Expansion Strategy and Establishing a Re-Order Point

Expansion Strategy and Establishing a Re-Order Point


September 30, 2019

Expansion Strategy and Establishing a Re-Order Point

“Many companies hesitate to enter export markets because of perceived risk. Certainly, there are some legitimate risks to be mitigated. There are also a number of “risks” which are exaggerated and promulgated with common myths. But there is one fundamental risk which has traditionally challenged export growth – market selection. Technology is quickly helping to obviate that risk and clear the path for more companies to expand internationally (Marsh, 2016).”
There are two cases we need to find statistical information for. The first case involves expansion strategy. The Bell Computer Company is trying to decide between a medium-scale or large-scale expansion. This will allow the opportunity to use the mean and standard deviation of probability distributions to make a decision on expansion strategy. The second case involves determining a re-order point for products. Kyle Bits and Bytes computer products needs to determine the re-order point for their most popular product, the HP Laser Printer. Kyle wants to ensure that he does not run out of stock and miss out on potential sales. This case will use normal distribution. The first case demonstrates application of statistics in finance and the second case demonstrates application of statistics in operations management.

Case 1: Bell Computer Company

Expected Value for Profit

    Medium-Scale Large-Scale
    Expansion Profits Expansion Profits
    Annual Profit ($1000s) P(x) Annual Profit ($1000s) P(x)
Demand Low 50 20% 0 20%
  Medium 150 50% 100 50%
  High 200 30% 300 30%
Demand Annual Profit (x)$1000s Probability P(x) (x – µ) (x – µ)2 (x – µ)2 * P(x)
Low 50 20% -95 9025 1805
Medium 150 50% 5 25 12.5
High 200 30% 55 3025 907.5
  Mean= 145   σ2 = 52.20153254
        σ = 2725
Demand Annual Profit (x)$1000s Probability P(x) (x – µ) (x – µ)2 (x – µ)2 * P(x)
Low 0 20% -140 19600 3920
Medium 100 50% -40 1600 800
High 300 30% 160 25600 7680
        σ2 = 111.3552873
  Mean= 140   σ = 12400

Bell Computer Company is looking to expand their operations. They are currently looking at two different expansion scenarios, medium and large scale expansion. For both expansion types, you could have 3 different demands. Low, Medium, or High. The probability of these demands would be 0.2, 0.5, and 0.3 respectively. There are profits associated with each level of demand as well. For the medium expansion, profits for low, medium, and high demand are $50,000, $150,000, and $200,000. For the large scale expansion there are different values for profit. For low, medium, or high demand the profits are $0, $100,000 and $300,000. Given these numbers management is trying to decide which expansion would be the most beneficial to the company. Looking at the numbers, and after doing some calculations, it’s clear to see that the large expansion could generate the highest profit if demands were high. However, it will actually produce a lower profit if the demand is only low or medium, with the medium scale expansion winning out in those scenarios. The large scale expansion has more risk associated to it.

Next, we need to put numbers and proof behind our preliminary prediction that large scale expansion has more risk. We need more than just base values. To do this we will determine the probability of occurrence for each outcome. The expected value is calculated by multiplying each possible outcomes by probability of occurrence of that outcome, and adding all those values (Black, 2017). Looking at the spreadsheet for Bell Computer Company it shows that the expected value of medium scale expansion is $145 and the expected value of large scale expansion is $140. This shows, and means, the medium scale expansion is preferred as this will help to maximize expected profit.

The next part of the puzzle involves variance. Variance in this case is vital as it will show how a company’s profits can deviate from the expected profit. The variance in the medium scale project is 2,725 while the variance in the large scale project is 12,400. Again we can see how the larger scale project has a larger variance, or larger chance of not obtaining expected results from a profit standpoint.

The next step of the process would be to look at standard deviation. Standard deviation is a measure of how spread out number are. Its Greek letter is sigma, and finding it is easy. It’s simply the square root of variance which we have already found (Pierce 2016). Higher standard deviation means more risk as lower standard variation means lower risk. The standard deviation for the medium size scale is 52.2, while the large scale expansion comes in at 111.3 for standard deviation. This shows, with calculations behind it for evidence/proof that the medium scale expansion is the “less risky” option of expansion and should be the one that Bell Computer Company chooses to go with.

Case 2: Kyle Bits and Bytes

Kyle Bits and Bytes is looking at determining a re-order point for their best-selling product. Kyle wants to ensure that he does not run out of stock on his HP Laser Printers. The average weekly demand of this product is 200 units. Lead time for the printer comes in at one week. The demand, like most products, is not constant and fluctuates with user’s needs. The company has recognized their standard deviation for demand is 30. Kyle has placed the stipulation on this re-order point that he wants the probability of running out of stock to be at 6%. With these targets and numbers in mind, we can calculate what the re-order point should be and make a recommendation accordingly.

According to Russell and Taylor, the reorder point R = dL + z*σ*√L, whereas d = Average daily demand, L = lead time, σ = Standard deviation of daily demand, z = Number of standard deviations corresponding to the service level probability (Russell & Taylor, 2011). In the case of Kyle Bits and Bytes, d = 200/7 units, L = 7 days and σ = 30/7. The maximum accepted probability of stock out is 6%. It means the service level is 0.94, Also, the z-table is used to determine the corresponding z- value, and in this case, it is observed to be 1.56. Therefore, with the data provided, the manager would order a total of 494 units (1.555 * 30 + 200 = 246.6 = rounded to 247 since the units do not come partially assembled * 2) on the first week to accommodate the order lead time and 247 units every subsequent week in order to maintain no more than six percent stock-out probability.


In conclusion, understanding what need is and being able to calculate future risk will help any organization. This means that when risk is factored in the preparation of outcomes can be made. This means that depending on the risk and variables the outcomes vary and the can prepare for each one in many ways.


Black, K. (2017). Business Statistics: For Contemporary Decision Making, (9th Edition). Hoboken, NJ: Wiley

Marsh, E. (2016, May 09). Take the gambling out of global expansion by making decisions based on real data. Retrieved February 04, 2018, from http://www.tradeready.ca/2016/trade-takeaways/take-gambling-global-expansion-making-decisions-based-real-data/

Pierce, R. (17 Oct 2016). “Standard Deviation and Variance”. Math Is Fun. Retrieved 21 Jun 2017 from http://www.mathsisfun.com/data/standard-deviation.html

Russell, R. S., & Taylor-Iii, B. W. (2008). Operations management along the supply chain. John Wiley & Sons.

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