Using Time Homogenous Markov Chain to maximise profit
up vote
0
down vote
favorite
Suppose there is a company with 30 printing machines and they need to hire staff to operate the machines such that the profit is maximised. The model is that each machine is either
1. Idle state (not operating)
2. Setup state (Operator is working on readying it for printing)
3. Working state (machine is printing, operator not needed)
When a machine completes a print job (working state), it enters either setup state (if there is a free operator available) or Idle state (if no operators are free).
When an operator finishes Setup state of a machine, the machine enters Working state and the Operator either selects an Idle machine and start Setup or if no machines are available, the operator waits until next machine becomes available.
The length of each print job (in days) follows Exp(7) and length of time (in days) to set up a machine follows Exp(1) dist. Setup times and print times are independent.
While in working, the machine earns $30/day and $0 in other states. Each operator costs $80 per day.
The question is how to maximise profit, by mainly using Time Homogenous Markov chains and R coding
stochastic-processes markov-chains markov-process transition-matrix
asked 2 days ago
TimMarkhov
1
New contributor
TimMarkhov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
Suppose there is a company with 30 printing machines and they need to hire staff to operate the machines such that the profit is maximised. The model is that each machine is either
1. Idle state (not operating)
2. Setup state (Operator is working on readying it for printing)
3. Working state (machine is printing, operator not needed)
When a machine completes a print job (working state), it enters either setup state (if there is a free operator available) or Idle state (if no operators are free).
When an operator finishes Setup state of a machine, the machine enters Working state and the Operator either selects an Idle machine and start Setup or if no machines are available, the operator waits until next machine becomes available.
The length of each print job (in days) follows Exp(7) and length of time (in days) to set up a machine follows Exp(1) dist. Setup times and print times are independent.
While in working, the machine earns $30/day and $0 in other states. Each operator costs $80 per day.
The question is how to maximise profit, by mainly using Time Homogenous Markov chains and R coding
stochastic-processes markov-chains markov-process transition-matrix
asked 2 days ago
TimMarkhov
1
New contributor
TimMarkhov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Suppose there is a company with 30 printing machines and they need to hire staff to operate the machines such that the profit is maximised. The model is that each machine is either
1. Idle state (not operating)
2. Setup state (Operator is working on readying it for printing)
3. Working state (machine is printing, operator not needed)
When a machine completes a print job (working state), it enters either setup state (if there is a free operator available) or Idle state (if no operators are free).
When an operator finishes Setup state of a machine, the machine enters Working state and the Operator either selects an Idle machine and start Setup or if no machines are available, the operator waits until next machine becomes available.
The length of each print job (in days) follows Exp(7) and length of time (in days) to set up a machine follows Exp(1) dist. Setup times and print times are independent.
While in working, the machine earns $30/day and $0 in other states. Each operator costs $80 per day.
The question is how to maximise profit, by mainly using Time Homogenous Markov chains and R coding
stochastic-processes markov-chains markov-process transition-matrix
asked 2 days ago
TimMarkhov
1
New contributor
TimMarkhov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Suppose there is a company with 30 printing machines and they need to hire staff to operate the machines such that the profit is maximised. The model is that each machine is either
1. Idle state (not operating)
2. Setup state (Operator is working on readying it for printing)
3. Working state (machine is printing, operator not needed)
When a machine completes a print job (working state), it enters either setup state (if there is a free operator available) or Idle state (if no operators are free).
When an operator finishes Setup state of a machine, the machine enters Working state and the Operator either selects an Idle machine and start Setup or if no machines are available, the operator waits until next machine becomes available.
The length of each print job (in days) follows Exp(7) and length of time (in days) to set up a machine follows Exp(1) dist. Setup times and print times are independent.
While in working, the machine earns $30/day and $0 in other states. Each operator costs $80 per day.
The question is how to maximise profit, by mainly using Time Homogenous Markov chains and R coding
stochastic-processes markov-chains markov-process transition-matrix
stochastic-processes markov-chains markov-process transition-matrix
asked 2 days ago
TimMarkhov
1
New contributor
TimMarkhov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
TimMarkhov
1
New contributor
TimMarkhov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
TimMarkhov
1
New contributor
TimMarkhov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
TimMarkhov
1
asked 2 days ago
TimMarkhov
1
1
New contributor
TimMarkhov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
TimMarkhov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
TimMarkhov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
TimMarkhov is a new contributor. Be nice, and check out our Code of Conduct.
TimMarkhov is a new contributor. Be nice, and check out our Code of Conduct.
TimMarkhov is a new contributor. Be nice, and check out our Code of Conduct.
TimMarkhov is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2999314%2fusing-time-homogenous-markov-chain-to-maximise-profit%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
