Scheduling Major League Baseball Umpires It used to be that major league baseball (MLB) umpires were scheduled on an Excel spreadsheet. The task took several weeks and had to be revised often. Now they use a scheduling system developed by researchers at the University of Miami, Carnegie Mellon, and Michigan State University. A variant of the classic Traveling Salesman problem, umpires, as shown in the photo, are assigned to crews that must visit all ballparks at least once during the year. Of course, there are many more constraints. Perspectives/Jeff Smith/Shutterstock MLB teams play 2430 games in a two- to four-game series during a six-month season. Each game requires a crew of four umpires. There are currently 70 umpires on MLB staff, and 22 AAA umpires who may be called up as needed to fill in for games. A typical umpire will handle 142 games a year. Unlike football referees, umpires are full-time employees of MLB. Umpires are normally assigned to crews, but the content of these crews can change during the year. Constraints to umpire crew scheduling include mandated vacations, overexposure to individual teams, prohibition to refereeing at home, and minimizing coast-to-coast travel. Examples of MLB rules used to enforce these constraints are: Crews should travel to all 30 ballparks at least once during a season. Crews should not umpire the same team’s series of games more than once every 18 days. Crews must not travel from the West Coast to the East Coast without an intermediate day off. Crews must not umpire consecutive series more than 1700 miles apart without an intermediate day off. Crews must not travel more than 300 miles preceding a series whose first game is a day game. Crews should not work more than 21 days without a day off. Crews should see each team at home and on the road at least once. Crews should have balanced schedules (i.e., travel approximately the same number of miles, umpire the same number of games, and have the same number of days off). Real-life scheduling problems, like umpire scheduling, can be quite complex. The general solution approach is similar to the assignment method of linear programming described in this chapter. There is an objective function of minimizing distance traveled subject to a number of constraints, as listed earlier. The variables are (0,1) meaning an umpire is either assigned to a game slot (i.e., 1), or not (i.e., 0), and the game slots are numerous (2430 × 4 = 9720). While this can be solved as an integer linear programming (LP) problem, the length of time to do so and the inability to relax constraints make it difficult to find a feasible solution. Academics use heuristics, or rules of thumb, to solve these types of problems. Heuristics do not necessarily satisfy all constraints and do not guarantee an optimal solution, but they can give satisficing or “good enough” solutions. The heuristics are evaluated against performance metrics, previous solutions, and “optimal” solutions (from mathematical programming such as LP). The heuristics are usually improved on with use until users accept them. Many are then coded into software and sold as scheduling systems for particular applications. Search the Internet for scheduling software specific to sports teams or referees. What functionality does the software promise?

Question

Want to see more full solutions like this?

Answer 1

Textbook Question

Chapter 17, Problem 1.1ASC

Scheduling Major League Baseball Umpires

It used to be that major league baseball (MLB) umpires were scheduled on an Excel spreadsheet. The task took several weeks and had to be revised often. Now they use a scheduling system developed by researchers at the University of Miami, Carnegie Mellon, and Michigan State University. A variant of the classic Traveling Salesman problem, umpires, as shown in the photo, are assigned to crews that must visit all ballparks at least once during the year. Of course, there are many more constraints.

Chapter 17, Problem 1.1ASC, Scheduling Major League Baseball Umpires It used to be that major league baseball (MLB) umpires were

Perspectives/Jeff Smith/Shutterstock

MLB teams play 2430 games in a two- to four-game series during a six-month season. Each game requires a crew of four umpires. There are currently 70 umpires on MLB staff, and 22 AAA umpires who may be called up as needed to fill in for games. A typical umpire will handle 142 games a year. Unlike football referees, umpires are full-time employees of MLB. Umpires are normally assigned to crews, but the content of these crews can change during the year. Constraints to umpire crew scheduling include mandated vacations, overexposure to individual teams, prohibition to refereeing at home, and minimizing coast-to-coast travel. Examples of MLB rules used to enforce these constraints are:

Crews should travel to all 30 ballparks at least once during a season.
Crews should not umpire the same team’s series of games more than once every 18 days.
Crews must not travel from the West Coast to the East Coast without an intermediate day off.
Crews must not umpire consecutive series more than 1700 miles apart without an intermediate day off.
Crews must not travel more than 300 miles preceding a series whose first game is a day game.
Crews should not work more than 21 days without a day off.
Crews should see each team at home and on the road at least once.
Crews should have balanced schedules (i.e., travel approximately the same number of miles, umpire the same number of games, and have the same number of days off).

