In an effort to maintain logistics costs low, the CEO of Riding Patriot has hired you as a consultant for their logistics department, and assigned you the task of looking into the cost of inventory at their Distribution Center (DC) located in Franklin, Massachusetts. Through some interviews and data collection on site you learn that Riding Patriot has several stores across the New England region. All of them are served from this single DC. You have been asked to define a (s, Q) policy for the inventory in this DC.

The demand of tires from taxi cabs is normally distributed and relatively stable at around 3,500 units per month, with a standard deviation of 375 units per month. The Sales department tells you that Riding Patriot pays $217 per unit. Through talks with Finance and Logistics personnel, you estimate that the firm's holding charge is about 16% of the item's cost per year.

Tires have to be shipped in full containers from the West Coast. Every time Riding Patriot places an order, it has to be in multiples of 100 units, and incurs an ordering cost of $1,650 for each order it places. Since the tires are moved by rail and truck, the lead time from the vendor is relatively long at 3 weeks. Payment is due at the moment the order is placed, and ownership of the items is transferred to you as soon as the order is placed. Riding Patriot's policy is to maintain a customer service level (CSL) of 95%.

Please enter all your numerical answers with 4 significant figures unless specifically told otherwise.

(Hint: Notice that some values above are given in terms of weeks, others in terms of months, and others in terms of years. For the sake of transforming values from one unit to the other, you can assume there are exactly 12 months in a year and exactly 4 weeks in a month.)

PART A

1. For orders from Riding Patriot to its supplier, what order size would you recommend? Use the economic order quantity (EOQ) formula, but subject to the constraint of ordering multiples of 100.

2. On an average, how frequently would Riding Patriot place these orders? Give your answer in terms of weeks, with one decimal.

PART B

1. What is your Reorder Point s? Give your answer rounded to the nearest multiple of 10.

2. What is the expected annual cost of carrying cycle stock? Round to the nearest multiple of $100.

3. What is the expected annual cost of carrying the safety stock? Round to the nearest multiple of $100.