Question

(All answers were generated using 1,000 trials and native Excel functionality.) Galaxy Co. sells virtual reality (VR) goggles, particularly targeting customers who like to play video games. Galaxy procures each pair of goggles for $150 from its supplier and sells each pair of goggles for $300. Monthly demand for the VR goggles is a normal random variable with a mean of 160 units and a standard deviation of 40 units. At the beginning of each month, Galaxy orders enough goggles from its supplier to bring the inventory level up to 140 goggles. If the monthly demand is less than 140, Galaxy pays $20 per pair of goggles that remains in inventory at the end of the month. If the monthly demand exceeds 140, Galaxy sells only the 140 pairs of goggles in stock. Galaxy assigns a shortage cost of $40 for each unit of demand that is unsatisfied to represent a loss-of-goodwill among its customers. Management would like to use a simulation model to analyze this situation.

(a) What is the average monthly profit resulting from its policy of stocking 140 pairs of goggles at the beginning of each month? Round your answer to the nearest dollar. $blank

(c) Use the simulation model to compare the profitability of monthly replenishment levels of 140 and 160 pairs of goggles. Use a 95% confidence interval on the difference between the average profit that each replenishment level generates to make your comparison. Round your answer to the nearest dollar. The average difference between the net profit generated by a replenishment level of 160 versus a replenishment level of 140 is $blank    . It means, that monthly replenishment level of 160 maximizes profitability.

Answer 1

Answer: Galaxy co.procures router at the rate of $150 and Sale the same at $300. The net profit by one router is $150. The mean demand is of 160 with the variance of 40. There are two conditions in this case.

1. When the demand is less than 140, Galaxy co. pays $20 per router

2. if the demand is more than 140, galaxy co. assign a cost of $40 for shortage of supply.

In such scenario, it is very necessary to have more inventory than the demand because a shortage of inventory will cost double than to have an excess of inventory.

a. If Galaxy co. has stocked 140 routers and they have demand also of 140 routers. In this case the profit Galaxy co. will make in that month will be = 140 * ($300 - $150)= 140 * $150 = $21000. (In this case, we have considered the supply is equal to the demand)

b. The proportion of month when the demand is completely fulfilled. Check the below diagram of the normal distribution with mean 160 and standard daviation 40.

Here,

P(120≤X≤200) = 0.68268

That is 68.28% of the area come under the desired portion, That means 31.72% of area is outside it. Therefore in general 34.14% is the chance when the demand will be met by the supply as the demand will get upto 200 by normal random variable distribution.

(c).

When the monthly replenshiment is in the order of 140,160.

Then the profit will be, if all the demand is met, in this case Galaxy co. every time make the inventory level upto 140, means in the month when the demand is 160, there had been an excess of demand for 20 routers.

1. Demand 140 , Profit = 140 * $150 = $21000

2. Demand 160 , Profit = (160*$150) - ($20*40)

= $24000-$800 = $23200