BIT 5664 - Problem Set #1 Inventory 1. Kumar Castings has been in the attractive situation in which it can obtain immediate delivery (i.e., 1 day) of a popular item it stocks for retail sale. The firm has therefore not bothered to order the item in any systematic way. However, recently profits have been squeezed due to competitive pressures and the firm has retained a consultant to study how inventory costs can be reduced. The consultant recommends establishing an inventory control system where ordering decisions are made in a consistent manner based on a balance of ordering and holding costs. It was determined that the various costs associated with making and receiving an order are approximately $70 per order. The cost of carrying an item in inventory amounts to approximately $27 per unit per year (primarily in direct storage costs and foregone investment profit on monies spent on inventory). Demand for an item is reasonably constant over time, and the forecast is for 16,500 units per year. The firm operates 6 days a week plus a few Sundays, or approximately 320 days per year. a. If Kumar uses a fixed quantity inventory system, what is the most economical quantity in which to order the item? What will be the resulting total inventory cost per year? How many times a year will Kumar order the item? What is the average amount of inventory held per year? What is the reorder point? b. The consultant further recommends that Kumar use a cheaper supplier located in Bangladesh. The leadtime for this new supplier is 16 weeks. The cost of each shipment is estimated at $2000. Kumar wants to maintain a customer service level of 95%. A closer look at demand determines that the annual demand is still 16,500 (or approximately 310 units per week) but the standard deviation of demand measured on a weekly basis is approximately 30 units. How much safety stock should Kumar hold for this item given the new supplier? What is the reorder point if safety stock is included? c. How does the order quantity and total annual inventory cost change with the new supplier? (Hint: be sure to add the cost of holding safety stock to the formula). How many orders per year are placed under this policy? What is the average amount of inventory held? d. Comment on the way inventory models are traditionally constructed and evaluated. Is there something amiss in the traditional view on inventory; i.e., what doesn't work in this model? Hint: Try graphing the sawtooth diagram for parts a and b, and you will notice the problem. NOTE: It does not matter whether you use weeks or days as units of measure, since both are referenced in the problem. You can actually keep days in the first part of the question and weeks in the second part because you are calculating reorder point, which is given in units. If you would like to use days for both parts, convert the standard deviation (given in weeks) to days by this formula: Standard deviation per week = (standard deviation per day * 6). Continued... 2. Mai Ka Trading is a Hong Kong manufacturer of electronic components. During the course of a year it requires container cargo space on ships leaving Hong Kong bound for the United States, Mexico and various ports in South America. The company needs 280,000 cubic feet of cargo space annually. The cost of reserving cargo space is $7000 and the cost of holding cargo space is $0.80/ft3. Determine how much storage space the company should optimally order, the total cost and how many times per year it should place an order to reserve space. 3. The daily demand for Hollingshead paint at Top Value Hardware Store is normally distributed with a mean of 30 gallons and a standard deviation of 10 gallons. The leadtime for receiving an order of paint from the paint distributor is 8 days. Since this is the only paint store in North Bay, the manager is interested in maintaining only a 75% service level. a. What reorder point should be used to meet this service level? b. Breaking news! A new paint store is opening in nearby West North Bay. Top Value knows it must improve its customer service in order to compete. What would be the reorder point for a 95% service level? What increase in safety stock is needed to support the increase in service level (compare on a % basis)? Continued... Transportation Method 4. Louderback Apparel has received an order for Olympic T-shirts. The company can purchase the T-shirts from textile factories in Mexico, Puerto Rico, and Haiti. The shirts are shipped from the factories to companies in the United States that silk-screen the shirts before they are shipped to distribution centers. The following tables provide the production and transportation costs ($/shirt) from the T-shirt factories to the silk-screen companies to the distribution centers, plus the supply of T-shirts at the factories and demand for the shirts at the distribution centers. Determine the optimal shipments that will minimize total production and transportation costs for the apparel company. Factory Mexico Puerto Rico Haiti Supply (1000's) 18 15 23 Silk-Screen Companies Miami Atlanta Houston 4 6 3 3 5 5 2 4 4 Distribution Centers Silk-Screen Companies Miami Atlanta Houston Demand (1000's) New York 5 7 8 20 St. Louis 7 6 6 12 Los Angeles 9 10 8 20 Location Analysis 5. The Sheibani restaurant chain uses a distribution center to prepare the food ingredients it provides to individual restaurants. The company is attempting to determine the location for a new distribution center that will service five restaurants. The grid-map coordinates of the five restaurants and the annual number of 40-foot trailer trucks transported to each restaurant are given below. Use the center of gravity technique to determine the coordinates of the best location for the distribution center. Plot the restaurants and the proposed distribution center on a grid. Restaurant 1 2 3 4 5 x 100 210 250 300 400 y 300 180 400 150 200 Shipments 35 24 15 19 38