Asked by Daija Talley on Jun 21, 2024
Verified
The president of a consulting firm wants to minimize the total number of hours it will take to complete four projects for a new client. Accordingly, she has estimated the time it should take for each of her top consultants-Charlie, Gerald, Johnny, and Rick-to complete any of the four projects, as follows:
Project Hours
Consultant A B C D Charlie 13161118 Gerald 13151012 Johnny 15112015 Rick 17171222\begin{array} { | l | l | l | l | l | } \hline \text { Consultant } & \text { A } & \text { B } & \text { C } & \text { D } \\\hline \text { Charlie } & 13 & 16 & 11 & 18 \\\hline \text { Gerald } & 13 & 15 & 10 & 12 \\\hline \text { Johnny } & 15 & 11 & 20 & 15 \\\hline \text { Rick } & 17 & 17 & 12 & 22 \\\hline\end{array} Consultant Charlie Gerald Johnny Rick A 13131517 B 16151117 C 11102012 D 18121522 a. In how many different ways can she assign these consultants to these projects?
b. What is the total number of hours required by the following arbitrary assignment?
Charlie-B; Gerald-A; Johnny-D; Rick-C
c. What is the optimal assignment of consultants to projects? (Use the assignment method; SHOW YOUR WORK!)
d. For the optimal schedule, what is the total number of hours it will take these consultants to complete these projects?
e. What is the significance, if any, of the fact that Gerald is the best performer at all four projects?
Consulting Firm
A professional services organization that provides expert advice to businesses or individuals in a specific field, such as management, finance, or technology.
Assignment Method
A mathematical technique used for optimal allocation of jobs to resources, minimizing cost or maximizing efficiency in operations.
Project Hours
The total amount of time allocated or spent on the completion of tasks within a project, often tracked for management, billing, or productivity purposes.
- Digest core principles of dispatching and their implementation in the process of scheduling.
- Assess the utility of various scheduling arrangements by studying their effects on average flow time, work-in-process, lateness, and makespan.
- Determine the optimal assignment of resources to maximize efficiency or minimize completion time.
Verified Answer
Project A Project B Project C Project D Charlie 1000 Gerald 0001 Johnny 0100 Rick 0010\begin{array} { | l | c | c | c | c | } \hline & \text { Project A } & \text { Project B } & \text { Project C } & \text { Project D } \\\hline \text { Charlie } & 1 & 0 & 0 & 0 \\\hline \text { Gerald } & 0 & 0 & 0 & 1 \\\hline \text { Johnny } & 0 & 1 & 0 & 0 \\\hline \text { Rick } & 0 & 0 & 1 & 0\\\hline\end{array} Charlie Gerald Johnny Rick Project A 1000 Project B 0010 Project C 0001 Project D 0100
Learning Objectives
- Digest core principles of dispatching and their implementation in the process of scheduling.
- Assess the utility of various scheduling arrangements by studying their effects on average flow time, work-in-process, lateness, and makespan.
- Determine the optimal assignment of resources to maximize efficiency or minimize completion time.
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