EOQ Economic Order Quantity

Peak-Sun, a beachwear boutique, is preparing to place its annual spring order for a line of limited-edition designer swimsuits featured in fashion magazines. The suits cost $30 each and sell for a retail price of $90. Because of the limited production run, only a single advance order can be placed, and the manufacturer will not take back any unsold merchandise. The store will sell the suits at full retail price for the first three months, then put the remaining suits "on sale" at half price (i.e., $45) for the following month. Any suits remaining at the end of the fourth month will be sold to a discount outlet at a price yet to be negotiated. The store managers are 95% sure that the total demand over the first three months will be between 100 and 400 units; empirical data shows that demand for such articles follows approximately a Normall distribution. During the half-price sale, it is most likely that another 80 suits will sell, although the demand in this period could be as low as 40 or as high as 160 (assuming enough suits were still on hand). The discount outlet will buy any leftover suits at a price that could be anywhere between $20 and $30 per unit. I Build a model and use Monte-Carlo Simulation to determine expected demand, profit, and optimal order quantity. Assume that the demand in the first three months and during the half-price sale period are independent, i.e., uncorrelated. Run simulation(s) with at least 5000 trials to answer the questions below.

a) What are the expected value and standard deviation of total demand over the entire four-month period?

b) If 300 suits are ordered, what is the probability distribution of total profit? Produce a histogram of the profit, and an estimate expected profit.

c) If 300 suits are ordered, what is the probability that they will all be sold within four months (either at full or half price)?

d) Determine the order quantity that maximizes the expected value of total profit. Give an answer that is accurate to within +/- 25 suits. Plot a graph of expected profit vs. order quantity.

e) Instead of a half-price sale, the store owner is thinking of taking only one-third off the regular price in the final month (i.e., selling the suits for $60 instead of $45). This would lead to lower demand in the final month: the demand would most likely be 50 suits, although it could be as low as 25 or as high as 100. Would this be better than a half-price sale?

Peak-Sun, a beachwear boutique, is preparing to place its annual spring order for a line of limited-edition designer swimsuits featured in fashion magazines. The suits cost $30 each and sell for a retail price of $90. Because of the limited production run, only a single advance order can be placed, and the manufacturer will not take back any unsold merchandise. The store will sell the suits at full retail price for the first three months, then put the remaining suits "on sale" at half price (i.e., \$45) for the following month. Any suits remaining at the end of the fourth month will be sold to a discount outlet at a price yet to be negotiated. The store managers are 95% sure that the total demand over the first three months will be between 100 and 400 units; empirical data shows that demand for such articles follows approximately a Normal distribution. During the half-price sale, it is most likely that another 80 suits will sell, although the demand in this period could be as low as 40 or as high as 160 (assuming enough suits were still on hand). The discount outlet will buy any leftover suits at a price that could be anywhere between $20 and $30 per unit. Build a model and use Monte-Carlo Simulation to determine expected demand, profit, and optimal order quantity. Assume that the demand in the first three months and during the half-price sale period are independent, i.e., uncorrelated. Run simulation(s) with at least 5000 trials to answer the questions below. a) What are the expected value and standard deviation of total demand over the entire four-month period? b) If 300 suits are ordered, what is the probability distribution of total profit? Produce a histogram of the profit, and an estimate of expected profit. c) If 300 suits are ordered, what is the probability that they will all be sold within four months (either at full or half price)? d) Determine the order quantity that maximizes the expected value of total profit. Give an answer that is accurate to within +/25 suits. Plot a graph of expected profit vs. order quantity. e) Instead of a half-price sale, the store owner is thinking of taking only one-third off the regular price in the final month (i.e., selling the suits for $60 instead of $45 ). This would lead to lower demand in the final month: the demand would most likely be 50 suits, although it could be as low as 25 or as high as 100 . Would this be better than a half-price sale