Let X ij = 1 if work i is assigned to job j, 0 otherwise. The constraint X 11 +

Question

Let Xij = 1 if work i is assigned to job j, 0 otherwise. The constraint X11 + X12 + X13 < 1 means

A. worker 1 can have 3 jobs assigned

B. worker 1 can have no jobs assigned

C. worker 1 can have 2 jobs assigned

D. there is no feasible solution

Let X1 and X2 be 0-1 variables whose values indicate whether projects 1 and 2 are not done or are done. Which answer below models a situation in which project 1 or 2 must be done, but not both?

A. X1 < X2    B. X1 + X2 < 1

C. X1 + X2 = 1 D. X1 + X2 > 1

Little's Law

A. is applicable to any waiting line model

B. is applicable to M/M/1 waiting model only

C. requires that arrivals follow Poisson and service times follow exponential distribution

D. None of the alternatives is correct

Explanation / Answer

1.

B. worker 1 can have no jobs assigned

Since, X11 + X12 + X13 < 1, it means that worker 1 is not assigned to any of the jobs.

2.                                                       

C. X1 + X2 = 1

If X1 is done and X2 is not done, then X1+X2 = 1+0 = 1

Similarly, If X2 is done and X1 is not done, then X1+X2 = 0+1 = 1

3.

None of the alternatives is correct as Little’s law is applicable to wide variety of arrival processes, service-time distributions and number of servers.

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