1) Consider a trading company located an industrial complex that sells electronic components. Due to its location, when an order is placed, it is instantaneously replenished. The most popular product is a RFID reader, which has an annual demand of 4,000 units and the purchasing price per unit is $80. The selling price of a RFID reader is $100. The annual interest rate is 10% and the average ordering cost is $40 per order. Compute the optimal total annual cost, the economic order quantity, and the optimal order interval for RFID readers.
2) Henny's Chocolates is well known for producing only one type of handmade chocolate and the unit price is $40. The annual demand is 5,000 chocolates on average and the expected inventory holding cost is 10% of the cost of each chocolate. On average, Henny's Chocolates can produce 1,000 chocolates per month. Because of difficulties in preparing kitchen tools, chocolates are produced in batch. The cost to set up the production process is $500. The unit production cost is $10. How many chocolates should the company produce in each batch?
3) Michael Scott is the owner of a small company that produces fresh bagels in New York. The daily demand for bagels appears to be normally distributed and it has been forecasted to be 450 units on average with a standard deviation of 50 bagels. Bagels are baked every morning at a cost of $2 per bagel and the selling price per bagel is $3. Bagels not sold on the day it is baked are relabeled as “day-old” and sold subsequently at a discount price of $1.50 per bagel. The day-old bagels are usually sold out in the morning right after the day they are baked. Determine the optimal number of bagels to bake each morning.
4) Arduino is one of the largest selling items in Adafruit, which deals in circuit boards. The circuit board sells for $150 per unit and costs $100 to purchase. Based on the previous sales data, the average monthly demand is 1,000 boards with a standard deviation of 200 boards and it appears to follow a normal distribution. Adafruit uses 10% annual interest rate to estimate inventory holding costs and the fixed cost per replenishment is $200. Assume that the replenishment lead time is a month, unfulfilled demands are backordered, and backorder cost is $10/unit/year. Compute the optimal replenishment quantity and reorder point.