The paper consists of three parts. The parts are only connected by the topic, not by the actual modeling results. Within Part I however, questions a) and b), build upon each other. In other words, the results from a) are inputs for b). If mistakes are made in part a), points are only reduced at this point. If part b) is solved correctly and is only leading to incorrect results because of the incorrect inputs from a), no further points are subtracted.
Make sure you are showing all steps of your work. For example, in part 2b) show how you calculated total profits, this is also worth points! Conclude all of your models with a written out answer.
Part One
A) K’s Brewery is selling its famous beers (K Lager, K-IPA, and K’s Black Belt Ale) in four sales regions throughout Germany. These four regions are Northeast, Northwest, Southeast and Southwest. Due to cultural, as well as historic and political differences, demand in the four regions differs. The firm uses two general marketing tools: advertisements and promotions (determined by the marketing budget) and signing up restaurants as contract distributors that exclusively sell K beers. Regional managers are allowed to employ varying emphasis on these two strategies, depending on what they think works best in a given region. The attached file includes sales data for the past 12 months, as well as marketing budgets and number of contracted restaurants for each region (also per month). Also included is the proposed marketing budget for each region for the next month, and the number of restaurants that are expected to be under contract in the next month.
K’s brewery’s management wants to develop a model to forecast future demand. Which of the three possible predicting variables (marketing budget, number of contracted restaurants, or time) alone or in any possible combination represents the best forecasting model? Choose your preferred model, explain your choice, and forecast demand for the next month (Note: although beer sales may be subject to seasonality, you do not need to consider this to solve this problem). Further hints: The forecasts are done by each of the four regional managers, i.e. demand for each region is forecasted separately. The best forecasting model may not be based on the same predicting variable for each region. (Total points 30)
B) K’s Brewery is currently brewing in three different locations: Koblenz, Bamberg and Oldenburg (please consult the map for the location of these cities). The firm is considering building a fourth brewery in either Magdeburg or Zwickau, as demand is outpacing capacity. The attached file includes production and transportation costs, as well as maximum monthly capacity for each of the facilities. Using the forecast for next month’s production as obtained in part a), determine if Magdeburg or Zwickau is the better location for an additional brewery (with respect to total production and transportation costs). Determine also how much beer should be brewed where and which brewery will deliver to which region.
Hint: based on the given information, you need to determine how to serve the forecasted demand given the available capacity. Two separate models are needed: one including the new brewery in Magdeburg, the other with the new brewery in Zwickau. (Total points 21)
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Part Two
K’s Brewery is evaluating where to locate another brewery (again, while this answers a similar question then Part One b), consider this to be a completely independent problem). Furthermore, the management of K’s brewery is contemplating if the currently planned additional capacity is sufficient (or too much). The plans include a capacity for Zwickau of 1250, 1500 or 1700 (in 1000 cases), and for Magdeburg 1500, 1700, or 2200. If capacity and demand do not match, the following happens: if capacity is above demand, the brewery will brew just according to demand; if capacity is below demand, K’s brewery needs to subcontract, which incurs subcontracting costs. Depending on the size of the new facility, productions costs per 1000 cases will change also (due to increased or decreased economies of scale). The Part2 input data file includes all relevant information. . The probability for a good economy is estimated at 0.3, for a medium economy also at 0.3 and 0.4 for a bad economy. A case of beer sells for Euro4. Determine which location should be chosen, and which size. Discuss your findings.
Hints: You need to calculate aggregated costs (i.e. totaled for aggregated production and then profits for the three different sizes of each facility, and for each economic state of nature. (total points 38)
Part Three
K’s brewery is sponsoring sports games and putting up “beer gardens”, selling drinks and snacks. For the first such event, the manager of the beer garden needs to determine how many pretzels to order. The local bakery offers a contract for 120, 150 or 180 pretzels, at a cost of Euro 0.40 each. The sales price is Euro 1.50. Any unsold pretzel is given to a charity.
If the game is interesting, the manager thinks that fewer people will come to the beer garden. In this case, demand is expected to be normally distributed, with a mean of 140 and a standard deviation of 20. However, if the game is boring, more people will come, with normally distributed demand (mean 190 and standard deviation 15). Based on the profile of the teams playing in the event, the manager thinks that there is a 40% chance that the game will end up being boring. Based on expected profit and expected percentage of unsold pretzels, how many pretzels should be ordered?
Acknowledgement: This last problem is inspired by N. Balakrishnan, B. Render and R.M. Stair, Jr.
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mba604_f15_1.docx
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