Question

A student group is producing activity calendars for sale at the beginning of the academic year and must decide how many to have printed. The calendars cost $2 each to print and sell for $5. Those not sold have no salvage value. Demand is normally distributed with a mean of 3000 and standard deviation of 100.

C_s = Sales price/unit – Cost/unit  C_o = Cost/unit – Salvage value  Service Level =
Q = µ + Z σ

1. What is the optimal service level?
2. How many calendars should the organization produce?

Answer 1

COST PRICE = 2
SALES PRICE = 5
SALVAGE VALUE = 0

Cost of shortage(Cs) = sales price - cost price = 5 - 2 = 3
Cost of overage(Co) = Cost price - salvage value = 2 - 0 = 2

Service level = Cs / (Cs + Co) = 3 / (3 + 2) = 0.6
The Z value that corresponds to a service level of 0.6 is = 0.25

Mean demand = 3000
Standard deviation = 100

Optimal stocking level = Mean demand + (Z * Standard deviation)

= 3000 + (0.25 * 100) = 3025

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