This assignment has two cases. The first case is on expansion strategy. Managers
ID: 3295076 • Letter: T
Question
This assignment has two cases. The first case is on expansion strategy. Managers constantly have to make decisions under uncertainty. This assignment gives students an opportunity to use the mean and standard deviation of probability distributions to make a decision on expansion strategy. The second case is on determining at which point a manager should re-order a printer so he or she doesn't run out-of-stock. The second case uses the normal distribution. The first case demonstrates application of statistics in finance and the second case demonstrates application of statistics in operations management. Assignment Steps Resources: Microsoft Excel®, Bell Computer Company Forecasts data set, Case Study Scenarios Using the provided Excel file, include answers to the following: Case 1: Bell Computer Company •Compute the expected value for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of maximizing the expected profit? Justify your answer. •Compute the variation for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of minimizing the risk or uncertainty? Justify your answer. Case 2: Kyle Bits and Bytes •Using the normal distribution, determine what the re-order point should be. In other words, how many HP laser printers should he have in stock when he re-orders from the manufacturer? Show your work.
Explanation / Answer
Case 1: Bell Computer Company
The Bell Computer Company has two expansion options: medium scale, and large scale. For both medium scale expansion and large scale expansion, demand can be low, medium, or high with probability of 0.2, 0.5, and 0.3 respectively. For medium scale expansion, profits in case of low, medium and high demand are $50,000 , $150,000 and $200,000 respectively. For large scale expansion, profits in case of low, medium, and high demand are $0, $100,000 and $300,000 respectively. Management is facing dilemma whether to go for medium scale expansion or large scale expansion. While large scale expansion has potential to generate higher profit in case of high demand, the large scale expansion will generate lower profit than medium scale expansion in case of low and medium demand. In case of low demand, the large scale expansion results in nil profit. Clearly, large-scale expansion bears more risk than the low-scale expansion.
The expected value is an anticipated value of an action. An action has multiple possible outcomes. First, we need to determine probability of occurrence of each outcome. The expected value is calculated by multiplying each possible outcomes by probability of occurrence of that outcome, and adding all those values. (Hossein, 2014) Expected value of medium scale expansion and large scale expansion will help the management choose the expansion option that is most likely to generate higher profit.
The expected value of two alternatives are:
Medium scale expansion: $145
Large scale expansion: $140
The medium scale expansion alternative has higher expected value than large-scale expansion project. Thus, medium-scale expansion is preferred for the objective of maximizing expected profit.
Merely knowing expected value is not enough to take an informed decision. It is also important to know how profits can deviate from the expected value. For this purpose, variance is used. Variance measures how far a set of random values are spread from the mean value. Higher variance means the random values are spread far from the mean. A low variance is desirable.
The variance of random variables is the expected value of squared deviation from the mean.
Mathematically, variance of discrete random variables is calculated as:
Var = E[(X-µ)2] = [P(X)* (X-µ)2]
(Hossein, 2014)
The variance of medium-scale and large-scale expansion projects are:
Medium-scale expansion: 2,725
Large-scale expansion: 12,400
The variation for profit associated with large-scale expansion is much higher than the variation for profit associated with medium-scale expansion.
Standard deviation is a measure of risk. Standard deviation is a measure used to quantify the amount of variation of a set of data values. Standard deviation is calculated as square root of variance. Low standard deviation indicates that random values tend to be close to the expected value. A lower standard deviation indicates lower risk and a higher standard deviation indicates higher risk.
The standard deviation of medium-scale and large-scale expansion projects are:
Medium-scale expansion: 52.202
Large-scale expansion: 111.355
Lower value of standard deviation of medium-scale expansion indicates that medium-scale expansion project is less risky than the large-scale expansion project. So, medium-scale expansion project is preferred for the objective of minimizing the risk or uncertainty.
Recommendation
The medium-scale expansion project has higher expected value, and lower risk. Thus, management should choose medium-scale expansion project.
Case 2: Kyle Bits and Bytes
Kyle Bits and Bytes is a retailer of computing products. Kyle’s most popular product is an HP laser printer. For this product, average weekly demand is 200 units, and lead time is one week. However, demand is not constant. Kyle has observed that weekly demand standard deviation is 30. Kyle need to know when should they place order (i.e. reorder point), and inventory level so that there is stock-out. If Kyle is not able to fulfill an order due to stock-out, Kyle will lose that sale and possibly additional sale. Kyle has set maximum acceptable probability of stock-out in any week to 6%. With this target, Kyle wants to know what should be the re-order point and how many HP laser printers should be in stock.
Reorder point is the inventory level at which order should be placed. In this case, demand is variable. For variable demand, it is assumed that demand can be described by a normal distribution. The average demand for the lead tine is the sum of average daily demand for the number of days in lead time period. This can be calculated by multiplying average daily demand by the lead time. The variance of the distribution is calculated as the sum of daily variance for the number of days in lead time.
Thus, reorder point R = dL + z**L
Where
d = Average daily demand
L = lead time
= Standard deviation of daily demand
z = Number of standard deviations corresponding to the service level probability
(Russell & Taylor, 2011)
Here,
d = 200/7 units
L = 7 days
= 30/7
Maximum accepted probability of stock out is 6%. It means, service level is 0.94
Using z-table, corresponding z- value is determined.
z = 1.56
Thus, reorder point R = (200/7)*7 + 1.56*(30/7)* 7 = 200 + 17.69 = 217.69
i.e. Kelly’s will place an order when inventory level reaches 218 units.
When demand is variable, there is chance of shortage (or stock out). Shortage can occur during the need time. I firm needs to maintain safety stock to avoid the risk of stock out. The safety stock is the additional inventory a firm maintains above expected demand to avoid stock out. Firms use service level to determine safety stock. A firm decides what probability it can afford of stock out. The service level is probability of no stock out during lead time. This probability is called service level. (Russell & Taylor, 2011) For example, a service level of 90% means there is 0.90 probability that firm will meet demand during lead time. It means, the probability of stock out is 10%.
Safety stock is determined as:
Safety stock = z**L
L = lead time
= Standard deviation of daily demand
z = Number of standard deviations corresponding to the service level probability
In this case,
L = 7 days
= 30/7
Maximum accepted probability of stock out is 6%. It means, service level is 0.94
Using z-table, corresponding z- value is determined.
z = 1.56
Thus, Safety stock =1.56*(30/7)* 7 = 17.69 = 18 units
Thus, Kelly’s should maintain 18 units safety stock of HP laser printer to avoid stock out.
References
Hossein, P. (2014). Introduction to Probability, Statistics, and Random Processes. Kappa Research.
Russell, R. S., Taylor, B. W. (2011). Operation Management. (7th ed.). Wiley Publication. John Wiley & Sons.
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