10.\" High Tech Inc. is a virtual store that stocks a variety of calculators in
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Question
10." High Tech Inc. is a virtual store that stocks a variety of calculators in its warehouse. Customer orders are placed the orders are picked and packaged; and then orders are shipped to the customers. A fixed-order-quantity inventory control system (FQS) helps monitor and control these SKUs. The following information is for one of the calculators that High Tech stocks, sells, and ships Average demand Lead time Order cost Unit cost Carrying charge rate Number of weeks Standard deviation of weekly demand SKU service level Current on-hand inventory 35 calculators Scheduled receipts Backorders 12.5 calculators per week 3 weeks $20/order $8.00 0.25 52 weeks per year 3.75 calculators 95 percent 20 calculators 2 calculators What are the economic order quantity? What are the total annual order and inventory- holding costs for the EOQ? a. b. c. What is the reorder point without safety stock? d. What is the reorder point with safety stock? e. Based on the previous information, should a fixed- order quantity be placed, and if so, for how many calculators?Explanation / Answer
We have following information
Average demand = 12.5 calculators per week
Number of weeks in a year = 52 weeks
Therefore Annual demand D = average demand * Number of week in a year
= 12.5 * 52 = 650 calculators per year
Ordering cost S = $ 20 per order
Unit cost = $8 per calculator
Holding or carrying cost H = 0.25 * unit cost = 0.25 * $8 = $2 per unit per annum
a. For minimum cost, calculate Optimum Order quantity per order which is Economic Order Quantity (EOQ)
EOQ = sqrt (2* D*S/H) = sqrt(2*650*$20/$2) = 114.02 or 114 calculators
Therefore EOQ is 114 calculators
b. Total Annual cost = total ordering cost + total carrying cost
= (D/Q)* S + (H*Q)/2 [where Q is Economic Order Quantity = 114]
= (650/114)*$20 + ($2*114)/2
= $114 + $114
= $228
Minimum total annual cost of this optimal order is $228
c. Reorder Point without safety stock
Reorder Point (ROP) = average demand * lead time
Where,
Reorder Point Q =?
D is average demand = 12.5 calculator
L is the lead time = 3 weeks
Therefore,
Reorder Point Q = 12.5 * 3 = 37.50 calculators
Reorder Point is 37.50 calculators
d. Formula for the Reorder Point calculation with safety stock
Reorder Point (ROP) = average demand * lead time + safety stock
OR,
Reorder Point Q = D L + z * st. dev. Of demand * sqrt (L)
Where
Reorder Point Q =?
D is average demand = 12.5 calculator
L is the lead time = 3 weeks
And safety stock = z * st. dev. Of demand * sqrt (L)
Where,
Value of z for the desired Service Level of 95% = 1.64
Standard deviation of weekly demand = 3.75 calculators
Let’s first calculate the safety stock at 95% of service level
Safety stock = 1.64 * 3.75 * sqrt (3) = 10.65
Therefore,
Reorder Point Q = 12.5 * 3 + 10.65 = 48.15 or 48 calculators (nearest whole number)
Reorder Point is 48 calculators
e. Yes, a fixed order quantity should be placed as economic order quantity is fixed order quantity and it is 114 calculators per order.
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