# Exercise 1- Forecasting

Using the data below, complete the following questions by hand (note: I want to see all of your work):

 Period Month Actual Issues Remediated 1 March 355 2 April 234 3 May 267 4 June 189 5 July 301 6 August 222 7 September 245 8 October 432 9 November 324 10 December 187

1. Use a 3-month moving average model to forecast issues remediated for periods 6-10. (15 points)

1. Use a 5-month moving average model to forecast issues remediated for periods 6-10. (15 points)

1. Use an exponential smoothing model with  a  =.2 to forecast issues remediated for periods 6-10.  (Assume a beginning forecast of 320 for period 5). (15 points)

1. Use an exponential smoothing model with  a  =.4 to forecast issues remediated for periods 6-10.  (Assume a beginning forecast of 320 for period 5) (15 points)

1. Compare the forecasts in questions 1 through 4.  Which is best?  Why?  Support your answer. (20 points)

1. Starting with your solution to question 4, complete a double smoothing model for periods 6-10 for issues remediated.  Again here, assume a beginning forecast of 320 for period 5.  How does this model perform compared to question 4?  Support you answer with statistics. (20 points)

# Study Guide- Exam 1

Review the Introduction chapter- there will be a few questions on the basic information

Forecasting- Chapter 3

1. Forecasting Definition
2. Smoothing Constant- Low Alpha vs High Alpha
1. Minimizing error
2. Reactions to changes
3. Forecasting Method Techniques
4. Weighted average moving forecast
1. How to work through this type of forecast- like the quiz
5. Moving Average Forecast
1. How to work through this type of forecast
2. What is needed for this forecast
6. Smoothing Forecast
1. How to work through this type of forecast
7. Double Smoothing Forecast
1. How to work through this type of forecast
8. Tracking Signal Definition
1. definition
2. How to calculate this
10. BIAS
1. definition
2. How to calculate this

Capacity- Chapter 5

1. Capacity Definition
2. Key capacity planning questions
3. Related capacity planning questions
4. Effective Capacity
1. Definition
2. How to work through the equation
5. Design Capacity
1. Definition
2. How to work through the equation
6. Capacity strategy
7. Actual Output definition
8. Inputs vs outputs
1. Examples of what these are
9. Efficiency Equations
1. Work through the examples from the slides
10. Utilization Equations
1. Work through the examples from the slides
11. Capacity Cushion Equations
12. Profit Equations
1. Work through all of the examples from the slides
13. Breakeven Equations
1. Work through all of the examples from the slides
14. Feasible solution space definition

Linear Programming- Chapter 19

1. Linear Programming Definition
2. Steps to setting the problem up
3. Constraints
1. How to find these in a word problem
4. Feasible solution definition
5. Objective Functions
1. The format of how this is written
2. How to find these in a word problem
6. Right Hand Side information from slides
7. Sensitivity Analysis
1. What’s included in this? From slides in class
8. Binding Constraints definition vs non-binding constraint definition
9. Redundant Constraint definition
10. Non- Negativity Constraint
1. How to find these in a word problem

# Exercise 2- Linear Programming

1. Answer the below problem using LINDO. Show all of your work where it is possible.

Banana Boat produces two similar products, Sun Block SPF 30 and Tanning Oil SPF 8. Sun Block is made of 40 pounds or raw material A and 60 pounds of raw material B, while Tanning Oil is made of 50 pounds of material A and 30 pounds of material B. For this production period, the company has a supply of only 75,000 pounds of material A and 88,000 pounds of material B. Based on demand, Banana Boat needs to sell at least 1200 Sun Blocks and 500 Tanning Oils each month. The profit contributions are \$10 and \$7 per product, respectively, for Sun Block and Tanning Oil. What is the number of each product to be produced to maximize total profit?

1. Describe the Decision Variables (5 points)
2. Describe the Objective Function (5 points)
3. List all of the Constraints (15 points)
4. Attach the LINDO Solution and describe the optimal solution. (15 points)

1. Answer the below problem using LINDO. Show all of your work where it is possible.

Yeti produces three products, Coolers, Water Bottles, and Dog Bowls. Coolers are made of 4 hours of Machine A and 3 hours of machine B. Water Bottles are made of 1 hour of Machine A, 2 hours of Machine B, and 1.5 hours of Machine C.  Dog Bowls are made of 1.5 hours of machine B and 2.5 hours of machine C. For this production period, the company has a supply of only 260 hours for Machine A, 230 hours of Machine B, and 75 hours of Machine C. Based on demand, Yetti needs to sell at least 35 Coolers and 20 Water Bottles each month. The profit contributions are \$40, \$22, and \$13 per product, respectively, for Coolers, Water Bottles, and Dog Bowls. What is the number of each product to be produced to maximize total profit?

