Suppose the programs for a Lions home game cost $2.00 to print and sell for $5.0

Question

Suppose the programs for a Lions home game cost $2.00 to print and sell for $5.00. Program demand is normally distributed with a mean of 30,000 and a standard deviation of 2000.

a. Based on the shortage cost and the overage cost, how many programs should be printed?

b. Suppose the service level for program sales is 95%.

i. How many programs should be printed?

ii. What is the implied shortage cost?

Part 2.Suppose the Tigers print programs for a series at a time. A three game weekend series with the Yankees is expected to draw 50,000 fans per game. For each game, the demand for the programs is normally distributed with a mean of 30,000 and a standard deviation of 3,000.

a. What is the three day demand distribution?

b. How many programs should be printed for the weekend series for a service level of 99%? Note: You must determine the three day demand distribution first.

Explanation / Answer

Solution of Part 1 –

Cost of the game = $ 3

Sale price = $ 5

Cs = Cost of a stock out = $ 5 - $ 2 = $ 3

Co = Cost of an overage =$ 2

SL= Service level = Cs / (Cs +Co) = 3 / (3+2) = 3/5 = 60%

Zsl at 60 % = 0.2533

Q= Batch size or number of units to order

Mean demand = m = 30,000

Standard deviation of demand= s = 2,000

If demand is normally distributed, the optimal number of units to order

Q = µ + * Zsl = 30,000 + 2,000 * 0.2533 = 30,000 +506.6 = 30,506.6

b. Suppose the service level for program sales is 95%.

i. How many programs should be printed?

ii. What is the implied shortage cost?

Zsl at 95% = 1.6449

If demand is normally distributed, the optimal number of units should be printed

Q = µ + * Zsl = 30,000 + 2,000 * 1.6449 = 30,000 +3,289.8 = 33,289.8

The implied shortage cost at 95% service level

Cs = Co * {SL / 1- SL} = $ 2 * {95% / (1-95%) } = $ 2 * 19 = $ 38

the implied shortage cost is $ 38

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