Supply Chain

1

BU.610.760: Supply Chain Analytics

Problem Set 1

1. Montreal Bagels is a famous bagel shop in Montreal, Canada. They bake fresh bagels each morning and the shop closes by 11 a.m. The selling price for a bagel is $5.50 and each bagel costs $2.50 to make. When the shop closes, if there are leftover bagels, a nearby school cafeteria buys them at $0.50 each. The daily demand for bagels is normally distributed with a mean of 80 and a standard deviation of 20. (a) Suppose that the shop bakes 100 bagels each morning. What is the minimum, mean,

median, and maximum daily profit they may expect to see?

(b) Run the simulation again, but this time evaluate the profit for five different bake quantities: 80, 90, 100, 110, 120.

(c) Among the five quantities you tried above, which order quantity would you prefer? This part does not have a right answer, but please explain the reasoning for your choice.

Hints and reminders:

(i) For this question, you can refer back to the video that discusses Module 0 Example 1(a) and (b).

(ii) In part (a) of the question, to set the demand equal to a normally distributed random input, you can use Distribution > Define > Continuous (from Categories) > Normal. Or, you can simply enter the formula RiskNormal(a,b), where a and b should be replaced with the mean and standard deviation.

(iii) In part (b) of the question, you can use @RISK’s RiskSimTable function to evaluate the profit for different quantities. After you run RiskSimTable, it will be helpful to generate a report using Reports > Output Reports > Overlay Simulations.

2. Return to the Montreal Bagels example discussed in the above question. This time, suppose

that we do not know the demand’s probability distribution. Instead, we have the daily demand data for the past 50 days, provided in “Homework 1 Question 2 Data.xlsx.” The shop would like to determine the number of bagels to bake every morning to maximize their average daily profit. Run the simulation and optimization to achieve this goal. Please answer the following questions: (a) What is the optimal quantity to bake every day?

(b) If Montreal Bagels uses this quantity, what would be the minimum, mean, median, and maximum daily profit they can expect to see?

Hints and reminders:

(i) For this question, you can refer back to the video that discusses Module 0 Example 1(c) and (d).

(ii) First, you need to fit a distribution to the daily demand data provided by Montreal Bagels, using @RISK’s Fit feature. Refer to the video for Module 0 Example 1 part (d) for an

2

example. One suggestion: When you are doing the fit, choose Continuous Sample Data as your data type. Because the demand for bagels is relatively large, there is no harm in approximating it as a continuous variable that can take fractional values.

(iii) To find the optimal quantity, you will use @RISK’s Optimize feature. See the video for Module 0 Example 1 part (c) for an example. To improve the speed of the optimization, please feel free to set Iterations to 100. After you run the optimization, you can answer part (b) by browsing the simulation results (choose the cell that holds the value of profit and click Explore > Browse Results).