Case 24 George's T-Shirts
Case 24 George’s T-shirts
Executive Summary
George Lassiter is project engineer for a major defensive contractor. For the last six years George has enjoyed an interesting and lucrative side business while designing, manufacturing, and hawking special event T-shirts. Some of these events include rock concerts, major sporting events, and special fund-raising events. His idea was very recognized within the community because his products were not only cheap but they were also cleverly designed and well produced. The shirts were sold in the streets surrounding the arenas and in the nearby parking lots with the appropriate licenses from the local authorities. George had a regular crew of vendors to whom he sold the shirts on consignment for $100 per …show more content…
dozen and the vendors would then offer these shirts to the public for $10 each thus making a profit of $1.67 on each shirt. George is working on several designs in various stages of development as he has a steady stream of T-shirts business.
George always had steady flow of job lined up because of the good quality and affordable prices of T-shirts he created and designed. But as one of the jobs came up he faced a problem on how many T-shirts to be produced for the event. He had been brought a deal of making shirts for a rock concert that was scheduled to be staged in two months. From his past experience in the business and the popularity of the performing group, George knew the concert was certainly going to be a big success. As an expert in this kind of business and from his past sales experience, George was able to come up with some prediction on how much a particular number of T-shirts would cost: ten thousand, seven thousand five hundred, or five thousand shirts. The orders’ costs were approximately $32,125, $25,250 and $17,750 respectively. Even though he was able to come up with some hard and reliable numbers there were also some unknowns that he had to figure out in order to adequately decide the volume to be produced and sold at the event.
George usually sells his t-shirts at special events or concerts. He must choose how many to order for an upcoming concert. One uncertainty that George will face is that he does not know the number of people that will be attending the concert. The other uncertainty that George will face is that he does not know the percentage of the attendees who will purchase a shirt. Although a certain number of tickets sold has been declared it still does not let George know exactly how many people will be in those seats. Expected monetary value comes to play in this case study. For instance, George must evaluate all probabilities and outcomes to produce the highest EMV possible. Like in most cases George’s final decision will have an effect on the cost and revenue generated from the number of shirts sold.
Decision Problem George’s major problem was the decision he had to make about how many T-shirts he should produce for the rock concert that was scheduled to be staged in two months. This was a big decision to be made by George since his T-shirts were not endorsed by the event sponsors and were not allowed to be sold within the arenas at which the events were held. Another problem that George faced while making the decision is the fact that the number of grandstand seats that would be sold were unknown. This means that he is not sure on how many T-shirts to produce since he does not know how many people will buy the tickets. Even though George believed that the grandstand sales were more likely to be at high, rather than the low, end of the spectrum, he still had to predict the total sales so that he can know the number of shirts to be manufactured. Another decision problem that George had to face had to deal with the fact that the percentage of the attendees who would buy one of his shirts was also unknown. From his past record he had never had a big number of shirts left over, but those that were left were sold to a discount clothing chain for $1.50 per shirt. This means that with the unknown grandstand seats to be sold, and the unknown number of fans that will buy his shirts, George still have to make a major decision on how many shirts to produce without having so many of them left over because he will end up selling them at a loss. George also had three different possibilities including a high, a medium, and a low value, specifically, 80,000, 50,000, and 20,000 grandstand seats. After considering the possibility of the number of those that will attend the concert and those that will buy his shirts, George had to decide the number of shirts to produce. He had to decide whether to make an order of ten thousand, seven thousand five hundred, or five thousand shirts. The orders’ costs were approximately $32,125, $25,250 and $17,750 respectively.
Decision Alternatives and Evaluation
Selling Price of Lassiter=$100 per dozen
Selling Price of vendors to customers=$10 a piece sold to people
20000 tickets would be sold for the standing area. (Most likely)
Number of grandstand seats sold was unknown-
High= 80000 p=p1 (aprrox.3, somewhat higher than .25)
Medium= 50000 P=.5
Low= 20000 p=.5-p1 (approx. .2, somewhat lesser than .25)
10% people who attend would buy with 60% probability)
5% people would buy (around 30% probability)
15% people would buy with 10% probability)
Cost of t shirt= Decreasing with increasing volume
5000pc --- $17750
7500pc ---$25250
10000pc---$32125
Unsold tee shirt sold at $1.5 per piece to discounting chain
He considered placing an order of 5000 shirts, which means 50000 people would attend, which is 50% probable
Placing 7500 means 75000 would attend, around 30% probability
We need to find the decision that has the best suitable outcome with highest probability.
Accordingly a decision can be taken. Hence we need to evaluate the expected outcomes of the different decisions.
This can be done by finding expected values, which can be calculated taking the probabilities of the outcomes and their return.
Let us assume that the decisions are of ordering 5000, 7500 and 10000 pieces of t-shirts.
Let us denote them by D1, D2 and D3.
Let us start with evaluating D1
If Lassiter orders for 5000pc
Cost of T shirts-$17750
For the number of Grand seats sold, we need to estimate a number. We know the probabilities of three figures-
High= 80000 p=p1 (aprrox.3, somewhat higher than .25)
Medium= 50000
P=.5
Low= 20000 p=.5-p1 (approx.2, somewhat lesser than .25)
We have assumed probabilities of high and low as .3 and .2.
The reason being Phigh >Plow
And Phigh + Plow=.5
Hence the Expected number of grandstand seats, by the theory of expected values
Summation (Probability of the number * the number)
=80000*.3+50000*.5+20000*.2=24000+25000+4000=53000
Hence the expected value of grandstand seats=53000
The expected value of standing area=20000
Hence total turnout expected=73000
Hence there should be a sale of 73000 T-shirts at 60% probability.
Now if he places an order of 5000, we can calculate the profits as follows
= Sales- cost=5000*100/12-17750= 41666.67-17750=23916$
Here we have assumed that sales of 5000 pieces have complete, since to sell 5000 pieces turnout must be 50000( with 60% probability), and here the expected turnout is 73000.
Now let us evaluate D2
Let us evaluate the outcome of buying 7500 t-shirts
The cost of these T-shirts is $25250.
For sales of 7500 T-shirts, there has to be sales of 75000 T-shirts.
We know that there is and expected turnout of 73000 people. Hence we can assume a sales of 7300 T-shirts at the concert.
