Expansion Strategy and Establishing a Reorder Point

Expansion Strategy and Establishing a Reorder Point

University of Phoenix

QNT/561 Applied Business Research & Statistics

Expansion Strategy and Establishing a Reorder Point

Case 1: Bell Computer Company

The Bell Computer Company is considering a plant expansion that will enable the company to begin the production of a new product. Since receiving my MBS from the University of Phoenix, I have become the vice president of Bell Computer Company and one of my duties is to determine whether the company should make the expansion on medium or a large scale project. Since the demand for a new product involves uncertainty we may use a low demand, medium demand, or high demand. Using the probability estimates for demands of 0.2, 0.5, and 0.3, I must perform some computation that will help the company in their decision of the plant expansion. I will compute the expected value for the profit and the variation for the profit of the two expansion alternatives.

The medium and large scales are two expansion options that Bell Computer considers will consider. The probability for the demand of low, medium, and large have a probability of 0.2, 0.5, and 0.3. Profit for the low, medium and high demand on the medium scale expansion with a $1000 annual profit is $50,000, $150,000, and $200,000. For the large scale expansion, the low, medium, and high demand on the large scale expansion is $0, $100,000, and $300,000. Choosing the correct expansion for Bell Computer Company will save the company money and time. Looking at the large scale expansion, it shows that if the company was to choose the large scale expansion, the company will produce lower profit than medium scale expansion when it comes to low and medium demands and the large scale expansion will produce higher profit in high demand. Because the large scale expansion have no profit for the low demand, the risk in using the large scale expansion is greater than the medium scale demand.

According to Black (2017), “forecasting is the art or science of predicting the future.” There the expected value is a forecasted value of a variable, meaning it is a predicted value of a variable. To find the expected value is to multiply each possible occurrence by the probability of occurrence which is as follows:

According to Black (2017), a variance is “the average of the squared deviations about the arithmetic mean for a set of numbers.” The variance is calculated as follows:

  • 50 x 0.20 + 150 x 0.50 + 200 x 0.30 = 145 (Medium Scale Expansion)
  • 0 x 0.20 + 100 x 0.50 + 300 x 0.30 = 140 (Large Scale Expansion)

Therefore the variance of the medium scale expansion is 2725 and the large scale expansion is 12,400. From the numbers you can see that the variance for the large scale expansion is a lot higher than the number for the medium scale expansion.

  • (50 – 145)² x 0.20 + (150 – 145)² x 0.50 + (200 – 145)² x 0.30 = 2725
  • (0 – 140)²z 0.20 + (100 – 140)² x 0.50 + (300 – 140)² x 0.30 = 12400

Case 2: Kyle Bits and Bytes

Kyle Bits and Bytes is a retailer of computer products whose most popular products is an HP laser printer. The weekly demand for this printer by Kyles Bits and Bytes customer is 200 units per week with a lead time of one week. In this case, the demand for the printer is not constant, so since taking an Operations Management class and learning that demand is a random variable, which according to Black (2017) is “variable that contains the outcomes of a chance experiment,” Kyle has been observing the weekly demand and realize that it standard deviation is 30. “The standard deviation is a popular measure of variability. It is used both as a separate entity and as a part of other analyses, such as computing confidence intervals and in hypothesis testing. The standard deviation is the square root of the variance. The population standard deviation is denoted by σ,” (Black, 2017). This information will give the company an insight of when to reorder the printers and the level of inventory in order for the company to have a stock-out, which will prevent the company from losing sales because there are no printers in stock. Kyle wants the probability of running short (stock-out) in any week to be no more than 6%. Keeping this information in mind will help the company with its reorder of printers and how many printers they should keep in stock. “The reorder point (ROP) is the level of inventory which triggers an action to replenish that particular inventory stock. It is a minimum amount of an item which a firm holds in stock, such that, when stock falls to this amount, the item must be reordered,” (Wikipedia, 2018). To determine what to reorder is as follows:

d = 200/7; L = 7; σ = 30/7; z = 1.56

  • Reorder Point – R = dl + z * σ * √L (d =daily demand; L = lead time)

The above answer concludes that Kyles Bits and Bytes should reorder printers when their inventory has 218 units. Keeping this amount of HP printers in stock will assure the company will not miss out on any sales.

  • R = (200/7) + 1.56 * (30/7) * √7 = 200 + 17.39 = 217.69

Since Kyle wants the probability of running short (stock-out) in any week to be no more than 6%, the service level will be 94%. This means that doing lead time, which is the amount of time between when the order id placed and when it is delivered; there is a 94% chance that Kyle will have the HP printers on hand. This is known as safety stock. “Safety stock is an additional quantity of an item held in inventory in order to reduce the risk that the item will be out of stock. Safety stock acts as a buffer in case the sales of an item are greater than planned and/or the supplier is unable to deliver additional units at the expected time.” (What is Safety Stock, 2019)

L = 7; σ = 30/7; z = 1.56

  • Safety Stock – z * σ * √7

The above answer concludes that 18 units safety stock of HP printers kept in stock to avoid stock out.

    • Safety Stock = 1.56 * (30/7) * √7 = 18 units


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

What is safety stock(2019). Retrieved from https://www.accountingcoach.com/blog/what-is-safety-stock

Wikipedia contributors. (2018, December 7). Reorder point. In Wikipedia, The Free Encyclopedia. Retrieved 22:44, April 16, 2019, from https://en.wikipedia.org/w/index.php?title=Reorder_point&oldid=872488838

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