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Practice Problems Module F—Simulation Problem 1: The time between arrivals at a drive-through window of a fast-food restaurant follows the distribution given below. The service time distribution is also given in the table. Use the random numbers provided to simulate the activities of the first five arrivals. Assume that the window opens at 11:00 A.M. and that the first arrival is after this, based on the first interarrival time. Time Between Arrivals Probability Service Time Probability 1 0.2 1 0.3 2 0.3 2 0.5 3 0.3 3 0.2 4 0.2 Random numbers for arrivals: 14, 74, 27, 03 Random numbers for service times: 88, 32, 36, 24 What time does the fourth customer leave the system? Problem 2: Average daily sales of a product are 8 units. The actual number of units each day is 7, 8, or 9 with probabilities 0.3, 0.4, and 0.3 respectively. The lead time for delivery of this product averages 4 days, although the time may be 3, 4, or 5 days with probabilities 0.2, 0.6, and 0.2. The company plans to place an order when the inventory level drops to 32 units (based on average demand and lead-time). The following random numbers have been generated: Set 1: 60, 87, 46, 63, 50, 76, 11, 04, 97, 96, 65 Set 2: 52, 78, 13, 06, 99, 98, 80, 09, 67, 89, 45 Use set 1 to generate lead-times and use set 2 to simulate daily demand. Simulate two ordering periods and determine how often the company runs out of stock before the shipment arrives. Use an order quantity of 32 and assume orders arrive early in the day prior to demand. ANSWERS Problem 1: Time Between Arrivals Probability Random Number Service Time Probability Random Number 1 0.2 01 - 20 1 0.3 01 - 30 2 0.3 21 - 50 2 0.5 31 - 80 3 0.3 51 - 80 3 0.2 81 - 00 4 0.2 81 - 00 Arrival Arrival Time Start of Service Service time End of Service Server Idle Wait Time 1 11:01 11:01 3 11:04 1 0 2 11:04 11:04 2 11:06 0 0 3 11:06 11:06 2 11:08 0 0 4 11:07 11:08 1 11:09 0 1 Therefore, the fourth arrival leaves at 11:09. Problem 2: Day Demand 0 Ending Inventory Order Placed? Lead-time 32 Order placed 4 days 1 8 24 2 9 15 3 7 8 4 7 33 Stock arrives 5 9 24 Order placed 6 9 15 7 9 6 8 7 0 Stockout - sales of one unit lost. 9 8 0 Stockout - sales of eight units lost 10 9 23 Stock arrives Order placed 5 days