Question

ABC's Fish Market buys fresh Boston bluefish daily for $4.20 per kilogram and sells it for $5.70 per kilogram. At the end of each business day, any remaining bluefish is sold to a producer of cat food for $2.4 per kilogram. Daily demand can be approximated by a normal distribution with a mean of 80 kilograms and a standard deviation of 10 kilograms. (a) What is the optimal stocking level? (b) What is the stockout risk?

plz, answer both question a) and b).

Answer 1

(a)

Cost price of bluefish = $4.20

Selling price of bluefish = $5.70

Salvage value of bluefish = $2.40

Mean demand = $\mu$ = 80 kgs

Standard deviation = $\sigma$ = 10 kgs

Underage Cost

If we order 1 fish less than the demand, the profit lost would be called the underage cost.

Underage cost = = $ 5.70 - $ 4.20 = $1.50

Cu

Overage Cost

If we order 1 fish more than the demand, the loss due to selling fish at a lower price would be called the overage cost.

Overage cost = $C_o$ = $ 4.20 - $ 2.40 = $1.80

Critical Ratio

$= \frac{C_u}{C_o+C_u}$

$= \frac{1.50}{1.80+1.50}$

=0.4545

From the normal distribution table (Z- table), the Z-value corresponding to 0.4545 is -0.115

Z= -0.115

The optimal order quantity is given by

$X=\mu+Z*\sigma$

$X=80+(-0.115)*10$

X= 78.85 kgs of bluefish

The optimal sticking level of bluefish is 78.85 kilograms.

(b)

The stockout risk is the probability that there is a demand but no inventory is available. This will happen when demand is greater than the stocking level.

Probabilty of stockout = P(Demand > Stocking level)

Probability of stockout = P(X > 78.85 )

= 1 - P(X < 78.85)

= 1 - P(Z < (78.85-80)/10)

=1 - P(Z < -0.115)

= 1- 0.4545

= 0.5455

The stockout risk is 0.5455 or 54.55%. Thus, there is possibility of stockout 54.55% of the days.