Hence we can calculate the profits as
= Sales of 7300 at concert+ sales of remaining 200 at discount –cost
=7300*100/12+200*1.5-25250= 35883.33
Hence the profit is $35883.
Let us evaluate D3
Now we evaluate the outcome of buying 10000 T-shirts
The cost of these T-shirts is 32125.
Here we know that 7300 shirts are expected to be sold.
Hence the remaining 2700 will be sold at discounted value.
Hence we can calculate the profit as
= Sales of 7300 at concert+ sales of remaining 2700 at discount-cost
= 7300*100/12+2700*1.5-35125
= 29758.33
Hence the expected profit is 29758.33
Here we have assumed that 10% of the people attending the concert will buy the t-shirt because
Probability of 10% =.6
Probability of 5%= Unknown
Probability of 15%=.1
Hence the probability is most likely to lie on near 10%, though on the lesser side.
Conclusively, here we have compared the outcomes of 3 situations. Lassiter could decide to buy either of 3 batches, however in most likely situation we see that buying 7500 pieces of T-shirt will give the highest outcome.
Hence I suggest that Mr. Lassiter places an order of 7500 T-shirts.
With such a large decision to be made, it is wise to look at different angles when making a final decision. Different information can sometimes reveal important details that could go undiscovered. George Lassiter 's decision comes down to one basic decision of how many shirts to buy. Yet, within that decision there are many variables that complicate the process. The two main variable that impact the decision are the number of attendees and the percentage that will buy his t-shirts. His best guest includes a 60,000 ticket spread on the number of attendants and a 10% spread of the number of buyers. Between all these options, there are 27 possible outcomes to this one decision. One way to reach an educated decisions is to follow each path to its respective outcome. The simplest way of doing that is to build a decision tree. A decision tree helps to map out the many turning points of a decision. By picking out a starting point, and then following the different branches as alternatives split off, all the possibilities can be seen from a 50,000 foot vantage point.
100,000 (25%)
40,000 (25%)
70,000 (50%)
3,500
7,000
6,000
2,000
4,000
(15%)
(5%)
(10%)
(10%)
(15%)
(5%)
(10%)
10%
60%
30%
60%
10%
60%
30%
30%
10%
(15%)
(5%)
10,000
10,500
15,000
5,000
Above is the decision tree that was created for this decision based on the information given. Now, the different branches of the decision tree are based on the George 's assumptions of what could happen. At this juncture, there are basic variables that George cannot control: how many people show up at the event and how many of those people will end up buying one of his shirts. Now, while George does not have any control over these variables, we will provide the data on which he will base his decision. First off, there is the variable of how many people will show up for the event. George believes there are three likely scenarios; he believes that there is a 50% chance that 50,000 people will attend the event, which leave 50% by which he believes can equally split between an attendance of 20,000 and 80,000 (Bodily, 481). The other variable focuses on the percentage of patrons that will buy his T-shirts. He believes that there is a 60% chance that 10% will buy one, a 30% chance that 5% will buy a shirt, and a 10% chance that 15% will buy his merchandise (Bodily, 481). This creates a dynamic, which can be seen in the decision tree, that in which there are nine different possibilities of which George believes could happen. He could have a low attendance rate, but a high T-shirt buyer rate. On the other hand, he could have a high attendance rate, but a low T-shirt buyer rate. I could also be one of the many alternatives in between. To complicate things even further, George 's decision, includes the variable that he does control: buying the T-shirts, must be taken into account. He has the option of buying shirts in 5,000, 7,500, or 10,000 batches at $17,750, $25,250, and $32,125, respectively. If this decision were to be added to decision tree it would have to go at the very top of the decision tree and the whole decision tree seen above would have to be replicated under each different options resulting in the 27 options mentioned earlier. While this may seem rather daunting, if each alternative, no matter how likely or unlikely, is broken down and examined based on what it will bring in verses what the associated costs would be, as well as the probability of it coming to fruition, a greater understanding of all the options can be gained which will result in a more educated decision. Only after fully engaging in each alternative can George hope to gain all the information that he needs to make the decision on how many shirts to buy. By doing the necessary research, George can help to mitigate any risk in having too many or too few shirts. George cannot hope to influence how many people attend the event or even what percentage of people buy his T-shirts, but he can make sure that he has done everything he can to make sure that he has the right number of shirts at the right time without ending up with too many leftovers for the discount rate. Even with decision trees and charts, all this information can still by quite overwhelming. Making the decision would be easier if it could all be boiled down to a simple figure. One tool that could be used to do this is Expected Monetary Value or EMV. Expected monetary value condenses all the outcomes of a decision into a single figure based on the money the outcomes bring in and their respective probability of occurring. According BusinessDictionary.com, expected monetary value is calculated as taking the sum of money brought in by each outcome multiplied by its chance of happening (BusinessDictionary.com, 2012, p. 1). By using EMV, George can get a since of what he can bring in based on the probability of certain situation happening. With such a complex decision tree, the EMV calculation will have to be done at many stages to get the numbers that George needs. All of these calculations will get rolled up into one number that George can use as a quick snapshot of what he can expect to bring in. On top of that, George can use the EMV numbers at various stages to compare the alternatives at the same point.
