Exercises
Classic EOQ Model
Exercise 1.1: Hospital Supplies A major hospital needs to manage its inventory of sterile surgical kits. The hospital uses an average of 40 kits per day, 365 days a year. The cost to place an order with their supplier is $50, and the annual cost of holding one kit in inventory is estimated to be $4. Your task is to determine the optimal number of kits the hospital should order each time to minimize costs.
Exercise 1.2: Automotive Parts An auto repair shop specializes in oil changes and uses a specific type of oil filter, "GoldFilter 7X". The shop has a steady demand of 2,500 filters per year. The administrative and shipping cost for placing an order is $30. The annual holding cost per filter is 20% of its purchase price, which is $10 per filter. Calculate the economic order quantity for this oil filter.
Exercise 1.3: University Bookstore The campus bookstore at a large university sells approximately 8,000 units of a popular statistics textbook annually. The cost of placing an order with the publisher is $120. The cost of storing one textbook for a year is $5. To prepare for the upcoming academic year, determine the optimal quantity of textbooks to order at one time.
EOQ with Quantity Discounts
Exercise 2.1: Coffee Bean Importer A specialty coffee shop, "The Daily Grind," imports premium coffee beans from Colombia. They have an annual demand of 5,000 pounds. The ordering cost is $60 per order, and the annual holding cost is $3 per pound. The supplier offers the following pricing structure: $10 per pound for orders under 1,000 pounds, $9.80 per pound for orders between 1,000 and 1,999 pounds, and $9.60 per pound for orders of 2,000 pounds or more. Determine the most cost-effective order quantity.
Exercise 2.2: Bicycle Manufacturer "Momentum Bikes" requires 12,000 specialized gear sets annually for its production line. The cost to place an order is $200, and the annual holding cost is 25% of the unit cost. The supplier provides the following discounts: for orders up to 2,999 units, the cost is $40 per unit; for orders of 3,000 units or more, the cost drops to $38.50 per unit. Should the company take advantage of the discount? Calculate the optimal order quantity.
Exercise 2.3: Electronics Retailer A consumer electronics store sells a popular model of wireless headphones with an annual demand of 3,000 units. The ordering cost is $45, and the annual holding cost is $8 per unit. The manufacturer has proposed a new pricing scheme to encourage larger orders: $150 per unit for orders less than 500, and $145 per unit for orders of 500 or more. What should the store's order quantity be?
EPQ (Economic Production Quantity) Model
Exercise 3.1: Bottling Plant A beverage company produces its signature energy drink in-house. The production line can bottle 800 cases per day, while the daily demand from distributors is 200 cases. The company operates 250 days a year. The cost to set up a production run is $500, and the annual cost to hold one case in inventory is $10. Calculate the optimal production lot size (EPQ).
Exercise 3.2: Custom Microchips A tech firm manufactures a specific microchip for its devices. The annual demand for the chip is 50,000 units. The machinery can produce chips at a rate of 250,000 units per year. The cost to initiate a production run is $1,000, and the annual holding cost per chip is $2.50. Determine the economic production quantity.
Exercise 3.3: Furniture Manufacturing A workshop produces a standard oak dining chair. Demand for the chair is stable at 40 units per week (assume 50 working weeks per year). The workshop can produce 100 chairs per week. The cost to set up the equipment for a production run of these chairs is $220, and the annual holding cost for a single chair is $15. Find the optimal number of chairs to produce in each run.
EOQ with Planned Shortages
Exercise 4.1: High-Fashion Apparel A boutique sells exclusive designer handbags. The annual demand is 600 bags. The ordering cost is $150, and the annual holding cost is $50 per bag. Because the customers are loyal, they are willing to wait for a bag if it's out of stock. The estimated cost of a shortage (due to loss of goodwill and administrative costs of backorders) is $80 per bag per year. Determine the optimal order quantity and the maximum shortage level the boutique should allow.
Exercise 4.2: Specialized Industrial Valve An industrial supplier deals with a specific type of high-pressure valve. Annual demand is 2,000 units, the ordering cost is $250, and the annual holding cost is $40 per unit. The supplier's main clients are large corporations that can tolerate backorders. The estimated cost of a backorder is $60 per unit per year. Calculate the optimal order policy, including the quantity that will be backordered in each cycle.
Exercise 4.3: Rare Book Dealer A dealer of rare books has a steady demand for a particular reprinted classic, totaling 300 books per year. The ordering cost from the publisher is $30, and the annual holding cost is $4 per book. The dealer knows that collectors are willing to be on a waiting list. The cost associated with managing this waiting list (shortage cost) is estimated at $10 per book per year. What is the optimal order quantity and the number of backorders that should be accumulated?
Probabilistic EOQ Models (Safety Stock)
Exercise 5.1: Pharmaceutical Distributor A distributor of a common antibiotic faces a variable demand. The average daily demand is 60 units, with a standard deviation of 15 units. The lead time for replenishment from the manufacturer is constant at 5 days. The company wants to ensure a 95% service level (Z = 1.65). Determine the safety stock required and the reorder point (ROP) for this antibiotic.
Exercise 5.2: Auto Glass Importer An auto glass company imports windshields for a popular car model. The demand is constant at 20 windshields per day. However, the lead time from the international supplier is uncertain, with an average of 10 days and a standard deviation of 3 days. To maintain a 99% service level (Z = 2.33), how much safety stock should the company hold, and what is the reorder point?
Exercise 5.3: Tech Component Supplier (Complex Scenario) A supplier of electronic components faces uncertainty in both demand and lead time. The average daily demand for a key component is 500 units with a standard deviation of 40 units. The lead time for receiving an order is, on average, 4 days with a standard deviation of 1 day. If the company aims for a 97% service level (Z = 1.88), calculate the required safety stock and the reorder point.
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