The Optimal Solution Is the Following (EXCEL SOLVER)
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Premier Consultant’s two consultants, Avery and Baker, Can be schedule 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 progress. The estimated hourly requirements for each of the clients over the four-week period are
Client Hours A 180 B 75 C 100 D 85
Hourly rate 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
Client Consultant A B C D Avery 100 125 115 100 Baker 120 135 115 120 Campbell 155 150 140 130 a. Develop a network representation of the problem. b. Formulate the problem as a linear program, with the optimal solution providing the hours each consultants should be schedule for each client to maximize the consulting firm’s billings. What is the schedule and what is the total billing? c. 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?
A 180 100
120 Avery 155 160
125
B 75 135 Baker 150 160 115 115 C 100 140 Campbell 120 140 100
130 D 85
Consultants Clients Linear programming problem
Maximize Z = 100 X11 + 125 X12 + 115 X13 + 100 X14 + 120 X21 + 135 X22 + 115 X23 + 120 X24 + 155 X31 + 150 X22 + 140 X23 + 130 X24
Subject to
X11 + X12 + X13 + X14 <= 160
X21 + X22 + X23 + X24 <= 160
X31 + X32 + X33 + X34 <= 140
X11 + X21 + X31 >= 180
X12 + X22 + X32 >=75
X13 + X23 + X33 >= 100
X14 + X24 +X34 >= 85
X11,X12,X13,X14,X21,X22,X23,X24,X31,X32,X33,X34 >=0
The optimal solution is the following (EXCEL SOLVER)
A B C D Avery 40 0 100 0 Baker 0 75 0 85 C bell 140 0 0 0
The total billing is 58325.
The consulting assignment of Avery to B is not used in the optimal schedule. So if this assignment is not permitted, the optimal schedule and total billing are not altered.