Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Anonymous
Anonymous asked in 電腦與網際網路軟體 · 1 decade ago

數量方法之線性規劃問題(餐館工作排程問題)

著名的張氏餐館每天營業24小時。侍者與雜役在上午3點、7點、11點、下午3點、7點、11點到班,每人每次輪班8小時。每天區分為6個工作時段,下表顯示每個時段所需最小的工作人數。該餐館工作排程問題,為當每個工作時段開始時,應決定需要多少侍者與雜役到班,以使每天總工作人數最少。(暗示:設Xi等於侍者與雜役的人數,開始工作為時段i,而i = 1,2,3,4,5,6)

工作時段時間 所需侍者與雜役的人數

1 03:00~07:00 3

2 07:00~11:00 12

3 11:00~15:00 16

4 15:00~19:00 9

5 19:00~23:00 11

6 23:00~03:00 4

想請問此題的目標函數以及問題限制式是否為 Min = X1 + X2+ X3+ X4+ X5+ X6

X1 + X2 >=12

X2 + X3 >=16

X3 + X4 >=16

X4 + X5 >=11

X5 + X6 >=11

X6 + X1 >=4

如果我寫錯了,那請問正確的限制式及目標函數的式子應該怎麼從題目當中萃取出來呢?敬請詳解嚕~感恩

Update:

(工作時段) (時間) (所需侍者與雜役的人數)

1 Answer

Rating
  • 1 decade ago
    Favorite Answer

    Decision variables:

    X1: 03:00~07:00 應聘僱人數

    X2: 07:00~11:00 應聘僱人數

    X3: 11:00~15:00 應聘僱人數

    X4: 15:00~19:00 應聘僱人數

    X5: 19:00~23:00 應聘僱人數

    X6: 23:00~03:00 應聘僱人數

    Objective function:

    X1 + X2+ X3+ X4+ X5+ X6 (min. 每日總員工數)

    Constrants:

    1) X1 + X6 >= 3

    2) X1 + X2 >= 12

    3) X2 + X3 >= 16

    4) X3 + X4 >= 9

    5) X4 + X5 >= 11

    6) X5 + X6 >= 4

    限制式歸納詳下表:

         03~07 07~11 11~15 15~19 19~23 23~03

    ----------------------------------------------------------------------------------------

     X1    ◎   ◎

     X2        ◎  ◎

     X3           ◎   ◎

     X4               ◎   ◎

     X5                   ◎   ◎

     X6    ◎                  ◎

    ----------------------------------------------------------------------------------------

    所需人數  3    12  16    9   11    4

Still have questions? Get your answers by asking now.