Question

You are the store manager for a store. One of your products is a desk. This desk comes in two colors: maple and black. Weekly demand for each desk color follows a Normal distribution with mean 100 and standard deviation 50. The demands for the two colors are independent. You order inventory replenishment's weekly, the lead-time from your supplier is 3 weeks and your supplier is quite reliable, i.e., you always receive your entire order in three weeks. You use the order up-to model to decide your order quantities.

A. Suppose your order up-to level is 500 for maple desks. With a 3-week lead time, what is your expected ending inventory of maple desks?

Choose the closest number. a. 98 b. 108 c. 208 d. 308 e. 408

Answer 1

P = review period = 1 week
L = average lead time = 3 weeks
d = weekly average demand = 100
s = std. dev. of weekly demand = 50

Optimum order up to level (T*) = d*(P+L) + Z*s*SQRT(P+L)
or, 500 = 100*(1+3) + Z*50*SQRT(1+3)
or, Z = 100/100 = 1 i.e. L(z) = 0.083 (from loss function tables)

Expected shortage per cycle (ESC) = L(z) x s*SQRT(P+L) = 0.083*50*SQRT(1+3) = 8.3

Exp. Inventory at the end of cycle = T* - d(P+L) + ESC = 500 - 100*(1+3) + 8.3 = 108.3 or 108 (rounded off)