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Problem 10-05 Premier Consulting’s two consultants, Avery and Baker, can be scheduled to work for clients up to a maxi...

  1. Problem 10-05

    Premier Consulting’s two consultants, Avery and Baker, can be scheduled to work for clients up to a maximum of 160 hours each over the next four weeks. A third consultant, Campbell, has some administrative assignments already planned and is available for clients up to a maximum of 140 hours over the next four weeks. The company has four clients with projects in process. The estimated hourly requirements for each of the clients over the four-week period are as follows:

    Client Hours

    A 180

    B 75

    C 100

    D 85

    1. Hourly rates vary for the consultant–client combination and are based on several factors, including project type and the consultant’s experience. The rates (dollars per hour) for each consultant–client combination are as follows:

      Client

      Consultant A B C D

      Avery 100 125 115 100

      Baker 120 135 115 120

      Campbell 155 150 140 130

      1. Choose the correct network representation of the problem.
      2. Formulate the problem as a linear program, with the optimal solution providing the hours each consultant should be scheduled for each client to maximize the consulting firm’s billings. What is the schedule and what is the total billing?

        Let xij = number of hours from consultant i assigned to client j.
        Max _x11 + _x12 + _x13 + _x14 + _x21 + _x22 + _x23
        + _x24 + _x31 + _x32 + _x33 + _x34
        s.t. _x11 + _x12 + _x13 + _x14 ≤ _
        _x21 + _x22 + _x23 + _x24 ≤ _
        _x31 + _x32 + _x33 + x34 ≤ _
        _x11 + _x21 + _x31 = _
        _x12 + _x22 + _x32 = _
        _x13 + _x23 + _x33 = _
        _x14 + _x24 + x34 = _
        xij ≥ 0 for all i, j
        Hours Assigned Billing
        Avery-Client A $
        Avery-Client B
        Avery-Client C
        Avery-Client D
        Baker-Client A
        Baker-Client B
        Baker-Client C
        Baker-Client D
        Campbell-Client A
        Campbell-Client B
        Campbell-Client C
        Campbell-Client D
        Total Billing $  
      3. New information shows that Avery doesn’t have the experience to be scheduled for client B. If this consulting assignment is not permitted, what impact does it have on total billings? What is the revised schedule?
        Hours Assigned Billing
        Avery-Client A $
        Avery-Client B
        Avery-Client C
        Avery-Client D
        Baker-Client A
        Baker-Client B
        Baker-Client C
        Baker-Client D
        Campbell-Client A
        Campbell-Client B
        Campbell-Client C
        Campbell-Client D
        Total Billing $
math   Statistics-And-Probability   
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Answer #1

(a)Develop a network representation of the problem Ans Avery S100 180 hours 160 hours S125 S120 S100 Si15 8 75 hours Baker S1

(b) Formulate the problem as a linear program, with the optimal solution providing the hours each consultant should be scheduL M 120 135 115 120 155 150 140 130 100 115 100 125 x21 x22 x23 x24 x31 x32 x33 x34 Total Billing Capacity x14 x13 x12 xll 5715 Hours Assigned|Hourly rateBiling 16 SO Avery-Client A Avery-Client B Avery-Client C Avery-ClientD 100 17 125S5,000 115 S11

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