5000 | 5,000 Shirts Purchased | Tickets Sold | 40,000 | 70,000 | 100,000 | % Who Buy Shirts | 10% | 5% | 15% | 10% | 5% | 15% | 10% | 5% | 15% | # of Shirts Sold | 4,000 | 2,000 | 5,000 | 5,000 | 3,500 | 5,000 | 5,000 | 5,000 | 5,000 | Price ($100/12) | 33,333 | 16,667 | 41,667 | 41,667 | 29,167 | 41,667 | 41,667 | 41,667 | 41,667 | Sold at Discount | 1,000 | 3,000 | 0 | 0 | 1,500 | 0 | 0 | 0 | 0 | at $1.50 p/u | $1,500.00 | $4,500.00 | $0.00 | $0.00 | $2,250.00 | $0.00 | $0.00 | $0.00 | $0.00 | Total Revenue | $34,833.33 | $21,166.67 | $41,666.67 | $41,666.67 | $31,416.67 | $41,666.67 | $41,666.67 | $41,666.67 | $41,666.67 | Costs | ($17,750.00) | ($17,750.00) | ($17,750.00) | ($17,750.00) | ($17,750.00) | ($17,750.00) | ($17,750.00) | ($17,750.00) | ($17,750.00) | Net Income | $17,083.33 | $3,416.67 | $23,916.67 | $23,916.67 | $13,666.67 | $23,916.67 | $23,916.67 | $23,916.67 | $23,916.67 | | | | | | | | | | | 7500 | 7,500 Shirts Purchased | Tickets Sold | 40,000 | 70,000 | 100,000 | % Who Buy Shirts | 10% | 5% | 15% | 10% | 5% | 15% | 10% | 5% | 15% | # of Shirts Sold | 4,000 | 2,000 | 6,000 | 5,000 | 3,500 | 5,000 | 7,500 | 5,000 | 7,500 | Price ($100/12) | $33,333 | $16,667 | $50,000 | $41,667 | $29,167 | $41,667 | $62,500 | $41,667 | $62,500 | Sold at Discount | 3,500 | 5,500 | 1,500 | 0 | 4,000 | 0 | 0 | 2,500 | 0 | at $1.50 p/u | $5,250 | $8,250 | $2,250 | $0 | $6,000 | $0 | $0 | $3,750 | $0 | Total Revenue | $38,583 | $24,917 | $52,250 | $41,667 | $35,167 | $41,667 | $62,500 | $45,417 | $62,500 | Costs | ($25,250) | ($25,250) | ($25,250) | ($25,250) | ($25,250) | ($25,250) | ($25,250) | ($25,250) | ($25,250) | Net Income | $13,333 | ($333) | $27,000 | $16,417 | $9,917 | $16,417 | $37,250 | $20,167 | $37,250 | | | | | | | | | | | 10000 | 10,000 Shirts Purchased | Tickets Sold | 40,000 | 70,000 | 100,000 | % Who Buy Shirts | 10% | 5% | 15% | 10% | 5% | 15% | 10% | 5% | 15% | # of Shirts Sold | 4,000 | 2,000 | 6,000 | 7,000 | 3,500 | 10,000 | 10,000 | 5,000 | 10,000 | Price ($100/12) | $33,333 | $16,667 | $50,000 | $58,333 | $29,167 | $83,333 | $83,333 | $41,667 | $83,333 | Sold at Discount | 6,000 | 8,000 | 4,000 | 0 | 6,500 | 0 | 0 | 5000 | 0 | at $1.50 p/u | $9,000 | $12,000 | $6,000 | $0 | $9,750 | $0 | $0 | $7,500 | $0 | Total Revenue | $42,333 | $28,667 | $56,000 | $58,333 | $38,917 | $83,333 | $83,333 | $49,167 | $83,333 | Costs | ($32,125) | ($32,125) | ($32,125) | ($32,125) | ($32,125) | ($32,125) | ($32,125) | ($32,125) | ($32,125) | Net Income | $10,208 | ($3,458) | $23,875 | $26,208 | $6,792 | $51,208 | $51,208 | $17,042 | $51,208 |
To begin the process of calculating all the EMV figures, George must start at the bottom or at the end of the tree and work up. In this case, the process must start where the final numbers have been calculated based on the percentage of attendee 's who buy shirts, taking into account the three different options for how many shirt George could buy. The final figures are multiplied by their chances of occurring. After this happens, the numbers can then be rolled up into the next level where they are applied towards the percentages of how many people will attend the event. This will result in a single number that accounts for all the different outcomes and their probabilities. George can then compare the different EMV 's based on the volume of shirts that he could buy and see which option holds the most promising EMV. Using this tool will not guarantee success, but it will give George a glimpse into what he will face based on what option he picks. One of the reasons that George 's decision is so complex is because of the risk involved with the outcomes. It has been mentioned before that the overall decision is rather straightforward; how many shirts should be bought. It is the uncertainty of the outcomes that makes the decision complex. One way of dismantling some of the complexity around the decision is to understand the risk and uncertainty surrounding the decision. In a small way, this has already been done through the assigning of probability to the different outcomes. This allows George not only to see the monetary outcome of the alternative, but also see how much he can expect a certain outcome to happen. This information, if correct, can point George in the most direction of the most likely outcome.
Overall EMV | 5,000 | | $19,816.67 | | | | 75,000 | | $17,914.58 | | | | 10,000 | | $23,550.00 |
EMV Based on 5,000 Shirts Ordered | | 40,000 | | 70,000 | | 10,000 | | Total EMV | | | | | | | | | 10% | $10,250.00 | | $14,350.00 | | $14,350.00 | | | | | | | | | | | 5% | $1,025.00 | | $4,100.00 | | $7,175.00 | | | | | | | | | | | 15% | $2,391.67 | | $2,391.67 | | $2,391.67 | | | | | | | | | | | | $13,666.67 | | $20,841.67 | | $23,916.67 | | $19,816.67 | | | | | | | | | EMV Based on 7,5000 Shirts Ordered | | 40,000 | | 70,000 | | 100,000 | | Total EMV | | | | | | | | | 10% | $8,000.00 | | $9,850.00 | | $22,350.00 | | | | | | | | | | | 5% | ($100.00) | | $2,975.00 | | $6,050.00 | | | | | | | | | | | 15% | $2,700.00 | | $1,641.67 | | $3,725.00 | | | | | | | | | | | | $10,600.00 | | $14,466.67 | | $32,125.00 | | $17,914.58 | | | | | | | | | EMV Based on 10,0000 Shirts Ordered | | 20,000 | | 50,000 | | 80,000 | | Total EMV | | | | | | | | | 10% | $6,125.00 | | $15,725.00 | | $30,725.00 | | | | | | | | | | | 5% | ($1,037.50) | | $2,037.50 | | $5,112.50 | | | | | | | | | | | 15% | $2,387.50 | | $5,120.83 | | $5,120.83 | | | | | | | | | | | | $7,475.00 | | $22,883.33 | | $40,958.33 | | $23,550.00 |
On the grand scale, George must understand how risk affects any of his projects. This begins with understanding how he himself feels about risk. In their discussion on risk, Cosmina-Simona Toader and colleagues in their paper, "Aspects Regarding Risk Management in Projects," mention how risk averse people tend to shy away of from dealing with Risk, and at the same time say that all managers must seek out risks associated with their projects so that they can be properly discarded (Toader & Ioan Brad, 2010, p. 454). Once George takes into account how he views risk, and can clearly see what risks he wants to take and one he wants to avoid or mitigate, he can then take a better decision. In George 's case, he cannot control the uncertainty of the number of attendees or the number of people who normally buy his shirts, but he can use different tools to analyze and manage the risks that he faces. One way is to use any number of different statistical theories that go beyond EMV figures and uses mathematical principles that will help point George in the right direction. One such model is the Statistical Decision Theory. It is described in the article, "Mathematical & Computer Modeling of Dynamic Systems" which focuses "optimizing" a certain (Bodily, 1988, p. 436)This is essentially what George 's decision is about; optimizing the number of shirts bought and sold. By using this or any other statistical model, perhaps George could gain a greater understanding of how risk can affect his business. One other way that George can focus on risk is to create a risk management solution for his business that seeks to recognize and manage risk throughout a project 's life. This process can be started by looking at some of the following questions that Toader and company produced. * "What does the risk mean to the project?" * "What types of risks exists?" * "What are the losses resulting from these risks." (Toader & Ioan Brad, 2010, p. 455).
