A law firm has six new cases for which it must conduct pre-trial preparations ov

Question

A law firm has six new cases for which it must conduct pre-trial preparations over the next week. To assist the attorneys with the preparation work, a legal assistant may be assigned to each case. There are currently five legal assistants with available time, and each legal assistant may only be assigned to one case. The time that each legal assistant would need to devote to a case is based on his or her expertise with the particular type of case and how complex it is. The firm's goal is to assign the legal assistants such that the total number of labor hours required to complete the entirety of the case preparation work is minimized. The table below provides the estimated times (in hours) the legal assistants will likely have to devote to the cases, based on their levels of experience and other factors. Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Arthur Brenda Chris Diana Ewan 21 25 29 20 18 24 21 24 26 27 26 21 24 25 27 25 27 27 23 26 23 26 24 29 23 Let 1, legal assistant i is assigned to case j rij-10, otherwise i = A,B,C,D,E and j = 1, 2, 3, 4, 5, 6. Formulate the problem as a binary programming model, and find the optimal labor allocation, i.e., determine which legal assistant the firm should assign to each case. (Include a print-out of your solved Excel spreadsheet.) Which case is not assigned a legal assistant (i.e., for which case will the attorney be responsible for the preparation work)?

Explanation / Answer

Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Arthur 22 26 21 27 18 23 Brenda 24 21 25 22 24 26 Chris 25 26 29 26 21 23 Diana 27 29 20 23 24 26 Ewan 25 27 27 23 26 24 This total should be equal to 1 because one person is alloted one case each Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Total Arthur 0 0 0 0 1 0 1 1 Brenda 0 1 0 0 0 0 1 1 Chris 0 0 0 0 0 1 1 1 Diana 0 0 1 0 0 0 1 1 Ewan 0 0 0 1 0 0 1 1 Total 0 1 1 1 1 1 This total should be less than or equal to 1 because one case is alloted to one person only Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Arthur 0 0 0 0 18 0 18 Brenda 0 21 0 0 0 0 21 Chris 0 0 0 0 0 23 23 Diana 0 0 20 0 0 0 20 Ewan 0 0 0 23 0 0 23 Total time 105 Assignment Arthur Case 5 Brenda Case 2 Chris Case 6 Diana Case 3 Ewan Case 4 Case 1 is not assigned a legal assistant and has to be handled by the attorney.

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