Question

The annual demand for a product is 17,200 units. The weekly demand is 331 units with a standard deviation of 85 units. The cost to place an order is $31.50, and the time from ordering to receipt is six weeks. The annual inventory carrying cost is $0.10 per unit. a. Find the reorder point necessary to provide a 95 percent service probability. (Round your answer to the nearest whole number.)

Reorder point
b. Suppose the production manager is asked to reduce the safety stock of this item by 60 percent. If she does so, what will the new service probability be? (Round your answer to 3 decimal places.)
Service probability

Answer 1

R = 2414 units

0.794

Explanation:

Given:

Weekly demand, D = 331 units

Lead time (L)= 6 weeks

Standard Deviation (SD) = 85 units

The reorder point is calculated using the relation :

R = D*L + z*(SDw)

SDw = the standard deviation with lead time of 6 weeks ; √6 * 85 = 208.21

z = NORMSINV(0.98) = 2.05

R = (331 * 6) + (2.05 * 208.21)

R = 1986 + 428.122

R = 2414.122

R = 2414 units

The Safety stock, SS

SS = z * SDw

SS = 2.05 * 208.21

SS = 426.8305 units

60% reduction :

426.8305 * (1 - 60%)

= 170.7322

= 171 units

The new service probability ;

SS = z * SDw

171 = z * 208.21

z = 171 / 208.21

z = 0.82

P(Z < 1.02) = 0.7938 = 0.794 = 79.4%