Question

A sporting goods company has a distribution center that maintains inventory of fishing rods. The fishing rods have the following demand, lead time, and cost characteristics: Average demand = 100 units per day, with a standard deviation of 12 units Average lead time = 12 days with a standard deviation of 2 days 250 days per year Unit cost = $25 Desired service level = 95% Ordering cost = $50 Inventory carrying cost = 20% The basic question: How many fishing rods should the distribution center carry to provide the desired service level? There are, of course, many other specific questions, such as EOQ? Average cycle stock?

Answer 1

Solution:

Average demand = 100 units per day, with a standard deviation of 12 units

Average lead time = 12 days with a standard deviation of 2 days

250 days per year

unit cost = $25 , desired service level = 95% , Ordering cost = $50 , Inventory carrying cost = 20%

Lets say

Average demand = Ad

Average lead time = At

Unit cost = U

Desired service level = Dl

Ordering cost = O

Inventory carrying cost = Icc

Standard deviation =S

Thus,

S of demand at Dl = $12 * 12^{\wedge} 2$ = 205 units

SS = 1.65 multiply with 205 = 339 units

Total units in a day = 250 multiply with 100 = 25000

EOQ = $(2 * 25000 \text { units per year } * 50 \text { per order }) /(25 \text { per unit* } 0.2)$ = 708 units

here 25 and 0.2 is unit cost and invetory cost

TAC

annual ordering cost

O = $50 * 25000 / 708$ = 1765.5

Annual inventory cost

Icc = $25^{*} 0.2^{*}(708 \text { units } / 2)$ = 1770

Annual product cost = Pc

25 multiply with 25000 = 625000

total = O +Icc+Pc

625000+1770+1765.5 = 628535.5

If the service level increases from 95% to 99%, cost will dec per unit