Expansion Strategy and Establishing a Re-Order Point

The Bell Computer Company is considering to start production of a new computer plant, and the company is weighing two options –medium scale and large scale expansion. The demand for both expansions can be low, medium, or high with a probability of 20%, 50%, and 30% respectively. The medium-scale expansion profits are $50,000, $150,000 and $200, 000 for low, medium, and high demand respectively. The large-scale expansion profits are $0, $100,000 and $300,000 for low, medium and high demand respectively. The management of Bell Computer Company is weighing between the two options –medium-scale expansion and large-scale expansion –which one to go for. In the case of high demand, the large-scale expansion option has the potential to generate higher profit than the medium scale expansion. But if the demand is medium, the large scale expansion option will generate lower profit and nil profit in case of low demand. Comparing the two options, it is clear that the large-scale expansion bears more risk than the low scale expansion. 

The expected value (EV) of an investment refers to the anticipated value for that investment at some point in the future (College of Business Administration, 2015). In this case, the EV refers to the expected value of investing in the two options. To calculate the EV for the two options, we first have to determine the probability of occurrence. Once the probability of occurrence is known the EV can be calculated by multiplying each possible outcome by the probability of occurrence of that outcome and then summing all those values (College of Business Administration, 2015). By determining the EV of the two options of expansions, the management of Bells Computer Company will be able to go for the option that is more likely to generate higher profit. The EVs for medium scale and large-scale expansion are calculated as shown below. 

Medium scale expansion 

Large Scale Expansion 

As seen, the option that has a higher EV is the medium scale. Thus, the medium-scale expansion is preferred for the objective of maximising profit. However, the profits can deviate from the EV, and for this reason, the management cannot solely base their decision on EV. Thus, it is crucial to calculate the variance and standard deviations of the two options. In statistics, variance is a measurement of the spread between numbers in a given set of data (Santos, 2015). Higher variance indicates that the data are spread far from the mean. A low variance is desirable. To calculate the variance of a given set of data, one has to calculate the difference between each data points and the mean and then square them. The square root of the sum of the squares is the variance. The variance of the medium-scale expansion and large-scale expansion are shown below. 

Risk Analysis for Medium-Scale Expansion
Demand	Annual Profit (x) $1000s	Probability P(x)	(x - µ)	(x - µ) 2	(x - µ) 2 * P(x)
Low	50	20%	83.33	6944.44	1388.89
Medium	150	50%	16.67	277.78	138.89
High	200	30%	66.67	4444.44	1333.33
	$ 133.33			σ 2 =	2861
				σ =
Risk Analysis for Large-Scale Expansion
Demand	Annual Profit (x) $1000s	Probability P(x)	(x - µ)	(x - µ) 2	(x - µ) 2 * P(x)
Low	0	20%	133.33	17777.78	3555.56
Medium	100	50%	33.33	1111.11	555.56
High	300	30%	166.67	27777.78	8333.33
	$ 133.33			σ 2 =	12444.44
				σ =

Medium-Scale Expansion 

Large-Scale Expansion 

From the calculations, the variance is higher with the large-scale expansion than with small-scale expansion. So, the medium-scale expansion option is preferred. 

Another measure of risk that can be used is the standard deviation. Just like variance, the standard deviation is used to show the degree of variation in a data set. Simply, the standard deviation is the square root of the variance (Santos, 2015) . A higher value of standard deviation indicates greater variability in the set of data, while low standard deviation indicates that the set of data are close to the expected value. A lower standard deviation is preferred because it indicates a lower risk. The standard deviation for medium scale expansion and large-scale expansion were calculated and are as shown below. 

Risk Analysis for Medium-Scale Expansion
Demand	Annual Profit (x) $1000s	Probability P(x)	(x - µ)	(x - µ) 2	(x - µ) 2 * P(x)
Low	50	20%	83.33	6944.44	1388.89
Medium	150	50%	16.67	277.78	138.89
High	200	30%	66.67	4444.44	1333.33
	$ 133.33			σ 2 =	2861
				σ =	53.49
Risk Analysis for Large-Scale Expansion
Demand	Annual Profit (x) $1000s	Probability P(x)	(x - µ)	(x - µ) 2	(x - µ) 2 * P(x)
Low	0	20%	133.33	17777.78	3555.56
Medium	100	50%	33.33	1111.11	555.56
High	300	30%	166.67	27777.78	8333.33
	$ 133.33			σ 2 =	12444.44
				σ =	111.55

Medium-scale expansion 

Large-scale expansion 

The standard deviation is lower for medium-scale expansion, and this indicates that the medium-scale expansion project is less risky than the large-scale expansion project. Therefore, based on this criteria, the management should go for the medium-scale project. 

Recommendation 

The management of Bell Computer Company should choose the medium-scale expansion project because it has higher expected value and lower risk. 

Case 2: Kyle Bits and Bytes 

Kyle Bits and Bytes is a retail firm that sells a variety of computer-related products, and the HP laser printer is one of its popular products. For this product, the weekly demand is 200 units, and the lead time for a new order to arrive from the manufacturer is one week. Due to the deviations in weekly demand, Kyle wants to know when his firm should place order and inventory level in order to ensure it is stock-out. This is because he fears losing sales, plus possibly additional sales if he fails to fulfil an order due to stock-out. Kyle wants the probability of running short in any given week to be equal to or less than 6%. With this target, Kyle wants to know what should be the reorder point as well as the number of HP laser printers that should be in stock. 

The reorder point (ROP) refers to the level of inventory, which triggers an action to replenish that particular inventory stock. If the demand for a given product is variable, the demand can be described by a normal distribution. The normal distribution can be described by two parameters –the mean and the standard deviation. The average demand for the lead time is calculated by multiplying average daily demand by the lead time. 

 (Russell & Taylor, 2011) 

Where; 

Using the z-table, 

Therefore, 

From the calculations, Kelly ought to place an order when the inventory levels reach 218 units. 

Stock out may occur when the demand is variable, and this can occur during the need time (Russell & Taylor, 2011). In order to avoid the risk of stock out, a business has to ensure that it maintains safety stock. Safety stock refers to the additional inventory a company need to maintain above the expected demand in order to ensure that there are no chances of stock out (Russell & Taylor, 2011). A company decides what probability it can afford of stock out. In the case of Kyle Bits and Bytes company, the probability is 6%. The probability of no stock is referred to as the service levels. Safety stock is calculated using the formula shown below. 

In this case, 

Therefore, 

Therefore, Kyle Bits and Bytes should maintain 18 units safety stock of HP laser print to avoid stock out. 

References 

College of Business Administration. (2015). Probability distributions & expected values. [Online]. Retrieved from: https://www.slideshare.net/duazara/probability-distributions-expected-values . Accessed 19 th August 2019. 

Russel, R., & Taylor, B. (2011). Operations management: Creating value along the supply chain. Wiley Publication. John Wiley & Sons, Inc. 

Santos, M. (2015). Measures of variability. [Online]. Available at: https://www.slideshare.net/marksantos7923/measures-of-variability-48369991 . Accessed 19 th August 2019.