Scenario 15.1 - The Jerk Store
George takes an eclectic mix of spices to make his authentic jerk seasoning as a rub for chicken,pork,and fish.The ingredients and packaging cost $1.50 and he sells the packets by the case to Jerk Stores in the Caribbean for $2.50 per packet.Tourists to the islands gladly pay $8.75 for these packets,eager to host their friends for an authentic Caribbean meal and bore them with vacation photos upon their return.The demand for the packets is normally distributed,with a mean of 2500 packets and a standard deviation of 600.
-If each Jerk Store location is acting independently,what is their expected overstock quantity if they order the optimal quantity?

Question

Quizplus · Accepted Answer

In order to find the expected overstock quantity and the optimal order quantity, we need to use the formula for the economic order quantity (EOQ):
EOQ = sqrt((2DS)/H)
where D is the demand (mean), S is the setup cost (packaging cost), and H is the holding cost (per unit cost of inventory).

Plugging in the given values, we get:
EOQ = sqrt((2*2500*1.5)/8.75) = sqrt(857.14) ≈ 29.29

This means the Jerk Stores should order 29 packets at a time for each location. To find the expected overstock quantity, we use the formula:
Expected overstock = sqrt((2DS^2)/H)
where D and S are the same as before, and we use the standard deviation, σ, rather than the mean for demand.

Plugging in the given values, we get:
Expected overstock = sqrt((2*2500*1.5^2)/8.75) = sqrt(642.86) ≈ 25.33

Therefore, the expected overstock quantity is 25.33 packets per order. To find the total expected overstock quantity for a year, we multiply by the number of orders per year, which is the annual demand divided by the order quantity:
Total expected overstock = (σ*sqrt(D))/sqrt(2)*EOQ = (600*sqrt(2500))/sqrt(2)*29.29 ≈ 372.67

Rounding to the nearest integer, we get an expected overstock of 373. Subtracting this from the order quantity, we get:
Optimal order quantity - expected overstock = 446 - 373 = 73

Therefore, the best choice for the expected overstock quantity is C) 446.

Scenario 15.1 - the Jerk Store