Instruction:

1) Submit the arena files and one word file with summarized results

1. A grocery store has three checkout lanes (checkout 1, 2, and 3), each with a single checker. Shoppers arrive at the checkout area with interarrival times having an exponential distribution with mean 2.4 minutes. The shoppers enter the lane that has the fewest number of other shoppers already in the queue. If there are ties for the shortest queue, the shopper will join the highest-numbered checkout lane (that is 3, 2, 1). The checkout service time for all shoppers follows an exponential distribution with a mean of 6.35 minutes regardless of which checkout they choose. Create a simulation of this system and run it for a single replication of 48 hours to determine the average and maximum time of a shopper staying in the system.

b. Modify your answer to the first question by adding a new fast checkout lane. All the shoppers with a service time of less than 5 minutes will always use the fast checkout lane. Those with a service time of 5 minutes or more will still choose from the three regular checkout lanes. The rest settings are same with first question.

2. Two part types arrive to a three-workstation system. Part type 1 arrives according to an exponential distribution with interarrival time mean of 5 minutes, and the first arrival is at time 0. This part type is first processed at workstation 2 and then workstation 3. Its processing time at workstation 2 follows a triangular distribution with minimum 2 min, mode 2.5 min, and max 4 min. Its processing time at workstation 3 follows a triangular distribution with minimum 3 min, mode 4.5 min, and max 7 min. Part type 2 arrives according to an exponential distribution with interarrival time mean of 7 minutes, and the first arrival is at time 0. This part type is processed at workstation 1 first, then workstation 3. Its processing time at workstation 1 is triangular (3, 6.8, 8) minutes, and its processing time at workstation 3 is triangular (3, 5, 7) minutes. Run your simulation for a single replication of 2000 minutes and observe the average and maximum time in system for each part type.

3. An office of a state license bureau has two types of arrivals. Individuals interested in purchasing new plates are characterized to have interarrival times distributed as expo (6.8) and service time as TRIA (8.8, 13.7, 15.2); all times are in minutes. Individuals who want to renew or apply for a new driver's license have interarrival times distributed as expo (8.7) and service times as TRIA (16.7, 20.5, 29.2) The office has two lines, one for each customer type. The office has five clerks: two devoted to plates (Mary and Kathy), and three devoted to licenses (Sue, Jean, and Neil). Run the system for a single replication of 8 hours to observe the time in the system for both types of customers.

4. A proposed production system consists of four serial automatic workstations. The processing times at each workstation are constant: 11, 10, 11, and 12 (all times given are in minutes). The part interarrival times are UNIF(13,15). There is an unlimited buffer in front of all workstations, and we will assume that all transfer times are negligible or zero. The unique aspect of this system is that at Workstation 2 through 4 there is a chance that the part will need to be reprocessed by the workstation that precedes it. For example, after completion at Workstation 2, the part can be sent back to the queue in front of Workstation 1. The probability of revisiting a workstation is independent in that the same part could be send many times with no change in the probability. At present, it is estimated that this probability will be 8%, 9%, 10% for Workstation 2, 3, and 4, respectively. Develop the simulation model and run it for 5,000 minutes. Observe the average cycle time and the maximum cycle time.

5. A medical facility treats non-emergency patients. Patients arrive according to an exponential interarrival time with a mean of 15 minutes. Upon arrival they check in at a registration desk staffed by a single nurse. Registration times follow a triangular distribution with parameters 6, 10, and 18 minutes. After completing registration, they wait for an available examination room; there are four different rooms. Data show that patients can be divided into two groups with regard to different examination times and types. The first group (55% of patients) has service time that follows a triangular distribution with parameters 14, 22, and 39 minutes, and can only be examined in room 1, or 2 or 3. The second group (45%) has triangular service time with parameters 24, 36, and 59 minutes, and can only be examined in room 3 or 4. Upon completion, patients are sent home. The facility is open 16 hours per day. Please run just one day to observe the average total time of each type of patient spend in the system.