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Mathematical formulation for a scheduling of tasks occurring more than once during a specific time horizon [closed]
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I would like to formulate a mathematical model for scheduling tasks. The tasks have specific properties, such as, due-date, cost, and labour hours. At the moment I have formulated parts of my model as a linear programming problem. My main objective is that given opportunities for maintenance I want to schedule the different maintenance tasks (to the maintenance opportunities) at the lowest possible cost. Cost of a task is lowest when it is scheduled closest to its due-date. The problem is subject to multiple constraints (i.e. maintenance task may not be scheduled at a maintenance opportunity exceeding the due-date of the task, each opportunity for maintenance has its maximum capacity). My main issue is that I need to schedule some of the task multiple times (also, the difference between the first scheduled task and the second scheduled same task may not be larger than its due date). However I do not know upfront where the task is allocated. I really need to figure out a way to constraint the distance between task_1_first and task_1_second to be within the limits of the due-date. Let me clarify this with an example:
There are 6 opportunities for maintenance given in months >> [2,5,6,9,13,16]
Task_1 needs to scheduled before its due date which is 5.2 months. Therefore there are two options either schedule Task_1_0 to opportunity in month 2 or month 5. In addition to this Task_1_1 needs to be scheduled again (since the time horizon is 16 months), in case it was allocated to month 2, there are two options (Month 5 and 6) and in case it was allocated to month 5 there are two options (Month 6 and 9).
Somehow I need to include this (dynamic?) behavior in my mathematical model. I strongly believe there is a solution, however I have not found it yet. Any suggestions or terminology of this kind of problem?
optimization linear-programming constraints
asked Jul 30 at 19:58
Engineering25
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closed as too broad by LinAlg, max_zorn, Isaac Browne, Leucippus, Taroccoesbrocco Jul 31 at 8:31
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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I would like to formulate a mathematical model for scheduling tasks. The tasks have specific properties, such as, due-date, cost, and labour hours. At the moment I have formulated parts of my model as a linear programming problem. My main objective is that given opportunities for maintenance I want to schedule the different maintenance tasks (to the maintenance opportunities) at the lowest possible cost. Cost of a task is lowest when it is scheduled closest to its due-date. The problem is subject to multiple constraints (i.e. maintenance task may not be scheduled at a maintenance opportunity exceeding the due-date of the task, each opportunity for maintenance has its maximum capacity). My main issue is that I need to schedule some of the task multiple times (also, the difference between the first scheduled task and the second scheduled same task may not be larger than its due date). However I do not know upfront where the task is allocated. I really need to figure out a way to constraint the distance between task_1_first and task_1_second to be within the limits of the due-date. Let me clarify this with an example:
There are 6 opportunities for maintenance given in months >> [2,5,6,9,13,16]
Task_1 needs to scheduled before its due date which is 5.2 months. Therefore there are two options either schedule Task_1_0 to opportunity in month 2 or month 5. In addition to this Task_1_1 needs to be scheduled again (since the time horizon is 16 months), in case it was allocated to month 2, there are two options (Month 5 and 6) and in case it was allocated to month 5 there are two options (Month 6 and 9).
Somehow I need to include this (dynamic?) behavior in my mathematical model. I strongly believe there is a solution, however I have not found it yet. Any suggestions or terminology of this kind of problem?
optimization linear-programming constraints
asked Jul 30 at 19:58
Engineering25
1
closed as too broad by LinAlg, max_zorn, Isaac Browne, Leucippus, Taroccoesbrocco Jul 31 at 8:31
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |Â
up vote
0
down vote
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up vote
0
down vote
favorite
I would like to formulate a mathematical model for scheduling tasks. The tasks have specific properties, such as, due-date, cost, and labour hours. At the moment I have formulated parts of my model as a linear programming problem. My main objective is that given opportunities for maintenance I want to schedule the different maintenance tasks (to the maintenance opportunities) at the lowest possible cost. Cost of a task is lowest when it is scheduled closest to its due-date. The problem is subject to multiple constraints (i.e. maintenance task may not be scheduled at a maintenance opportunity exceeding the due-date of the task, each opportunity for maintenance has its maximum capacity). My main issue is that I need to schedule some of the task multiple times (also, the difference between the first scheduled task and the second scheduled same task may not be larger than its due date). However I do not know upfront where the task is allocated. I really need to figure out a way to constraint the distance between task_1_first and task_1_second to be within the limits of the due-date. Let me clarify this with an example:
There are 6 opportunities for maintenance given in months >> [2,5,6,9,13,16]
Task_1 needs to scheduled before its due date which is 5.2 months. Therefore there are two options either schedule Task_1_0 to opportunity in month 2 or month 5. In addition to this Task_1_1 needs to be scheduled again (since the time horizon is 16 months), in case it was allocated to month 2, there are two options (Month 5 and 6) and in case it was allocated to month 5 there are two options (Month 6 and 9).
Somehow I need to include this (dynamic?) behavior in my mathematical model. I strongly believe there is a solution, however I have not found it yet. Any suggestions or terminology of this kind of problem?
optimization linear-programming constraints
asked Jul 30 at 19:58
Engineering25
1
I would like to formulate a mathematical model for scheduling tasks. The tasks have specific properties, such as, due-date, cost, and labour hours. At the moment I have formulated parts of my model as a linear programming problem. My main objective is that given opportunities for maintenance I want to schedule the different maintenance tasks (to the maintenance opportunities) at the lowest possible cost. Cost of a task is lowest when it is scheduled closest to its due-date. The problem is subject to multiple constraints (i.e. maintenance task may not be scheduled at a maintenance opportunity exceeding the due-date of the task, each opportunity for maintenance has its maximum capacity). My main issue is that I need to schedule some of the task multiple times (also, the difference between the first scheduled task and the second scheduled same task may not be larger than its due date). However I do not know upfront where the task is allocated. I really need to figure out a way to constraint the distance between task_1_first and task_1_second to be within the limits of the due-date. Let me clarify this with an example:
There are 6 opportunities for maintenance given in months >> [2,5,6,9,13,16]
Task_1 needs to scheduled before its due date which is 5.2 months. Therefore there are two options either schedule Task_1_0 to opportunity in month 2 or month 5. In addition to this Task_1_1 needs to be scheduled again (since the time horizon is 16 months), in case it was allocated to month 2, there are two options (Month 5 and 6) and in case it was allocated to month 5 there are two options (Month 6 and 9).
Somehow I need to include this (dynamic?) behavior in my mathematical model. I strongly believe there is a solution, however I have not found it yet. Any suggestions or terminology of this kind of problem?
optimization linear-programming constraints
asked Jul 30 at 19:58
Engineering25
1
asked Jul 30 at 19:58
Engineering25
1
asked Jul 30 at 19:58
Engineering25
1
asked Jul 30 at 19:58
Engineering25
1
1
closed as too broad by LinAlg, max_zorn, Isaac Browne, Leucippus, Taroccoesbrocco Jul 31 at 8:31
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as too broad by LinAlg, max_zorn, Isaac Browne, Leucippus, Taroccoesbrocco Jul 31 at 8:31
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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