By understanding these and other questions and putting into place a strong risk management strategy, George can harness the information that is available , and in doing so be in a better situation to handle the risks and uncertainties that could pop up during the event. This information coupled with both the probabilities that George assigned to the different alternatives as well as with the EMV figures from earlier in the paper will help to give George more in depth view of what is going on with this project. If George can take into account all the information that is available, and then apply correctly to the decision at hand, George will be able to make a better educated decision, and that in turn will lead to a higher possibility of success for this project.
Conclusion and Recommendation
It’s a fact of human nature that what we receive, for either good or bad, depends in part on what actions we choose to take and in part on circumstances beyond our control. George Lassiter based his decision technique on decisions under uncertainty on a set of alternative actions, states of nature, and outcomes. Lassiter was certain that the rock concert was going to be a huge success. He knew that 20,000 tickets were going to be bought by the rock group devoted fans. The two unknowns at hand were the grandstand seats that would be sold and the percentage of the attendees who would buy his shirts.
In most situations, the idea of Decision Making under Risk makes a lot more sense than Decision Making under Uncertainty. There are a few situations where someone has the responsibility to make a decision of great consequence with no knowledge of the relative likelihood of the outcome involved. Lassiter assigned the probability to each State of Nature. By research and past sales he was able to reveal relative information that he concluded in the underlying probabilities. Lassiter relied on subjective probabilities, which should not be dismissed as a mere intuition. In fact, there is a sense, in which all probabilities are subjective, since the only absolutely probability that something will happen is 1 if it happens or 0 if it doesn’t.
George Lassiter estimated three possibilities (a high, a medium, and a low value), 100,000, 70,000, and 40,000 grandstand seats being sold (Bodily, 1988, p. 481). He figures the concert will draw 70,000 devoted fans and likely as the other two possibilities combined. The second unknown was the percentage of the attendees who would buy one of the shirts. As Lassiter’s formal analysis and memory served (about 6 out of 10) which is 10% of the attendance will buy his shirts (Bodily, 1988, p. 481). Our group decided that the Decision Tree, a “simple” stage problem like George’s T-shirt problem was needed. First, we went to the outermost chance nodes, the little boxes, the possible attendees that branched to the percentages of possible sales of t-shirts, and the probabilities to the payoffs to compute the EMV. Based on the decision tree we determined our decision rule on how George Lassiter came up with his decision to sell 10,000 shirts at the concert event.
George will have to wait and see as to what will actually happen. George decided to go with the expected monetary value projections. Time will bear out if these projections will hold true. Going forward, George could take steps towards minimizing his risks in a number of ways. He could find ways to reduce production costs, such as finding a cheaper shirt (with the same quality). He could find a way to sell the left over shirts at a higher price by either finding a different outlet. He could even look at a different direction by perhaps trying to connect with a band or team to sell his shirts officially across a season or tour. Either way, George should seek to find ways to minimize his costs, boost his revenue, and manage his risks. If George can do these things effectively and efficiently, He can grow his business in ways he could never imagine.
Based on the Decision Tree analysis, we noticed that Lassiter went the safer route with this investment to avoid risk. Although, George placed the order for the 10,000 shirts we thought of a couple of ideas to increase revenue. The recommendations we suggested for George’s T-shirts is that he can consider partnering up with the arena where the events were held to be allowed to sell within the arena as well as outside. Lassiter would be able to attract more consumers inside the events, and he will be able to order more shirts plus have customers inside the events and outside the event. With this recommendation he would have the advantage above the other vendors on the outside.
Another recommendation is on the number of shirts left over from any of the events instead of George selling to the discount clothing chain for $1.50 per shirt; he can also sell to music stores for rock concerts and local sporting goods stores for higher price like $3.00 per shirt. Also, he can put on EBay because some devoted fan may want to buy for memorabilia. The reason for this recommendation is there may be fans that were unable to go to the events, but still want to purchase a shirt for a souvenir. In this case study our group supported George’s T-shirt decision of how he placed his order.
Bibliography
Bodily, S. E. (1988). Quantitiave Business Analysis: Text and Cases. Boston: McGraw Hill Custom Publishing.
BusinessDictionary.com. (2012 йил 25-11). Expected Monetary Value. From BusinessDictionary.com: http://www.businessdictionary.com/definition/expected-monetary-value.html
Jokinen, H., & Kimmo Konkarikoski, P. P. (2009). Operations ' decision making under uncertainty: case studies on papermaking. . Mathematical & Computer Modelling of Dynamical Systems , 435-452.
Toader, C., & Ioan Brad, A. M. (2010 йил 12). Aspects Regarding Risk Management in Projects. Animal Sience and Biotechnologies , 454-457.
