Respuesta :
Answer:
a) 138 units
b) 17 units
c) 17 units
d) Total Cost = $353.35
Explanation:
Given:
Average pizzas delivered = 200
Charge of inventory holding = 30% of cost
Lead time = 7 days
Now,
a) Economic Order Quantity = [tex]\sqrt\frac{2\times\textup{Annual Demand}\times\textup{Cost per Order}}{\textup{Carrying cost}}[/tex]
also,
Annual Demand = 200 × 12 = 2400
Cost per Order = Cost of Box + Processing Costs
= 30 cents + $10
= $10.30
and, Carrying Cost = [tex]\frac{\textup{Total Inventory Cost}}{\textup{total annual demand}}[/tex]
=[tex]\frac{\textup{Total Cost per order}\times\textup{Annual demand}\times\frac{25}{100}}{\textup{Annual demand}}[/tex]
= [tex]\frac{\$10.30\times2400}\times\frac{25}{100}}{2400}[/tex]
= $2.575
Therefore,
Economic Order Quantity = [tex]\sqrt\frac{2\times\textup{2400}\times\textup{10.30}}{\textup{2.575}}[/tex]
= 138.56 ≈ 138 units
b) Reorder Point
= (average daily unit sales × the lead time in days) + safety stock
= ([tex]\frac{200}{30}\times7[/tex]
= 46.67 ≈ 47 units
c) Number of orders per year = [tex]\frac{\textup{Annual Demand}}{\textup{Economic order quantity}}[/tex]
= [tex]\frac{\textup{2400}}{\textup{138}}[/tex]
= 17.39 ≈ 17 units
d) Total Annual Cost (Total Inventory Cost)
= Ordering Cost + Holding Cost
Now,
The ordering Cost = Cost per Order × Total Number of orders per year
= $10.30 × 17
= $175.1
and,
Holding Cost = Average Inventory Held × Carrying Cost per unit
Average Inventory Held = [tex]\frac{\textup{0+138}}{\textup{2}}[/tex] = 69
Carrying Cost per unit = $2.575
Holding Cost = 69 × $2.575 =
$177.675
Therefore,
Total Cost = Ordering Cost + carrying cost
= $175.1 + $177.675 = $353.35
Answer:
Q´ = 894 pizzas per order
Reorder point r = 2.68 cycles/year
D = 2400 pizzas/year
Total annual inventory cost TAC = $53.66 per year
Explanation:
having the following:
D = 2400 pizzas/year
Ch = ($0.2/unit)*0.3 = $0.06/unit
Co = $10/order
calculating pizza quantities in order:
Q´ = E*O*Q = ((2*D*Co)/Ch)^1/2 = ((2*2400*10)/0.06)^1/2 = 894.4 = 894 pizzas per order
calculating the reorder point:
Reorder point r = (2400 pizzas/year)*(1/894 cycles/pizza) = 2.68 cycles/year
Calculating the total annual inventory cost:
Total annual inventory cost TAC = (D*Co/Q) + ((Q/2)*Ch) = (2400*10/894) + (0.06*(894/2)) = 26.85 + 26.82 = $53.66 per year
It can be seen that when the TAC is calculated using Q´, the annual order costs are similar to the annual maintenance costs. Can be done for $0.25/unit pizza cost.
