• Perform 10 simulation runs for the PortaCom problem and determine the probability of loss, the maximum profit, the maximum loss, and the average profit. Also draw the histograms of c1, c2, x & Profit.
• Perform 1,000,000 simulation runs for the PortaCom problem and determine the probability of loss, the maximum profit, the maximum loss, and the average profit. Also draw the histograms of c1, c2, x & Profit.
• Compare your results for the 10 runs and 1,000,000 runs.
Develop a pseudo-random number generator (PRNG) Function
Input: Seed Output: Sequence of 100 pseudo-random numbers (between 0 and 1)
Code the inventory simulation problem -- explained in the lecture today -- to decide how many PCs to order per week. (either 1 or 2). Simulation Time: 500 weeks
In the lecture you saw the the 2 ATM case-study Now, you are asked to develop a program to simulate the 3 ATM case study (multi-server queuing model).
Required statistics: Average waiting time Probability of waiting Probability of waiting more than 1 minute Maximum waiting time Utilization of the first ATM machine Utilization of the second ATM machine Utilization of the third ATM machine
In this case, you have the following assumptions: 3 ATM machines (i.e. 3 servers) A single queue for all 3 serves Inter-arrival time follows an exponential distribution (mean = 1 minute). Service time of the first ATM machine: uniform distribution (minimum value = 2 minutes & maximum value = 4 minutes). Service time of the second ATM machine: triangular distribution (a = 2 minutes, b = 4 minutes & c =3.3 minutes). Service time of the third ATM machine: normal distribution (mean = 3 minutes, standard deviation = 0.5 minutes). Run the model for 1 million customers.
Tie One On, an exclusive men’s clothing store specializing in ties, is planning to develop a store in a new shopping mall. Customers are expected to arrive at the store location at random at an average rate of 40 per hour. I.e. IAT : Normal Distr. {60/40;6/40} (minutes).The store will be open 10 hours per day. Service time (of a customer) is assumed to follow a normal distribution {6,1} (minutes). The average sale to a customer is $22. Clerks are paid $20/hr. (including all benefits), and the cost of having a waiting customer is estimated to be $10 per customer per hour. One possibility is to have a small store staffed by 2 clerks This store, however, will only have room for a maximum of 3 customers to be present. Another possibility is to have a larger store with 6 clerks. The larger store can accommodate up to a total of 15 customers. It is believed that customers who arrive when the store is full will shop elsewhere. If the small store leases for $200 per day and the large store leases for $ 2000 per day, which configuration should be used?
Soup Herman is a restaurant that serves soup and salad. Customers first line up in a cash register line to pay for their meals. After paying, they proceed to one of four salad bars. While all customers purchase salad, only 60% of customers go on to take the soup from one of the two soup stations. Assume that the IAT (of customers to the restaurant) can be modeled by a Normal Distribution: {1;0.2} minutes. The time it takes to pay the cashier, get the salad, and get soup each follows a Normal Distribution. If the cashier takes an average of 40 seconds to collect money from a customer (assume std 10 seconds}; and the customer averages two minutes to get a salad (assume std 20 seconds}; and one minute to get soup (assume std 15 seconds}.
Determine the average time a customer spends paying for and getting food if; (i) the customer is getting salad only; and (ii) the customer is getting both soup and salad.