Homework answers / question archive / A typical assignment problem (similar to, but different from, the transportation problem) GOS Consulting  has just won four proposals for new clients it wants very much to impress

A typical assignment problem (similar to, but different from, the transportation problem) GOS Consulting  has just won four proposals for new clients it wants very much to impress

Health Science

Share With

A typical assignment problem (similar to, but different from, the transportation problem)

GOS Consulting  has just won four proposals for new clients it wants very much to impress. They have decided to put their top people to work on these projects over the next six weeks: Greg, Osiris and Son.  Each consultant works 40 hours a week, so there are 120 total consultant- hours available per week and 720 consultant-hours available for the entire period. Abracadabra requires 230 hours of consulting time over the next six weeks; Bestfone requires 240 hours; Clowdnine requires 120, and Dine2Eat requires 115 hours.  Hourly rates depend upon various factors, including the consultant’s experience for that type of project. The following table gives the hourly rate charged for each client/consultant combination:

The objective is to assign consultants to projects in such a way as to MAXimize the company’s billings.  Consultants may work on more than one project.

This is similar to the transportation problem. The difference here is that the ‘supply’ is the number of hours each consultant can provide, and the demand is the number of hours each project requires.  Your DVs can have a similar Xij notation where Xij means the number of hours worked by consultant i for project j.

1. Draw a network diagram similar to the transportation diagram showing the possible consultant/project combinations. Be sure to label the arcs, and provide the supply, demand, and units.
2. Set up the DVs using NUN.
3. Set up the objective function using dimensional analysis.
4. Set up the constraints using dimensional analysis.
5. Summarize the LP in algebraic form (i., without units)
6. Put the problem into solver and solve it. Then answer the questions below on the ANSWER report:
7. Give a brief summary of which consultant is working for which client.
8. Summarize the total amount billed for this combination of consultants and clients