Exam 5 November, questions and answers PDF

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Logistics Management and Planning Practice Questions & Solutions 1. A specialty coffeehouse sells Colombian coffee at a fairly steady rate of 280 pounds annually. The beans are purchased from a local supplier for $2 per pound. The coffeehouse estimates that it costs $45 in paperwork ...

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Logistics Management and Planning Practice Questions & Solutions 1.

A specialty coffeehouse sells Colombian coffee at a fairly steady rate of 280 pounds annually. The beans are purchased from a local supplier for $2.40 per pound. The coffeehouse estimates that it costs $45 in paperwork and labor to place an order for the coffee, and holding costs are based on a 20 percent annual interest rate.

(1) (a) (b) (c) (d)

Determine the optimal order quantity for Colombian coffee. What is the time between placement of orders? What is the average annual cost of holding and setup due to this item? If replenishment lead time is three weeks, determine the reorder level based on the on-hand inventory.

Solution: For this problem, we have the following parameters: The fixed ordering cost K = 45 dollars per pound, the demand rate D = 280 pounds per year, and the holding cost h = 2.40 × 0.2 = 0.48 dollars per pound per year. 2KD (a) The optimal order quantity is Q* = = 229.13 pounds. h Q* (b) The optimal order cycle is T * = = 0.82 year. D (c) The average annual cost of holding and setup is $109.98. (d) Because we assume there are 52 weeks in one year, three weeks is L = 3/52 years. Note that τ < T*, so the lead time is shorter than the optimal order cycle. Therefore, the reorder quantity should be R = D*L = 16.15 pounds.

(2) Consider the coffeehouse discussed in Problem 1. Suppose that its setup cost for ordering was really only $15. Determine the error made in calculating the annual cost of holding and setup incurred as a result of its using the wrong value of K. (Note that this implies that its current order policy is suboptimal)

Solution: Under the true fixed ordering cost K’ = 15 dollars, the total cost calculated in using the “wrong” order K ' D hQ* + quantity Q* = 229.13 is = $73.32 . 2 Q* However, the optimal total cost should be G'  2K' h  $63.50 . Therefore, the error is $73.32 - $63.50 = $9.82, or ($73.32 – $63.50)/$63.50 = 15.5%.

2.

Next week, Super Discount Airlines has a flight from New York to Los Angeles that will be booked to capacity. The airline knows from past history that an average of 25 customers (with a standard deviation of 15) cancel their reservation or do not show for the flight. Revenue from a ticket on the flight is $125. If the flight is overbooked, the airline has a policy of getting the customer on the next available flight and giving the person a free round‐trip ticket on a future flight. The cost of this free round‐trip ticket averages $250. Super Discount considers the cost of flying the plane from New York to Los Angeles a sunk cost. By how many seats should Super Discount overbook the flight?

Solution: Cu = $125 Co = $250 P(D...