Case 7.4 Maximart Sales The inventory manager of Maximart Sales wants to establish optimum ordering policies. Weekly demand for a particular item follows a normal distribution with a mean of 300 units and a standard deviation of 70 units. The supplier will sell Maximart up to 999 units in an order at a price of $100/unit. If Maximart orders between 1000 and 3999 units per order, they can get the product for $95/unit. If Maximart is willing to order 4000 or more units with each order, they can get the product at $90/unit. Maximart sells the item for $200 per unit. It costs Maximart $125 to place an order, and $0.60 to hold a unit of inventory from one week to the next. The lead time between placing an order and receiving it, inspected and ready for sale, is two weeks. When demand cannot be satisfied from stock, some customers are willing to accept back order, and wait another week or two for delivery. Other customers will not wait. The percentage of customers who are willing to accept a backorder varies uniformly between 10% and 50%. Maximart estimates that they will lose $60 in future profit from each lost sale. The current inventory policy is an order quantity of 4000 units, to take advantage of the quantity discounts. Further, the inventory manager has also set the reorder point at the average weekly demand, 300 units. An order will be placed in any week for which the ending inventory is less than the reorder point, provided that there is not already an outstanding order from the previous week. a. Simulate 40 weeks of operation. Assume that the inventory at the beginning of week 1 is 1000 units. Provide a breakdown of the average net profit and the average weekly costs for ordering, holding, lost future profits, and average total weekly costs. b. Repeat part a. with an order quantity of 1000 units and a reorder point of 700 units. c. Using the results from part a. and b. investigate a couple other combinations of reorder point and order quantity, in an attempt to determine the combination of the two that will lead to the greatest profit. Report your recommendations. Case 7.2 Skyhigh Airlines Skyhigh Airlines flight 708 from New York to Los Angeles is a popular flight that is usually sold out. Unfortunately, some ticketed passengers change their plans at the last minute and cancel or re-book on another flight. Subsequently, the airline loses the $450 for every empty seat that the plane flies. To limit their losses from no-shows, the airline routinely overbooks flight 708, and hopes that the number of no-shows will equal the number of seats oversold. However, things seldom work out that well. Sometimes flight 708 has empty seats, and other times there are more passengers than the airplane has seats. When the latter happens, the airline must \"bump\" pre-ticketed passengers; they estimate that this will cost them $275 in later accommodations to bumped passengers. Fortunately for the airline, hopeful passengers usually show up at flight time without tickets and want to get on the flight. The airline classifies these passengers as standbys while it waits to determine how many seats, if any will be available. Standby passengers can help offset the loss associated with flying an empty seat, but the airline suffers no penalty when a standby passenger is not able to receive a seat. Airline records indicate that the number of No-shows and Standbys will vary according to the probability tables below: Number of No-shows 0 1 2 3 4 5 6 Relative Frequency 0.04 0.08 0.14 0.25 0.30 0.13 0.06 Number of Standbys 0 1 2 3 4 Relative Frequency 0.26 0.34 0.24 0.11 0.05 Simulate 25 flights with each of several different overbooking decisions (assume that the best overbooking number will be between 1 and 6) to determine the optimal number of seats to overbook this flight, to minimize the airline's losses. Tabulate your results and use them to justify your recommendations. You should report, for each scenario, the average loss per flight, and the percentage of flights that suffer a loss