Assignment:
A bank with 5 tellers - A bank with five tellers opens its doors at 9 a.m. and closes its doors at 5pm, but it operates until all the customers are in the line by 5 p.m. have been served. Assume that the interarrival times of customers are exponentially distributed with a mean of 1 min and that the service times of customers are exponentially distributed with a mean of 4.5 min. In the current configuration, each teller has a separate queue (see figure 8.64). An arriving customer joins the shortest queue, choosing the shortest queue furthest to the left in case of ties.
The bank's management team is concerned with operating costs as well as the quality of service currently being provided to customers, and they are thinking about changing the system to a single queue. In the proposed system, all arriving customers would join single queue. The first customer in the queue goes to the first available teller. Simulate 5 days of operation of the current and proposed systems and compare their expected performance.
2. Airline ticket counter - At an airline ticket counter, the current practice is to allow queues to form in front of each ticket agent. Time between arrivals to the agents is exponentially distributed with a mean of 5 minutes. Customer join the shortest queue at the time of their arrival. The service time for the ticket agents is uniformly distributed between 2 and 10 minutes.
a. Develop an ExtendSim model to determine the minimum number of agents that will result in an average waiting time of 5 min or less.
b. The airline has decided to change the procedure involved in processing customers by the ticket agents. A single line is formed, and customers are rooted to the ticket agent who becomes free next. Modify the simulation model in part (a) to simulate the process change. Determine the number of agents needed to achieve an average waiting time of 5 min or less.
c. Compare the systems in parts (a) and (b) in terms of the number of agents needed to achieve a maximum waiting time of 5 minutes.
d. It has been found that a subset of the customers purchasing tickets is taking a long period of time. By separating ticket holders from non-ticket holders, management believes that improvements can be made in the processing of customers. The time needed to check back in a person is uniformly distributed between 2 and 4 min. The time to purchase a ticket is uniformly distributed between 12 and 18 min. Assume that 15% of the customers will purchase tickets and develop a model to simulate this situation. As before, the time between all arrivals is exponentially distributed with a mean of 5 min. suggest staffing levels for both counters, assuming that the average waiting time should not exceed 5 min.
3. Grocery Store - You are hired by Safeway to help them build a number of simulation models to better understand the customer flows and queuing processes in a grocery store setting. The pilot project at hand focuses on an off-peak setting where at most two checkouts are open.
To better understand the necessary level of detail and the complexities involved, Safeway wants a whole battery of increasingly more realistic and complex models. For each model, Safeway wants to keep track of (i.e., pilot) the average cycle time, queue length, and waiting time in the queue. To understand the variability, they also want to see the standard deviation of these three metrics.
In addition, they would like to track the maximum waiting time and maximum number of customers in line. Furthermore, to better understand the system dynamics, pilot of the actual queue lengths over time are required features of the model. The off-peak setting is valid for about 4 hours, so it is reasonable to run the simulation to 240 min, Furthermore, to facilitate an easier first-cut comparison between the models, a fixed random seed is recommended. Because Safewayplans to use these different models later, it is important that each model sheet has limit of one model.
a) In the first model your only interest is the queues building up at the checkout counters. Empirical investigation has indicated that it is reasonable to model the arrival process (to the checkout counters) as a Poisson process with a constant arrival intensity of 3 customers per minute. The service time in a checkout station is on average 30 seconds per customer and will, in this initial model, be considered constant. Inspired by the successes of a local bank. Safeway wants to model a situation with one single line to both checkout counters. As soon as a checkout is available the first person in the queue will go to this counter. After the customers have paid for their goods they immediately leave the store.
b) Upon closer investigation, it is clear that the service time is not constant but rather normally distributed with mean 14=30 seconds and standard deviation cr=10 seconds. (Hint: This can be set directly in the Activity blocks.) What is the effect of the additional variability compared to the results in a)?
c) To be able to analyze the effect of different queuing configurations, Safeway wants a model in which each checkout counter has its own queue. When a customer arrives to the checkout point, he or she will choose the shortest line. The customer is not allowed to switch queues after making the initial choice. Can you see any differences in system performance compared to the results in part (b)?
d) To make the model more realistic, Safeway also wants to include the time customers spend in the store walking around and picking up their groceries. Empirical investigation has shown that there are basically two types of customers, and they need to be treated somewhat differently.
Type 1: The light shopper who buys only a few items (fewer than 15)
• About 60% of the customers arriving to the store
• The shopping time follows a triangular distribution with a most likely value of 5 min, a minimum value of 2 min, and a maximum value of 8 min.
• The service times for these customers at the checkout counter are exponentially distributed with a mean of 15 s.
Type 2: The heavy shopper who buys several items (more than 15)
• Represents about 40% of the arriving customers.
• The shopping time is triangularly distributed with a most likely value of 10 min, a minimum value of 5 min, and a maximum value of 15 min.
• The service times for these customers at the checkout counter are exponentially distributed with a mean of 52 s.
The total arrival process to the store is still a Poisson process with a mean of three customers per minute. As for the queue configuration, Safeway feels that the setup in b with one line for each checkout is better for psychological reasons; one long line might deter customers from entering the store.
Modify the simulation model to incorporate the described elements and make it more realistic. Analyze the performance of the current process using the performance measures discussed earlier as well as the following additional measures:
• The time spent shopping (average and standard deviation)
• The number of customers (average and standard deviation)
• The separate cycle times for heavy and light shoppers (average and standard deviation)
e) To improve the service for the light shoppers, Safeway is thinking about dedicating one of the checkout counters to this customer group. In other word, only light shoppers are allowed to use checkout 1. The other checkout (checkout 2) will handle both heavy and light shoppers. However, empirical interviews indicate that no light shoppers are waiting in line at the express lane. How does this design change affect the cycle times for the two customer groups and for the average customer?