Rivoli, P., (2005, November 22). Lessons from the T-Shirt Industry: Arm Chair Capitalist. Retrieved July 1, 2006, from http://armchaircapitalists.blogspot.com/2005/11/what-actually-drives-t-shirt-industry.html
McElwain, J., (2001, May 1). American Apparel Takes on the 1 Shirt Market. Retrieved July 1, 2006, from http://www.findarticles.com/p/articles/mi_m3638/is_9_42/ai_76473285
Executive Summary
George Lassiter is project engineer for a major defensive contractor. For the last six years George has enjoyed an interesting and lucrative side business while designing, manufacturing, and hawking special event T-shirts. Some of these events include rock concerts, major sporting events, and special fund-raising events. His idea was very recognized within the community because his products were not only cheap but they were also cleverly designed and well produced. The shirts were sold in the streets surrounding the arenas and in the nearby parking lots with the appropriate licenses from the local authorities. George had a regular crew of vendors to whom he sold the shirts on consignment for $100 per …show more content…
dozen and the vendors would then offer these shirts to the public for $10 each thus making a profit of $1.67 on each shirt. George is working on several designs in various stages of development as he has a steady stream of T-shirts business.
George always had steady flow of job lined up because of the good quality and affordable prices of T-shirts he created and designed. But as one of the jobs came up he faced a problem on how many T-shirts to be produced for the event. He had been brought a deal of making shirts for a rock concert that was scheduled to be staged in two months. From his past experience in the business and the popularity of the performing group, George knew the concert was certainly going to be a big success. As an expert in this kind of business and from his past sales experience, George was able to come up with some prediction on how much a particular number of T-shirts would cost: ten thousand, seven thousand five hundred, or five thousand shirts. The orders’ costs were approximately $32,125, $25,250 and $17,750 respectively. Even though he was able to come up with some hard and reliable numbers there were also some unknowns that he had to figure out in order to adequately decide the volume to be produced and sold at the event.
George usually sells his t-shirts at special events or concerts. He must choose how many to order for an upcoming concert. One uncertainty that George will face is that he does not know the number of people that will be attending the concert. The other uncertainty that George will face is that he does not know the percentage of the attendees who will purchase a shirt. Although a certain number of tickets sold has been declared it still does not let George know exactly how many people will be in those seats. Expected monetary value comes to play in this case study. For instance, George must evaluate all probabilities and outcomes to produce the highest EMV possible. Like in most cases George’s final decision will have an effect on the cost and revenue generated from the number of shirts sold.
Decision Problem George’s major problem was the decision he had to make about how many T-shirts he should produce for the rock concert that was scheduled to be staged in two months. This was a big decision to be made by George since his T-shirts were not endorsed by the event sponsors and were not allowed to be sold within the arenas at which the events were held. Another problem that George faced while making the decision is the fact that the number of grandstand seats that would be sold were unknown. This means that he is not sure on how many T-shirts to produce since he does not know how many people will buy the tickets. Even though George believed that the grandstand sales were more likely to be at high, rather than the low, end of the spectrum, he still had to predict the total sales so that he can know the number of shirts to be manufactured. Another decision problem that George had to face had to deal with the fact that the percentage of the attendees who would buy one of his shirts was also unknown. From his past record he had never had a big number of shirts left over, but those that were left were sold to a discount clothing chain for $1.50 per shirt. This means that with the unknown grandstand seats to be sold, and the unknown number of fans that will buy his shirts, George still have to make a major decision on how many shirts to produce without having so many of them left over because he will end up selling them at a loss. George also had three different possibilities including a high, a medium, and a low value, specifically, 80,000, 50,000, and 20,000 grandstand seats. After considering the possibility of the number of those that will attend the concert and those that will buy his shirts, George had to decide the number of shirts to produce. He had to decide whether to make an order of ten thousand, seven thousand five hundred, or five thousand shirts. The orders’ costs were approximately $32,125, $25,250 and $17,750 respectively.
Decision Alternatives and Evaluation
Selling Price of Lassiter=$100 per dozen
Selling Price of vendors to customers=$10 a piece sold to people
20000 tickets would be sold for the standing area. (Most likely)
Number of grandstand seats sold was unknown-
High= 80000 p=p1 (aprrox.3, somewhat higher than .25)
Medium= 50000 P=.5
Low= 20000 p=.5-p1 (approx. .2, somewhat lesser than .25)
10% people who attend would buy with 60% probability)
5% people would buy (around 30% probability)
15% people would buy with 10% probability)
Cost of t shirt= Decreasing with increasing volume
5000pc --- $17750
7500pc ---$25250
10000pc---$32125
Unsold tee shirt sold at $1.5 per piece to discounting chain
He considered placing an order of 5000 shirts, which means 50000 people would attend, which is 50% probable
Placing 7500 means 75000 would attend, around 30% probability
We need to find the decision that has the best suitable outcome with highest probability.
Accordingly a decision can be taken. Hence we need to evaluate the expected outcomes of the different decisions.
This can be done by finding expected values, which can be calculated taking the probabilities of the outcomes and their return.
Let us assume that the decisions are of ordering 5000, 7500 and 10000 pieces of t-shirts.
Let us denote them by D1, D2 and D3.
Let us start with evaluating D1
If Lassiter orders for 5000pc
Cost of T shirts-$17750
For the number of Grand seats sold, we need to estimate a number. We know the probabilities of three figures-
High= 80000 p=p1 (aprrox.3, somewhat higher than .25)
Medium= 50000
P=.5
Low= 20000 p=.5-p1 (approx.2, somewhat lesser than .25)
We have assumed probabilities of high and low as .3 and .2.
The reason being Phigh >Plow
And Phigh + Plow=.5
Hence the Expected number of grandstand seats, by the theory of expected values
Summation (Probability of the number * the number)
=80000*.3+50000*.5+20000*.2=24000+25000+4000=53000
Hence the expected value of grandstand seats=53000
The expected value of standing area=20000
Hence total turnout expected=73000
Hence there should be a sale of 73000 T-shirts at 60% probability.
Now if he places an order of 5000, we can calculate the profits as follows
= Sales- cost=5000*100/12-17750= 41666.67-17750=23916$
Here we have assumed that sales of 5000 pieces have complete, since to sell 5000 pieces turnout must be 50000( with 60% probability), and here the expected turnout is 73000.
Now let us evaluate D2
Let us evaluate the outcome of buying 7500 t-shirts
The cost of these T-shirts is $25250.
For sales of 7500 T-shirts, there has to be sales of 75000 T-shirts.
We know that there is and expected turnout of 73000 people. Hence we can assume a sales of 7300 T-shirts at the concert.
