Exam 12: Introduction to Simulation Using Analytic Solver Platform

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -What function should be used for generating random numbers from a normal distribution with mean μ and standard deviation σ between the values of a and b only?

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -What function should be used for generating random numbers between 1 and 12 from a continuous uniform distribution?

Large sample size, n, is desirable because

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -Sal, from Exhibit 12.5, has produced the following spreadsheet to compute confidence intervals on his income. What formula should go in cell B8 to compute the upper limit on a 95% confidence interval for the true population mean?

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -University Florists makes bouquets from a variety of materials. The Daily Special Bouquet is priced at $20. The florist assembles this bouquet each day from a variety of low cost flowers he buys from his flower supplier. The actual cost of flowers ranges uniformly from $2 to $7, with all intermediate values being equally likely. The florist (who studied management science many years ago) knows that the time to assemble a bouquet is normally distributed with a mean time of 5 minutes and standard deviation of 1 minute. This will be the time required for all of the Daily Special Bouquets for that day. The florist values his labor time at $10 per hour. Sales are normally distributed with a mean of 10 bouquets per day with a standard deviation of 1 bouquet. What formulas should go in cells B8:B14 to simulate daily profits for the store? Instructions: Answer the following questions using the Analytic Solver Platform Excel add-in.

If chance or uncertainty is present in a system then there is an element of ____ in the decision-making problem.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -Jim Johnson operates a bus service to take college students to "The Big City" on Friday night and bring them back to school on Sunday night. The bus has 45 seats but sometimes there are empty seats. His records show that about 5% of ticket holders do not show up for their ride. Tickets cost $20 and are non-refundable. If Jim overbooks the bus and more than 45 passengers show up, some of them will be bumped and have to miss the trip. This bumping costs the company $40 because Jim has a double-your-money back policy for bumped passengers. Jim plans to accept 48 reservations (overbook 3 seats). What is Jim Johnson's expected marginal profit?

Exhibit 12.4. The following questions use the information below. The manager of a Washington, DC sightseeing tour company is concerned about overbooking for one of his bus tours. The bus has 15 seats but sometimes there are empty seats. His records show that about 20% of ticket holders do not show up for their tour. Tickets cost $10 and are non-refundable. If the manager overbooks the tour and more than 15 passengers show up, some of them will be bumped to a later tour. This bumping costs the company $25 in various expenses to keep the customer happy until the next tour. The manager wants to see what happens to profits if 18 reservations are accepted. -Using the information in Exhibit 12.4, what formula should go in cell C15 of the worksheet to determine the Marginal Profit?

Exhibit 12.4. The following questions use the information below. The manager of a Washington, DC sightseeing tour company is concerned about overbooking for one of his bus tours. The bus has 15 seats but sometimes there are empty seats. His records show that about 20% of ticket holders do not show up for their tour. Tickets cost $10 and are non-refundable. If the manager overbooks the tour and more than 15 passengers show up, some of them will be bumped to a later tour. This bumping costs the company $25 in various expenses to keep the customer happy until the next tour. The manager wants to see what happens to profits if 18 reservations are accepted. -Using the information in Exhibit 12.4, what formula should go in cell C14 of the worksheet to determine the Cost of Bumping Passengers?

In general there are two primary issues involved in risk. What are these two issues?

​The term "risk" also implies the potential for loss.

Exhibit 12.3 The following questions use the information below. An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending. -A simulation model was replicated 100 times yielding a mean of 82.59 with variance of 17.66. Of the 100 replications, 11 replications yielded an outcome over a value of 100. What is the 90% confidence interval on the mean? Instructions: Answer the following questions using the Analytic Solver Platform Excel add-in.

The best-case analysis approach to risk analysis

Exhibit 12.4. The following questions use the information below. The manager of a Washington, DC sightseeing tour company is concerned about overbooking for one of his bus tours. The bus has 15 seats but sometimes there are empty seats. His records show that about 20% of ticket holders do not show up for their tour. Tickets cost $10 and are non-refundable. If the manager overbooks the tour and more than 15 passengers show up, some of them will be bumped to a later tour. This bumping costs the company $25 in various expenses to keep the customer happy until the next tour. The manager wants to see what happens to profits if 18 reservations are accepted. -Using the information in Exhibit 12.4, what Analytic Solver Platform function should be used in cell C10 to determine the number of Passengers to Board?

The PsiTarget(.) function in Analytic Solver Platform

A good way to fit the distribution to historical patterns when historical data is available is to

Several techniques are available to help managers analyze risk. Three of the most common are best-case/worst-case analysis, what-if analysis, and simulation. Of these methods, what-if analysis the most powerful.

Uncertainty

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -What function should be used for generating random numbers from the following distribution on the number of phone calls per hour?

Which Analytic Solver Platform function will generate random integer numbers between 2 and 8?