1. Per-item cost of overestimating demand: $3.28 2. Per-item cost of underestimating demand: $14.23 3. Probability that the value of demand is lower than the optimal order quantity: 0.50 4. Optimal order quantity for uniform distribution: 470 items 5. Optimal order quantity for normal distribution: 543 items
Added by Dawn A.
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28 and the probability that the value of demand is lower than the optimal order quantity is 0.50, we can calculate the expected cost of overestimating demand as follows: Expected cost of overestimating demand = Per-item cost of overestimating demand * Probability Show more…
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Sri K.
The beer store sells potato chips and has does so for a long time. Over the last four years, it has observed that its weekly demand for potato chips varies quite a bit from week to week, but does not follow any seasonal or predictable pattern. The volume of potato chips is much higher than beer, and the store estimates that weekly demand can be modeled as being normally distributed with a mean of 35 bags per week, and a standard deviation of 7. Assume that the store has a given amount of inventory at the start of a week, and has no opportunity to replenish this inventory during the week. In particular for each of the question we’ll assume that the store has 34 bags of inventory at the start of the week. 1. What is the probability that it will sell all 34 bags? (rounded to three decimal places) 2. What is the probability that it has at least 2 bags of chips leftover at the end of the week? (rounded to three decimal places) 3. What is the probability that unmet demand equals or exceeds 3 bags? (rounded to three decimal places) 4. What is the expected number of bags that the store will sell? (rounded to three decimal places) 5. What is the expected number of bags in inventory at the end of the week? (rounded to three decimal places) 6. What is the expected unmet demand? (rounded to three decimal places)
Supreeta N.
Patty Gonia is trying to sell a rain coat to two interested buyers, who each have value for the coat drawn independently from U[50,150]. (a) If Patty sells the coat through a second price auction, what is her expected revenue? And what is the probability that she sells the jacket for at least $100? (b) Patty wonders whether setting a ‘reserve price’ would increase her expected revenue. A reserve price is a value R, where if the second price is below R then the item is sold at price R. If the highest bid is less than R, the item is not sold. What will Patty’s expected revenue be if she runs a second price auction with reserve price R = $100? (Hint: look at the three case for how many bidders bid above $100. What is the probability that a bidder bids above $100? Also, note that given that a bidder bids above $100, their bid will be distributed U[100,150].) (c) Patty decides to set a reserve price of $100. Suppose that unknown to Patty, the two bidders are her competitors, Ari I. and Cole Umbia. Ari and Cole decide that they will collude to buy the coat at a cheaper price, by agreeing that they will each only bid the minimum of their value and $100. (So for example, if Ari’s value is $80 he should bid $80, but if his value is $120 he should bid $100.) Is this strategy a Bayes-Nash Equilibrium? Why or why not? (d) Patty is considering using either a first-price-sealed bid auction or an ascending auction. Patty learns that one customer is a busy working mother, who can only come try on the coat at a specified time, and the other customer is an MS&E 260 student with plenty of time. What advantages/disadvantages should Patty consider when deciding on the auction format? Please provide both qualitative and quantitative/theorem-based reasoning in your response.
Dominador T.
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