What is the objective function and constraints of this problem?
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1
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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
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up vote
1
down vote
favorite
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
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
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
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 at 10:56
nbro
2,38353169
2,38353169
asked Sep 18 '17 at 13:03
Janice
63
63
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1 Answer
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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.
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
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.
add a comment |
up vote
0
down vote
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.
add a comment |
up vote
0
down vote
up vote
0
down vote
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.
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
callculus
17.6k31427
17.6k31427
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