Exercises Series 2 Logistics Management - course code: 345 Exercise 1: A few years ago, Heineken, the Dutch brewing company, decided to reduce the length of its average lead-time from 16 weeks to 6 weeks. Assume that the standard deviation of LT is also changed from 3 weeks to 1 week. To make this change, Heineken invested about $1 million. Yet, the service level (97.7%) and weekly demand (50,000 boxes of beer) did not change. Assuming an inventory cost of $2 for each box, what your opinion is about this investment? (z=2) Exercise 2: Leaving Spaces is a furniture retailer that buys its items from different suppliers. They should purchase a mattress from a manufacturer at $ 600 per each. The holding cost for each mattress is only 1% of the price. Assuming an ordering cost of $ 2000 and an estimated yearly demand of 1500 (a) find the optimal order quantity that minimizes inventory costs for Leaving Spaces and, (b) how much the total annual cost of Leaving Spaces changes if they order 200 mattresses every time instead of optimal number? Exercise 3: Daily demand for a product of a computer manufacturer is 400,000 units. The company, on average, makes $150 net profit for each computer. The current fill rate is 86%. About 70% of their incomplete orders are back-ordered, and the rests are cancelled. The company is considering to improve the fill rate to 90% whose estimated daily additional operating cost (e.g., improving the warehousing and transportation) is $ 2,000,000. What should be the minimum backorder cost to make this investment reasonable? 1 Eftekhar: SCM Exercises 2 Exercise 4: We have a hostel near a university in Amsterdam that always fills up on the evening before soccer matches. Data shows us that when our hostel is fully booked, the number of lastminute cancellations has a mean of 8 and standard deviation of 4. The average room rate is $50. When our hostel is overbooked, the policy is to find a room in a nearby hostel and to pay for the room for the customer-we prefer not to loose our customers. This usually costs us $70-because we have to book rooms on late notice which are expensive. How many rooms should our hostel overbook? Exercise 5: How many Parkas L.L. Bean to order if cost per parka is $45, sale price per parka is $100, discount price per parka is $35. Assume that the mean of demand for this parka is 2,000 and standard deviation is 400. Exercise 6: A product at Macy's is priced to sell at $500 per unit. Macy's buys it from the supplier at $300 per unit. Each unsold unit has a salvage value of $200. Demand is expected to be between 30 and 35 units for the week. The demand probabilities and the associated cumulative probability distribution for this case are demonstrated below: Units demanded Probability of the demand Cumulative probability 30 0.10 0.10 31 0.15 0.25 32 0.25 0.50 33 0.25 0.75 34 0.15 0.90 35 0.10 1.00 What is the optimal fill rate that minimizes Macy's inventory costs? How many units should be ordered? Exercise 7: Find the economic order quantity and the reorder point, given Annual demand: D =1,000 Ordering cost: A=$4.9 Eftekhar: SCM Exercises 3 Holding cost per unit per year: h=$2 LT=5 days Purchasing price, p =$12. Exercise 8: A copy store in a university uses 5,000 boxes of paper every year. Assume that standard deviation of demand during a lead time of 2 weeks is about 50 boxes and the average demand per week is 100. To keep a 95% service level (i.e., z=1.645), calculate the reorder point. Remark: \"In a fixed time period system, reorders are placed at the time of review (T), and the safety stock that must be reordered is: safety stock= zT+L where, L is lead time. In this case, the quantity to order is: Q=average demand over the vulnerable period+safety stockinventory on hand Q=d (L+T)+zT+LI Exercise 9: Daily demand for a particular coffee at Target store is 100 units with standard deviation of 25. The review period is 5 days, and lead time is 4 days. The management has set a policy of fulfilling 98% of demand from its stock. At the beginning of this review period, there are 389 units in inventory. How many units should be ordered? (z =2.05)