Suppose the cafeteria's current ordering policy is to purchase beans every 13 weeks. The manager says that the ordering cost of S = $50 is just a guess. Therefore, he insists on using the current policy. Find the range of S for which the EOQ he found in part (a) would be preferable (in terms of lower total replenishment and transportation costs) to the current policy of buying beans every 13 weeks.

to. Economic order quantity is the optimal order size to minimize all inventory costs. The formula is written as

EOQ = [2FD/C]^1/2

Where C = Cost of maintenance per unit per year = In our problem, the cost of maintenance is 20% of the purchase price

which is 0.20(65 units*$4*52) = 2704

F=Fixed cost per order that is $50 for procedures and others
D=Demand in units per year is 65*52 =3380

Solving the above formula = ((2*50*3380)/2704)^(1/2) = (125)^(1/2) = 11.18

(b) Optimum number of orders per year

The optimal order quantity (Q*) is found when annual holding cost = ordering cost

solving the above equation = Sqrt ((2*3380*50)/0.8) = 650

maintenance cost per unit per year = 0.2*4 =0.8

What is the optimal interval ( in weeks ) between orders?

T* = Q* /D = 650 /3380 = 0.1923 years

Assuming 52 weeks