every time she places an order. Orders take exactly 10 days to arrive. Allison estimates her annual per unit holding costs at 10% of the cost of the guns (to her).

a) What type of inventory management problem is this? Explain your answer.

i. Newsvendor (single period) model
ii. EPQ model
iii. MRP model
iv. ABC Classification
v. EOQ model with discrete demand distribution
vi. EOQ model with continuous demand distribution

b. How many guns should Allison order at a time in order to minimize holding and ordering costs?

c. Calculate the level at which she should reorder guns if she is willing to experience at most an 8% chance of stocking out.

d. Fill in: When inventory drops to __________ guns, Allison should place an order for ____________ more guns.

e. The supplier offers Allison a discount of $2/gun if she orders 1000 guns at a time. Is it worth taking the discount? (If you were unable to answer part b), use 1300 guns as the optimal order quantity.)

Explanation / Answer

a. The correct answer is Option vi - EOQ model with continuous demand distribution b. Annual Demand (30 * 365) 10950 Ordering Cost $       100.00 Holding Cost ( 15 * 10%) $           1.50 EOQ = 2AO / H where A = Annual Demand O = Ordering Cost per order H = Holding Cost per unit per annum EOQ = 2AO / H = (2 * 10950 * 100) / 1.50 = 1208.305 or, 1208 units c. Mean Demand (per day) 30 Standard Deviation of Daily Demand (SDd) 10 Lead Time (days) 10 Standard Deviation of Lead Time (SDl) = SDd * Lead Time = 10*10 = 31.62 31.62 Service Level Desired (1 - Stock Out = 1 - 0.08) 92% Z Value at 92% 1.405 Safety Stock for 92% service level Z value * Standard Deviation (Demand Lead Time) (31.62 * 1.405) 44 Lead Time Demand ( Lead Time * Avg Demand) 300 Reorder Point = Lead Time Demand + Safety Stock 344 d. When inventory drops to 344 guns, Allison should place an order for 1208 more guns. e. Inventory Order Size (a) 1208 1000 Price (b) 15.00 13.00 Product Cost (Price * Annual Demand = b * 10950) ( c) $164,250.00 $142,350.00 # Orders (Annual Demand / Order Size = 10950 / a) (d) 9 11 Ordering Cost (No orders * $ 100 = d* $100) (e) $906.46 $1,095.00 Carrying Cost per unit (f) $1.50 $1.30 Carrying Cost (Order Size / 2 * Carrying Cost per unit per annum = a/2 * f) (g) $906.00 $650.00 Total Cost (c + e + g) $166,062.46 $144,095.00 Yes it is worth taking the discount as overall cost reduces from $166062.46 to $144095

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