Exam 8: The Mathematics of Scheduling: Chasing the Critical Path

Suppose that you work at a local convenience store. The store has just closed and you and three other co-workers must complete a list of tasks before any of you can leave for the night. Each task may only be worked on by one person. What is the optimal amount of time that it will take to complete the list of tasks knowing that all tasks are independent from one another? (a) 18 (b) 22 (c)25 (d)27 (e)None of the

Suppose that you work at a local convenience store. The store has just closed and you and one other co-worker must complete a list of tasks before any of you can leave for the night. Each task may only be worked on by one person. What is the optimal amount of time that it will take to complete the list of tasks knowing that all tasks are independent from one another?

A project consists of seven tasks labeled A through G . The table shown below gives the processing times and precedence relations. Which project digraph represents this situation?

-Consider the digraphs shown above ; which of the digraphs have an outdegree of 3 at vertex O?

A project consists of seven tasks labeled A through G . The table shown below gives the processing times and precedence relations. Which project digraph represents this situation? -Consider the project above; use the priority list A, C, B, F, G, D, E to find the project finish time fin using N = 3 processors.

Consider the project digraph shown below; apply the critical-path algorithm to find the project finish time f i n using N=2 processors.

Suppose that you work at a local convenience store. The store has just closed and you and two other co-workers must complete a list of tasks before any of you can leave for the night. Each task may only be worked on by one person. What is the optimal amount of time that it will take to complete the list of tasks knowing that all tasks are independent from one another?

-Consider the digraphs shown above ; how many arcs from the digraph shown in figure 2 are adjacent to arc HT?

-Consider the digraph shown above ; which arcs, if any, are adjacent to BO?

A project consists of seven tasks labeled A through G. The table shown below gives the processing times and precedence relations. Which project digraph represents this situation?

Consider the digraph with vertex set V = {I, C, H, A, B, O, D} and arc set A = {IC, ID, CH, HA, HO, AI, AB, BO, BD, OD}. Draw the digraph.

Consider the project digraph shown below; you plan on applying the critical-path algorithm to complete the project. However, you have a choice of using either N = 2 processors or N = 3 processors. Is it more efficient to use three processors as opposed to two? Explain.

Consider the digraph shown below; give the arc set A.

Suppose that you work at a local convenience store. The store has just closed and you and one other co-worker must complete a list of tasks before any of you can leave for the night. Each task may only be worked on by one person. What is the optimal amount of time that it will take to complete the list of tasks knowing that all tasks are independent from one another? Hint: You are guaranteed that a project finish time is optimal if there is zero idle time.

-Consider the digraph shown above ; what is the indegree of vertex B?

-Consider the digraph shown above ; which arcs, if any, are adjacent to AD?

In a specific project, the addition of more processors will always cause the optimal time to decrease.

Which of the digraphs below have arc OS as part of its arc set?

Consider the project digraph shown below; apply the decreasing-time algorithm to find the project finish time fin using N = 3 processors.

-Consider the project digraph from problem 8; apply the critical-path algorithm to find the project finish time fin using N = 2 processors.