Quantitative Business Analysis (MGMT 715) 2015/2016 Essay PDF

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Quantitative Business Analysis (MGMT 715) 2015/2016 George's T Shirts Final Essay...

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Background: George Lassiter is a project engineer for a major defense contractor. He owns a lucrative side business where he designs, manufactures, and hawks “special event” t-shirts. These shirts are sold at rock concerts, major sporting events, and special fundraising events. The shirts are neither endorsed by event sponsors nor allowed to be sold inside the arenas. Their competitive advantage lies in their product design, quality, and price. The product is strategically distributed in streets surrounding the arenas and nearby parking lots. The shirts are sold to vendors for $100 per dozen; Vendors sell them to the public for $10 per shirt. Unsold shirts are purchased by a discount clothing store for $1.50 per shirt. George uses a silk screener/shirt supply house to produce the shirts on a large scale. He purchases batches of 2,500 shirts with the following volume discounts: Order Size

Cost

10,000

$32,125

7500

$25,250

5000

$17,750

The Problem: George Lassiter faces a dilemma about the number of shirts to produce for a rock concert scheduled in two months. George Lassiter is certain about the sale of 20,000 tickets for the standing area around the stage. His primary concern is the number of grandstand seats that will be sold. Based upon his view of the group’s popularity and advance hype, he thinks that there are three possibilities for the sale of grandstand seats-80,000, 50,000 and 20,000. In addition, George is unsure the percentage of attendees who will buy one of his shirts. Typically, fifteen, ten, or five percent of the total attendees purchase a shirt. George puts the

probabilities of those percentages occurring at .1, .3, and .6. George Lassiter is unsure of the quantity of t-shirts to purchase from his supplier to earn the most profit. The Solution: To figure out the quantity of t-shirts to purchase from the supplier so that the quantity results in the most profit, we calculated the different scenarios in an Excel spreadsheet and drew a decision tree shown in Appendix Figure-1. Since George thinks there are three possibilities for the number of grandstand seats to be sold, we made three charts categorized by the order sizes. We broke down the charts by the potential number of tickets sold per possibility. The sales of 20,000 standing tickets have been taken for granted. In addition to 20,000 tickets, there are three possibilities of the number of grandstand tickets likely to be sold. We assumed the following probabilities for high, medium and low value. Items Grandstand Attendance-High Grandstand Attendance-Medium Grandstand Attendance-Low

Quantity 80,000 50,000 20,000

Probability (assumptions) .3 .5 .2

Since the concert is very likely to be a huge success, the high demand of 80,000 is more likely than the low demand of 20,000. We assigned a higher degree of probability to the quantity of 80,000 in attendance than to 20,000. As detailed in the Appendix-Figure 2.1-2.3, the charts revolved around these 3 possibilities because typically fifteen, ten, or five percent of the total attendees purchase a shirt. This is labeled as percentage of demand on the charts. Next we calculate the demand by multiplying the demand percentage by total attendance. The order sizes manufactured by the supplier are 10,000, 7500, and 5000. We multiply the smaller of demand or order size by the sales price to get total sales. If orders exceed demand, the shirts are sold at a discounted price of $1.50. This resale is added to total sales to get total revenue. The costs are then subtracted from total revenue to get gross profit. Probabilities have been applied to calculate the expected monetary value for each of the order size.

Expected monetary value analysis: As shown in the decision tree in the appendix, the different combinations of demands and the number of attendees have been calculated. Using the expected Monetary Value Criterion, we propose that George Lassiter choose the strategy that produces the highest profit. According to the calculation shown in the

Order Expected Highest Lowest Size value of Profit Profit Profit tabular format in appendix-Figure 10000 26552.85 51175 -3465 7500 25238.35 37225 -340 2.1-2.3, Order size 10,000 provides 5000 20314.25 23900 3410 the highest EMV. The second best EMV is generated by the order size 7500. The summarized table shown in figure says that the highest profit the 10,000 order size can produce is 51175, much higher than the EMV. EMV EVUC EVPI

26552 28502 1950

However, the probability of getting the highest profit is only 10%. The EMV calculations must consider the probability of experiencing varying demand scenarios and number of attendees. At the same time, it is also possible that the 10,000 order size produces a loss of 3465. Order Size 7500 provides a fair amount of profit, slightly lower than the order size 10,000. Although the amount of profit generated by order size 10,000 and 7500 is similar, the highest profit scenario for order size 10,000 is higher than that of 7500 order size. The highest profit for this order size may reach up to 37,225 while the lowest profit can go as low as -340. As the EMV calculation doesn’t consider only the single scenario for decision making, the expected value of profit for 7500 order size turned out to be 25,238. Order size 5000 provides the lowest expected value of profit. However, the lowest possible profit for this order size was found to be higher than those for previous two order sizes. The

worst case scenario for order size 5000 is the profit of 3410, better than the losses incurred by order size 10000 and 7500. Expected value of Perfect Information: We have calculated the expected value of perfect information which is the price Lassiter can spend to gain access to perfect information. The EVPI is the difference between EMV and EVUC. To calculate the EVPI, expected value under certainty needs to be calculated. As shown in the decision tree in Appendix, the EVUC in this case is 28,502. EVUC = (40930*0.3+26980*0.5+13665*0.2) = 28502 EMV= (40930*0.3+25563*0.5+7463*0.2) =26553 [Assuming the probability .3, .5 & .2 for High, Medium and Low demand] EVPI= EVUC-EMV = (28,502-26,553) = 1950. Theoretically, perfect information eliminates uncertainty. If Lassiter has the opportunity to get the perfect information he can spend no more than 1950 to get it. Factors contributing to the highest EMV: The factors that contributed to the highest EMV for order size 10,000 include a. 10% chance of 15% buying shirts and 60% chance of 10% buying shirts provided scenarios with no shirts left over. The full price of 8.33 for bulk of the shirts increased the revenue for this order size. b. Lower (0.2) chance of 40,000 attendees also increased the chance of higher attendance, affecting the profitability positively.

An Alternative Scenario: We have also calculated the alternative scenario with 25% chance of 40k attendance, 50% chance of 70k attendance and 25% chance of 100k attendance. Although we did not show this alternative calculation scenario in our decision tree and tables, the summarized expected value for all three order size is given below. Order size 10000 7500 5000

Expected Value 24900 24181.25 19816.67

Probability .25 .50 .25

Under the alternative probability scenario, as shown above, the optimum order size with the highest EMV still remains the 10,000 with an expected monetary value of 24900. Conclusion: Based on the probability and percentage of the attendees who would buy one of his shirts, George’s decision to order for 5,000 shirts will not be the most effective one. Possible per unit profit, considering the best case scenario, for the high value demand is also higher than the per unit profit for low value demand. As the George’s optimism about the popularity of the event is neither very high not very low, any order quantity higher than 10,000 is not suggested in order to avoid losses. Considering all the factors and estimations, we suggest that George order 10,000 shirts....