Question

The College of Business office buys copy paper from Office Depot and places and order every Monday morning. Office Depot charges $10 for delivery of each order. The leadtime to get an order is 2 days. The usage per day (during the five-day work week) can be modeled with a Normal distribution with a mean of 10 reams of paper and a standard deviation of 2 reams of paper.

(a) What inventory model is appropiate?

(b) What is the length of the protection interval? (Assume 1 week = 5 work days.)

(C) On Monday morning the office manager checks the inventory of copy paper and finds that there are 30 reams of paper in stock. How many reams of paper should she order if the acceptable stock out risk is 5%?

Answer 1

Periodic interval, P = 5 work days (order is placed every monday morning)  

Lead time, L = 2 days

Mean demand, m = 10 reams per day

Std deviation of daily demand, s = 2 reams

(a) Periodic review inventory model is appropriate.

(b) Protection interval = P + L = 5 workdays + 2 days = 7 workdays

(c) For 5% stockout risk, value of z = NORMSINV(1-0.05) = 1.645

Target Inventory level = m*(P+L) + z*s*SQRT(P+L) = 10*(5+2) + 1.645*2*SQRT(5+2) = 78.7 ~ 78 reams

Number of reams to order = Target inventory - Current Inventory = 78 - 30 = 48 reams