Write a linear program to achieve our objective

Assignment Help Engineering Mathematics

Reference no: EM131162794

A lot of three identical items is to be sequenced through three machines. Each item must be processed first on machine 1, then on machine 2, and finally on machine 3. It takes 20 minutes to process one item on machine 1, 12 minutes on machine 2, and 25 minutes on machine 3. The objective is to minimize the total work span to complete all the items.

a) Write a linear program to achieve our objective. (Hint. Let xi j be the starting time of processing item i on machine j. Two items may not occupy the same machine at the same time; also, an item may be processed on machine (j + 1) only after it has been completed on machine j.)

b) Cast the model above as a network problem. Draw the associated network and give an interpretation in terms of flow in networks. (Hint. Formulate and interpret the dual problem of the linear program obtained in (a).)

c) Find an initial feasible solution; solve completely.

Reference no: EM131162794

Questions Cloud

Formulate the problem as a linear program : Formulate the problem as a linear program. Interpret the resulting model as a network-flow problem. Draw the corresponding network diagram.

Analyze the data on recognition and the data on reported use : In addition, they asked participants in the first group to indicate the degree to which they used textbook pictures in general as study aids. How would you analyze the data on recognition and the data on reported use of pictures?

How can formulation be manipulated to become network problem : If the answer to (a) is no, how can the formulation be manipulated to become a network problem? Draw the associated network. (Hint. Add a redundant constraint introducing a fictitious node.)

Calculate the optimal staffing pattern : Assuming that both service rates approximate Poisson distribution, calculate the optimal staffing pattern for the clinic and the system performance measures.

Write a linear program to achieve our objective : Write a linear program to achieve our objective. Cast the model above as a network problem. Draw the associated network and give an interpretation in terms of flow in networks.

Describe the social factors that contribute to the problem : Identify and describe the social factors that contribute to the problem. Identify and examine a federal or state social welfare policy that aims to address this social problem.

Determine the service utilization : Simulate the process for the first twenty persons arriving for flu shots.- Determine the average time in queue.- Determine the service utilization.

How does this affect the mean weight of the packages : Is the sample mean always equal to one of the values in the sample? If so, explain why. If not, give an example.

Determine the minimum-cost exploration scheme : As the leader of an oil-exploration drilling venture, you must determine the least-cost selection of 5 out of 10 possible sites. Formulate an integer program to determine the minimum-cost exploration scheme that satisfies these restrictions.

User Account

All Pages