Find the value of the minimum setup time

Assignment Help Mathematics

Reference no: EM132230003

Question 1 - Consider the following graph G.

Find -

i. δ(G) =

ii. λ(G) =

iii. κ(G) =

iv. number of edge-disjoint AC-paths.

v. number of vertex-disjoint AC-paths.

Question 2 - The table given below shows the setup time of each job assigned to the four different machines.

	Job 1	Job 2	Job 3	Job 4
Machine 1	14	5	8	7
Machine 2	3	11	6	5
Machine 3	7	8	3	9
Machine 4	3	4	10	10

Use Hungarian algorithm to determine how the four jobs should be assigned to different machines to minimize the total setup time, and then find the value of the minimum setup time.

Question 3 - The following diagram shows a general network N with lower and upper capacities. An initial flow is given as such that the numbers next to each arc are the lower capacity, the values of the flow through the arc, and the upper capacity of the arc.

(a) Write down the value of the current flow from S to T.

(b) Starting with the initial flow, use the maximum flow algorithm to find a maximum flow from S to T and draw a diagram to indicate the flow along each arc.

(d) If the upper capacity of arc GT increases by 2 units (while leaving all other capacities unchanged), what will be the value of a maximum flow from S to T? (Explain you answer briefly.)

(e) If the upper capacity of arc GT decreases by 2 units (while leaving all other capacities unchanged), what will be the value of a maximum flow from S to T? (Explain you answer briefly)

(f) If the upper capacity of arc EF increases by 2 units (while leaving all other capacities unchanged), what will be the value of a maximum flow from S to T? (Explain you answer briefly.)

(g) If the upper capacity of arc EF decreases by 2 units (while leaving all other capacities unchanged), what will be the value of a maximum flow from S to T? (Explain you answer briefly.)

Reference no: EM132230003

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