Given an EOQ model with shortages in which annual demand is 4200 units, C_o=$160, C_c=$7 per unit per year, and C_s=$25, what is the optimal stock out level? A) 96.44 B) 102.36 C) 108.44 D) 114.64

Question

Quizplus · Accepted Answer

The formula for calculating the optimal stock out level in an EOQ model with shortages is given by:

Tc = (2DCo / (CcCs)) ^ 0.5

where,
Tc = optimal cycle time
D = annual demand
Co = cost of placing an order
Cc = carrying cost per unit per year
Cs = cost of a stock out per unit

Plugging in the values given in the question, we get:

Tc = (2*4200*160 / (7*25)) ^ 0.5 = 36.84

The optimal order quantity can be calculated as:

Q* = (2DCo / Cs(1-(D/Q)/Tc)) ^ 0.5

Plugging in the values, we get:

Q* = (2*4200*160 / 25(1-(4200/Q)/36.84)) ^ 0.5 = 300

The optimal stock out level can be calculated as:

S* = D(Tc-Q*) / Tc

Plugging in the values, we get:

S* = 4200(36.84-300)/36.84 = 108.44

Hence, the optimal stock out level is 108.44 units.

Given an EOQ Model with Shortages in Which Annual Demand