Real-life scheduling problems, like umpire scheduling, can be quite complex. The general solution approach is similar to the assignment method of linear programming described in this chapter. There is an objective function of minimizing distance traveled subject to a number of constraints, as listed earlier. The variables are (0,1) meaning an umpire is either assigned to a game slot (i.e., 1), or not (i.e., 0), and the game slots are numerous (2430 × 4 = 9720). While this can be solved as an integer linear programming (LP) problem, the length of time to do so and the inability to relax constraints make it difficult to find a feasible solution.

Academics use heuristics, or rules of thumb, to solve these types of problems. Heuristics do not necessarily satisfy all constraints and do not guarantee an optimal solution, but they can give satisficing or “good enough” solutions. The heuristics are evaluated against performance metrics, previous solutions, and “optimal” solutions (from mathematical programming such as LP). The heuristics are usually improved on with use until users accept them. Many are then coded into software and sold as scheduling systems for particular applications.

Search the Internet for scheduling software specific to sports teams or referees. What functionality does the software promise?

Expert Solution & Answer

Summary Introduction

Case summary:

The league of baseball has a complex scheduling system need to do umpire management. A six month season requires use of a system developed by researchers to manage the umpires, manage crew change, vacation management, minimizing travel and many more constraints. This complex situation cannot be handled through linear programming because it can be a time consuming approach because of its inflexibility due to these many constraints. A heuristic model or thumb of rule system helps find a good solution easily which might not be the best but is a practical and faster approach.

To determine:

Research on the web about sport management software that helps to schedule sports teams.

Explanation of Solution

Sports management software:

These days there are multiple softwares available that are specifically designed for sports industry that will help the managing organization bodies to satisfy their scheduling needs.

The software “MCS” is an ideal solution to manage the team activity scheduling, providing efficient communication tool to coordinate the members.

LR software solution also analysis the scheduling process and provides statistical modelling to help future planning. The payment processing, leave and vacation management, travel itinerary solutions are also provided by this software.

Company “A” is an umpire assigning software that helps to schedule umpires by handling multiple constraints, include communication to them as well as their payroll processing.

These solutions provide faster and effective management and are able to handle multiple variables that are specific to the sports industry.

Conclusion

There are dedicated softwares available in the sports industry that helps to make the process of scheduling easier and optimal. Some of the solution providers are discussed above.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

Develop and implement a complex and scientific project for an organisation of your choice. please include report include the following: Introduction Background research to the project The 5 basic phases in the project management process Project Initiation Project Planning Project Execution Project Monitoring and Controlling Project Closing Conclusion

Not use ai please

Sam's Pet Hotel operates 51 weeks per year, 6 days per week, and uses a continuous review inventory system. It purchases kitty litter for $11.00 per bag. The following information is available about these bags: > Demand 95 bags/week > Order cost $52.00/order > Annual holding cost = 25 percent of cost > Desired cycle-service level = 80 percent >Lead time 4 weeks (24 working days) > Standard deviation of weekly demand = 15 bags > Current on-hand inventory is 320 bags, with no open orders or backorders. a. Suppose that the weekly demand forecast of 95 bags is incorrect and actual demand averages only 75 bags per week. How much higher will total costs be, owing to the distorted EOQ caused by this forecast error? The costs will be $ higher owing to the error in EOQ. (Enter your response rounded to two decimal places.)

Answer 2

Textbook Question

Chapter 17, Problem 1.1ASC

Scheduling Major League Baseball Umpires

It used to be that major league baseball (MLB) umpires were scheduled on an Excel spreadsheet. The task took several weeks and had to be revised often. Now they use a scheduling system developed by researchers at the University of Miami, Carnegie Mellon, and Michigan State University. A variant of the classic Traveling Salesman problem, umpires, as shown in the photo, are assigned to crews that must visit all ballparks at least once during the year. Of course, there are many more constraints.

