Hi,
I'm most of the way through setting up a linear programming problem but I realized I'm missing part of the calculation. I'm solving it in LINDO so that's why it's formatted this way. I'm trying to find the optimal number of workers to minimize cost per week - there are 6 types of workers. I have the demand for each item and production rate for each worker for each of the 6 types of items I'm trying to produce and the cost of each worker per week.
The objective function is:
minimize 5L + 5B + 6E + 5W + 7S + 8G subject to
2) 4Lw + 2Lb + 1Lbg + 2Lsp - Le = 0 (production rate of worker type 1 for all 6 items)
3) 3Bw + 3Bb + 1Bbg + 2Bsp - Be = 0 (production rate of worker type 2 for all 6 items)
4) 2Ew + 2Eb + 5Ebg + 1Esp - Ee = 0 (production rate of worker type 3 for all 6 items)
5) 2Ww + 3Wb + 2Wbg + 4Wsp - We = 0 (production rate of worker type 4 for all 6 items)
6) 6Ssi - Se = 0 (production rate of worker type 5 for all 6 items)
7) 7Gg - Ge = 0 (production rate of worker type 6 for all 6 items)
11) Lw +Bw + Ew + Ww >= 240 (demand of item 1)
12) Lb + Bb+ Eb + Wb >= 228 (demand of item 2)
13) Lbg + Bbg + Ebg + Wbg >= 48 (demand of item 3)
14) Lsp + Bsp + Esp + Wsp >= 60 (demand of item 4)
15) Ssi - Dsi = 48 (demand of item 5)
16) Gg >= 42 (demand of item 6)
17) E >= 15 (worker type 3 constraint)
18) S >= 12 (worker type 5 constraint)
19) G >= 8 (worker type 7 constraint)
I know this is only part of the solution, I haven't tied the production rates back to calculate a quantity for each type of worker. From there the cost will need to be calculated from the objective function. Can someone help me with the piece I'm missing? Usually staffing type problems give the number of required workers up front so I'm a little stuck. I've tried to include all the relevent info - sorry if I left something out!
Thanks!!
I'm most of the way through setting up a linear programming problem but I realized I'm missing part of the calculation. I'm solving it in LINDO so that's why it's formatted this way. I'm trying to find the optimal number of workers to minimize cost per week - there are 6 types of workers. I have the demand for each item and production rate for each worker for each of the 6 types of items I'm trying to produce and the cost of each worker per week.
The objective function is:
minimize 5L + 5B + 6E + 5W + 7S + 8G subject to
2) 4Lw + 2Lb + 1Lbg + 2Lsp - Le = 0 (production rate of worker type 1 for all 6 items)
3) 3Bw + 3Bb + 1Bbg + 2Bsp - Be = 0 (production rate of worker type 2 for all 6 items)
4) 2Ew + 2Eb + 5Ebg + 1Esp - Ee = 0 (production rate of worker type 3 for all 6 items)
5) 2Ww + 3Wb + 2Wbg + 4Wsp - We = 0 (production rate of worker type 4 for all 6 items)
6) 6Ssi - Se = 0 (production rate of worker type 5 for all 6 items)
7) 7Gg - Ge = 0 (production rate of worker type 6 for all 6 items)
11) Lw +Bw + Ew + Ww >= 240 (demand of item 1)
12) Lb + Bb+ Eb + Wb >= 228 (demand of item 2)
13) Lbg + Bbg + Ebg + Wbg >= 48 (demand of item 3)
14) Lsp + Bsp + Esp + Wsp >= 60 (demand of item 4)
15) Ssi - Dsi = 48 (demand of item 5)
16) Gg >= 42 (demand of item 6)
17) E >= 15 (worker type 3 constraint)
18) S >= 12 (worker type 5 constraint)
19) G >= 8 (worker type 7 constraint)
I know this is only part of the solution, I haven't tied the production rates back to calculate a quantity for each type of worker. From there the cost will need to be calculated from the objective function. Can someone help me with the piece I'm missing? Usually staffing type problems give the number of required workers up front so I'm a little stuck. I've tried to include all the relevent info - sorry if I left something out!
Thanks!!