Problem 10-31 (Algorithmic) A product with an annual demand of 1000 units has Co
ID: 2494972 • Letter: P
Question
Problem 10-31 (Algorithmic)
A product with an annual demand of 1000 units has Co = $24.50 and Ch = $5. The demand exhibits some variability such that the lead-time demand follows a normal probability distribution with µ = 24 and = 4.
Note: Use Appendix B to identify the areas for the standard normal distribution.
What is the recommended order quantity? Round your answer to the nearest whole number.
Q* =
What are the reorder point and safety stock if the firm desires at most a 7% probability of stock-out on any given order cycle? If required, round your answers to the nearest whole number.
Record point =
Safety stock =
If a manager sets the reorder point at 29, what is the probability of a stock-out on any given order cycle? If required, round your answer to four decimal places.
P(Stockout/cycle) =
How many times would you expect a stock-out during the year if this reorder point were used? Round your answer to the nearest whole number.
Number of Orders =
Explanation / Answer
Given
Annual Demand (D) = 1000 units /year,
Ordering Costs Co = $24.50/order
Holding Costs Ch = $5/unit/year
What is the recommended order quantity?
Ans:- The Optimal Ordering Quantity is
Q1* = (2DCo)/(Ch) = (2*1000*24.50)/5 = 98.99 units
What are the reorder point and safety stock if the firm desires at most a 7% probability of stock-out on any given order cycle?
Ans:- Using a normal distribution table, a 7-percent probability of a stockout on any given order cycle implies 93% service level. This implies that 7% upper tail area. This corresponds to a standard normal z-value of 1.47.
The Recorder point is r = mean demand during replenishment lead time + Zd
= d + Z d = 24+ 1.47*4 = 29.88 30 units
Safety stock = Zd = 1.47*4 = 5.88 6 units
If a manager sets the reorder point at 29, what is the probability of a stock-out on any given order cycle?
Ans:- If R = 29, the standardized z-value is (29 – 24)/4 = 1.25, giving a tail area under the normal distribution of 0.1056. This is the probability of a stock-out each cycle.
How many times would you expect a stock-out during the year if this reorder point were used?
Ans:-
Annual ordering/ setting up cost = Co(D/Q)
Where D/Q is the number of order or setup per year (D = annual
usage, Q = lot size in units)
The number of stockouts per year is therefore 0.1056 times the number of orders per year = 0.1056(D/Q) = 2.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.