Hence we can calculate the profits as
= Sales of 7300 at concert+ sales of remaining 200 at discount –cost
=7300*100/12+200*1.5-25250= 35883.33
Hence the profit is $35883.
Let us evaluate D3
Now we evaluate the outcome of buying 10000 T-shirts
The cost of these T-shirts is 32125.
Here we know that 7300 shirts are expected to be sold.
Hence the remaining 2700 will be sold at discounted value.
Hence we can calculate the profit as
= Sales of 7300 at concert+ sales of remaining 2700 at discount-cost
= 7300*100/12+2700*1.5-35125
= 29758.33
Hence the expected profit is 29758.33
Here we have assumed that 10% of the people attending the concert will buy the t-shirt because
Probability of 10% =.6
Probability of 5%= Unknown
Probability of 15%=.1
Hence the probability is most likely to lie on near 10%, though on the lesser side.
Conclusively, here we have compared the outcomes of 3 situations. Lassiter could decide to buy either of 3 batches, however in most likely situation we see that buying 7500 pieces of T-shirt will give the highest outcome.
Hence I suggest that Mr. Lassiter places an order of 7500 T-shirts.
With such a large decision to be made, it is wise to look at different angles when making a final decision. Different information can sometimes reveal important details that could go undiscovered. George Lassiter 's decision comes down to one basic decision of how many shirts to buy. Yet, within that decision there are many variables that complicate the process. The two main variable that impact the decision are the number of attendees and the percentage that will buy his t-shirts. His best guest includes a 60,000 ticket spread on the number of attendants and a 10% spread of the number of buyers. Between all these options, there are 27 possible outcomes to this one decision. One way to reach an educated decisions is to follow each path to its respective outcome. The simplest way of doing that is to build a decision tree. A decision tree helps to map out the many turning points of a decision. By picking out a starting point, and then following the different branches as alternatives split off, all the possibilities can be seen from a 50,000 foot vantage point.
100,000 (25%)
40,000 (25%)
70,000 (50%)
3,500
7,000
6,000
2,000
4,000
(15%)
(5%)
(10%)
(10%)
(15%)
(5%)
(10%)
10%
60%
30%
60%
10%
60%
30%
30%
10%
(15%)
(5%)
10,000
10,500
15,000
5,000
Above is the decision tree that was created for this decision based on the information given. Now, the different branches of the decision tree are based on the George 's assumptions of what could happen. At this juncture, there are basic variables that George cannot control: how many people show up at the event and how many of those people will end up buying one of his shirts. Now, while George does not have any control over these variables, we will provide the data on which he will base his decision. First off, there is the variable of how many people will show up for the event. George believes there are three likely scenarios; he believes that there is a 50% chance that 50,000 people will attend the event, which leave 50% by which he believes can equally split between an attendance of 20,000 and 80,000 (Bodily, 481). The other variable focuses on the percentage of patrons that will buy his T-shirts. He believes that there is a 60% chance that 10% will buy one, a 30% chance that 5% will buy a shirt, and a 10% chance that 15% will buy his merchandise (Bodily, 481). This creates a dynamic, which can be seen in the decision tree, that in which there are nine different possibilities of which George believes could happen. He could have a low attendance rate, but a high T-shirt buyer rate. On the other hand, he could have a high attendance rate, but a low T-shirt buyer rate. I could also be one of the many alternatives in between. To complicate things even further, George 's decision, includes the variable that he does control: buying the T-shirts, must be taken into account. He has the option of buying shirts in 5,000, 7,500, or 10,000 batches at $17,750, $25,250, and $32,125, respectively. If this decision were to be added to decision tree it would have to go at the very top of the decision tree and the whole decision tree seen above would have to be replicated under each different options resulting in the 27 options mentioned earlier. While this may seem rather daunting, if each alternative, no matter how likely or unlikely, is broken down and examined based on what it will bring in verses what the associated costs would be, as well as the probability of it coming to fruition, a greater understanding of all the options can be gained which will result in a more educated decision. Only after fully engaging in each alternative can George hope to gain all the information that he needs to make the decision on how many shirts to buy. By doing the necessary research, George can help to mitigate any risk in having too many or too few shirts. George cannot hope to influence how many people attend the event or even what percentage of people buy his T-shirts, but he can make sure that he has done everything he can to make sure that he has the right number of shirts at the right time without ending up with too many leftovers for the discount rate. Even with decision trees and charts, all this information can still by quite overwhelming. Making the decision would be easier if it could all be boiled down to a simple figure. One tool that could be used to do this is Expected Monetary Value or EMV. Expected monetary value condenses all the outcomes of a decision into a single figure based on the money the outcomes bring in and their respective probability of occurring. According BusinessDictionary.com, expected monetary value is calculated as taking the sum of money brought in by each outcome multiplied by its chance of happening (BusinessDictionary.com, 2012, p. 1). By using EMV, George can get a since of what he can bring in based on the probability of certain situation happening. With such a complex decision tree, the EMV calculation will have to be done at many stages to get the numbers that George needs. All of these calculations will get rolled up into one number that George can use as a quick snapshot of what he can expect to bring in. On top of that, George can use the EMV numbers at various stages to compare the alternatives at the same point.
