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Quality Electronics, Inc. (QE) sells high-end electronic game consoles, competing with the Sony Playstation, Nintendo Wii, and  the Microsoft Xbox lines. Management learned that the pre-holiday season is the best time to introduce a new game console, because many families use this time to look for new ideas for December holiday gifts. When QE discovers a new console with good market potential it chooses an October market entry date getting a jump on competitors who often wait until November to introduce their new models.

In order to get toys in its stores by October, QE places one time orders with its Chinese manufacturers in June or July of each year. Demand for electronic game consoles can be highly volatile.  If developers like the features of a new console, many games will be developed for it. In addition, if a new consoles catches on, a sense of shortage in the market place often increases the demand to high levels and large profits can be realized. However, new consoles can also flop, with few games written for it, leaving QE stuck with high levels of inventory that must be sold at reduced prices. The most important question the company faces is deciding how many units of a new game console should be purchased to meet anticipated sales demand. If too few are purchased, sales will be lost; if too many are purchased, profits will be reduced because of low prices realized in clearance sales. 

For the coming season, QE plans to introduce a new console called the ZFactor 5000. In addition, to a state of the art hand-held controller, this computer game console features a virtual reality helmet with built-in microphone and voice-controlled voice-over Internet cell phone features to enhance game play experience and communication with other players. It also features a ‘hired gun’ option that connects the player to a group of ‘for hire’ game players (in southeast Asia) that will complete a given level in a game or rapidly level up a game character for you, allowing the game character to acquire more advanced skills, abilities and equipment, and thereby allowing players to skip the easy beginning levels and take on the more challenging levels for a minimal charge. 

As usual, QE faces the decision of how many ZFactor 5000 console units to order for the coming holiday season. Members of the management team suggested order quantities of 920,000, 950,000, 1,040,000, or 1,100,000 units. The relatively wide range of order quantities suggested indicate considerable disagreement concerning the market potential. The product management team asks you for an analysis of the stock-out probabilities for various order quantities, an estimate of the profit potential and to help make an order quantity recommendation. QE expects to sell the ZFactor 5000 for $300 based on a cost of $120 per unit. If console inventory remains after the holiday season, QE will sell all surplus inventory for $50 per unit. After reviewing the sales history of similar products, QE’s senior sales forecaster predicted an expected demand of 1,000,000 units with a 0.90 probability that demand would be between 840,000 units and 1,160,000 units. The senior sales forecaster did not provide the standard deviation but indicated it could be computed from this information with the following hint: The Z score for a 90 percent interval such as this is 1.645.   


Prepare a managerial report that addresses the following issues and recommends an order quantity for the ZFactor 5000 game console. The target audience for this report is your boss, a senior manager who has a basic understanding of business statistics. Of course, if the report is exemplary you may expect it to be circulated more widely in the company to your credit. 

1)    Use the senior sales forecaster’s prediction to define a normal probability distribution that can be used to approximate the demand distribution. In particular, state the mean and standard deviation for a normal distribution based on the information provided by the senior sales forecaster.   

2)    Use Minitab to create a graph of the distribution and show its mean and standard deviation. To make a graph, follow these steps:

a.        use a column in the worksheet for the random variable. Call it ‘X’.

b.        use a column in the worksheet for the function value. Call it ‘f(x)’. 

c.        use calc/make patterned data/simple set of numbers, store data in x, values from 800,000 to 1,200,000 in steps of 20,000, list the sequence once.

d.        use calc/probability distributions/Normal; use probability density and the mean and standard deviation you have determined in part 1, input column X, optional storage f(x).

e.        Make a scatterplot with connect line using X = X and Y = f(x). Give it an appropriate title, x-axis label, and put your name in the footer. 

3)    Use Minitab to compute the probability of a stock-out for the order quantities suggested by the members of the management team. Include a table in your document that summarizes the results of your computations. 

4)    Using Excel, compute the projected profit for the order quantities suggested by the management team under three scenarios: worst case in which sales = 850,000 units, most likely case in which sales = 1,000,000 units and best case in which sales = 1,150,000 units. Calculate an overall expected profit for each of the four order quantities if it is assumed the worst case and best case each have a 5% chance of occurring, respectively. Include a table in your document that summarizes the results of your computations.  

5)    Use Minitab to address this issue. One of QE’s managers felt that the profit potential was so great that the order quantity should have a 75% chance of meeting demand and only a 25% chance of any stock-outs. What quantity would be ordered under this policy, and what is the projected profit under the three sales scenarios? 

Provide your own personal recommendation for an order quantity and note the associated profit projections. Explain all of the reasons for your recommendation. You are welcome to include in your explanation any additional analysis that you performed in support of your recommendation.

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