Timeline for RCPS with time buckets for resource capacity constraints
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Oct 13, 2022 at 15:34 | comment | added | David Torres | A bit late and probably not that relevant but it seems quite similar to event-based models: Tesch (2020) (original papers cited within). | |
| Mar 2, 2022 at 12:08 | vote | accept | Rutger | ||
| Feb 25, 2022 at 14:06 | answer | added | LINDO Systems | timeline score: 1 | |
| Feb 23, 2022 at 13:19 | comment | added | A.Omidi | Thanks for the provided example. It seems with defining a subset of the planning horizon to capture overlap, [5,8], and also declaring the related variable to use the resource exactly on the subset by adding the appropriate penalties would work. Do you try that? | |
| Feb 23, 2022 at 13:13 | comment | added | A.Omidi | For more details please, see this and this links. | |
| Feb 23, 2022 at 13:12 | comment | added | A.Omidi | this is a variant of the RCPSP with the time-index formulation. Where $J$ is the set of the jobs, $R$ is the set of the resources, $T$ is the planning duration, $P_j$ is the processing time of job $j$, $U_{(r,j)}$ is the amount of resource $r$ required for processing job $j$, $C_r$ is the capacity of renewable resource $r$. | |
| Feb 23, 2022 at 12:23 | comment | added | Rutger | @A.Omidi I added a small example. Could you maybe elaborate a bit more on the last inequality that you mention? Does $x_{j,t_2}$ refer to the resource usage of activity $j$ in bucket $t_2$, or what does the index $t_2$ exactly represent | |
| Feb 23, 2022 at 12:17 | history | edited | Rutger | CC BY-SA 4.0 |
added 625 characters in body
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| Feb 23, 2022 at 10:52 | comment | added | A.Omidi | Also, you can use $\sum_{j\in J}\sum_{t_2=t-p_{j}+1}^{t} u_{(j,r)}x_{(j,t_2)} \leq c_{r} \,\,\, \forall t\in \mathcal{T}, r \in R$ resource capacity constraints instead of what you mentioned to mirror what you are trying to do better. Where $j$ referred to tasks and $t$ referred to time bucket. | |
| Feb 23, 2022 at 10:47 | comment | added | A.Omidi | If you define the available time in each time bucket around $24$ hours, the tasks should be performed in $2$ days without any extra resources. (actually if the resource is being available in $24$ hours). Indeed, for achieving more resources you would need to pay violation penalties. | |
| Feb 23, 2022 at 10:46 | comment | added | A.Omidi | Welcome to OR.SE. Would you please, more elaborate to understand the problem a bit better by a numerical simple example? What exactly do you mean by ` if an operation overlaps multiple buckets?`? As a simple explanation, suppose a task has consumed $2$ days to be performed on the specific resource and the time bucket is daily. | |
| S Feb 23, 2022 at 9:38 | review | First questions | |||
| Feb 23, 2022 at 13:59 | |||||
| S Feb 23, 2022 at 9:38 | history | asked | Rutger | CC BY-SA 4.0 |