5000 | 5,000 Shirts Purchased | Tickets Sold | 40,000 | 70,000 | 100,000 | % Who Buy Shirts | 10% | 5% | 15% | 10% | 5% | 15% | 10% | 5% | 15% | # of Shirts Sold | 4,000 | 2,000 | 5,000 | 5,000 | 3,500 | 5,000 | 5,000 | 5,000 | 5,000 | Price ($100/12) | 33,333 | 16,667 | 41,667 | 41,667 | 29,167 | 41,667 | 41,667 | 41,667 | 41,667 | Sold at Discount | 1,000 | 3,000 | 0 | 0 | 1,500 | 0 | 0 | 0 | 0 | at $1.50 p/u | $1,500.00 | $4,500.00 | $0.00 | $0.00 | $2,250.00 | $0.00 | $0.00 | $0.00 | $0.00 | Total Revenue | $34,833.33 | $21,166.67 | $41,666.67 | $41,666.67 | $31,416.67 | $41,666.67 | $41,666.67 | $41,666.67 | $41,666.67 | Costs | ($17,750.00) | ($17,750.00) | ($17,750.00) | ($17,750.00) | ($17,750.00) | ($17,750.00) | ($17,750.00) | ($17,750.00) | ($17,750.00) | Net Income | $17,083.33 | $3,416.67 | $23,916.67 | $23,916.67 | $13,666.67 | $23,916.67 | $23,916.67 | $23,916.67 | $23,916.67 | | | | | | | | | | | 7500 | 7,500 Shirts Purchased | Tickets Sold | 40,000 | 70,000 | 100,000 | % Who Buy Shirts | 10% | 5% | 15% | 10% | 5% | 15% | 10% | 5% | 15% | # of Shirts Sold | 4,000 | 2,000 | 6,000 | 5,000 | 3,500 | 5,000 | 7,500 | 5,000 | 7,500 | Price ($100/12) | $33,333 | $16,667 | $50,000 | $41,667 | $29,167 | $41,667 | $62,500 | $41,667 | $62,500 | Sold at Discount | 3,500 | 5,500 | 1,500 | 0 | 4,000 | 0 | 0 | 2,500 | 0 | at $1.50 p/u | $5,250 | $8,250 | $2,250 | $0 | $6,000 | $0 | $0 | $3,750 | $0 | Total Revenue | $38,583 | $24,917 | $52,250 | $41,667 | $35,167 | $41,667 | $62,500 | $45,417 | $62,500 | Costs | ($25,250) | ($25,250) | ($25,250) | ($25,250) | ($25,250) | ($25,250) | ($25,250) | ($25,250) | ($25,250) | Net Income | $13,333 | ($333) | $27,000 | $16,417 | $9,917 | $16,417 | $37,250 | $20,167 | $37,250 | | | | | | | | | | | 10000 | 10,000 Shirts Purchased | Tickets Sold | 40,000 | 70,000 | 100,000 | % Who Buy Shirts | 10% | 5% | 15% | 10% | 5% | 15% | 10% | 5% | 15% | # of Shirts Sold | 4,000 | 2,000 | 6,000 | 7,000 | 3,500 | 10,000 | 10,000 | 5,000 | 10,000 | Price ($100/12) | $33,333 | $16,667 | $50,000 | $58,333 | $29,167 | $83,333 | $83,333 | $41,667 | $83,333 | Sold at Discount | 6,000 | 8,000 | 4,000 | 0 | 6,500 | 0 | 0 | 5000 | 0 | at $1.50 p/u | $9,000 | $12,000 | $6,000 | $0 | $9,750 | $0 | $0 | $7,500 | $0 | Total Revenue | $42,333 | $28,667 | $56,000 | $58,333 | $38,917 | $83,333 | $83,333 | $49,167 | $83,333 | Costs | ($32,125) | ($32,125) | ($32,125) | ($32,125) | ($32,125) | ($32,125) | ($32,125) | ($32,125) | ($32,125) | Net Income | $10,208 | ($3,458) | $23,875 | $26,208 | $6,792 | $51,208 | $51,208 | $17,042 | $51,208 |
To begin the process of calculating all the EMV figures, George must start at the bottom or at the end of the tree and work up. In this case, the process must start where the final numbers have been calculated based on the percentage of attendee 's who buy shirts, taking into account the three different options for how many shirt George could buy. The final figures are multiplied by their chances of occurring. After this happens, the numbers can then be rolled up into the next level where they are applied towards the percentages of how many people will attend the event. This will result in a single number that accounts for all the different outcomes and their probabilities. George can then compare the different EMV 's based on the volume of shirts that he could buy and see which option holds the most promising EMV. Using this tool will not guarantee success, but it will give George a glimpse into what he will face based on what option he picks. One of the reasons that George 's decision is so complex is because of the risk involved with the outcomes. It has been mentioned before that the overall decision is rather straightforward; how many shirts should be bought. It is the uncertainty of the outcomes that makes the decision complex. One way of dismantling some of the complexity around the decision is to understand the risk and uncertainty surrounding the decision. In a small way, this has already been done through the assigning of probability to the different outcomes. This allows George not only to see the monetary outcome of the alternative, but also see how much he can expect a certain outcome to happen. This information, if correct, can point George in the most direction of the most likely outcome.
Overall EMV | 5,000 | | $19,816.67 | | | | 75,000 | | $17,914.58 | | | | 10,000 | | $23,550.00 |
EMV Based on 5,000 Shirts Ordered | | 40,000 | | 70,000 | | 10,000 | | Total EMV | | | | | | | | | 10% | $10,250.00 | | $14,350.00 | | $14,350.00 | | | | | | | | | | | 5% | $1,025.00 | | $4,100.00 | | $7,175.00 | | | | | | | | | | | 15% | $2,391.67 | | $2,391.67 | | $2,391.67 | | | | | | | | | | | | $13,666.67 | | $20,841.67 | | $23,916.67 | | $19,816.67 | | | | | | | | | EMV Based on 7,5000 Shirts Ordered | | 40,000 | | 70,000 | | 100,000 | | Total EMV | | | | | | | | | 10% | $8,000.00 | | $9,850.00 | | $22,350.00 | | | | | | | | | | | 5% | ($100.00) | | $2,975.00 | | $6,050.00 | | | | | | | | | | | 15% | $2,700.00 | | $1,641.67 | | $3,725.00 | | | | | | | | | | | | $10,600.00 | | $14,466.67 | | $32,125.00 | | $17,914.58 | | | | | | | | | EMV Based on 10,0000 Shirts Ordered | | 20,000 | | 50,000 | | 80,000 | | Total EMV | | | | | | | | | 10% | $6,125.00 | | $15,725.00 | | $30,725.00 | | | | | | | | | | | 5% | ($1,037.50) | | $2,037.50 | | $5,112.50 | | | | | | | | | | | 15% | $2,387.50 | | $5,120.83 | | $5,120.83 | | | | | | | | | | | | $7,475.00 | | $22,883.33 | | $40,958.33 | | $23,550.00 |
On the grand scale, George must understand how risk affects any of his projects. This begins with understanding how he himself feels about risk. In their discussion on risk, Cosmina-Simona Toader and colleagues in their paper, "Aspects Regarding Risk Management in Projects," mention how risk averse people tend to shy away of from dealing with Risk, and at the same time say that all managers must seek out risks associated with their projects so that they can be properly discarded (Toader & Ioan Brad, 2010, p. 454). Once George takes into account how he views risk, and can clearly see what risks he wants to take and one he wants to avoid or mitigate, he can then take a better decision. In George 's case, he cannot control the uncertainty of the number of attendees or the number of people who normally buy his shirts, but he can use different tools to analyze and manage the risks that he faces. One way is to use any number of different statistical theories that go beyond EMV figures and uses mathematical principles that will help point George in the right direction. One such model is the Statistical Decision Theory. It is described in the article, "Mathematical & Computer Modeling of Dynamic Systems" which focuses "optimizing" a certain (Bodily, 1988, p. 436)This is essentially what George 's decision is about; optimizing the number of shirts bought and sold. By using this or any other statistical model, perhaps George could gain a greater understanding of how risk can affect his business. One other way that George can focus on risk is to create a risk management solution for his business that seeks to recognize and manage risk throughout a project 's life. This process can be started by looking at some of the following questions that Toader and company produced. * "What does the risk mean to the project?" * "What types of risks exists?" * "What are the losses resulting from these risks." (Toader & Ioan Brad, 2010, p. 455).