Chapter 17, Problem 1.1ASC, Scheduling Major League Baseball Umpires It used to be that major league baseball (MLB) umpires were

Perspectives/Jeff Smith/Shutterstock

MLB teams play 2430 games in a two- to four-game series during a six-month season. Each game requires a crew of four umpires. There are currently 70 umpires on MLB staff, and 22 AAA umpires who may be called up as needed to fill in for games. A typical umpire will handle 142 games a year. Unlike football referees, umpires are full-time employees of MLB. Umpires are normally assigned to crews, but the content of these crews can change during the year. Constraints to umpire crew scheduling include mandated vacations, overexposure to individual teams, prohibition to refereeing at home, and minimizing coast-to-coast travel. Examples of MLB rules used to enforce these constraints are:

Crews should travel to all 30 ballparks at least once during a season.
Crews should not umpire the same team’s series of games more than once every 18 days.
Crews must not travel from the West Coast to the East Coast without an intermediate day off.
Crews must not umpire consecutive series more than 1700 miles apart without an intermediate day off.
Crews must not travel more than 300 miles preceding a series whose first game is a day game.
Crews should not work more than 21 days without a day off.
Crews should see each team at home and on the road at least once.
Crews should have balanced schedules (i.e., travel approximately the same number of miles, umpire the same number of games, and have the same number of days off).

Real-life scheduling problems, like umpire scheduling, can be quite complex. The general solution approach is similar to the assignment method of linear programming described in this chapter. There is an objective function of minimizing distance traveled subject to a number of constraints, as listed earlier. The variables are (0,1) meaning an umpire is either assigned to a game slot (i.e., 1), or not (i.e., 0), and the game slots are numerous (2430 × 4 = 9720). While this can be solved as an integer linear programming (LP) problem, the length of time to do so and the inability to relax constraints make it difficult to find a feasible solution.

Academics use heuristics, or rules of thumb, to solve these types of problems. Heuristics do not necessarily satisfy all constraints and do not guarantee an optimal solution, but they can give satisficing or “good enough” solutions. The heuristics are evaluated against performance metrics, previous solutions, and “optimal” solutions (from mathematical programming such as LP). The heuristics are usually improved on with use until users accept them. Many are then coded into software and sold as scheduling systems for particular applications.

Search the Internet for scheduling software specific to sports teams or referees. What functionality does the software promise?

Expert Solution & Answer

Summary Introduction

Case summary:

The league of baseball has a complex scheduling system need to do umpire management. A six month season requires use of a system developed by researchers to manage the umpires, manage crew change, vacation management, minimizing travel and many more constraints. This complex situation cannot be handled through linear programming because it can be a time consuming approach because of its inflexibility due to these many constraints. A heuristic model or thumb of rule system helps find a good solution easily which might not be the best but is a practical and faster approach.

To determine:

Research on the web about sport management software that helps to schedule sports teams.

Explanation of Solution

Sports management software:

These days there are multiple softwares available that are specifically designed for sports industry that will help the managing organization bodies to satisfy their scheduling needs.

The software “MCS” is an ideal solution to manage the team activity scheduling, providing efficient communication tool to coordinate the members.

LR software solution also analysis the scheduling process and provides statistical modelling to help future planning. The payment processing, leave and vacation management, travel itinerary solutions are also provided by this software.

Company “A” is an umpire assigning software that helps to schedule umpires by handling multiple constraints, include communication to them as well as their payroll processing.

These solutions provide faster and effective management and are able to handle multiple variables that are specific to the sports industry.

Conclusion

There are dedicated softwares available in the sports industry that helps to make the process of scheduling easier and optimal. Some of the solution providers are discussed above.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 17, Problem 1.1ASC

Scheduling Major League Baseball Umpires

It used to be that major league baseball (MLB) umpires were scheduled on an Excel spreadsheet. The task took several weeks and had to be revised often. Now they use a scheduling system developed by researchers at the University of Miami, Carnegie Mellon, and Michigan State University. A variant of the classic Traveling Salesman problem, umpires, as shown in the photo, are assigned to crews that must visit all ballparks at least once during the year. Of course, there are many more constraints.

