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Osprey Sports stocks everything that a musky fisherman could want in the Great North Woods. A particular musky lure has been very popular with local fishermen as well as those who buy lures on the Internet from Osprey Sports. The cost to place orders with the supplier $40/order; the demand averages 5 lures per day, with a standard deviation of 1 lure and the inventory holding cost is 1.00/lure/year. The lead time form the supplier is 9 days, with a standard deviation of 3 days. It is important to maintain a 95 Percent cycle-service level to properly balance service with inventory holding costs. Osprey Sports is open 350 days a year to allow the owners the opportunity to fish for muskies during the prime season. The owners want to use a continuous review inventory system for this item. Refer to the standard normal table for z-values.
a. What order quantity should be used?
374 lures. (Enter your response rounded to the nearest whole number.)
b. What reorder point should be used? 70 lures. (Enter your response rounded to the nearest whole number.)
****c. What is the total annual cost for this inventory system?**** $
Expert Answer
The optimal order quantity depends on demand rate, fixed cost and inventory holding cost and variable cost of the unit.
It is governed by the equation,
Where Q = Optimal order size/quantity, D = Demand per unit period, S = Fixed cost of ordering, H = Inventory holding cost per unit per unit time period
With this given data,
Demand, D = 5 lures per day = 350 * 5 = 1750 lures /year
S = $40 per order
H = $1 per lure
On substituting the values in the equation,
we get optimal order quantity = Q = 374.16 ≈ 374 units
b) Re-order point
Reorder point is the point at which the order is triggered depending leadtime to delivery and demand.
Reorder point = Demand * Leadtime + safety stock
Reorder point = D * L + Is
Where L is the lead time and D is the demand per unit (day)
Safety stock for 95% level of service (Is) = Z * σ * L0.5
We know that here in this case,
Z for 95% service level= 1.645
σ, standard deviation = 1 lure / day
L = 9 days
Upon substituting the values, we get
Reorder point = D * L + Z * (L * σd2 + d * σl2)0.5 = (5 * 9) + 1.645 * (9 * 12 + 5 * 32)0.5 = 45 + 12.08 ≈ 57 lures
Thus, Reorder point is 57 lures
c) Annual ordering cost and holding cost
Total costs is sum of annual ordering cost and annual holding cost
We know that, Annual ordering cost = S x (D / Q)
Substituting in the above equation, we get,
Annual ordering cost = S x (D / Q) = 40 * (1750 / 374) = $ 187
Also, we know that, Annual holding cost = H x (Q / 2)
Thus, Annual holding cost = 1 x (374 / 2) = $187
Total costs = 187 + 187 = $374
Thus, total annual cost for this inventory system is $374
