What is the objective function and constraints of this problem?
$begingroup$
How to solve this problem? This is what I know so far.
Let A be the no. of drivers at the beginning of the year.
Let B be the no. of drivers fired.
Let C be the no. of drivers recruited
Is the objective function 12000A + 2000B + 1000C
Am I on the correct track? What is next?
SBS bus company just won the tender to run premium bus services from the east of New York. The company predicts that they need to have at least the following numbers of bus drivers in coming 5 years: Year 1: 100 drivers; Year 2: 90 drivers; Year 3: 110 drivers; Year 4: 120 drivers and Year 5: 90 drivers.
Recruiting one driver costs the company 1,000 USD which includes pre-deployment training. Firing one driver costs the company 2,000 USD including the severance pay. Each driver on payroll costs the company 12,000 USD per year. The company currently has 60 bus drivers on payroll. Apply linear programming model to develop a formulation to minimize the total recruiting, firing and payroll cost for the bus company. List assumptions you made in the formulation. Note that you are not required to solve the problem.
linear-programming
edited Apr 14 '18 at 10:56
nbro
2,41653173
asked Sep 18 '17 at 13:03
JaniceJanice
63
$endgroup$
add a comment |
$begingroup$
How to solve this problem? This is what I know so far.
Let A be the no. of drivers at the beginning of the year.
Let B be the no. of drivers fired.
Let C be the no. of drivers recruited
Is the objective function 12000A + 2000B + 1000C
Am I on the correct track? What is next?
SBS bus company just won the tender to run premium bus services from the east of New York. The company predicts that they need to have at least the following numbers of bus drivers in coming 5 years: Year 1: 100 drivers; Year 2: 90 drivers; Year 3: 110 drivers; Year 4: 120 drivers and Year 5: 90 drivers.
Recruiting one driver costs the company 1,000 USD which includes pre-deployment training. Firing one driver costs the company 2,000 USD including the severance pay. Each driver on payroll costs the company 12,000 USD per year. The company currently has 60 bus drivers on payroll. Apply linear programming model to develop a formulation to minimize the total recruiting, firing and payroll cost for the bus company. List assumptions you made in the formulation. Note that you are not required to solve the problem.
linear-programming
edited Apr 14 '18 at 10:56
nbro
2,41653173
asked Sep 18 '17 at 13:03
JaniceJanice
63
$endgroup$
add a comment |
$begingroup$
How to solve this problem? This is what I know so far.
Let A be the no. of drivers at the beginning of the year.
Let B be the no. of drivers fired.
Let C be the no. of drivers recruited
Is the objective function 12000A + 2000B + 1000C
Am I on the correct track? What is next?
SBS bus company just won the tender to run premium bus services from the east of New York. The company predicts that they need to have at least the following numbers of bus drivers in coming 5 years: Year 1: 100 drivers; Year 2: 90 drivers; Year 3: 110 drivers; Year 4: 120 drivers and Year 5: 90 drivers.
Recruiting one driver costs the company 1,000 USD which includes pre-deployment training. Firing one driver costs the company 2,000 USD including the severance pay. Each driver on payroll costs the company 12,000 USD per year. The company currently has 60 bus drivers on payroll. Apply linear programming model to develop a formulation to minimize the total recruiting, firing and payroll cost for the bus company. List assumptions you made in the formulation. Note that you are not required to solve the problem.
linear-programming
edited Apr 14 '18 at 10:56
nbro
2,41653173
asked Sep 18 '17 at 13:03
JaniceJanice
63
$endgroup$
How to solve this problem? This is what I know so far.
Let A be the no. of drivers at the beginning of the year.
Let B be the no. of drivers fired.
Let C be the no. of drivers recruited
Is the objective function 12000A + 2000B + 1000C
Am I on the correct track? What is next?
SBS bus company just won the tender to run premium bus services from the east of New York. The company predicts that they need to have at least the following numbers of bus drivers in coming 5 years: Year 1: 100 drivers; Year 2: 90 drivers; Year 3: 110 drivers; Year 4: 120 drivers and Year 5: 90 drivers.
Recruiting one driver costs the company 1,000 USD which includes pre-deployment training. Firing one driver costs the company 2,000 USD including the severance pay. Each driver on payroll costs the company 12,000 USD per year. The company currently has 60 bus drivers on payroll. Apply linear programming model to develop a formulation to minimize the total recruiting, firing and payroll cost for the bus company. List assumptions you made in the formulation. Note that you are not required to solve the problem.
linear-programming
linear-programming
edited Apr 14 '18 at 10:56
nbro
2,41653173
asked Sep 18 '17 at 13:03
JaniceJanice
63
edited Apr 14 '18 at 10:56
nbro
2,41653173
asked Sep 18 '17 at 13:03
JaniceJanice
63
edited Apr 14 '18 at 10:56
nbro
2,41653173
edited Apr 14 '18 at 10:56
nbro
2,41653173
edited Apr 14 '18 at 10:56
nbro
2,41653173
2,41653173
asked Sep 18 '17 at 13:03
JaniceJanice
63
asked Sep 18 '17 at 13:03
JaniceJanice
63
asked Sep 18 '17 at 13:03
JaniceJanice
63
63
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
It´s not enough. You have to regard each period (year). The most important thing in (linear) programming is to define the variables:
$h_i$: Number of drivers, who are hired at the beginning of year $i in {1,2,3,4,5}$
$f_i$: Number of drivers, who are fired at the end of year $i-1 in {1,2,3,4,5}$
$d_i=h_i-f_i:$ Difference of hired and fired drivers in year $i in {1,2,3,4,5}$
$d_1=60$ is the initial number of drivers.