1. Describe the Decision Variables (5 points)
2. Describe the Objective Function (5 points)
3. List all of the Constraints (15 points)
4. Attach the LINDO Output and describe the optimal solution. (15 points)
5. What would it take to produce Dog Bowls? Explain how you found your solution. (5 points)

1. The below output came from the optimal solution of a toy manufacturing company. The printer had problems and wasn’t able to appropriately fill out the LINDO output. Without using LINDO/LINO, please fill in the blank answers and explain how you got to your answer. (15 Points)

INPUT:

OUTPUT:

Grasso

Exercise 5- PERT/CPM

Grasso Construction Company

In 2018, Grasso Construction Company had received a contract to construct a water purification system for the city of Wilmington.  By the fall of 2019, work was nearly complete on the main system; however, it was apparent that work on a special remote control building would have to be finished earlier than originally planned if the main system was to be completed on time.

Mr. Jason Barnes, field construction supervisor for Grasso Construction Company had arranged a meeting with Ms. Addison Lee, project engineer, to restudy the arrow diagram of their critical path schedule for the construction of the remote-control building in an effort to determine the shortest possible time in which the job could be done without spending more money than necessary.

Grasso Construction used the Critical Path Method as a tool to assist in project planning and control.  A list of the activities for the remote-control site is in Exhibit 1.  The Cost Table, Exhibit 2, lists the activities and their duration along with the cost needed to complete them in this “normal time”.  The Cost Table also lists the minimum amount of time that each activity will require, called the “crash” time.  In addition, a final listing in the Cost Table shows how much it will cost to shorten each activity by one week.  The sequence of consecutive activities requiring the longest time to complete before the end of the project is known as the “critical path” for that project.  The path is considered “critical” because any delay in the particular sequence will delay the completion of the entire project.

Exhibit 1

 Job Label Job Description Immediately Preceding Job Normal Time te tp A Procure materials Start 3 4 B Prepare site Start 6 8 C Prepare request for Wilmington Engineering department approval Start 2 5 3 D Prefabricate building and deliver to site A 5 7 E Obtain Wilmington Engineering department approval C 2 3 F Install connecting lines to main system A 7 8 G Erect building and equipment on site B, D, E 4 6

Exhibit 2

# Cost Table for Remote Control Building Project

 Normal Crash Activity te  (Weeks) Dollars to (Weeks) * Dollars** A 3 \$        5,000 2 \$      5,000 B 6 \$      14,000 4 \$      6,000 C 2 \$        2,500 1 \$      2,500 D 5 \$      10,000 3 \$      4,000 E 2 \$        8,000 2 – F 7 \$      11,500 5 \$      3,000 G 4 \$      10,000 2 \$      7,000 Total Project Cost (No Crashing) \$      61,000

*Crash weeks shown represent the minimum possible time for the given activity, to.

**This is the cost of gaining one week over the normal time by use of “crash” methods.

Answer the following questions regarding Grasso Construction Company. Be sure to answer every single question in each individual part.:

1. (25 points) Draw a PERT/CPM diagram of this building project. I need to see your drawing.
1. What is the critical path?
2. How long will it take to complete the project without crashing?
3. What is the associated cost?
4. Revise the schedule in order to complete the job within 10 weeks using the crashing method.  Indicate the new cost and critical path or paths.

1. (25 points) Starting from the original tables listed in the exhibits above, Grasso Construction will need to use a new 10-week schedule. However, it became obvious that it would take not two but five weeks to prepare the necessary data for Activity C and that this step alone would now cost \$7,000.
1. What steps would you take to keep on schedule?
2. What would be your new critical path or paths?
3. What would happen to project costs?  (Assume that activity C cannot be crashed.)

1. (25 points) Assume that the project was planned for completion in six weeks and that activity C, the preparation for approval, would take two weeks as described in the case (i.e., go back to where you left off at the end of part 1).
1.  If there is a penalty cost of \$10,000 per week for every week the project is late, what action would you take?
2.  Can you expedite the project so as to finish in 6 weeks?

1. (25 points) What is the probability of completing this building project in 9 weeks?