Chapter 17, Problem 1.1ASC, Scheduling Major League Baseball Umpires It used to be that major league baseball (MLB) umpires were

Perspectives/Jeff Smith/Shutterstock

MLB teams play 2430 games in a two- to four-game series during a six-month season. Each game requires a crew of four umpires. There are currently 70 umpires on MLB staff, and 22 AAA umpires who may be called up as needed to fill in for games. A typical umpire will handle 142 games a year. Unlike football referees, umpires are full-time employees of MLB. Umpires are normally assigned to crews, but the content of these crews can change during the year. Constraints to umpire crew scheduling include mandated vacations, overexposure to individual teams, prohibition to refereeing at home, and minimizing coast-to-coast travel. Examples of MLB rules used to enforce these constraints are:

Crews should travel to all 30 ballparks at least once during a season.
Crews should not umpire the same team’s series of games more than once every 18 days.
Crews must not travel from the West Coast to the East Coast without an intermediate day off.
Crews must not umpire consecutive series more than 1700 miles apart without an intermediate day off.
Crews must not travel more than 300 miles preceding a series whose first game is a day game.
Crews should not work more than 21 days without a day off.
Crews should see each team at home and on the road at least once.
Crews should have balanced schedules (i.e., travel approximately the same number of miles, umpire the same number of games, and have the same number of days off).

Real-life scheduling problems, like umpire scheduling, can be quite complex. The general solution approach is similar to the assignment method of linear programming described in this chapter. There is an objective function of minimizing distance traveled subject to a number of constraints, as listed earlier. The variables are (0,1) meaning an umpire is either assigned to a game slot (i.e., 1), or not (i.e., 0), and the game slots are numerous (2430 × 4 = 9720). While this can be solved as an integer linear programming (LP) problem, the length of time to do so and the inability to relax constraints make it difficult to find a feasible solution.

Academics use heuristics, or rules of thumb, to solve these types of problems. Heuristics do not necessarily satisfy all constraints and do not guarantee an optimal solution, but they can give satisficing or “good enough” solutions. The heuristics are evaluated against performance metrics, previous solutions, and “optimal” solutions (from mathematical programming such as LP). The heuristics are usually improved on with use until users accept them. Many are then coded into software and sold as scheduling systems for particular applications.

Search the Internet for scheduling software specific to sports teams or referees. What functionality does the software promise?

Expert Solution & Answer

Summary Introduction

Case summary:

The league of baseball has a complex scheduling system need to do umpire management. A six month season requires use of a system developed by researchers to manage the umpires, manage crew change, vacation management, minimizing travel and many more constraints. This complex situation cannot be handled through linear programming because it can be a time consuming approach because of its inflexibility due to these many constraints. A heuristic model or thumb of rule system helps find a good solution easily which might not be the best but is a practical and faster approach.

To determine:

Research on the web about sport management software that helps to schedule sports teams.

Explanation of Solution

Sports management software:

These days there are multiple softwares available that are specifically designed for sports industry that will help the managing organization bodies to satisfy their scheduling needs.

The software “MCS” is an ideal solution to manage the team activity scheduling, providing efficient communication tool to coordinate the members.

LR software solution also analysis the scheduling process and provides statistical modelling to help future planning. The payment processing, leave and vacation management, travel itinerary solutions are also provided by this software.

Company “A” is an umpire assigning software that helps to schedule umpires by handling multiple constraints, include communication to them as well as their payroll processing.

These solutions provide faster and effective management and are able to handle multiple variables that are specific to the sports industry.

Conclusion

There are dedicated softwares available in the sports industry that helps to make the process of scheduling easier and optimal. Some of the solution providers are discussed above.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 17, Problem 1.1ASC

Scheduling Major League Baseball Umpires

It used to be that major league baseball (MLB) umpires were scheduled on an Excel spreadsheet. The task took several weeks and had to be revised often. Now they use a scheduling system developed by researchers at the University of Miami, Carnegie Mellon, and Michigan State University. A variant of the classic Traveling Salesman problem, umpires, as shown in the photo, are assigned to crews that must visit all ballparks at least once during the year. Of course, there are many more constraints.

