Quick Print Inc. uses plain and three-hole-punched paper for copying needs. Dema

Question

Quick Print Inc. uses plain and three-hole-punched paper for copying needs. Demand for each type of paper is highly variable. Weekly demand for the plain paper is estimated to be normally distributed with mean 100 and standard deviation 65 (measure in boxes). Each week a replenishment order is placed to the paper factory and the order arrives five weeks later. All copying orders that cannot be satisfied immediately due to lack of paper are back ordered. The inventory holding cost is about $1 per box per year.

A- Again, suppose that Quick Print uses an order-up-to level of 700 for plain paper. What is Quick print’s fill rate?

B- What is Quick Print’s optimal order-up-to level for plain paper if it operates with 99% fill rate?

Explanation / Answer

Given,

Average daily demand (d)= 100

sd=65

Lead time (L)=5 days

a) Safety Stock (SS) = sd* (L^0.5) = 65 * (5^0.5) = 65*2.23 = 145.34

Reorder Point = dL + SS = (100*5) + 145.34 = 645.34

b) z= 99% = 2.58

Safety Stock (SS) = z*sd*(L^0.5) = 2.58* 65* 2.23 = 373.97 paper

Reorder point = dL+ SS = 100*5 + 373.97 = 873.97 paper

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