A Case Study on Bell Computer Company and Kyle Bits and Bytes
ACase Study on Bell Computer Company and Kyle Bits and Bytes
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ACase Study on Bell Computer Company and Kyle Bits and Bytes
CaseStudy 1: Bell Computer Company
TheBell Computer Company is interested in expanding its plant so that itcan commence the production of a new product. After graduating withan MBA from the University of Phoenix I have been requested to applymy knowledge in determining whether the expansion to be implementedshould be a medium or largescale project. The new product’s demandis uncertain. This demand can be categorized as being low, medium orhigh with probability estimates of 0.2, 0.5 and 0.3 respectively.
Question1
Theexpected value describes the return or results one can expect toreceive for a particular form of action (Peck,Olsen, & Devore, 2015).The formula used in calculating the expected value (µ) is given by:
Expectedvalue (profit) (µ) = ∑xP(x) where:
xis the variable (in this case it is the annual profit in $1000s)
P(x)is the probability of the event in the variable occurring (in thiscase it is the probability of annual profits falling under (50, 150,and 200) and (0, 100, and 300) in mediumscale and largescaleexpansion scenarios).
TheMicrosoft Excel function used to calculate the expected value in aset of data with variables and probabilities is“=SUMPRODUCT(Ax:Ay,Bx:By)”. In this function Ax:Ay is thelocation of the cells with the variables corresponding to x, andBx:By is the location of the cells with P(x) variables. The functionused to compute the expected profits for the mediumscale expansionplan is “=SUMPRODUCT(C4:C6,D4:D6)”, and it gives a result of$145,000. The function used to compute the expected profits for thelargescale expansion plan is “=SUMPRODUCT(E4:E6,F4:F6)”, and itgives a result of $140,000. According to these results, it would beadvisable for the company to undertake a mediumscale expansionexercise since it will bring in more profits to the company comparedto a largescale expansion exercise.
Question2
Thevariance (variation) (δ^{2})shows how numbers in a dataset are spread. It describes how far anumber in the dataset is from the average. It is computed by findingthe difference between every variable in the dataset (x) and theexpected value (µ), and then finding its square, multiplying thesquares (x µ)^{2}by the probability of the event in the variable occurring (P(x)),followed by summing the results of these multiplications(Peck, Olsen, & Devore, 2015).The formula is:
Inthe case of the data relating to the Bell Computer Company’sexpansion plans, the expected values (µ) (in $1000s) used are 145and 140 for mediumscale and largescale expansion plans. Tocalculate the variance for the mediumscale expansion plan thefunction “=SUM(F12:F14)” is used. This will calculate the sum∑(xµ)^{2}P(x)for the cells (F12:F14). These three cells contain (xµ)^{2}P(x)for the three cells with different probabilities (20%, 50%, and 30%)of different annual profits (50, 150, 200) for the different Low,Medium and High Demands in the case of a mediumscale expansion plan.
TheExcel function yields a variance (δ^{2})^{}of2,725. The standard deviation is 52.20153254 and is given by thesquare root of the variance. The Excel function used is “=SQRT(F15)”.The cell F15 contains the variance (sum ∑(xµ)^{2}P(x)of the cells (F12:F14)).
Tocalculate the variance for the largescale expansion plan thefunction “=SUM(F20:F22)” is used. This will calculate the sum∑(xµ)^{2}P(x)for the cells (F20:F22). These three cells contain (xµ)^{2}P(x)for the three cells with different probabilities (20%, 50%, and 30%)of different annual profits (0, 100, 300) for the different Low,Medium and High Demands in the case of a largescale expansion plan.
TheExcel function yields a variance (δ^{2})^{}of12,400. The standard deviation is 111.3552873 and is given by thesquare root of the variance. The Excel function used is “=SQRT(F23)”.The cell F23 contains the variance (sum ∑(xµ)^{2}P(x)of the cells (F20:F22)).
Thestandard deviation values can be used to guide the company in itsquest to minimize risk and uncertainty. A higher standard deviationindicates that the annual profits for the Low, Medium and Highdemands will differ from the expected profit (µ) by a huge margin,pointing to a bigger risk and uncertainty. Therefore, it would beadvisable for the Bell Computer Company to undertake a mediumscaleexpansion plan since it has the lower standard deviation(52.20153254) of the two expansion plans.
CaseStudy 2: Kyle Bits and Bytes
KyleBits and Bytes is a company specializing in the sale of differentcomputer products. Its best product is an HP laser printer that has amean weekly demand of 200 units with a lead time of 1 week. Kyle hasrequested the computation of a reorder point given that the demandfor the printers is not constant.
Thegiven figures state mean demand is 200 printers, and that thestandard deviation is 30. By stating that the probability of astockout occurring should not exceed 6% means that the probabilityof stocks not running out is 94%. This is the probability to be usedto find the area under the curve. The test used is a onetailed testsince we are testing the likelihood of the relationship happeningtowards one direction (no stockouts), and entirely disregarding thelikelihood of a relationship happening towards the other direction(stockouts). The 94% can also be taken as the confidence level(Peck, Olsen, & Devore, 2015).To find the zscore:
Theconfidence level (94%) is subtracted from 100% to find its αlevel:
Thisis then converted into decimal 0.06.
Theconcerted αlevelis then divided by 2 to find the area under each tail:
Thearea under each tail is then subtracted from 1 since it is ofinterest to find the area in the middle of the curve rather than thearea of the tail:
Lookingup 0.97 in the ztable yields a zscore of 1.88
z= 1.88
Thiszscore is of importance in finding the safety stock required tocompute the reorder point. The reorder point model assumes that

the demand is fairly constant

the lead time is constant

suppliers can meet the demand for the product
Theconditions above are met in the case of Kyle Bits and Bytes. Thesafety stock is the number of printers that will be required by thecompany to avoid stockouts (Bragg,2015).It is given by:
Safetystock = zscore x standard deviation * √lead time
Safetystock = 1.88*30*√1
Safetystock = 56.4 ≈ 57 printers
Thereorder point is given by:
Reorderpoint = (Mean demand x Lead time) + Safety stock
Reorderpoint = (200×1) + 57 = 257 printers.
Kyleshould have 257 printers in stock when he orders others from themanufacturer.
References
Bragg,S. (2015). InventoryManagement: Second Edition.Accounting Tools.
Peck,R., Olsen, C., & Devore, J. (2015). Introductionto Statistics and Data Analysis.Boston: Cengage Learning.
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