The constraints for the minimum of drivers in year $1$ is
$$sumlimits_{i=1}^{1}d_igeq 100$$
The constraints for the minimum of drivers in year $2$ is
$$sumlimits_{i=1}^{2}d_igeq 90$$
And so on.
And the objective function is
$$texttt{min}quad 1000cdot sum_{i=1}^5 h_i+2000cdot sum_{i=1}^5 f_i+12000cdot( sum_{k=1}^5 sum_{i=1}^k d_i)$$
$h_i,f_i in mathbb N$
If you have any questions feel free to ask.
answered Sep 18 '17 at 14:48
callculuscallculus
18.1k31427
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
It´s not enough. You have to regard each period (year). The most important thing in (linear) programming is to define the variables:
$h_i$: Number of drivers, who are hired at the beginning of year $i in {1,2,3,4,5}$
$f_i$: Number of drivers, who are fired at the end of year $i-1 in {1,2,3,4,5}$
$d_i=h_i-f_i:$ Difference of hired and fired drivers in year $i in {1,2,3,4,5}$
$d_1=60$ is the initial number of drivers.
The constraints for the minimum of drivers in year $1$ is
$$sumlimits_{i=1}^{1}d_igeq 100$$
The constraints for the minimum of drivers in year $2$ is
$$sumlimits_{i=1}^{2}d_igeq 90$$
And so on.
And the objective function is
$$texttt{min}quad 1000cdot sum_{i=1}^5 h_i+2000cdot sum_{i=1}^5 f_i+12000cdot( sum_{k=1}^5 sum_{i=1}^k d_i)$$
$h_i,f_i in mathbb N$
If you have any questions feel free to ask.
answered Sep 18 '17 at 14:48
callculuscallculus
18.1k31427
$endgroup$
add a comment |
$begingroup$
It´s not enough. You have to regard each period (year). The most important thing in (linear) programming is to define the variables:
$h_i$: Number of drivers, who are hired at the beginning of year $i in {1,2,3,4,5}$
$f_i$: Number of drivers, who are fired at the end of year $i-1 in {1,2,3,4,5}$
$d_i=h_i-f_i:$ Difference of hired and fired drivers in year $i in {1,2,3,4,5}$
$d_1=60$ is the initial number of drivers.
The constraints for the minimum of drivers in year $1$ is
$$sumlimits_{i=1}^{1}d_igeq 100$$
The constraints for the minimum of drivers in year $2$ is
$$sumlimits_{i=1}^{2}d_igeq 90$$
And so on.
And the objective function is
$$texttt{min}quad 1000cdot sum_{i=1}^5 h_i+2000cdot sum_{i=1}^5 f_i+12000cdot( sum_{k=1}^5 sum_{i=1}^k d_i)$$
$h_i,f_i in mathbb N$
If you have any questions feel free to ask.
answered Sep 18 '17 at 14:48
callculuscallculus
18.1k31427
$endgroup$
add a comment |
$begingroup$
It´s not enough. You have to regard each period (year). The most important thing in (linear) programming is to define the variables:
$h_i$: Number of drivers, who are hired at the beginning of year $i in {1,2,3,4,5}$
$f_i$: Number of drivers, who are fired at the end of year $i-1 in {1,2,3,4,5}$
$d_i=h_i-f_i:$ Difference of hired and fired drivers in year $i in {1,2,3,4,5}$
$d_1=60$ is the initial number of drivers.
The constraints for the minimum of drivers in year $1$ is
$$sumlimits_{i=1}^{1}d_igeq 100$$
The constraints for the minimum of drivers in year $2$ is
$$sumlimits_{i=1}^{2}d_igeq 90$$
And so on.
And the objective function is
$$texttt{min}quad 1000cdot sum_{i=1}^5 h_i+2000cdot sum_{i=1}^5 f_i+12000cdot( sum_{k=1}^5 sum_{i=1}^k d_i)$$
$h_i,f_i in mathbb N$
If you have any questions feel free to ask.
answered Sep 18 '17 at 14:48
callculuscallculus
18.1k31427
$endgroup$
It´s not enough. You have to regard each period (year). The most important thing in (linear) programming is to define the variables:
$h_i$: Number of drivers, who are hired at the beginning of year $i in {1,2,3,4,5}$
$f_i$: Number of drivers, who are fired at the end of year $i-1 in {1,2,3,4,5}$
$d_i=h_i-f_i:$ Difference of hired and fired drivers in year $i in {1,2,3,4,5}$
$d_1=60$ is the initial number of drivers.
The constraints for the minimum of drivers in year $1$ is
$$sumlimits_{i=1}^{1}d_igeq 100$$
The constraints for the minimum of drivers in year $2$ is
$$sumlimits_{i=1}^{2}d_igeq 90$$
And so on.
And the objective function is
$$texttt{min}quad 1000cdot sum_{i=1}^5 h_i+2000cdot sum_{i=1}^5 f_i+12000cdot( sum_{k=1}^5 sum_{i=1}^k d_i)$$
$h_i,f_i in mathbb N$
If you have any questions feel free to ask.
answered Sep 18 '17 at 14:48
callculuscallculus
18.1k31427
answered Sep 18 '17 at 14:48
callculuscallculus
18.1k31427
answered Sep 18 '17 at 14:48
callculuscallculus
18.1k31427
answered Sep 18 '17 at 14:48
callculuscallculus
18.1k31427
18.1k31427
add a comment |
add a comment |
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