In question (iii) you need to find the probability that the single bottle ordered is sold, the probability that the single bottle remains unsold, and, using the profits found in (ii), the expected profit. For the two probabilities you may use the norm.dist Excel formula.
MGT 3730 (11353-FMWA) Analysis of Management Processes Benedetto C. Valenti Fall 2015 Assignment 3 Due Friday, December 18 by email at email@example.com, or in my mailbox (please hand your work to the staff at the front desk). This is an individual assignment. You may discuss it with others, but never in front of a piece of paper, board, or screen. No spreadsheet need be submitted. Each Roman letter holds one tenth of the full score. 1. A supermarket sells soy milk bottles at $2.00 each to the customers and buys them at $0.80 each with a sixty-day expiration. When expired, they are returned to the supplier for $0.20 each (the supplier pays the supermarket). For the order arrived today, the store manager expects a demand of 1,000 bottles, normally distributed with standard deviation 200. (i) Suppose 1,200 bottles arrived today, what is the profit if the demand turns out to be exactly 1,000? (ii) Suppose only one bottle arrived today, what is the profit if it is sold and what is the profit if it remains unsold? (iii) What is the probability that these two events happen? What is the expected profit for ordering that single bottle? (iv) Using marginal analysis, show how to find the optimal order quantity. (v) Would that change if the standard deviation increased? If so, how and why? 2. During peak demand, an airline check-in with two desks and a single waiting line receives one customer every 1.5 minutes on average, with standard deviation of 0.4 minutes. Service times are 2.5 minutes on average, with standard deviation of 0.9 minutes. (vi) Find the throughput, the utilization rate and the efficiency rate of the system. (vii) Find the average queue length and the average flow time of the system. (viii) Would the average queue length change if one desk closed? If so, how and why? (ix) If the system was divided in two separate queues, one waiting line and one desk for priority passengers (30% of the total), and one waiting line and one desk for all other passengers, what would be the average queue length for the two types of passengers? (x) Assuming that a priority passenger’s wait costs twice the wait of a regular passenger, is it better to keep one single waiting line with two servers or two separate queues? Why?