Homework Assignment 2. "New Due Date:" Please make sure you work in Groups. The following fundamental result is useful frequently throughout the assignment (and in general): If X and Y are two normally distributed random variables with means µx and µy and standard deviations σx and σy respectively, then Z=X+Y is normally distributed with mean µz =µx + µy and standard deviation σz = (σx²+σy²)0.5. Question 1 Having noticed a continuing increase in tourism to his native Sydney, Bruce decided in August 1994 to put his degree in Mathematics "on hold" and instead to pursue a career as street vendor. Since then, he has been selling T-shirts with Sydney motifs in the tourist trodden vicinity of the Opera House. Using his knowledge of mathematics, he used past sales data (see spreadsheet, "Sidney Shirts.xls") to place monthly orders with his T-shirt supplier. The coming 4 weeks (weeks 35 to 38 in 2000) will be different though. For those 4 weeks Sydney will host the Olympic Games and his supplier has offered Bruce a special Sydney 2000 edition T-shirt. Since the supply of those shirts is limited, Bruce can at most purchase 550 units for AU $10 each. Bruce decides to only offer the special edition T-shirts during the next 4 weeks. After that, he estimates that demand for special edition T-shirts will virtually disappear and he plans to return to the traditional style. Sheila, another Street vendor who is unable to obtain any special edition shirts at all, offers to buy any leftover shirts from him in October for AU $5. At a sales price of AU $25 for each shirt, he wonders how many to buy. Given the limited supply, he knows that his supplier's offer is his only chance to get special edition T-shirts. What would you recommend? Why? Hint: Use the standard deviation of the sales data. Question 2 FWX imports Monitors from South East Asia, at a price of $83 per unit. Ordering & Shipping cost an additional $13,000 per shipment, inventory holding costs at FWX are 20% p.a. Daily demand (Monday through Friday) is normally distributed and averages 1000 units, with a standard deviation of 600. Due to changing suppliers, complicated customs procedures and the resurfacing of high sea piracy, delivery times also fluctuate, around an average of 21 working days. The standard deviation of demand during lead time, σDDLT, has been determined as 10,000 units. To facilitate a desired service level of 99%, FWX spends $ 30,000 per year in administering a perpetual review system. a) Determine an appropriate order size and reorder point1. b) To avoid the high monitoring costs for the perpetual system, Anton, a young Industrial Engineer, has proposed to change to a Periodic Review system. Without any additional investment, Anton found that administrative costs would drop by approximately 75%. What do you think about his suggestion? c) A local supplier promises to deliver any order within exactly 7 working days. Order costs would decrease to $5,000 per order, but the unit price increases by 2%. Should FWX switch suppliers? If so, which Review System do you recommend? Explain what you observe. 1 Use the Average Inventory (on Hand) approximation to calculate inventory holding costs.