16 Screen Custom View tioncomhmtpx Michigan State Figurine i

16 Screen Custom View tion.com/hm.tpx Michigan State Figurine inc. (MSF) selis crystal figurines to Spartan fans. MSF buys the figurines from a manufacturer for $12 per unit. They send orders electronically to the manufacturer, costing $25 per order and they experlence an average lead time of seven days for each order to arrive from the manufacturer Their inventory carrying cost is 20 percent. The average daily demand for the figurines is four units per day They are open for business 250 days a year. The supplier decides to offer a volume discount. They will sell the crystal figurines at $10 per unit for orders of 500 units or more. Answer the following questions a. How many units should the firm order each time? Assume there is no uncertainty at all about the demand or the lead time. (Round your answer to the nearest whole number.,) b. How many orders will they place in a year? c. What is the ntory? d. What s the ennual ordering cost? esc tab

Solution

Given data:

Order cost (S) = $25

Material cost/unit = $12 for 0-499 units order & $10 for 500+ units order lot

Holding cost(H) = 20% of $12 = $2.4

Daily demand = 4 units

Days operation = 250

Lead time = 7 Days

Annual Demand = 250*4 = 1000 Units

Solution:

a)To determine the ideal units that should be ordered, we follow the following steps:

Step 1:

Calculating the EOQ at both $12 & $10 material cost, we have:

EOQ₁₂ = Sqrt (( 2*D*S)/H) = Sqrt (2*1000*25)/(0.2*12) = 144

And, EOQ₁₀ = Sqrt (( 2*D*S)/H) = Sqrt (2*1000*25)/(0.2*10) = 158

Clearly, we find that a 158 order quantity actually costs $12 per unit. Hence EOQ₁₀ is not feasible.

Step 2:

As we see from step 1 that the feasible EOQ is 144. But this doesn’t correspond to lowest cost. Hence, we have to compare its total cost with the price break quantity – 500 units at lower price level i.e $10

Now, we know that:

Total cost = Total Holding cost + Total Ordering cost + Total material cost

Therefore,

TC₁₄₄ = ((q/2)*H)+((D/q)*S)+(C*D) = ((144/2)*2.4)+((1000/144)*25)+(12*1000) = $12346.41

And, TC₅₀₀ = ((500/2)*2)+((1000/500)*25)+(10*1000) = $10550

Clearly, we find that total cost is minimum when the order quantity is 500 units.

Thus, the firm should order 500 units each time.

b) Number of orders placed in a year = Annual Demand/order lot size = 1000/500 = 2 orders/year

c)Average inventory = Lot size/2 = 500/2 = 250 units

d)Annual ordering cost = (D/q)*S = (1000/500)*25 = $50

e)Annual Inventory carrying cost = (q/2)*H = (1000/2)*(0.2*10) = $1000

Hope the explanation helps. Thanks