Chapter 17, Problem 1.1ASC, Scheduling Major League Baseball Umpires It used to be that major league baseball (MLB) umpires were

Perspectives/Jeff Smith/Shutterstock

MLB teams play 2430 games in a two- to four-game series during a six-month season. Each game requires a crew of four umpires. There are currently 70 umpires on MLB staff, and 22 AAA umpires who may be called up as needed to fill in for games. A typical umpire will handle 142 games a year. Unlike football referees, umpires are full-time employees of MLB. Umpires are normally assigned to crews, but the content of these crews can change during the year. Constraints to umpire crew scheduling include mandated vacations, overexposure to individual teams, prohibition to refereeing at home, and minimizing coast-to-coast travel. Examples of MLB rules used to enforce these constraints are:

Crews should travel to all 30 ballparks at least once during a season.
Crews should not umpire the same team’s series of games more than once every 18 days.
Crews must not travel from the West Coast to the East Coast without an intermediate day off.
Crews must not umpire consecutive series more than 1700 miles apart without an intermediate day off.
Crews must not travel more than 300 miles preceding a series whose first game is a day game.
Crews should not work more than 21 days without a day off.
Crews should see each team at home and on the road at least once.
Crews should have balanced schedules (i.e., travel approximately the same number of miles, umpire the same number of games, and have the same number of days off).

Real-life scheduling problems, like umpire scheduling, can be quite complex. The general solution approach is similar to the assignment method of linear programming described in this chapter. There is an objective function of minimizing distance traveled subject to a number of constraints, as listed earlier. The variables are (0,1) meaning an umpire is either assigned to a game slot (i.e., 1), or not (i.e., 0), and the game slots are numerous (2430 × 4 = 9720). While this can be solved as an integer linear programming (LP) problem, the length of time to do so and the inability to relax constraints make it difficult to find a feasible solution.

Academics use heuristics, or rules of thumb, to solve these types of problems. Heuristics do not necessarily satisfy all constraints and do not guarantee an optimal solution, but they can give satisficing or “good enough” solutions. The heuristics are evaluated against performance metrics, previous solutions, and “optimal” solutions (from mathematical programming such as LP). The heuristics are usually improved on with use until users accept them. Many are then coded into software and sold as scheduling systems for particular applications.

Search the Internet for scheduling software specific to sports teams or referees. What functionality does the software promise?

Expert Solution & Answer

Summary Introduction

Case summary:

The league of baseball has a complex scheduling system need to do umpire management. A six month season requires use of a system developed by researchers to manage the umpires, manage crew change, vacation management, minimizing travel and many more constraints. This complex situation cannot be handled through linear programming because it can be a time consuming approach because of its inflexibility due to these many constraints. A heuristic model or thumb of rule system helps find a good solution easily which might not be the best but is a practical and faster approach.

To determine:

Research on the web about sport management software that helps to schedule sports teams.

Explanation of Solution

Sports management software:

These days there are multiple softwares available that are specifically designed for sports industry that will help the managing organization bodies to satisfy their scheduling needs.

The software “MCS” is an ideal solution to manage the team activity scheduling, providing efficient communication tool to coordinate the members.

LR software solution also analysis the scheduling process and provides statistical modelling to help future planning. The payment processing, leave and vacation management, travel itinerary solutions are also provided by this software.

Company “A” is an umpire assigning software that helps to schedule umpires by handling multiple constraints, include communication to them as well as their payroll processing.

These solutions provide faster and effective management and are able to handle multiple variables that are specific to the sports industry.

Conclusion

There are dedicated softwares available in the sports industry that helps to make the process of scheduling easier and optimal. Some of the solution providers are discussed above.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

Summary Introduction

Case summary:

The league of baseball has a complex scheduling system need to do umpire management. A six month season requires use of a system developed by researchers to manage the umpires, manage crew change, vacation management, minimizing travel and many more constraints. This complex situation cannot be handled through linear programming because it can be a time consuming approach because of its inflexibility due to these many constraints. A heuristic model or thumb of rule system helps find a good solution easily which might not be the best but is a practical and faster approach.

To determine:

Research on the web about sport management software that helps to schedule sports teams.

Explanation of Solution

Sports management software:

These days there are multiple softwares available that are specifically designed for sports industry that will help the managing organization bodies to satisfy their scheduling needs.