Grasso

# Exercise 2- Linear Programming

1. Answer the below problem using LINDO. Show all of your work where it is possible.

Banana Boat produces two similar products, Sun Block SPF 30 and Tanning Oil SPF 8. Sun Block is made of 40 pounds or raw material A and 60 pounds of raw material B, while Tanning Oil is made of 50 pounds of material A and 30 pounds of material B. For this production period, the company has a supply of only 75,000 pounds of material A and 88,000 pounds of material B. Based on demand, Banana Boat needs to sell at least 1200 Sun Blocks and 500 Tanning Oils each month. The profit contributions are \$10 and \$7 per product, respectively, for Sun Block and Tanning Oil. What is the number of each product to be produced to maximize total profit?

1. Describe the Decision Variables (5 points)
• X1= # of sun blocks
• X2= # of tanning oil
2. Describe the Objective Function (5 points)
• MAX 10×1+ 7×2
3. List all of the Constraints (15 points)
• Raw material A 40×1+ 50X2 <= 75000
• Raw material B 60×1+ 30×2 <= 88000
• Demand Sunblock                 x1>= 1200
• Demand Tanning Oil x2>= 500
4. Attach the LINDO Solution and describe the optimal solution. (15 points)

1. Answer the below problem using LINDO. Show all of your work where it is possible.

Yeti produces three products, Coolers, Water Bottles, and Dog Bowls. Coolers are made of 4 hours of Machine A and 3 hours of machine B. Water Bottles are made of 1 hour of Machine A, 2 hours of Machine B, and 1.5 hours of Machine C.  Dog Bowls are made of 1.5 hours of machine B and 2.5 hours of machine C. For this production period, the company has a supply of only 260 hours for Machine A, 230 hours of Machine B, and 75 hours of Machine C. Based on demand, Yeti needs to sell at least 35 Coolers and 20 Water Bottles each month. The profit contributions are \$40, \$22, and \$13 per product, respectively, for Coolers, Water Bottles, and Dog Bowls. What is the number of each product to be produced to maximize total profit?

1. Describe the Decision Variables (5 points)
• X1= Coolers
• X2= Water Bottles
• X3= Dog Bowls
2. Describe the Objective Function (5 points)
• MAX 40X1+22X2+ 13X3

1. List all of the Constraints (15 points)
• Machine A 4X1+ 1X2 <= 260
• Machine B 3X1 + 2X2 + 1.5X3 <= 230
• Machine C 5X2+ 2.5X3 <=75
• Demand Coolers X1 >= 35
• Demand Water Bottles X2 >=20
• Non-Negativity Dog Bowls X3 >=0
2. Attach the LINDO Output and describe the optimal solution. (15 points)

1. What would it take to produce Dog Bowls? Explain how you found your solution. (5 points)

The price would need to go up by 1.4 (reduced cost) since that is the improvement needed in the coefficient for a current zero variable to become positive

1. The below output came from the optimal solution of a toy manufacturing company. The printer had problems and wasn’t able to appropriately fill out the LINDO output. Please fill in the blank answers and explain how you got to your answer. (15 Points)

INPUT:

OUTPUT:

1. By using the values and plugging them into the objective function, you would get the following input: 3(8)+7(5)+4(13)= 111.00
2. Since the slack or surplus value has a number other than 0, your dual price would be 0.00
3. By looking at the original objective function equation, you would see that the current coefficient is 4.00

Exercise 3- Location Planning and Analysis

A firm has four manufacturing plants and four warehouses.  It is trying to determine the optimal way to ship from its plants to the warehouses.

The plant capacities and warehouse requirements are as follows:

Plant Capacity                      Warehouse requirement

1 = 1200                                  A = 3100

2 = 4200                                   B = 1800

3 = 5000                                   C = 2000

4 = 2000                                   D = 4400

The freight charges per unit from each plant to each warehouse are as follows:

 Plant Warehouse A B C D 1 2 3 4 \$9 \$6 \$8 \$7 \$5 \$8 \$9 \$9 \$6 \$11 \$9 \$8 \$7 \$6 \$5 \$8

1. Find an initial feasible solution using Northwest Corner and find the cost of this solution. Set this up with Warehouse going across the columns at the top and Plants going down the rows as it is shown in the picture above. (18 Points)

1. Find an initial feasible solution using the North-South rule and find the cost of this solution. Set this up with Warehouse going across the columns at the top and Plants going down the rows as it is shown in the picture above. (18 Points)

1. Find an initial feasible solution using the Difference method and find the cost of this solution. Set this up with Warehouse going across the columns at the top and Plants going down the rows as it is shown in the picture above. (18 Points)

1. Formulate this problem as a transportation Linear Programming problem using LINDO. Show me the decision variables, objective function, constraints and the LINDO output. Find the cost of this solution and describe the optimal solution. (26 Points)

1. How does the Linear Programming solution compare to the solutions found in questions 1-3? Describe the different outcomes.  (20 Points)