By understanding these and other questions and putting into place a strong risk management strategy, George can harness the information that is available , and in doing so be in a better situation to handle the risks and uncertainties that could pop up during the event. This information coupled with both the probabilities that George assigned to the different alternatives as well as with the EMV figures from earlier in the paper will help to give George more in depth view of what is going on with this project. If George can take into account all the information that is available, and then apply correctly to the decision at hand, George will be able to make a better educated decision, and that in turn will lead to a higher possibility of success for this project.
Conclusion and Recommendation
It’s a fact of human nature that what we receive, for either good or bad, depends in part on what actions we choose to take and in part on circumstances beyond our control. George Lassiter based his decision technique on decisions under uncertainty on a set of alternative actions, states of nature, and outcomes. Lassiter was certain that the rock concert was going to be a huge success. He knew that 20,000 tickets were going to be bought by the rock group devoted fans. The two unknowns at hand were the grandstand seats that would be sold and the percentage of the attendees who would buy his shirts.
In most situations, the idea of Decision Making under Risk makes a lot more sense than Decision Making under Uncertainty. There are a few situations where someone has the responsibility to make a decision of great consequence with no knowledge of the relative likelihood of the outcome involved. Lassiter assigned the probability to each State of Nature. By research and past sales he was able to reveal relative information that he concluded in the underlying probabilities. Lassiter relied on subjective probabilities, which should not be dismissed as a mere intuition. In fact, there is a sense, in which all probabilities are subjective, since the only absolutely probability that something will happen is 1 if it happens or 0 if it doesn’t.
George Lassiter estimated three possibilities (a high, a medium, and a low value), 100,000, 70,000, and 40,000 grandstand seats being sold (Bodily, 1988, p. 481). He figures the concert will draw 70,000 devoted fans and likely as the other two possibilities combined. The second unknown was the percentage of the attendees who would buy one of the shirts. As Lassiter’s formal analysis and memory served (about 6 out of 10) which is 10% of the attendance will buy his shirts (Bodily, 1988, p. 481). Our group decided that the Decision Tree, a “simple” stage problem like George’s T-shirt problem was needed. First, we went to the outermost chance nodes, the little boxes, the possible attendees that branched to the percentages of possible sales of t-shirts, and the probabilities to the payoffs to compute the EMV. Based on the decision tree we determined our decision rule on how George Lassiter came up with his decision to sell 10,000 shirts at the concert event.
George will have to wait and see as to what will actually happen. George decided to go with the expected monetary value projections. Time will bear out if these projections will hold true. Going forward, George could take steps towards minimizing his risks in a number of ways. He could find ways to reduce production costs, such as finding a cheaper shirt (with the same quality). He could find a way to sell the left over shirts at a higher price by either finding a different outlet. He could even look at a different direction by perhaps trying to connect with a band or team to sell his shirts officially across a season or tour. Either way, George should seek to find ways to minimize his costs, boost his revenue, and manage his risks. If George can do these things effectively and efficiently, He can grow his business in ways he could never imagine.
Based on the Decision Tree analysis, we noticed that Lassiter went the safer route with this investment to avoid risk. Although, George placed the order for the 10,000 shirts we thought of a couple of ideas to increase revenue. The recommendations we suggested for George’s T-shirts is that he can consider partnering up with the arena where the events were held to be allowed to sell within the arena as well as outside. Lassiter would be able to attract more consumers inside the events, and he will be able to order more shirts plus have customers inside the events and outside the event. With this recommendation he would have the advantage above the other vendors on the outside.
Another recommendation is on the number of shirts left over from any of the events instead of George selling to the discount clothing chain for $1.50 per shirt; he can also sell to music stores for rock concerts and local sporting goods stores for higher price like $3.00 per shirt. Also, he can put on EBay because some devoted fan may want to buy for memorabilia. The reason for this recommendation is there may be fans that were unable to go to the events, but still want to purchase a shirt for a souvenir. In this case study our group supported George’s T-shirt decision of how he placed his order.
Bibliography
Bodily, S. E. (1988). Quantitiave Business Analysis: Text and Cases. Boston: McGraw Hill Custom Publishing.
BusinessDictionary.com. (2012 йил 25-11). Expected Monetary Value. From BusinessDictionary.com: http://www.businessdictionary.com/definition/expected-monetary-value.html
Jokinen, H., & Kimmo Konkarikoski, P. P. (2009). Operations ' decision making under uncertainty: case studies on papermaking. . Mathematical & Computer Modelling of Dynamical Systems , 435-452.
Toader, C., & Ioan Brad, A. M. (2010 йил 12). Aspects Regarding Risk Management in Projects. Animal Sience and Biotechnologies , 454-457.
Rivoli, P., (2005, November 22). Lessons from the T-Shirt Industry: Arm Chair Capitalist. Retrieved July 1, 2006, from http://armchaircapitalists.blogspot.com/2005/11/what-actually-drives-t-shirt-industry.html
McElwain, J., (2001, May 1). American Apparel Takes on the 1 Shirt Market. Retrieved July 1, 2006, from http://www.findarticles.com/p/articles/mi_m3638/is_9_42/ai_76473285