The software “MCS” is an ideal solution to manage the team activity scheduling, providing efficient communication tool to coordinate the members.

LR software solution also analysis the scheduling process and provides statistical modelling to help future planning. The payment processing, leave and vacation management, travel itinerary solutions are also provided by this software.

Company “A” is an umpire assigning software that helps to schedule umpires by handling multiple constraints, include communication to them as well as their payroll processing.

These solutions provide faster and effective management and are able to handle multiple variables that are specific to the sports industry.

Conclusion

There are dedicated softwares available in the sports industry that helps to make the process of scheduling easier and optimal. Some of the solution providers are discussed above.

Answer 8

Expert Solution & Answer

Summary Introduction

Case summary:

The league of baseball has a complex scheduling system need to do umpire management. A six month season requires use of a system developed by researchers to manage the umpires, manage crew change, vacation management, minimizing travel and many more constraints. This complex situation cannot be handled through linear programming because it can be a time consuming approach because of its inflexibility due to these many constraints. A heuristic model or thumb of rule system helps find a good solution easily which might not be the best but is a practical and faster approach.

To determine:

Research on the web about sport management software that helps to schedule sports teams.

Explanation of Solution

Sports management software:

These days there are multiple softwares available that are specifically designed for sports industry that will help the managing organization bodies to satisfy their scheduling needs.

The software “MCS” is an ideal solution to manage the team activity scheduling, providing efficient communication tool to coordinate the members.

LR software solution also analysis the scheduling process and provides statistical modelling to help future planning. The payment processing, leave and vacation management, travel itinerary solutions are also provided by this software.

Company “A” is an umpire assigning software that helps to schedule umpires by handling multiple constraints, include communication to them as well as their payroll processing.

These solutions provide faster and effective management and are able to handle multiple variables that are specific to the sports industry.

Conclusion

There are dedicated softwares available in the sports industry that helps to make the process of scheduling easier and optimal. Some of the solution providers are discussed above.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Summary Introduction

Case summary:

The league of baseball has a complex scheduling system need to do umpire management. A six month season requires use of a system developed by researchers to manage the umpires, manage crew change, vacation management, minimizing travel and many more constraints. This complex situation cannot be handled through linear programming because it can be a time consuming approach because of its inflexibility due to these many constraints. A heuristic model or thumb of rule system helps find a good solution easily which might not be the best but is a practical and faster approach.

To determine:

Research on the web about sport management software that helps to schedule sports teams.

Answer 12

Explanation of Solution

Sports management software:

These days there are multiple softwares available that are specifically designed for sports industry that will help the managing organization bodies to satisfy their scheduling needs.

The software “MCS” is an ideal solution to manage the team activity scheduling, providing efficient communication tool to coordinate the members.

LR software solution also analysis the scheduling process and provides statistical modelling to help future planning. The payment processing, leave and vacation management, travel itinerary solutions are also provided by this software.

Company “A” is an umpire assigning software that helps to schedule umpires by handling multiple constraints, include communication to them as well as their payroll processing.

These solutions provide faster and effective management and are able to handle multiple variables that are specific to the sports industry.

Answer 13

Conclusion

There are dedicated softwares available in the sports industry that helps to make the process of scheduling easier and optimal. Some of the solution providers are discussed above.

Answer 14

Ch. 17 - Scheduling Major League Baseball Umpires It used...Ch. 17 - Scheduling Major League Baseball Umpires It used...Ch. 17 - Solving Tough Scheduling Problems in Healthcare...Ch. 17 - Solving Tough Scheduling Problems in Healthcare...Ch. 17 - Analytics at Airbnb Airbnb is a global community...Ch. 17 - Analytics at Airbnb Airbnb is a global community...Ch. 17 - Analytics at Airbnb Airbnb is a global community...Ch. 17 - Analytics at Airbnb Airbnb is a global community...Ch. 17 - How do scheduling activities differ for projects,...Ch. 17 - Why is scheduling a job shop so difficult?

Concept explainers

Videos

Explanation of Solution

Want to see more full solutions like this?

Chapter 17 Solutions

Additional Business Textbook Solutions